diff --git a/README.md b/README.md
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--- a/README.md
+++ b/README.md
@@ -1,31 +1,179 @@
-# Maths Digital Mentoring
+# Math Digital Mentoring
-A moodle-based training area for maths aiming to prepare students for their studies with the help of AI- and gamification-aspects.
+This repository offers material to enrich mathematical exercises in the Learning Management Systems (LMS) Moodle and ILIAS with interactive elements, e.g., gamification or adaptive learning. This lightweight solution can be implemented by lecturers in their courses using the on-board tools of the learning management system. No installation of an additional plugin is needed.
-## Live Demo
-[Click here](https://hsbo-clone.ebwl-oer.de/mod/quiz/view.php?id=145) for a live demo.
+There are several ways to get started.
+- Take a look on some working examples in the [Live Demos Section](#live-demos).
+- Load a stable version of the material in your LMS and adapt it to your needs: [LMS-readable Packages Section](#lms-readable-packages).
+- Copy and paste the code directly in questions of your LMS: Check the [Insertable Code Section](#insertable-code).
+- Once applied at your university, the resulted effects of the tested versions can be measured with analytics tools offered in the [Effect Measurement Section](#effect-measurement). This can also be done by lecturers, but Python knowledge is helpful.
+- Check the [Paper Section](#papers) for findings from research related to this approach.
-## Screenhot
-
+Apart form that, the repository also contains [Screenshots](#screenhots) and information about [Troubleshooting](#troubleshooting), [Exercise Generation](#exercise-generation) and the [License](#license) (MIT).
-## Getting started
+[//]: # (<REPLACE < with open and > with closed paranthesis>For ILIAS some special features have to be considered, which are detailed in the [ILIAS Section]<#ilias>.)
-- Create a new course in your moodle system.
-- Navigate to the course administration and pick the restore-option.
-- Pick one of the `*.mbz`-files (according to your preferred language) of this repository for restoring. It contains a moodle-course-backup-file. Perform the restore in your newly created moodle-course. *Please choose one of the `*.mbz-files` according to your preferred language.*
-- The course you imported contains a single activity: The training area. Check it out in the dashboard of your course.
-- Be free to edit the quiz as you like and import it into other courses of your moodle-system.
+## Screenshots from LMS
+
+Examples of the same exercise in the pedagogical agent design (left) and in the fantasy game design (right).
+
+
+Example of three different feedbacks offered by the STACK plugin in the pedagogical agent design.
+
+## Live Demos
+[Moodle course with all demos](https://hsbo-clone.ebwl-oer.de/course/view.php?id=14)
+
+The demos run in an open Moodle system of Bochum UAS. You are logged in automatically after a short period of time. Then the learning material can be started by clicking the "Attempt quiz" button.
+
+- The version [Pedagogical Agent (Adaptive)](https://hsbo-clone.ebwl-oer.de/mod/quiz/view.php?id=145) is characterized by learners being directed to different questions depending on whether or not they correctly solve the "boss" tasks.
+- The version [Pedagogical Agent (Instant Tutoring)](https://hsbo-clone.ebwl-oer.de/mod/quiz/view.php?id=1699) is characterized by immediate feedback that is provided to the learners while they are still solving the exercise.
+- The [Fantasy Game](https://hsbo-clone.ebwl-oer.de/mod/quiz/view.php?id=1700) version ties the tasks into a medieval story and adapts the learning environment accordingly.
+- The [Plain](https://hsbo-clone.ebwl-oer.de/mod/quiz/view.php?id=1698) version shows how the questions appear by default and serves as a control design for research projects with an experimental approach.
+
+## LMS-readable Packages
+
+You can either import all versions or some selected versions with the help of the LMS' "restore" option. In this case, the [Moodle Backup files](#moodle-backup-files-mbz) are needed.
+
+Or you can import the questions in the question bank of your course and create the learning material from that. In this case you can make use of the [question files](#question-files-xml). You should choose this option when you work with ILIAS.
+
+Or you can parse the exercises for any of the versions from an editable table file. In this case, please refer to the [Exercise Generation Section](#exercise-generation).
+
+If you want to apply this frontend-oriented approach to other questions than the here presented, check the [Insertable Code Section](#insertable-code).
+
+To get an overview of the differenct versions, please refer to the [Live Demos](#live-demos) and [Screenshots](#screenhots) sections.
+
+[//]: # (Which ever way you choose, please consider the respective requirements and the step by step guides.)
+
+### Moodle Backup Files (mbz)
+
+#### Step by Step Guide
+
+
+
+1. Download one of the `*.mbz`-files (according to your preferred version and language) of this repository.
+1. Create a new course in your Moodle system or navigate to an existing one where you want to embed the activities.
+1. Navigate to the course administration and pick the restore option.
+1. Pick the downloaded `*.mbz`-file in the "Upload File" dialogue.
+1. Perform the restore in your Moodle course. Watch out to pick the right option to not delete any existing content of your course during the restore accidentally.
+
+
+#### Files
+| Version | File (german) | File (english) | Tested with |
+|---------|-------------- |-----------------|-----------------|
+| Normal | [backup-quiz-normal_ger.mbz](backup-files/backup-quiz-normal_ger.mbz) | Planned for Winter 2023-24| Moodle 4.1 |
+| Pedagogical Agent (Adaptive) | [backup-quiz-normal_ger.mbz](backup-files/backup-pa-simple_ger.mbz) | [backup-quiz-normal_en.mbz](backup-files/backup-pa-simple_en.mbz) | Moodle 4.1 |
+| Pedagogical Agent (Instant Tutoring) | [backup-quiz-instant-tutoring_ger.mbz](backup-files/backup-pa-instant-tutoring_ger.mbz) | Planned for Winter 2023-24 | Moodle 4.1 |
+| Fantasy Game | [backup-fantasy_ger.mbz](backup-files/backup-fantasy_ger.mbz) | Planned for Winter 2023-24 | Moodle 4.1 |
+| All Versions | [backup-complete-course_ger.mbz](backup-files/backup-complete-course_ger.mbz) | Planned for Winter 2023-24 | Moodle 4.1 |
+
+
+### Question Files (xml)
+
+#### Step by Step Guide
+
+1. Download one of the `*.xml`-files (according to your preferred version and language) of this repository.
+1. Create a new course in your Moodle system or navigate to an existing one where you want to embed the activities.
+1. Navigate to the course's question bank.
+1. Navigate to the question bank's import page.
+1. Pick the downloaded `*.xml`-file in the "Upload File" dialogue.
+1. Perform the import.
+
+It is preferred to create a quiz from these questions in the following way.
+1. In your course's main page turn editing on.
+1. Create a quiz element at an arbitrary position of your course.
+1. Navigate to the "Add questions" page of the newly created quiz.
+1. Choose "Add from question bank".
+1. Choose the category of the selected version (see table).
+1. Go for sure that the option "Also show elements from subcategories" is checked.
+1. Sort the questions alphabetically in ascending order.
+1. Click on "Show all ... questions".
+1. Select all questions that are currently shown.
+1. Click on "Add."
+1. You may now want to preview the quiz to see if the questions are properly included.
+
+#### Files
+| Version | File (german) | File (english) | Question Category | Tested with |
+|---------|-------------- |-----------------|-------------|----|
+| Normal | [questions-normal_ger.xml](question-files/questions-normal_ger.xml) | Planned for Winter 2023-24| test | Moodle 4.1 |
+| Pedagogical Agent (Adaptive) | Planned for Winter 2023-24 | Planned for Winter 2023-24| Adaptive Learning Test| Moodle 4.1 |
+| Pedagogical Agent (Instant Tutoring) | [questions-pa-its_ger.xml](question-files/questions-pa-its_ger.xml) | Planned for Winter 2023-24| instant-tutoring | Moodle 4.1 |
+| Fantasy Game | [questions-rpg_ger.xml](question-files/questions-rpg_ger.xml) | Planned for Winter 2023-24| rpg | Moodle 4.1 |
+| All Versions | [questions-all_ger.xml](question-files/questions-all_ger.xml) | Planned for Winter 2023-24| choose from above one by one | Moodle 4.1 |
+
+## Insertable Code
+
+Instead of using a given set of questions as in the [LMS-readable Packages Section](#lms-readable-packages) the code can also be applied to other questions. Currently, only questions of the type STACK are supported. If you want to apply one of the designs to other question types (e.g., multiple-choice, fill-the-gap, ...) please contact the [repository owner](mailto:malte.neugebauer@hs-bochum.de) for support.
+
+It is important to consider that each design carries additional information that are either saved in the script or in an additional configuration element that is included in the LMS by importing the exercise files. These information are e.g., how exercises relate to each other in the "Pedagogical Agent (Adaptive)" design or the colors of the fairies in the "Fantasy Game" design.
+
+When applying the code directly to other exercises, these information have to be included and adapted to ensure compatibility. Thus, it is preferred to generate the exercises from a table as described in the [Exercise Generation Section](#exercise-generation). By doing so the configuration elements are automatically parsed.
+
+[//]: # (To achieve this, download the file of your preferred version and language and follow the steps below.)
+
+[//]: # (### Files)
+
+| Version | File (german) | File (english) | Yet empty column | Tested with |
+|---------|-------------- |-----------------|-------------|----|
+| Normal | No JavaScript included | No JavaScript included | | Moodle 4.1 |
+| Pedagogical Agent (Adaptive) | [alquiz.js](script/alquiz.js) | [alquiz_en.js](script/alquiz_en.js) | | Moodle 4.1 |
+| Pedagogical Agent (Instant Tutoring) | [alquiz-qpool-instant-tutoring.js](script/alquiz-qpool-instant-tutoring.js) | Planned for Winter 2023-24| | Moodle 4.1 |
+| Fantasy Game | [alquiz-fantasy-bg-ver3.js](script/alquiz-fantasy-bg-ver3.js) | Planned for Winter 2023-24| | Moodle 4.1 |
+
+
+
+[//]: # (<REPLACE < with open and > with closed paranthesis and REPLACE -- with line break>### Step by Step Guide----1. In your LMS navigate to a question of your choice.--1. In the input field for changing the question text of this question, switch to the code level.--1. In the first line of the code level question text, insert the following line: `<script src="https://marvin.hs-bochum.de/~mneugebauer/{name of chosen file with ending}`. Where `{name of chosen file with ending}` has to be replaced according to your chosen version and language, e.g., `alquiz.js` for the german "Pedagogical Agent <Adaptive>" version. Some LMS do not allow including scripts from a foreign domain. In this case do the following instead:-- 1. Open the preferred [file]<#files-2> with a text editor and copy its content.-- 1. In the first line of the code level question text, insert a script tag `<script></script>` and paste the beforehand copied text between `<script>` and `</script>`.--1. Create a test with the created exercise.)
+
+
+## Exercise Generation
+
+The question files for the different versions are automatically parsed with the script [create_question_versions_from_csv.py](exercise-generation/create_question_versions_from_csv.py) with the information from the table [exercises.csv](exercise-generation/exercises.csv). Thus, for changes in the exercise content only one file has to be modified. The modifications will affect the question file of each version.
+
+
+
+## Effect Measurement
+[//]: # (There are various ways to address the effects of this approach on learners. We propose an experimental setting and test at least two versions: One serves as a control condition and at least one other serves as the treatment condition.)
+
+[//]: # (<REPLACE < with open and > with closed paranthesis>The LMS offers various learning data to lecturers <e. g. grade statistics> by default that may address the question, what effect this approach has on learners. We propose to focus on learners' usage patterns among different designs. The following excerpt from the file [overview.pdf]<> visualizes the data from the datasets [alquiz-analysis-control.csv]<>, [alquiz-analysis-test_its.csv]<> and [alquiz-analysis-test_rpg.csv]<> from the folders [university1]<./analysis/university_1> and [university2]<./analysis/university_1>. The latter files include each movement of several users within the three different designs <normal, pedagogical agent <instant tutoring> and fantasy game>. These files can be generated by lecturers by running the scripts [alquiz-analyisis-control.js]<> or [alquiz-analyisis-test.js]<> respectively for either the control design or the pa/fantasy designs in the LMS attempt overview page. The Python script [visualize_patterns.py]<> generates several Latex files from that, that are included in the [overview.tex]<> file. For further information about the measurement of effects with this approach please refer to the [Papers Section]<#papers>)
+
+The LMS offers various learning data to lecturers (e. g. grade statistics) by default that may address the question, what effect this approach has on learners. To get a deeper understanding learners' usage patterns can additionally visualized as shown in the screenshot by following the steps below. The following excerpt from the file [overview.pdf](./analysis/tex/overview.pdf) visualizes the data from the exemplary dataset [hops.csv](./analysis/hops.csv).
+
+
+
+1. In your LMS, navigate to the attempt overview page of one of the quizzes. You should see here a list of attempts users made with the learning material.
+1. Go for sure that all attempts are listed here and not only a selection (not: page 1 of ...). In Moodle you can achieve this by adjusting the page size to a large number, e.g., 999.
+1. Download either the script [alquiz-analysis-control.js](./analysis/alquiz-analysis-control.js) for the versions "Normal" and "Pedagogical Agent (Adaptive)" or the script [alquiz-analysis-test.js](./analysis/alquiz-analysis-test.js) for the versions with instant feedback, i.e., "Fantasy Game" and "Pedagogical Agent (Instant Tutoring)."
+1. The downloaded script files can be opened with any text editor. Copy the script's content and paste it in the console of your browser on the attempt overview page.
+1. Run the command `loadUsers();` in the console.
+1. The script loads the usage data, as if you would click on the attempts one by one. Check the current download state by running the command `getFetchState();` in the console.
+1. When the output of `getFetchState();` doesn't change, you can run `loadAndDownloadCSV();` in the console to download the data as a `*.csv` file. The script anonymizes the downloaded data by default. If you want to take a look on the data file, consider the appropriate options: `;` as cell delimiter, `'` as string delimiter.
+1. Give the file a descriptive name, e.g., `usage-data-version-A.csv` and store it on your device.
+1. Download the python script [visualize_hops.py](./analysis/visualize_hops.py) and store it in the same folder as the usage data file.
+1. Open the python script in a text editor. Find the line of code in the python script that is responsible for the name of the included data file and change it according to the previously saved usage data file.
+1. Run the python script. Several Latex files will be generated in a folder named `tex`, located in the same folder as the just executed python script file.
+1. Download the file [overview.tex](./analysis/tex/overview.tex) and place it in the just generated `tex` folder.
+1. Parse a pdf from the file [overview.tex](./analysis/tex/overview.tex). The resulting file [overview.pdf](./analysis/tex/overview.pdf) contains the usage pattern visualizations.
+
+[//]: # (<REPLACE < with open and > with closed paranthesis>The latter can be generated by running the scripts [alquiz-analysis-control.js]<./analysis/alquiz-analysis-control.js> or [alquiz-analysis-test.js]<./analysis/alquiz-analysis-test.js> for the control design or the pedagogical agent/fantasy game design respectively. The generated file can then by read by the script [visualize-patterns.py]<./analysis/visualize_patterns.py>, which generates several Latex files that are included by the file [overview.tex]<./analysis/tex/overview.tex>.)
## Troubleshooting
-### Ressources won't load
-It may appear that for security reasons, your moodle-system can't fetch the script from the server. In this case the training area exists in your moodle-system, but will behave like any other test-element in moodle. For example, the maths-worlds-cluster and the endboss-symbols in the navigation bar (see screenshot above) won't appear. If so, download the script (choose `script/alquiz.js` for german or `script/alquiz_en.js` for english) from this repository and move it to a place on your own server. Afterwards you have to change the `<script src="...">`-url in the beginning of each(!) question.
-The same may appear for images used in the trigonometry-questions and the avatar-icon(s). Download them from this repository (`img`-directory), move them to your server and change the urls in the regarding questions. Please note, that for the english version the file with the ending `_en`
+Since the approach is based on Javascript, the regulations for using JavaScript inside the LMS are of high importance for the functionality of the approach.
+
+If for any reasons JavaScript is not allowed in question texts of your LMS, the training area exists in your LMS, but will behave like any other test element in the LMS. As an example for the "Pedagogical Agent" version, the math worlds cluster and the endboss symbols in the navigation bar (see screenshots above) won't appear.
+
+In this case, you may want to ask your LMS administrator to allow the usage of JavaScript in question texts for your specific use case.
+
+If you chose to implement the code directly as described in the [Insertable Code Section](#insertable-code) please ensure that the according configuration information for your preferred version align with the question setting as described there. It may be more desired to choose either one of the pre-generated [LMS-readable packages](#lms-readable-packages) or to [generate the exercises](#exercise-generation) from a table. These latter procedures exclude the configuration setting as the cause of the error.
+
+[//]: # (### Training area looks messy or does not work properly)
+[//]: # (<REPLACE < with open and > with closed paranthesis and REPLACE -- with line break>The script-file `alquiz.js` adds additional CSS-styling information to the loaded page. These stylings are optimized for the Moodle-system of Hochschule Bochum. It may not fit to the stylings of your Moodle-system. This may cause troubles for up to two cases:--1. If this only relates to the desgin of the training area, you have to identify the two lines, where `alquiz.js` adds the styling information to the page and adapt them to your Moodle-system. To do so, search for `document.createElement<"style">;` and edit the related variable declaration `.innerHTML = "..."`.--1. If this also applies to the functionality of the training area <e. g. the question feedback is not shown in the speech bubble above the question, but below the question>, you have to adapt any `querySelector`, `querySelectorAll` and `getElementById` function in `alquiz.js` to operate correctly with your Moodle-system.)
+
+[//]: # (## ILIAS)
+[//]: # (Since the approach is based on Javascript, the regulations for using JavaScript inside the LMS are of high importance for the functionality of the approach.)
-### Training area looks messy or does not work properly
-The script-file `alquiz.js` adds additional CSS-styling information to the loaded page. These stylings are optimized for the moodle-system of Hochschule Bochum. It may not fit to the stylings of your moodle-system. This may cause troubles for up to two cases:
-1. If this only relates to the desgin of the training area, you have to identify the two lines, where `alquiz.js` adds the styling information to the page and adapt them to your moodle-system. To do so, search for `document.createElement("style");` and edit the related variable declaration `.innerHTML = "..."`.
-1. If this also applies to the functionality of the training area (e. g. the question feedback is not shown in the speech bubble above the question, but below the question), you have to adapt any `querySelector`, `querySelectorAll` and `getElementById` function in `alquiz.js` to operate correctly with your moodle-system.
+## Papers
+ - Neugebauer, M., Tousside, B., Frochte, J. (2023). *Success Factors for Mathematical E-Learning Exercises Focusing First-Year Students.* In: Proceedings of the 15th International Conference on Computer Supported Education (CSEDU). https://doi.org/10.5220/0011858400003470
+ - Neugebauer, M, Frochte, J. (2023). *Steigerung von Lernerfolg und Motivation durch gamifizierte Mathematik-Aufgaben in Lernmanagementsystemen.* In: 21. Fachtagung Bildungstechnologien (DELFI). https://doi.org/10.18420/delfi2023-39
## License
diff --git a/analysis/alquiz-analysis-control.js b/analysis/alquiz-analysis-control.js
new file mode 100644
index 0000000000000000000000000000000000000000..71b341165ceb14fd25af389411462c3783a1ad7f
--- /dev/null
+++ b/analysis/alquiz-analysis-control.js
@@ -0,0 +1,1290 @@
+console.log("start alquiz analysis");
+//----------------QUIZ OBJECTS--------------------
+//In control design, questions section_09_check_in_modified2_6 and section_09_check_in_modified2_7 are merged in one question section_09_check_in_modified2_6and7.
+/* WiMa SoSe 2023*/
+let quizObject = {
+ groups: {
+ start: "Start",
+ s3: "3 Elementare Funktionen",
+ s4: "4 Eigenschaften von Funktionen",
+ s5: "5 Grenzwerte, Stetigkeit und Definitionslücken",
+ s6: "6 Differentialrechnung I (Ableitungsregeln)",
+ s7: "7 Differentialrechnung II (Anwendung)",
+ s8: "8 Differentialrechnung in mehreren Variablen",
+ s9: "9 Finanzmathematik I",
+ s10: "10 Finanzmathematik II",
+ s11: "11 Lineare Algebra Grundlagen",
+ s12: "12 Weiterführende Matrixrechnung",
+ s13: "13 Lineare Optimierung"
+
+ },
+ questions: {
+ start: {
+ name: "Home",
+ group: "start",
+ onsuccess: "s3_1",
+ onfailure: "s3_1"
+ },
+ s3_1: {
+ /*orange*/
+ name: "Geradengleichung aufstellen 1",
+ onsuccess: "s3_2",
+ onfailure: "s3_2",
+ variants: 4,
+ color: "#fbc02d",
+ filter: "invert(75%) sepia(32%) saturate(1024%) hue-rotate(352deg) brightness(102%) contrast(97%)"
+ },
+ s3_2: {
+ /*red-orange*/
+ name: "Geradengleichung aufstellen 2",
+ onsuccess: "s3_3",
+ onfailure: "s3_3",
+ variants: 4,
+ color: "#ff3d00",
+ filter: "invert(31%) sepia(93%) saturate(4185%) hue-rotate(7deg) brightness(105%) contrast(110%)"
+ },
+ s3_3: {
+ /*light orange*/
+ name: "Scheitelpunkt aus Graphik ablesen",
+ variants: 4,
+ color: "#ffcc80",
+ filter: "invert(94%) sepia(80%) saturate(1438%) hue-rotate(304deg) brightness(109%) contrast(101%)"
+ },
+ s3_4: {
+ /*???*/
+ name: "Erlösfunktion",
+ variants: 4,
+ color: "#CF7D35",
+ filter: "invert(61%) sepia(55%) saturate(1048%) hue-rotate(339deg) brightness(88%) contrast(83%)"
+ },
+ s3_5: {
+ /*???*/
+ name: "Abschnittsweise def Funktion",
+ variants: 4,
+ color: "#34BC98",
+ filter: "invert(64%) sepia(14%) saturate(1723%) hue-rotate(114deg) brightness(94%) contrast(93%)"
+ },
+ s3_6: {
+ /*???*/
+ name: "Gewinnfunktion aufstellen",
+ variants: 4,
+ color: "#E9FCEE",
+ filter: "invert(100%) sepia(5%) saturate(4521%) hue-rotate(53deg) brightness(102%) contrast(96%)"
+ },
+ section_03_check_out_modified2_1: {
+ name: "Angebot und Nachfrage",
+ variants: 4,
+ color: "#573036",
+ filter: "invert(20%) sepia(11%) saturate(2292%) hue-rotate(301deg) brightness(88%) contrast(87%)",
+ group: "s3"
+ },
+ section_03_check_out_modified2_2: {
+ name: "Scheitelpunktform DOMAINUID 4 ACEA29",
+ variants: 4,
+ color: "#1BA1C7",
+ filter: "invert(46%) sepia(89%) saturate(419%) hue-rotate(147deg) brightness(97%) contrast(96%)",
+ group: "s3"
+ },
+ section_03_check_out_modified2_3: {
+ name: "Erlösfunktion E(p) aufstellen",
+ variants: 4,
+ color: "#B38ABB",
+ filter: "invert(67%) sepia(28%) saturate(423%) hue-rotate(244deg) brightness(85%) contrast(89%)",
+ group: "s3"
+ },
+ section_03_check_out_modified2_4: {
+ name: "Produktionsfunktion Def ök",
+ variants: 4,
+ color: "#D558A8",
+ filter: "invert(50%) sepia(90%) saturate(907%) hue-rotate(290deg) brightness(87%) contrast(90%)",
+ group: "s3"
+ },
+ section_03_check_out_modified2_5: {
+ name: "Gewinnschwelle & Gewinngrenze Kap. 2.7 (TF) (Duplikat Malte)",
+ variants: 4,
+ color: "#1B5658",
+ filter: "invert(26%) sepia(12%) saturate(2407%) hue-rotate(133deg) brightness(95%) contrast(86%)",
+ group: "s3"
+ },
+ section_03_check_out_modified2_6: {
+ name: "Definitionsbereich Ök. Kap. 2.7 (TF)",
+ variants: 4,
+ color: "#810311",
+ filter: "invert(8%) sepia(64%) saturate(6140%) hue-rotate(346deg) brightness(93%) contrast(104%)",
+ group: "s3"
+ },
+ section_04_check_in_modified_6: {
+ name: "Nullstelle abspalten (Duplikat Malte)",
+ variants: 4,
+ color: "#74CD27",
+ filter: "invert(68%) sepia(76%) saturate(507%) hue-rotate(42deg) brightness(95%) contrast(83%)",
+ group: "s4"
+ },
+ s4_1: {
+ /*very light green*/
+ name: "NS reverse",
+ onsuccess: "s4_2",
+ onfailure: "s4_2",
+ variants: 4,
+ color: "#ccff90",
+ filter: "invert(88%) sepia(22%) saturate(727%) hue-rotate(38deg) brightness(103%) contrast(107%)"
+ },
+ s4_2: {
+ /*light green*/
+ name: "NS bei Def",
+ onsuccess: "s4_3",
+ onfailure: "s4_3",
+ variants: 4,
+ color: "#b2ff59",
+ filter: "invert(96%) sepia(97%) saturate(787%) hue-rotate(29deg) brightness(100%) contrast(108%)"
+ },
+ s4_3: {
+ /*green*/
+ name: "NS Wurzelfkt",
+ onsuccess: "s4_4",
+ onfailure: "s4_4",
+ variants: 4,
+ color: "#76ff03",
+ filter: "invert(67%) sepia(72%) saturate(618%) hue-rotate(43deg) brightness(110%) contrast(103%)"
+ },
+ s4_4: {
+ /*dimmed green*/
+ name: "4.2 Polynom von Grad 4 her bestimmen",
+ onsuccess: "s4_5",
+ onfailure: "s4_5",
+ variants: 4,
+ color: "#64dd17",
+ filter: "invert(79%) sepia(18%) saturate(3453%) hue-rotate(45deg) brightness(97%) contrast(91%)"
+ },
+ s4_5: {
+ /*dark green*/
+ name: "4.1 Funktion ablesen Grad 4",
+ variants: 4,
+ color: "#689f38",
+ filter: "invert(54%) sepia(21%) saturate(1222%) hue-rotate(49deg) brightness(99%) contrast(83%)"
+ },
+ section_05_check_in_3: {
+ name: "Grenzwert gegen inf ablesen",
+ variants: 4,
+ color: "#3CF48A",
+ filter: "invert(72%) sepia(40%) saturate(699%) hue-rotate(89deg) brightness(101%) contrast(98%)",
+ group: "s5"
+ },
+ section_05_check_in_modified2_7: {
+ name: "Stetigkeit abschnittsw def Funktion (Duplikat Malte)",
+ variants: 4,
+ color: "#E249B2",
+ filter: "invert(52%) sepia(64%) saturate(4425%) hue-rotate(292deg) brightness(93%) contrast(90%)",
+ group: "s5"
+ },
+ section_05_check_in_6: {
+ name: "Polstelle",
+ variants: 4,
+ color: "#77B211",
+ filter: "invert(64%) sepia(52%) saturate(5261%) hue-rotate(48deg) brightness(107%) contrast(87%)",
+ group: "s5"
+ },
+ section_05_check_in_modified2_8: {
+ name: "Hebbare Lücke (Duplikat Malte)",
+ variants: 4,
+ color: "#D57774",
+ filter: "invert(81%) sepia(50%) saturate(3032%) hue-rotate(305deg) brightness(86%) contrast(94%)",
+ group: "s5"
+ },
+ section_05_check_in_8: {
+ name: "Asymptote",
+ variants: 4,
+ color: "#FD9C80",
+ filter: "invert(84%) sepia(53%) saturate(4565%) hue-rotate(313deg) brightness(115%) contrast(108%)",
+ group: "s5"
+ },
+ section_05_check_out_1: {
+ name: "Grenzwertaufgabe mögliche Polstellen (TU)",
+ variants: 4,
+ color: "#E249B2",
+ filter: "invert(52%) sepia(64%) saturate(4425%) hue-rotate(292deg) brightness(93%) contrast(90%)",
+ group: "s5"
+ },
+ section_05_check_out_2: {
+ name: "Nullstellen und Polstellen von sqrt(P/Q-1) Kap. 2.4 & 2.6 (TF)",
+ variants: 4,
+ color: "#D57774",
+ filter: "invert(81%) sepia(50%) saturate(3032%) hue-rotate(305deg) brightness(86%) contrast(94%)",
+ group: "s5"
+ },
+ section_05_check_out_3: {
+ name: "Nullstellen, Polstellen und Asymptoten einer gebrochenrationalen Funktion Kap. 2.4 & 2.6 (TF)",
+ variants: 4,
+ color: "#944A6C",
+ filter: "invert(34%) sepia(25%) saturate(1028%) hue-rotate(280deg) brightness(96%) contrast(89%)",
+ group: "s5"
+ },
+ section_05_check_out_5: {
+ name: "Asymptote VWL",
+ variants: 4,
+ color: "#9B49A2",
+ filter: "invert(35%) sepia(65%) saturate(573%) hue-rotate(248deg) brightness(92%) contrast(92%)",
+ group: "s5"
+ },
+ section_05_check_out_6: {
+ name: "Sprungstelle abschnittsw def Funktion",
+ variants: 4,
+ color: "#FA00D1",
+ filter: "invert(54%) sepia(100%) saturate(7435%) hue-rotate(298deg) brightness(97%) contrast(127%)",
+ group: "s5"
+ },
+ s6_1: {
+ /*very light purple*/
+ name: "Ableitungsfunktion Konstante",
+ onsuccess: "s6_2",
+ onfailure: "s6_2",
+ variants: 4,
+ color: "#ea80fc",
+ filter: "invert(76%) sepia(34%) saturate(6604%) hue-rotate(231deg) brightness(102%) contrast(98%)"
+ },
+ s6_2: {
+ /*light purple*/
+ name: "Ableitungsfunktion Potenzfunktion",
+ onsuccess: "s6_3",
+ onfailure: "s6_3",
+ variants: 4,
+ color: "#e040fb",
+ filter: "invert(37%) sepia(85%) saturate(3762%) hue-rotate(272deg) brightness(104%) contrast(97%)"
+ },
+ s6_3: {
+ /*purple*/
+ name: "Ableitungsfunktion Potenzfunktion gebrochener Exponent",
+ variants: 4,
+ color: "#d500f9",
+ filter: "invert(26%) sepia(92%) saturate(2035%) hue-rotate(275deg) brightness(86%) contrast(153%)"
+ },
+ section_06_check_out_1: {
+ name: "01 Summen- und konstanter Faktor",
+ variants: 4,
+ color: "#E2AFDA",
+ filter: "invert(96%) sepia(86%) saturate(2059%) hue-rotate(203deg) brightness(96%) contrast(83%)",
+ group: "s6"
+ },
+ section_06_check_out_2: {
+ name: "02 Produktregel (TF)",
+ variants: 4,
+ color: "#EB3E57",
+ filter: "invert(33%) sepia(19%) saturate(6570%) hue-rotate(328deg) brightness(97%) contrast(89%)",
+ group: "s6"
+ },
+ section_06_check_out_3: {
+ name: "03 Quotientenregel[neu](TF)",
+ variants: 4,
+ color: "#7E182C",
+ filter: "invert(14%) sepia(27%) saturate(5843%) hue-rotate(328deg) brightness(98%) contrast(98%)",
+ group: "s6"
+ },
+ section_06_check_out_4: {
+ name: "05 Logarithmisches Ableiten",
+ variants: 4,
+ color: "#3960A7",
+ filter: "invert(33%) sepia(56%) saturate(621%) hue-rotate(180deg) brightness(96%) contrast(95%)",
+ group: "s6"
+ },
+ section_06_check_out_5: {
+ name: "04 Kettenregel",
+ variants: 4,
+ color: "#E44FCD",
+ filter: "invert(76%) sepia(58%) saturate(7362%) hue-rotate(280deg) brightness(93%) contrast(93%)",
+ group: "s6"
+ },
+ section_07_check_in_1: {
+ name: "Newtonverfahren",
+ variants: 4,
+ color: "#278495",
+ filter: "invert(40%) sepia(10%) saturate(2946%) hue-rotate(142deg) brightness(107%) contrast(86%)",
+ group: "s7"
+ },
+ section_07_check_in_2: {
+ name: "Stationäre kritische Stelle",
+ variants: 4,
+ color: "#6D9D29",
+ filter: "invert(53%) sepia(90%) saturate(357%) hue-rotate(43deg) brightness(87%) contrast(88%)",
+ group: "s7"
+ },
+ section_07_check_in_modified2_4: {
+ name: "Extrema und Wendestelle (Duplikat Malte)",
+ variants: 4,
+ color: "#A3717F",
+ filter: "invert(51%) sepia(4%) saturate(3367%) hue-rotate(293deg) brightness(95%) contrast(75%)",
+ group: "s7"
+ },
+ section_07_check_out_1: {
+ name: "Grenzkostenfunktion",
+ variants: 4,
+ color: "#302FFF",
+ filter: "invert(12%) sepia(96%) saturate(6720%) hue-rotate(247deg) brightness(102%) contrast(101%)",
+ group: "s7"
+ },
+ section_07_check_out_2: {
+ name: "Kurvendiskussion: gebrochenrationale Funktion",
+ variants: 4,
+ color: "#BBCBC4",
+ filter: "invert(93%) sepia(3%) saturate(752%) hue-rotate(102deg) brightness(89%) contrast(85%)",
+ group: "s7"
+ },
+ section_07_check_out_3: {
+ name: "Maximalen Gewinn bestimmen",
+ variants: 4,
+ color: "#C5F99B",
+ filter: "invert(100%) sepia(16%) saturate(5613%) hue-rotate(328deg) brightness(109%) contrast(92%)",
+ group: "s7"
+ },
+ section_07_check_out_4: {
+ name: "Optimierung Gewinn",
+ variants: 4,
+ color: "#A3717F",
+ filter: "invert(51%) sepia(4%) saturate(3367%) hue-rotate(293deg) brightness(95%) contrast(75%)",
+ group: "s7"
+ },
+ section_07_check_out_5: {
+ name: "Optimierung Umsatz",
+ variants: 4,
+ color: "#395C44",
+ filter: "invert(28%) sepia(21%) saturate(737%) hue-rotate(86deg) brightness(102%) contrast(87%)",
+ group: "s7"
+ },
+ section_08_check_in_2: {
+ name: "01 partiell Diff",
+ variants: 4,
+ color: "#10F046",
+ filter: "invert(52%) sepia(95%) saturate(903%) hue-rotate(88deg) brightness(115%) contrast(90%)",
+ group: "s8"
+ },
+ section_08_check_in_3: {
+ name: "02 partiell Diff",
+ variants: 4,
+ color: "#E39FB2",
+ filter: "invert(78%) sepia(4%) saturate(2863%) hue-rotate(296deg) brightness(88%) contrast(102%)",
+ group: "s8"
+ },
+ section_08_check_out_2: {
+ name: "06 partiell Diff",
+ variants: 4,
+ color: "#01D504",
+ filter: "invert(43%) sepia(74%) saturate(1175%) hue-rotate(89deg) brightness(106%) contrast(114%)",
+ group: "s8"
+ },
+ section_08_check_out_3: {
+ name: "7.03 Det 3x3 Folie 16",
+ variants: 4,
+ color: "#C6F237",
+ filter: "invert(96%) sepia(38%) saturate(4597%) hue-rotate(13deg) brightness(104%) contrast(89%)",
+ group: "s8"
+ },
+ section_09_check_in_1: {
+ name: "wann ver-x-facht sich K",
+ variants: 4,
+ color: "#B64537",
+ filter: "invert(36%) sepia(12%) saturate(4301%) hue-rotate(324deg) brightness(93%) contrast(92%)",
+ group: "s9"
+ },
+ section_09_check_in_2: {
+ name: "Zinssatz i berechnen",
+ variants: 4,
+ color: "#8C9BF5",
+ filter: "invert(64%) sepia(5%) saturate(3975%) hue-rotate(195deg) brightness(98%) contrast(96%)",
+ group: "s9"
+ },
+ section_09_check_in_modified2_6and7: {
+ name: "Barwert Zahlungsstrom (Duplikat Malte)(Kopiert aus Barwert Endwert Zahlungsstrom)",
+ },
+ /*section_09_check_in_modified2_6: {
+ name: "Barwert Zahlungsstrom (Duplikat Malte)(Kopiert aus Barwert Endwert Zahlungsstrom)",
+ variants: 4,
+ color: "#910602",
+ filter: "invert(11%) sepia(63%) saturate(4965%) hue-rotate(14deg) brightness(103%) contrast(124%)",
+ group: "s9"
+ },
+ section_09_check_in_modified2_7: {
+ name: "Endwert Zahlungsstrom (Duplikat Malte)(Kopiert aus Barwert Endwert Zahlungsstrom)",
+ variants: 4,
+ color: "#C8B210",
+ filter: "invert(72%) sepia(81%) saturate(1388%) hue-rotate(8deg) brightness(93%) contrast(87%)",
+ group: "s9"
+ },*/
+ section_09_check_in_4: {
+ name: "BW",
+ variants: 4,
+ color: "#9F6D55",
+ filter: "invert(49%) sepia(5%) saturate(4049%) hue-rotate(334deg) brightness(89%) contrast(72%)",
+ group: "s9"
+ },
+ section_09_check_in_5: {
+ name: "EW",
+ variants: 4,
+ color: "#65D794",
+ filter: "invert(80%) sepia(24%) saturate(818%) hue-rotate(88deg) brightness(91%) contrast(88%)",
+ group: "s9"
+ },
+ section_09_check_in_6: {
+ name: "Grundbegriffe",
+ variants: 4,
+ color: "#162095",
+ filter: "invert(18%) sepia(23%) saturate(6913%) hue-rotate(217deg) brightness(94%) contrast(98%)",
+ group: "s9"
+ },
+ section_09_check_out_1: {
+ name: "Äquivalenzprinzip",
+ variants: 4,
+ color: "#DD5BE4",
+ filter: "invert(46%) sepia(92%) saturate(1381%) hue-rotate(268deg) brightness(96%) contrast(85%)",
+ group: "s9"
+ },
+ section_09_check_out_2: {
+ name: "Effektivzins 1",
+ variants: 4,
+ color: "#A4FFDC",
+ filter: "invert(91%) sepia(24%) saturate(563%) hue-rotate(85deg) brightness(103%) contrast(103%)",
+ group: "s9"
+ },
+ section_09_check_out_3: {
+ name: "Impl. Terminzinss.",
+ variants: 4,
+ color: "#BA9DCC",
+ filter: "invert(70%) sepia(13%) saturate(705%) hue-rotate(233deg) brightness(94%) contrast(91%)",
+ group: "s9"
+ },
+ section_09_check_out_4: {
+ name: "Barwert und Endwert eines Zahlungsstroms",
+ variants: 4,
+ color: "#D34FDB",
+ filter: "invert(45%) sepia(84%) saturate(1892%) hue-rotate(259deg) brightness(88%) contrast(94%)",
+ group: "s9"
+ },
+ section_09_check_out_5: {
+ name: "Endwert berechnen",
+ variants: 4,
+ color: "#910602",
+ filter: "invert(11%) sepia(63%) saturate(4965%) hue-rotate(14deg) brightness(103%) contrast(124%)",
+ group: "s9"
+ },
+ section_09_check_out_6: {
+ name: "Kapitalwert bestimmen",
+ variants: 4,
+ color: "#C8B210",
+ filter: "invert(72%) sepia(81%) saturate(1388%) hue-rotate(8deg) brightness(93%) contrast(87%)",
+ group: "s9"
+ },
+ section_10_check_in_3: {
+ name: "Rentenbarwertfaktor",
+ variants: 4,
+ color: "#3BDBAA",
+ filter: "invert(92%) sepia(80%) saturate(1117%) hue-rotate(82deg) brightness(101%) contrast(69%)",
+ group: "s10"
+ },
+ section_10_check_in_4: {
+ name: "Rentenendwertfaktor",
+ variants: 4,
+ color: "#916F06",
+ filter: "invert(43%) sepia(44%) saturate(6440%) hue-rotate(38deg) brightness(93%) contrast(95%)",
+ group: "s10"
+ },
+ section_10_check_out_1: {
+ name: "Rente n berechnen",
+ variants: 4,
+ color: "#C5B6C7",
+ filter: "invert(80%) sepia(6%) saturate(490%) hue-rotate(246deg) brightness(91%) contrast(96%)",
+ group: "s10"
+ },
+ section_10_check_out_modified2_6: {
+ name: "Rentenbarwert, Rentenendwert (Duplikat Malte)",
+ variants: 4,
+ color: "#DA8376",
+ filter: "invert(76%) sepia(76%) saturate(1360%) hue-rotate(305deg) brightness(86%) contrast(86%)",
+ group: "s10"
+ },
+ section_10_check_out_3: {
+ name: "Annuität berechnen",
+ variants: 4,
+ color: "#88383B",
+ filter: "invert(27%) sepia(85%) saturate(439%) hue-rotate(308deg) brightness(84%) contrast(94%)",
+ group: "s10"
+ },
+ section_10_check_out_4: {
+ name: "Annutätentilgung, Tilgungsplan",
+ variants: 4,
+ color: "#71BC2E",
+ filter: "invert(61%) sepia(95%) saturate(366%) hue-rotate(48deg) brightness(91%) contrast(84%)",
+ group: "s10"
+ },
+ section_10_check_out_5: {
+ name: "Laufzeit eines Darlehens",
+ variants: 4,
+ color: "#B20EE3",
+ filter: "invert(22%) sepia(84%) saturate(4934%) hue-rotate(280deg) brightness(90%) contrast(116%)",
+ group: "s10"
+ },
+ section_10_check_out_6: {
+ name: "Restschuld eines Darlehens",
+ variants: 4,
+ color: "#C751FB",
+ filter: "invert(41%) sepia(23%) saturate(6695%) hue-rotate(255deg) brightness(101%) contrast(97%)",
+ group: "s10"
+ },
+ section_11_check_in_modified_7: {
+ name: "MatrixMultiplikation",
+ variants: 4,
+ color: "#496108",
+ filter: "invert(32%) sepia(17%) saturate(2438%) hue-rotate(36deg) brightness(96%) contrast(94%)",
+ group: "s11"
+ },
+ section_11_check_in_modified_8: {
+ name: "Transponieren",
+ variants: 4,
+ color: "#4DA97E",
+ filter: "invert(54%) sepia(42%) saturate(476%) hue-rotate(100deg) brightness(100%) contrast(84%)",
+ group: "s11"
+ },
+ section_11_check_in_modified_9: {
+ name: "8.12 LGS Matrix-Form Folie 11 (5.1 LGS) (Duplikat Malte)",
+ variants: 4,
+ color: "#F8C255",
+ filter: "invert(76%) sepia(85%) saturate(388%) hue-rotate(335deg) brightness(100%) contrast(95%)",
+ group: "s11"
+ },
+ section_11_check_out_1: {
+ name: "6.02 extern Matrizenrechnung",
+ variants: 4,
+ color: "#642E0E",
+ filter: "invert(18%) sepia(12%) saturate(6525%) hue-rotate(354deg) brightness(97%) contrast(92%)",
+ group: "s11"
+ },
+ section_11_check_out_2: {
+ name: "6.03 Matrix-Vektor-Produkt",
+ variants: 4,
+ color: "#16C9D7",
+ filter: "invert(67%) sepia(27%) saturate(3791%) hue-rotate(137deg) brightness(101%) contrast(83%)",
+ group: "s11"
+ },
+ section_11_check_out_3: {
+ name: "6.06 Addition von 2 Linearkombi",
+ variants: 4,
+ color: "#C768E5",
+ filter: "invert(51%) sepia(33%) saturate(1489%) hue-rotate(239deg) brightness(96%) contrast(86%)",
+ group: "s11"
+ },
+ section_11_check_out_4: {
+ name: "6.08 Folie S.18 Matrixprodukt",
+ variants: 4,
+ color: "#DA8376",
+ filter: "invert(76%) sepia(76%) saturate(1360%) hue-rotate(305deg) brightness(86%) contrast(86%)",
+ group: "s11"
+ },
+ section_11_check_out_5: {
+ name: "6.11 Operationen von 3 Matrizen",
+ variants: 4,
+ color: "#93916B",
+ filter: "invert(62%) sepia(7%) saturate(1282%) hue-rotate(19deg) brightness(91%) contrast(88%)",
+ group: "s11"
+ },
+ section_11_check_out_6: {
+ name: "8.05 LGS 2x2",
+ variants: 4,
+ color: "#A4AA17",
+ filter: "invert(57%) sepia(80%) saturate(463%) hue-rotate(23deg) brightness(95%) contrast(84%)",
+ group: "s11"
+ },
+ section_11_check_out_7: {
+ name: "8.06 LGS 3x3",
+ variants: 4,
+ color: "#62CB69",
+ filter: "invert(99%) sepia(33%) saturate(3140%) hue-rotate(51deg) brightness(87%) contrast(79%)",
+ group: "s11"
+ },
+ section_12_check_in_4: {
+ name: "Inverse 2x2",
+ variants: 4,
+ color: "#CD51BA",
+ filter: "invert(52%) sepia(46%) saturate(3109%) hue-rotate(280deg) brightness(85%) contrast(86%)",
+ group: "s12"
+ },
+ section_12_check_in_5: {
+ name: "Streichungsmatrix",
+ variants: 4,
+ color: "#877931",
+ filter: "invert(51%) sepia(15%) saturate(1482%) hue-rotate(13deg) brightness(88%) contrast(89%)",
+ group: "s12"
+ },
+ section_12_check_in_6: {
+ name: "7.01 Det 2x2",
+ variants: 4,
+ color: "#DDB76F",
+ filter: "invert(77%) sepia(47%) saturate(395%) hue-rotate(353deg) brightness(90%) contrast(91%)",
+ group: "s12"
+ },
+ section_12_check_out_modified_1: {
+ name: "7.03 Det 3x3 Folie 16",
+ variants: 4,
+ color: "#C14532",
+ filter: "invert(29%) sepia(72%) saturate(1119%) hue-rotate(334deg) brightness(100%) contrast(91%)",
+ group: "s12"
+ },
+ section_12_check_out_modified_2: {
+ name: "Inverse 3x3",
+ variants: 4,
+ color: "#70C3CA",
+ filter: "invert(72%) sepia(7%) saturate(2161%) hue-rotate(136deg) brightness(100%) contrast(88%)",
+ group: "s12"
+ },
+ section_12_check_out_modified_3: {
+ name: "Inverse singulär 3x3",
+ variants: 4,
+ color: "#6AC2E3",
+ filter: "invert(67%) sepia(76%) saturate(312%) hue-rotate(161deg) brightness(93%) contrast(90%)",
+ group: "s12"
+ },
+ section_12_check_out_modified_4: {
+ name: "Laplace 4x4 (TF) (Duplikat Malte)",
+ variants: 4,
+ color: "#8F822E",
+ filter: "invert(44%) sepia(53%) saturate(494%) hue-rotate(15deg) brightness(101%) contrast(89%)",
+ group: "s12"
+ },
+ section_13_check_out_modified_1: {
+ name: "Simplex Pivotelement Dualer Simplex",
+ variants: 4,
+ color: "#040237",
+ filter: "invert(5%) sepia(65%) saturate(6178%) hue-rotate(225deg) brightness(82%) contrast(117%)",
+ group: "s13"
+ },
+ section_13_check_out_modified_2: {
+ name: "Simplex Pivotelement+Neue Basis angeben",
+ variants: 4,
+ color: "#AEC069",
+ filter: "invert(74%) sepia(10%) saturate(1407%) hue-rotate(32deg) brightness(95%) contrast(97%)",
+ group: "s13"
+ },
+ section_13_check_out_modified_3: {
+ name: "Simplex dual",
+ variants: 4,
+ color: "#C6E2B2",
+ filter: "invert(99%) sepia(25%) saturate(1040%) hue-rotate(32deg) brightness(96%) contrast(83%)",
+ group: "s13"
+ },
+ section_13_check_out_modified_4: {
+ name: "Simplex Tableau aufstellen (Duplikat Malte)",
+ variants: 4,
+ color: "#0EE073",
+ filter: "invert(74%) sepia(55%) saturate(3187%) hue-rotate(95deg) brightness(100%) contrast(89%)",
+ group: "s13",
+ onsuccess: "_finish",
+ onfailure: "_finish"
+ }
+ }
+};
+
+/*Preparatory courses WiSe 2023-24*/
+let quizObjectAsString = '{"groups": {"start": "Start", "t0_syn_1": "Syntax", "t1_fra_1": "Bruchrechnung", "t3_frabin_1": "Binom. Formeln", "t4_pq_1": "pq-Formel", "t5_rul_1": "Potenzrechenregeln", "t7_der_1": "Ableitungen"}, "questions": {"start": {"name": "Start", "group": "start"}, "t0_syn_1_a": {"name": "Gleichung eingeben (Multiplikation)", "variants": 4, "color": "#573036", "filter": "invert(20%) sepia(11%) saturate(2292%) hue-rotate(301deg) brightness(88%) contrast(87%)"}, "t0_syn_1_b": {"name": "Gleichung eingeben (Division)", "variants": 4, "color": "#1BA1C7", "filter": "invert(46%) sepia(89%) saturate(419%) hue-rotate(147deg) brightness(97%) contrast(96%)"}, "t0_syn_1_c": {"name": "Potenzen", "variants": 4, "color": "#B38ABB", "filter": "invert(67%) sepia(28%) saturate(423%) hue-rotate(244deg) brightness(85%) contrast(89%)"}, "t0_syn_1_d": {"name": "Rationale Ausdr\u00fccke", "variants": 3, "color": "#D558A8", "filter": "invert(50%) sepia(90%) saturate(907%) hue-rotate(290deg) brightness(87%) contrast(90%)"}, "t0_syn_1_e": {"name": "Wurzelzeichen", "variants": 4, "color": "#1B5658", "filter": "invert(26%) sepia(12%) saturate(2407%) hue-rotate(133deg) brightness(95%) contrast(86%)"}, "t0_syn_1_f": {"name": "Mehrere L\u00f6sungen", "variants": 4, "color": "#810311", "filter": "invert(8%) sepia(64%) saturate(6140%) hue-rotate(346deg) brightness(93%) contrast(104%)"}, "t0_syn_1_g": {"name": "Gleichung mehrschrittig l\u00f6sen", "variants": 4, "color": "#74CD27", "filter": "invert(68%) sepia(76%) saturate(507%) hue-rotate(42deg) brightness(95%) contrast(83%)"}, "t0_syn_1_h": {"name": "Griechische Buchstaben", "variants": 4, "color": "#3CF48A", "filter": "invert(72%) sepia(40%) saturate(699%) hue-rotate(89deg) brightness(101%) contrast(98%)"}, "t0_syn_1_i": {"name": "Syntax-Endboss", "variants": 4, "color": "#77B211", "filter": "invert(64%) sepia(52%) saturate(5261%) hue-rotate(48deg) brightness(107%) contrast(87%)"}, "t1_fra_1_bi-a": {"name": "K\u00fcrzen zweier einfacher Br\u00fcche", "variants": 4, "color": "#FD9C80", "filter": "invert(84%) sepia(53%) saturate(4565%) hue-rotate(313deg) brightness(115%) contrast(108%)"}, "t1_fra_1_bi-b": {"name": "K\u00fcrzen zweier Br\u00fcche mit Variablen", "variants": 4, "color": "#E249B2", "filter": "invert(52%) sepia(64%) saturate(4425%) hue-rotate(292deg) brightness(93%) contrast(90%)"}, "t1_fra_1_bi-c": {"name": "K\u00fcrzen zweier Br\u00fcche mit Variablen und Zahlen", "variants": 4, "color": "#D57774", "filter": "invert(81%) sepia(50%) saturate(3032%) hue-rotate(305deg) brightness(86%) contrast(94%)"}, "t1_fra_1_bi-d": {"name": "K\u00fcrzen zweier Br\u00fcche mit Termen", "variants": 4, "color": "#944A6C", "filter": "invert(34%) sepia(25%) saturate(1028%) hue-rotate(280deg) brightness(96%) contrast(89%)"}, "t1_fra_1_bii-a": {"name": "Einfachen Bruch erweitern", "variants": 4, "color": "#9B49A2", "filter": "invert(35%) sepia(65%) saturate(573%) hue-rotate(248deg) brightness(92%) contrast(92%)"}, "t1_fra_1_bii-b": {"name": "Bruch mit Variablen erweitern", "variants": 4, "color": "#FA00D1", "filter": "invert(54%) sepia(100%) saturate(7435%) hue-rotate(298deg) brightness(97%) contrast(127%)"}, "t1_fra_1_bii-c": {"name": "Bruch mit Variablen und Zahlen erweitern", "variants": 4, "color": "#E2AFDA", "filter": "invert(96%) sepia(86%) saturate(2059%) hue-rotate(203deg) brightness(96%) contrast(83%)"}, "t1_fra_1_ca": {"name": "Einfache Addition von Br\u00fcchen", "variants": 4, "color": "#EB3E57", "filter": "invert(33%) sepia(19%) saturate(6570%) hue-rotate(328deg) brightness(97%) contrast(89%)"}, "t1_fra_1_cb": {"name": "Addition von Br\u00fcchen mit Variablen und gleichem Nenner", "variants": 4, "color": "#7E182C", "filter": "invert(14%) sepia(27%) saturate(5843%) hue-rotate(328deg) brightness(98%) contrast(98%)"}, "t1_fra_1_cc": {"name": "Addition von Br\u00fcchen mit Variablen und unterschiedlichen Nennern", "variants": 4, "color": "#3960A7", "filter": "invert(33%) sepia(56%) saturate(621%) hue-rotate(180deg) brightness(96%) contrast(95%)"}, "t1_fra_1_cd": {"name": "Addition von Br\u00fcchen mit einer Variablen und unterschiedlichen Nennern", "variants": 4, "color": "#E44FCD", "filter": "invert(76%) sepia(58%) saturate(7362%) hue-rotate(280deg) brightness(93%) contrast(93%)"}, "t1_fra_1_ce": {"name": "Addition von Br\u00fcchen mit Variablen und unterschiedlichen Nennern I", "variants": 4, "color": "#278495", "filter": "invert(40%) sepia(10%) saturate(2946%) hue-rotate(142deg) brightness(107%) contrast(86%)"}, "t1_fra_1_cf": {"name": "Addition von Br\u00fcchen mit Variablen und unterschiedlichen Nennern II", "variants": 4, "color": "#6D9D29", "filter": "invert(53%) sepia(90%) saturate(357%) hue-rotate(43deg) brightness(87%) contrast(88%)"}, "t1_fra_1_da": {"name": "Multiplikation zweier einfacher Br\u00fcche", "variants": 4, "color": "#302FFF", "filter": "invert(12%) sepia(96%) saturate(6720%) hue-rotate(247deg) brightness(102%) contrast(101%)"}, "t1_fra_1_db": {"name": "Multiplikation zweier Br\u00fcche mit Variablen", "variants": 4, "color": "#BBCBC4", "filter": "invert(93%) sepia(3%) saturate(752%) hue-rotate(102deg) brightness(89%) contrast(85%)"}, "t1_fra_1_dc": {"name": "Multiplikation Bruch mit Zahlen, Bruch mit Variablen, Ganzzahl", "variants": 4, "color": "#C5F99B", "filter": "invert(100%) sepia(16%) saturate(5613%) hue-rotate(328deg) brightness(109%) contrast(92%)"}, "t1_fra_1_dd": {"name": "Multiplikation zweier Br\u00fcche mit Termen", "variants": 4, "color": "#A3717F", "filter": "invert(51%) sepia(4%) saturate(3367%) hue-rotate(293deg) brightness(95%) contrast(75%)"}, "t1_fra_1_de": {"name": "Einfacher Doppelbruch", "variants": 4, "color": "#395C44", "filter": "invert(28%) sepia(21%) saturate(737%) hue-rotate(86deg) brightness(102%) contrast(87%)"}, "t1_fra_1_df": {"name": "Bruch und Geteilt-Rechnung", "variants": 4, "color": "#10F046", "filter": "invert(52%) sepia(95%) saturate(903%) hue-rotate(88deg) brightness(115%) contrast(90%)"}, "t1_fra_1_dg": {"name": "Doppelbruch mit Zahlen und Variablen", "variants": 4, "color": "#E39FB2", "filter": "invert(78%) sepia(4%) saturate(2863%) hue-rotate(296deg) brightness(88%) contrast(102%)"}, "t1_fra_1_dh": {"name": "Doppelbruch mit Termen", "variants": 4, "color": "#23F5CC", "filter": "invert(100%) sepia(72%) saturate(2181%) hue-rotate(84deg) brightness(106%) contrast(91%)"}, "t1_fra_1_ea": {"name": "Bruchrechnung Kombination I", "variants": 4, "color": "#01D504", "filter": "invert(43%) sepia(74%) saturate(1175%) hue-rotate(89deg) brightness(106%) contrast(114%)"}, "t1_fra_1_eb": {"name": "Bruchrechnung Kombination II", "variants": 4, "color": "#C6F237", "filter": "invert(96%) sepia(38%) saturate(4597%) hue-rotate(13deg) brightness(104%) contrast(89%)"}, "t1_fra_1_ec": {"name": "Bruchrechnung Kombination III", "variants": 4, "color": "#B64537", "filter": "invert(36%) sepia(12%) saturate(4301%) hue-rotate(324deg) brightness(93%) contrast(92%)"}, "t3_frabin_1_g": {"name": "Binomische Formeln Ia - Erste binomische Formel", "variants": 4, "color": "#8C9BF5", "filter": "invert(64%) sepia(5%) saturate(3975%) hue-rotate(195deg) brightness(98%) contrast(96%)"}, "t3_frabin_1_h": {"name": "Binomische Formeln Ib - Zweite binomische Formel", "variants": 4, "color": "#9F6D55", "filter": "invert(49%) sepia(5%) saturate(4049%) hue-rotate(334deg) brightness(89%) contrast(72%)"}, "t3_frabin_1_i": {"name": "Binomische Formeln Ic - Dritte binomische Formel", "variants": 4, "color": "#65D794", "filter": "invert(80%) sepia(24%) saturate(818%) hue-rotate(88deg) brightness(91%) contrast(88%)"}, "t3_frabin_1_j": {"name": "Binomische Formeln I - Anwendungsaufgabe", "variants": 4, "color": "#162095", "filter": "invert(18%) sepia(23%) saturate(6913%) hue-rotate(217deg) brightness(94%) contrast(98%)"}, "t3_frabin_1_k": {"name": "Bruchrechenregeln Ig2 - Bruch mit binomischem Term erweitern 2 (copy)", "variants": 3, "color": "#DD5BE4", "filter": "invert(46%) sepia(92%) saturate(1381%) hue-rotate(268deg) brightness(96%) contrast(85%)"}, "t4_pq_1_a": {"name": "p-q-Formal Ia - Termumformung", "variants": 4, "color": "#A4FFDC", "filter": "invert(91%) sepia(24%) saturate(563%) hue-rotate(85deg) brightness(103%) contrast(103%)"}, "t4_pq_1_b": {"name": "p-q-Formel Ib - pq-Formel", "variants": 4, "color": "#BA9DCC", "filter": "invert(70%) sepia(13%) saturate(705%) hue-rotate(233deg) brightness(94%) contrast(91%)"}, "t4_pq_1_c": {"name": "p-q-Formel I - Endboss", "variants": 4, "color": "#D34FDB", "filter": "invert(45%) sepia(84%) saturate(1892%) hue-rotate(259deg) brightness(88%) contrast(94%)"}, "t5_rul_1_a": {"name": "Potenzrechenregeln Ia \u2013 Exponenten addieren", "variants": 2, "color": "#910602", "filter": "invert(11%) sepia(63%) saturate(4965%) hue-rotate(14deg) brightness(103%) contrast(124%)"}, "t5_rul_1_b": {"name": "Potenzrechenregeln Ib \u2013 Exponenten subtrahieren", "variants": 2, "color": "#C8B210", "filter": "invert(72%) sepia(81%) saturate(1388%) hue-rotate(8deg) brightness(93%) contrast(87%)"}, "t5_rul_1_c": {"name": "Potenzrechenregeln Ic - Wurzel als Potenz darstellen", "variants": 4, "color": "#3BDBAA", "filter": "invert(92%) sepia(80%) saturate(1117%) hue-rotate(82deg) brightness(101%) contrast(69%)"}, "t5_rul_1_d": {"name": "Potenzrechenregeln Id \u2013 Exponenten multiplizieren", "variants": 2, "color": "#916F06", "filter": "invert(43%) sepia(44%) saturate(6440%) hue-rotate(38deg) brightness(93%) contrast(95%)"}, "t5_rul_1_e": {"name": "Potenzrechenregeln Ie - Potenzrechenregeln anwenden", "variants": 2, "color": "#C5B6C7", "filter": "invert(80%) sepia(6%) saturate(490%) hue-rotate(246deg) brightness(91%) contrast(96%)"}, "t5_rul_1_f": {"name": "Potenzrechenregeln I - Endboss", "variants": 2, "color": "#88383B", "filter": "invert(27%) sepia(85%) saturate(439%) hue-rotate(308deg) brightness(84%) contrast(94%)"}, "t7_der_1_a": {"name": "Ganzzahlige Summanden ableiten", "variants": 4, "color": "#71BC2E", "filter": "invert(61%) sepia(95%) saturate(366%) hue-rotate(48deg) brightness(91%) contrast(84%)"}, "t7_der_1_b": {"name": "Gebrochenrationale Summanden ableiten", "variants": 4, "color": "#B20EE3", "filter": "invert(22%) sepia(84%) saturate(4934%) hue-rotate(280deg) brightness(90%) contrast(116%)"}, "t7_der_1_c": {"name": "Produkte ableiten I", "variants": 4, "color": "#C751FB", "filter": "invert(41%) sepia(23%) saturate(6695%) hue-rotate(255deg) brightness(101%) contrast(97%)"}, "t7_der_1_d": {"name": "Produkte ableiten II", "variants": 4, "color": "#496108", "filter": "invert(32%) sepia(17%) saturate(2438%) hue-rotate(36deg) brightness(96%) contrast(94%)"}, "t7_der_1_e": {"name": "Division ableiten I", "variants": 4, "color": "#4DA97E", "filter": "invert(54%) sepia(42%) saturate(476%) hue-rotate(100deg) brightness(100%) contrast(84%)"}, "t7_der_1_f": {"name": "Division ableiten II", "variants": 4, "color": "#F8C255", "filter": "invert(76%) sepia(85%) saturate(388%) hue-rotate(335deg) brightness(100%) contrast(95%)"}, "t7_der_1_g": {"name": "Kettenregel I", "variants": 4, "color": "#642E0E", "filter": "invert(18%) sepia(12%) saturate(6525%) hue-rotate(354deg) brightness(97%) contrast(92%)"}, "t7_der_1_h": {"name": "Kettenregel II", "variants": 4, "color": "#16C9D7", "filter": "invert(67%) sepia(27%) saturate(3791%) hue-rotate(137deg) brightness(101%) contrast(83%)"}, "t7_der_1_i": {"name": "Gemischtes I", "variants": 4, "color": "#C768E5", "filter": "invert(51%) sepia(33%) saturate(1489%) hue-rotate(239deg) brightness(96%) contrast(86%)"}, "t7_der_1_j": {"name": "Gemischtes II", "variants": 4, "color": "#DA8376", "filter": "invert(76%) sepia(76%) saturate(1360%) hue-rotate(305deg) brightness(86%) contrast(86%)"}, "t7_der_1_k": {"name": "Gemischtes III", "variants": 4, "color": "#93916B", "filter": "invert(62%) sepia(7%) saturate(1282%) hue-rotate(19deg) brightness(91%) contrast(88%)"}, "t7_der_1_l": {"name": "Gemischtes IV", "variants": 4, "color": "#A4AA17", "filter": "invert(57%) sepia(80%) saturate(463%) hue-rotate(23deg) brightness(95%) contrast(84%)"}, "t7_der_1_m": {"name": "Gemischtes V", "variants": 4, "color": "#62CB69", "filter": "invert(99%) sepia(33%) saturate(3140%) hue-rotate(51deg) brightness(87%) contrast(79%)"}, "t7_der_1_n": {"name": "Gemischtes VI", "variants": 4, "color": "#CD51BA", "filter": "invert(52%) sepia(46%) saturate(3109%) hue-rotate(280deg) brightness(85%) contrast(86%)"}}}';
+quizObject = JSON.parse(quizObjectAsString);
+
+var processedAttempts = 0;
+var allAttempts = 0;
+//var CryptoObj =
+var fetches = {};
+var urls = {};
+
+//Paginate quiz objects
+let page = 0;
+for(let i in quizObject.questions) {
+ quizObject.questions[i].page = page;
+ let toAdd = quizObject.questions[i].variants == undefined ? 1 : quizObject.questions[i].variants;
+ page += toAdd;
+}
+
+let Encoder = new TextEncoder();
+//Hash functions to encrypt user id
+async function sha256(message) {
+ // encode as UTF-8
+ const msgBuffer = Encoder.encode(message);
+
+ // hash the message
+ const hashBuffer = await crypto.subtle.digest('SHA-256', msgBuffer);
+
+ // convert ArrayBuffer to Array
+ const hashArray = Array.from(new Uint8Array(hashBuffer));
+
+ // convert bytes to hex string
+ const hashHex = hashArray.map(b => ('00' + b.toString(16)).slice(-2)).join('');
+ return hashHex;
+}
+
+let monthTranslator = {
+ "Januar":0,
+ "Februar":1,
+ "März":2,
+ "März":2,
+ "April":3,
+ "Mai":4,
+ "Juni":5,
+ "Juli":6,
+ "August":7,
+ "September":8,
+ "Oktober":9,
+ "November":10,
+ "Dezember":11
+};
+//----------------CLASSES-------------------------
+class CQuestionAttempt {
+ constructor(timestampOrString, questionId, action, outcome, variant) {
+ this.variant = variant;
+ if(this.variant == undefined) {
+ this.variant = 1;
+ }
+ //Check timestampOrString
+ this.timestamp;
+ if(Number.isInteger(timestampOrString)) {
+ this.timestamp = timestampOrString;
+ }
+ else if(timestampOrString instanceof String || typeof timestampOrString === 'string') {
+ //German with full months written?
+ this.timestamp = this.getTimestampFromGermanTime(timestampOrString);
+ }
+ this.questionId = questionId;
+ this.action = action;
+ this.outcome = outcome;
+ if(!this.timestamp) {
+ //console.log("timestring could not be converted");
+ this.timestamp = timestampOrString;
+ }
+ }
+
+ getTimestampFromGermanTime(timestring) {
+ let hasAmPm = ((timestring.search(/ am/i) + timestring.search(/ pm/i)) > -2);
+ let time;
+ if(hasAmPm == true) {
+ console.log("special handling for AM / PM time string is neccessary");
+ return false;
+ }
+ //let matchAllResult = timestring.matchAll(/(\d+)\. (.{4,}?) (\d{2,4}), (\d+):(\d+):(\d+)/g);
+ let matchAllResult = timestring.matchAll(/(\d+)\.* (.{4,}?) (\d{2,4}),* (\d+):(\d+):*(\d*)/g);
+ let matches = Array.from(matchAllResult)[0];
+ if(!matches) {
+ //Give it another try, matching e. g. 18/09/23, 11:55:42
+ matchAllResult = timestring.matchAll(/(\d+)[\.\/-](\d+)[\.\/-](\d+),* (\d+):(\d+):*(\d*)/g);
+ matches = Array.from(matchAllResult)[0];
+ if(!matches) {
+ //probably not german, try Date
+ //console.log(timestring)
+ time = new Date(timestring);
+ }
+ else {
+ let year = matches[3]
+ if(matches[3].length == 2) {
+ year = "20"+year;
+ }
+ let month = parseInt(matches[2])-1;
+ time = new Date(year, month, matches[1], matches[4], matches[5], matches[6]);
+ }
+ }
+ else {
+ //1: day of month, 2: month in words, 3: year, 4: hours, 5: minutes, 6:seconds
+ if(monthTranslator[matches[2]] == undefined) {
+ //probably not german
+ return false;
+ }
+
+ time = new Date(matches[3], monthTranslator[matches[2]], matches[1], matches[4], matches[5], matches[6]);
+ }
+ if(isNaN(time)) {
+ return false;
+ }
+ return time.getTime();
+ }
+}
+
+class CUser {
+ constructor(idOrNode) {
+ let object = this;
+ this.Parser = new DOMParser();
+ this.QuestionAttempts = [];
+
+ if(idOrNode instanceof String || typeof idOrNode === 'string') {
+ this.id = idOrNode;
+ }
+ else if(idOrNode instanceof Element) {
+ if(idOrNode.tagName == "TR") {
+ let idNode = idOrNode.querySelector(".c3");
+ if(idNode == undefined) {
+ console.log("no id found for this row");
+ return;
+ }
+ this.id = idNode.innerHTML;
+
+ let reviewLink = idOrNode.querySelector(".reviewlink");
+ if(reviewLink == undefined) {
+ console.log("no review link found for this row");
+ return;
+ }
+ this.addAttempt(reviewLink.href);
+ }
+ }
+ else {
+ console.log("unknown type");
+ }
+ }
+
+ addAttempt(reviewUrl) {
+ let object = this;
+ if(reviewUrl == undefined) {
+ return;
+ }
+ fetch(reviewUrl)
+ .then(function(response) {
+ return response.text();
+ })
+ .then(function(htmlText) {
+ let fetchedPage = object.Parser.parseFromString(htmlText, "text/html");
+
+ let allQuestions = fetchedPage.querySelectorAll(".que");
+ if(allQuestions.length <= 1) {
+ //Sometimes, default is to show questions by pages. In this case, reload the page with all questions shown.
+ //Get url from .othernav or simply add "&showall=1" to the url.
+ return fetch(reviewUrl+"&showall=1").then(function(responseShowAll) {
+ return responseShowAll.text();
+ })
+ .then(function(htmlTextShowAll) {
+ let fetchedPageShowAll = object.Parser.parseFromString(htmlTextShowAll, "text/html");
+ //console.log(fetchedPageShowAll.querySelectorAll(".que"));
+ return fetchedPageShowAll;
+ });
+ }
+ else {
+ return fetchedPage;
+ }
+ })
+ .then(function(fetchedPageOrShowAll) {
+ //test = fetchedPageOrShowAll;
+ let allQuestions = fetchedPageOrShowAll.querySelectorAll(".que");
+ //console.log(allQuestions);
+ if(allQuestions.length < 1) {
+ throw new Error("bad amount of questions");
+ }
+
+ //Assume each question is shown, even the unattended. Then, allQuestions can be paginated as in quizObject.
+ //Loop through questions and variants in quiz object and append question information one by one.
+ let page = 0;
+ let questionIds = Object.keys(quizObject.questions);
+ let lastPage = questionIds.length-1;
+ for(let questionName in quizObject.questions) {
+ //The variant part here differs in control group analysis.
+ //let variants = quizObject.questions[questionName].variants == undefined ? 1 : quizObject.questions[questionName].variants;
+ //for(let i = 0;i<variants;i++) {
+ //console.log(page);
+ let relevantQuestionNode = allQuestions[page];
+ //console.log(page);
+ //fetch all question attempts from history
+ let previousQuestionAttemptUrls = relevantQuestionNode.querySelectorAll(".history a[id*='action_link']:not(.history tr a)");
+ for(let j=0;j<previousQuestionAttemptUrls.length;j++) {
+ let fetchId = Date.now().toString(36) + Math.random().toString(36).slice(2);
+ fetches[fetchId] = 0;
+ urls[fetchId] = previousQuestionAttemptUrls[j].href;
+ fetch(previousQuestionAttemptUrls[j].href)
+ .then(function(response) {
+ return response.text();
+ })
+ .then(function(htmlText) {
+ let fetchedQuestionAttemptHistoryPage = object.Parser.parseFromString(htmlText, "text/html");
+ let infoTable = fetchedQuestionAttemptHistoryPage.querySelector(".history .generaltable");
+ if(infoTable == undefined) {
+ throw new Error("no table found for history number "+i);
+ }
+
+ let questionAttemptInfo = object.getQuestionAttemptInfoFromTable(infoTable);
+
+ //Get variant from Seed: (.*?) info in action field.
+ let variant = 1;
+ let matchAllResult = questionAttemptInfo.action.matchAll(/Seed: (.*?);/g);
+ if(!!matchAllResult) {
+ let matches = Array.from(matchAllResult)[0]
+ //console.log(matches);
+ if(matches != undefined && matches[1] != undefined && matches[1] != "") {
+ variant = matches[1];
+ }
+ }
+
+ object.QuestionAttempts.push(new CQuestionAttempt(questionAttemptInfo.timestring, questionName, questionAttemptInfo.action, questionAttemptInfo.status, /*i+1*/variant));
+ fetches[fetchId] = 1;
+ })
+ .catch(function(error) {
+ console.log("Error fetching question attempt from history.");
+ console.log(error);
+ });
+ }
+
+ //Fetch most recent question attempt. This one is found on the overview page without clicking.
+ let shownTable = allQuestions[page].querySelector(".generaltable");
+ if(shownTable == undefined) {
+ throw new Error("no table found for question "+questionName);
+ }
+ let questionAttemptInfo = object.getQuestionAttemptInfoFromTable(shownTable);
+
+ //Get variant from Seed: (.*?) info in action field.
+ let variant = 1;
+ let matchAllResult = questionAttemptInfo.action.matchAll(/Seed: (.*?);/g);
+ if(!!matchAllResult) {
+ let matches = Array.from(matchAllResult)[0]
+ //console.log(matches);
+ if(matches != undefined && matches[1] != undefined && matches[1] != "") {
+ variant = matches[1];
+ }
+ }
+
+ object.QuestionAttempts.push(new CQuestionAttempt(questionAttemptInfo.timestring, questionName, questionAttemptInfo.action, questionAttemptInfo.status, variant));
+
+ if(page == lastPage) {
+ processedAttempts++;
+ console.log("(Nearly) processed "+processedAttempts+" of "+allAttempts+ " attempts.");
+ }
+
+ page++;
+ //}
+ }
+ })
+ .catch(function(error) {
+ console.log("error in promise chain");
+ console.log(error);
+ });
+ }
+
+ getQuestionAttemptInfoFromTable(tableNode) {
+ if(tableNode == undefined) {
+ return false;
+ }
+ let lastRow = tableNode.querySelector(".current.lastrow");
+ if(lastRow == undefined) {
+ return false;
+ }
+ //Assume c1 be the time, c2 be the action text and c3 be the status
+ let timestringNode = lastRow.querySelector(".c1");
+ let actionNode = lastRow.querySelector(".c2");
+ let statusNode = lastRow.querySelector(".c3");
+
+ if(timestringNode == undefined || statusNode == undefined) {
+ return false;
+ }
+
+ return {timestring:timestringNode.innerHTML, action:(actionNode.innerHTML == undefined ? "" : actionNode.innerHTML), status:statusNode.innerHTML};
+ }
+
+ async getAttemptsAsCSV(addUserCol, addHeadingRow, encryptId, getRidOfInitializationAttempts) {
+ let csvString = "";
+ if(addUserCol == undefined) {
+ addUserCol = true;
+ }
+ if(addHeadingRow == undefined) {
+ addHeadingRow = false;
+ }
+ if(encryptId == undefined) {
+ encryptId = true;
+ }
+ let id = this.id;
+ if(encryptId == true) {
+ //Because by default, Moodle's export results function returns Matrikelnummern as int, we encrypt the int too to ensure consistent results.
+ let toEncrypt = parseInt(id);
+ if(!isNaN(toEncrypt)) {
+ id = await sha256(""+toEncrypt);
+ }
+ else {
+ //In case not the Matricel Id is listed, the e-mail-address will be hashed here to identify unique users.
+ id = await sha256(""+id);
+ }
+ }
+ if(getRidOfInitializationAttempts == undefined) {
+ getRidOfInitializationAttempts = true;
+ }
+
+
+ if(addHeadingRow == true) {
+ if(addUserCol == true) {
+ csvString += "user_id;";
+ }
+ csvString += "timestamp;question_id;variant;action;outcome;next_timestamp;next_question_id;next_variant\n";
+ }
+
+ //Sort attempts by time. To add next question attribute.
+ let SortedAttempts = this.getSanitizedAttempts(getRidOfInitializationAttempts);
+
+ for(let i=0;i<SortedAttempts.length;i++) {
+ let relevantVars = []
+ if(addUserCol == true) {
+ relevantVars.push(id);
+ }
+ relevantVars.push(SortedAttempts[i].timestamp, SortedAttempts[i].questionId, SortedAttempts[i].variant, SortedAttempts[i].action, SortedAttempts[i].outcome);
+ if(SortedAttempts[i+1] != undefined) {
+ relevantVars.push(SortedAttempts[i+1].timestamp, SortedAttempts[i+1].questionId, SortedAttempts[i+1].variant);
+ //relevantVars.push(SortedAttempts[i+1].questionId)
+ }
+ else {
+ relevantVars.push("", "_finish", "");
+ }
+ //csvString += "\""+relevantVars.join("\";\"")+"\"\n";
+ csvString += "'"+relevantVars.join("';'")+"'\n";
+ }
+
+ //csvString += "\n";
+ return csvString;
+ }
+
+ /*Leave the calculations up to python.
+ async getOverallInfoAsCSVRow(addHeadingRow, encryptId, getRidOfInitializationAttempts) {
+ let csvString = "";
+ if(addHeadingRow == undefined) {
+ addHeadingRow = false;
+ }
+ if(encryptId == undefined) {
+ encryptId = true;
+ }
+ let id = this.id;
+ if(encryptId == true) {
+ id = await sha256(this.id);
+
+ }
+ if(getRidOfInitializationAttempts == undefined) {
+ getRidOfInitializationAttempts = true;
+ }
+
+ if(addHeadingRow == true) {
+ if(addUserCol == true) {
+ csvString += "id,";
+ }
+ csvString += "started_working_amount,solved_amount,calls,first_action,last_action";
+ }
+
+ //Sort attempts by time. To add next question attribute.
+ let SortedAttempts = this.getSanitizedAttempts(getRidOfInitializationAttempts);
+
+ if(getRidOfInitializationAttempts == true) {
+ let initialTimestamp = SortedAttempts[0].timestamp;
+ let SortedAttemptsCopy = JSON.parse(JSON.stringify(SortedAttempts));
+ SortedAttempts = [];
+ for(let j=0;j<SortedAttemptsCopy.length;j++) {
+ if(SortedAttemptsCopy[j].timestamp != initialTimestamp) {
+ SortedAttempts.push(SortedAttemptsCopy[j]);
+ }
+ }
+ }
+
+ for(let i=0;i<SortedAttempts.length;i++) {
+ let relevantVars = []
+ if(addUserCol == true) {
+ relevantVars.push(id);
+ }
+ relevantVars.push(SortedAttempts[i].timestamp, SortedAttempts[i].questionId, SortedAttempts[i].variant, SortedAttempts[i].action, SortedAttempts[i].outcome);
+ if(SortedAttempts[i+1] != undefined) {
+ relevantVars.push(SortedAttempts[i+1].timestamp, SortedAttempts[i+1].questionId, SortedAttempts[i+1].variant);
+ //relevantVars.push(SortedAttempts[i+1].questionId)
+ }
+ else {
+ relevantVars.push("", "_finish", "");
+ }
+ csvString += "\""+relevantVars.join("\";\"")+"\"\n";
+ }
+
+ //csvString += "\n";
+ return csvString;
+ }*/
+
+ getSanitizedAttempts(getRidOfInitializationAttempts, getRidOfFinishedAttemptAttempts) {
+ //Will sort the question attempts and get rid of initialization attempts.
+ if(getRidOfInitializationAttempts == undefined) {
+ getRidOfInitializationAttempts = true;
+ }
+ if(getRidOfFinishedAttemptAttempts == undefined) {
+ getRidOfFinishedAttemptAttempts = true;
+ }
+
+ if(this.QuestionAttempts.length == 0) {
+ console.log("error: no attempts to sanitize");
+ return [];
+ }
+
+ let SanitizedAttempts = JSON.parse(JSON.stringify(this.QuestionAttempts));
+ SanitizedAttempts.sort(function(a, b) { return parseInt(a.timestamp) - parseInt(b.timestamp); });
+
+ if(getRidOfFinishedAttemptAttempts == true) {
+ let SanitizedAttemptsCopy = JSON.parse(JSON.stringify(SanitizedAttempts));
+ SanitizedAttempts = [];
+ for(let i=0;i<SanitizedAttemptsCopy.length;i++) {
+ if(SanitizedAttemptsCopy[i].action != "Versuch beendet" && SanitizedAttemptsCopy[i].action != "Attempt finished") {
+ SanitizedAttempts.push(SanitizedAttemptsCopy[i]);
+ }
+ }
+ }
+
+ if(!getRidOfInitializationAttempts) {
+ return SanitizedAttempts;
+ }
+
+ if(SanitizedAttempts.length == 0) {
+ console.log("no attempts after sanitizing");
+ return [];
+ }
+
+ let initialTimestamp = SanitizedAttempts[0].timestamp;
+ let SanitizedAttemptsCopy = JSON.parse(JSON.stringify(SanitizedAttempts));
+ SanitizedAttempts = [];
+ for(let j=0;j<SanitizedAttemptsCopy.length;j++) {
+ if(SanitizedAttemptsCopy[j].timestamp != initialTimestamp) {
+ SanitizedAttempts.push(SanitizedAttemptsCopy[j]);
+ }
+ }
+ return SanitizedAttempts;
+ }
+}
+
+
+//----------------MAIN-------------------------
+//Classic theme?
+//let rows = document.querySelectorAll("#responses tbody tr:not(.emptyrow)");
+//Alternative for HS BO Moodle Theme?
+let rows = document.querySelectorAll("#attempts tbody tr:not(.emptyrow)");
+allAttempts = rows.length;
+let Users = {};
+
+console.log("There are "+allAttempts+" rows. Run 'loadUsers();' or 'loadUsers(from, to);' or 'loadUsersStepwise();' to start processing.");
+
+//for(let i=7;i<8;i++) {
+function loadUsers(from, to) {
+ if(from == undefined) {
+ from = 0;
+ }
+ if(to == undefined) {
+ to = rows.length;
+ }
+ for(let i=from;i<to;i++) {
+ let id;
+ let idNode = rows[i].querySelector(".c3");
+ if(idNode == undefined) {
+ console.log("no id found for row "+i);
+ continue;
+ }
+ id = idNode.innerHTML;
+ if(id == "") {
+ console.log("empty id in row "+i);
+ continue;
+ }
+ if(Users[id] == undefined) {
+ Users[id] = new CUser(rows[i]);
+ }
+ else {
+ //Get review link and add attempt to already existing user.
+ let reviewLink = rows[i].querySelector(".reviewlink");
+ if(reviewLink != undefined) {
+ Users[id].addAttempt(reviewLink.href);
+ }
+ else {
+ console.log("Found user row of already existing user, but didn't find review link.");
+ }
+ }
+ }
+}
+
+var csvText = "";
+async function loadCSV(UsersObject) {
+ if(UsersObject == undefined) {
+ if(Users == undefined) {
+ return false;
+ }
+ UsersObject = Users;
+ }
+ //let csvText = "";
+ csvText = "";
+ let first = true;
+ for(let i in UsersObject) {
+ csvText += await UsersObject[i].getAttemptsAsCSV(true, first);
+ if(first == true) { first = false; }
+ }
+
+ /*let c = document.createElement("a");
+ c.download = "alquiz-analysis-control.csv";
+ var t = new Blob([csvText], {
+ type: "text/plain"
+ });
+ c.href = window.URL.createObjectURL(t);
+ c.click();*/
+}
+
+function downloadCSV() {
+ let c = document.createElement("a");
+ c.download = "alquiz-analysis-control.csv";
+ var t = new Blob([csvText], {
+ type: "text/plain"
+ });
+ c.href = window.URL.createObjectURL(t);
+ c.click();
+}
+
+async function loadAndDownloadCSV() {
+ return await loadCSV().then(function(response) {
+ downloadCSV();
+ return response;
+ });
+}
+
+function getFetchState() {
+ /*let overallFetches = Object.keys(fetches).length;
+ let solvedFetches = 0;
+ for(let fetchId in fetches) {
+ if(fetches[fetchId] == 1) {
+ solvedFetches++;
+ }
+ }*/
+ infoObject = getFetchStateMachineReadable();
+ console.log("Fetched "+infoObject.solved+" of "+infoObject.overall+".");
+}
+
+function getFetchStateMachineReadable() {
+ let overallFetches = Object.keys(fetches).length;
+ let solvedFetches = 0;
+ for(let fetchId in fetches) {
+ if(fetches[fetchId] == 1) {
+ solvedFetches++;
+ }
+ }
+ return {"solved":solvedFetches, "overall":overallFetches};
+}
+
+//----------------TEST--------------------------
+function showAllAttemptsOf018345157(questionId) {
+ if(questionId == undefined) {
+ questionId = "start";
+ }
+ let OnlyStartAttempts = [];
+ if(Users["018345157"] != undefined) {
+ Users["018345157"].QuestionAttempts.forEach(function(QuestionAttempt) {
+ if(QuestionAttempt.questionId == questionId) {
+ OnlyStartAttempts.push(QuestionAttempt);
+ }
+ });
+ }
+ console.log(OnlyStartAttempts);
+}
+
+var processCount = 0;
+function processStepByStep() {
+ fetchInfoObject = getFetchStateMachineReadable();
+ if(fetchInfoObject.solved == fetchInfoObject.overall) {
+ if(processCount == allAttempts) {
+ console.log("Successfully processed all attempts.")
+ if(interval != undefined) {
+ clearInterval(interval);
+ }
+ return;
+ }
+ else {
+ loadUsers(processCount, processCount+1);
+ processCount++;
+ }
+ }
+}
+
+var interval;
+function loadUsersStepwise() {
+ interval = setInterval(processStepByStep, 5000);
+}
\ No newline at end of file
diff --git a/analysis/alquiz-analysis-test.js b/analysis/alquiz-analysis-test.js
new file mode 100644
index 0000000000000000000000000000000000000000..c21a6f4d164e36f3264445f04d2edad31e7a3ab6
--- /dev/null
+++ b/analysis/alquiz-analysis-test.js
@@ -0,0 +1,1424 @@
+console.log("start alquiz analysis");
+//----------------QUIZ OBJECTS--------------------
+//WiMa SoSe 2023
+let quizObject = {
+ groups: {
+ start: "Start",
+ s3: "3 Elementare Funktionen",
+ s4: "4 Eigenschaften von Funktionen",
+ s5: "5 Grenzwerte, Stetigkeit und Definitionslücken",
+ s6: "6 Differentialrechnung I (Ableitungsregeln)",
+ s7: "7 Differentialrechnung II (Anwendung)",
+ s8: "8 Differentialrechnung in mehreren Variablen",
+ s9: "9 Finanzmathematik I",
+ s10: "10 Finanzmathematik II",
+ s11: "11 Lineare Algebra Grundlagen",
+ s12: "12 Weiterführende Matrixrechnung",
+ s13: "13 Lineare Optimierung"
+
+ },
+ questions: {
+ start: {
+ name: "Home",
+ group: "start",
+ onsuccess: "s3_1",
+ onfailure: "s3_1"
+ },
+ s3_1: {
+ /*orange*/
+ name: "Geradengleichung aufstellen 1",
+ onsuccess: "s3_2",
+ onfailure: "s3_2",
+ variants: 4,
+ color: "#fbc02d",
+ filter: "invert(75%) sepia(32%) saturate(1024%) hue-rotate(352deg) brightness(102%) contrast(97%)"
+ },
+ s3_2: {
+ /*red-orange*/
+ name: "Geradengleichung aufstellen 2",
+ onsuccess: "s3_3",
+ onfailure: "s3_3",
+ variants: 4,
+ color: "#ff3d00",
+ filter: "invert(31%) sepia(93%) saturate(4185%) hue-rotate(7deg) brightness(105%) contrast(110%)"
+ },
+ s3_3: {
+ /*light orange*/
+ name: "Scheitelpunkt aus Graphik ablesen",
+ variants: 4,
+ color: "#ffcc80",
+ filter: "invert(94%) sepia(80%) saturate(1438%) hue-rotate(304deg) brightness(109%) contrast(101%)"
+ },
+ s3_4: {
+ /*???*/
+ name: "Erlösfunktion",
+ variants: 4,
+ color: "#CF7D35",
+ filter: "invert(61%) sepia(55%) saturate(1048%) hue-rotate(339deg) brightness(88%) contrast(83%)"
+ },
+ s3_5: {
+ /*???*/
+ name: "Abschnittsweise def Funktion",
+ variants: 4,
+ color: "#34BC98",
+ filter: "invert(64%) sepia(14%) saturate(1723%) hue-rotate(114deg) brightness(94%) contrast(93%)"
+ },
+ s3_6: {
+ /*???*/
+ name: "Gewinnfunktion aufstellen",
+ variants: 4,
+ color: "#E9FCEE",
+ filter: "invert(100%) sepia(5%) saturate(4521%) hue-rotate(53deg) brightness(102%) contrast(96%)"
+ },
+ section_03_check_out_modified2_1: {
+ name: "Angebot und Nachfrage",
+ variants: 4,
+ color: "#573036",
+ filter: "invert(20%) sepia(11%) saturate(2292%) hue-rotate(301deg) brightness(88%) contrast(87%)",
+ group: "s3"
+ },
+ section_03_check_out_modified2_2: {
+ name: "Scheitelpunktform DOMAINUID 4 ACEA29",
+ variants: 4,
+ color: "#1BA1C7",
+ filter: "invert(46%) sepia(89%) saturate(419%) hue-rotate(147deg) brightness(97%) contrast(96%)",
+ group: "s3"
+ },
+ section_03_check_out_modified2_3: {
+ name: "Erlösfunktion E(p) aufstellen",
+ variants: 4,
+ color: "#B38ABB",
+ filter: "invert(67%) sepia(28%) saturate(423%) hue-rotate(244deg) brightness(85%) contrast(89%)",
+ group: "s3"
+ },
+ section_03_check_out_modified2_4: {
+ name: "Produktionsfunktion Def ök",
+ variants: 4,
+ color: "#D558A8",
+ filter: "invert(50%) sepia(90%) saturate(907%) hue-rotate(290deg) brightness(87%) contrast(90%)",
+ group: "s3"
+ },
+ section_03_check_out_modified2_5: {
+ name: "Gewinnschwelle & Gewinngrenze Kap. 2.7 (TF) (Duplikat Malte)",
+ variants: 4,
+ color: "#1B5658",
+ filter: "invert(26%) sepia(12%) saturate(2407%) hue-rotate(133deg) brightness(95%) contrast(86%)",
+ group: "s3"
+ },
+ section_03_check_out_modified2_6: {
+ name: "Definitionsbereich Ök. Kap. 2.7 (TF)",
+ variants: 4,
+ color: "#810311",
+ filter: "invert(8%) sepia(64%) saturate(6140%) hue-rotate(346deg) brightness(93%) contrast(104%)",
+ group: "s3"
+ },
+ section_04_check_in_modified_6: {
+ name: "Nullstelle abspalten (Duplikat Malte)",
+ variants: 4,
+ color: "#74CD27",
+ filter: "invert(68%) sepia(76%) saturate(507%) hue-rotate(42deg) brightness(95%) contrast(83%)",
+ group: "s4"
+ },
+ s4_1: {
+ /*very light green*/
+ name: "NS reverse",
+ onsuccess: "s4_2",
+ onfailure: "s4_2",
+ variants: 4,
+ color: "#ccff90",
+ filter: "invert(88%) sepia(22%) saturate(727%) hue-rotate(38deg) brightness(103%) contrast(107%)"
+ },
+ s4_2: {
+ /*light green*/
+ name: "NS bei Def",
+ onsuccess: "s4_3",
+ onfailure: "s4_3",
+ variants: 4,
+ color: "#b2ff59",
+ filter: "invert(96%) sepia(97%) saturate(787%) hue-rotate(29deg) brightness(100%) contrast(108%)"
+ },
+ s4_3: {
+ /*green*/
+ name: "NS Wurzelfkt",
+ onsuccess: "s4_4",
+ onfailure: "s4_4",
+ variants: 4,
+ color: "#76ff03",
+ filter: "invert(67%) sepia(72%) saturate(618%) hue-rotate(43deg) brightness(110%) contrast(103%)"
+ },
+ s4_4: {
+ /*dimmed green*/
+ name: "4.2 Polynom von Grad 4 her bestimmen",
+ onsuccess: "s4_5",
+ onfailure: "s4_5",
+ variants: 4,
+ color: "#64dd17",
+ filter: "invert(79%) sepia(18%) saturate(3453%) hue-rotate(45deg) brightness(97%) contrast(91%)"
+ },
+ s4_5: {
+ /*dark green*/
+ name: "4.1 Funktion ablesen Grad 4",
+ variants: 4,
+ color: "#689f38",
+ filter: "invert(54%) sepia(21%) saturate(1222%) hue-rotate(49deg) brightness(99%) contrast(83%)"
+ },
+ section_05_check_in_3: {
+ name: "Grenzwert gegen inf ablesen",
+ variants: 4,
+ color: "#3CF48A",
+ filter: "invert(72%) sepia(40%) saturate(699%) hue-rotate(89deg) brightness(101%) contrast(98%)",
+ group: "s5"
+ },
+ section_05_check_in_modified2_7: {
+ name: "Stetigkeit abschnittsw def Funktion (Duplikat Malte)",
+ variants: 4,
+ color: "#E249B2",
+ filter: "invert(52%) sepia(64%) saturate(4425%) hue-rotate(292deg) brightness(93%) contrast(90%)",
+ group: "s5"
+ },
+ section_05_check_in_6: {
+ name: "Polstelle",
+ variants: 4,
+ color: "#77B211",
+ filter: "invert(64%) sepia(52%) saturate(5261%) hue-rotate(48deg) brightness(107%) contrast(87%)",
+ group: "s5"
+ },
+ section_05_check_in_modified2_8: {
+ name: "Hebbare Lücke (Duplikat Malte)",
+ variants: 4,
+ color: "#D57774",
+ filter: "invert(81%) sepia(50%) saturate(3032%) hue-rotate(305deg) brightness(86%) contrast(94%)",
+ group: "s5"
+ },
+ section_05_check_in_8: {
+ name: "Asymptote",
+ variants: 4,
+ color: "#FD9C80",
+ filter: "invert(84%) sepia(53%) saturate(4565%) hue-rotate(313deg) brightness(115%) contrast(108%)",
+ group: "s5"
+ },
+ section_05_check_out_1: {
+ name: "Grenzwertaufgabe mögliche Polstellen (TU)",
+ variants: 4,
+ color: "#E249B2",
+ filter: "invert(52%) sepia(64%) saturate(4425%) hue-rotate(292deg) brightness(93%) contrast(90%)",
+ group: "s5"
+ },
+ section_05_check_out_2: {
+ name: "Nullstellen und Polstellen von sqrt(P/Q-1) Kap. 2.4 & 2.6 (TF)",
+ variants: 4,
+ color: "#D57774",
+ filter: "invert(81%) sepia(50%) saturate(3032%) hue-rotate(305deg) brightness(86%) contrast(94%)",
+ group: "s5"
+ },
+ section_05_check_out_3: {
+ name: "Nullstellen, Polstellen und Asymptoten einer gebrochenrationalen Funktion Kap. 2.4 & 2.6 (TF)",
+ variants: 4,
+ color: "#944A6C",
+ filter: "invert(34%) sepia(25%) saturate(1028%) hue-rotate(280deg) brightness(96%) contrast(89%)",
+ group: "s5"
+ },
+ section_05_check_out_5: {
+ name: "Asymptote VWL",
+ variants: 4,
+ color: "#9B49A2",
+ filter: "invert(35%) sepia(65%) saturate(573%) hue-rotate(248deg) brightness(92%) contrast(92%)",
+ group: "s5"
+ },
+ section_05_check_out_6: {
+ name: "Sprungstelle abschnittsw def Funktion",
+ variants: 4,
+ color: "#FA00D1",
+ filter: "invert(54%) sepia(100%) saturate(7435%) hue-rotate(298deg) brightness(97%) contrast(127%)",
+ group: "s5"
+ },
+ s6_1: {
+ /*very light purple*/
+ name: "Ableitungsfunktion Konstante",
+ onsuccess: "s6_2",
+ onfailure: "s6_2",
+ variants: 4,
+ color: "#ea80fc",
+ filter: "invert(76%) sepia(34%) saturate(6604%) hue-rotate(231deg) brightness(102%) contrast(98%)"
+ },
+ s6_2: {
+ /*light purple*/
+ name: "Ableitungsfunktion Potenzfunktion",
+ onsuccess: "s6_3",
+ onfailure: "s6_3",
+ variants: 4,
+ color: "#e040fb",
+ filter: "invert(37%) sepia(85%) saturate(3762%) hue-rotate(272deg) brightness(104%) contrast(97%)"
+ },
+ s6_3: {
+ /*purple*/
+ name: "Ableitungsfunktion Potenzfunktion gebrochener Exponent",
+ variants: 4,
+ color: "#d500f9",
+ filter: "invert(26%) sepia(92%) saturate(2035%) hue-rotate(275deg) brightness(86%) contrast(153%)"
+ },
+ section_06_check_out_1: {
+ name: "01 Summen- und konstanter Faktor",
+ variants: 4,
+ color: "#E2AFDA",
+ filter: "invert(96%) sepia(86%) saturate(2059%) hue-rotate(203deg) brightness(96%) contrast(83%)",
+ group: "s6"
+ },
+ section_06_check_out_2: {
+ name: "02 Produktregel (TF)",
+ variants: 4,
+ color: "#EB3E57",
+ filter: "invert(33%) sepia(19%) saturate(6570%) hue-rotate(328deg) brightness(97%) contrast(89%)",
+ group: "s6"
+ },
+ section_06_check_out_3: {
+ name: "03 Quotientenregel[neu](TF)",
+ variants: 4,
+ color: "#7E182C",
+ filter: "invert(14%) sepia(27%) saturate(5843%) hue-rotate(328deg) brightness(98%) contrast(98%)",
+ group: "s6"
+ },
+ section_06_check_out_4: {
+ name: "05 Logarithmisches Ableiten",
+ variants: 4,
+ color: "#3960A7",
+ filter: "invert(33%) sepia(56%) saturate(621%) hue-rotate(180deg) brightness(96%) contrast(95%)",
+ group: "s6"
+ },
+ section_06_check_out_5: {
+ name: "04 Kettenregel",
+ variants: 4,
+ color: "#E44FCD",
+ filter: "invert(76%) sepia(58%) saturate(7362%) hue-rotate(280deg) brightness(93%) contrast(93%)",
+ group: "s6"
+ },
+ section_07_check_in_1: {
+ name: "Newtonverfahren",
+ variants: 4,
+ color: "#278495",
+ filter: "invert(40%) sepia(10%) saturate(2946%) hue-rotate(142deg) brightness(107%) contrast(86%)",
+ group: "s7"
+ },
+ section_07_check_in_2: {
+ name: "Stationäre kritische Stelle",
+ variants: 4,
+ color: "#6D9D29",
+ filter: "invert(53%) sepia(90%) saturate(357%) hue-rotate(43deg) brightness(87%) contrast(88%)",
+ group: "s7"
+ },
+ section_07_check_in_modified2_4: {
+ name: "Extrema und Wendestelle (Duplikat Malte)",
+ variants: 4,
+ color: "#A3717F",
+ filter: "invert(51%) sepia(4%) saturate(3367%) hue-rotate(293deg) brightness(95%) contrast(75%)",
+ group: "s7"
+ },
+ section_07_check_out_1: {
+ name: "Grenzkostenfunktion",
+ variants: 4,
+ color: "#302FFF",
+ filter: "invert(12%) sepia(96%) saturate(6720%) hue-rotate(247deg) brightness(102%) contrast(101%)",
+ group: "s7"
+ },
+ section_07_check_out_2: {
+ name: "Kurvendiskussion: gebrochenrationale Funktion",
+ variants: 4,
+ color: "#BBCBC4",
+ filter: "invert(93%) sepia(3%) saturate(752%) hue-rotate(102deg) brightness(89%) contrast(85%)",
+ group: "s7"
+ },
+ section_07_check_out_3: {
+ name: "Maximalen Gewinn bestimmen",
+ variants: 4,
+ color: "#C5F99B",
+ filter: "invert(100%) sepia(16%) saturate(5613%) hue-rotate(328deg) brightness(109%) contrast(92%)",
+ group: "s7"
+ },
+ section_07_check_out_4: {
+ name: "Optimierung Gewinn",
+ variants: 4,
+ color: "#A3717F",
+ filter: "invert(51%) sepia(4%) saturate(3367%) hue-rotate(293deg) brightness(95%) contrast(75%)",
+ group: "s7"
+ },
+ section_07_check_out_5: {
+ name: "Optimierung Umsatz",
+ variants: 4,
+ color: "#395C44",
+ filter: "invert(28%) sepia(21%) saturate(737%) hue-rotate(86deg) brightness(102%) contrast(87%)",
+ group: "s7"
+ },
+ section_08_check_in_2: {
+ name: "01 partiell Diff",
+ variants: 4,
+ color: "#10F046",
+ filter: "invert(52%) sepia(95%) saturate(903%) hue-rotate(88deg) brightness(115%) contrast(90%)",
+ group: "s8"
+ },
+ section_08_check_in_3: {
+ name: "02 partiell Diff",
+ variants: 4,
+ color: "#E39FB2",
+ filter: "invert(78%) sepia(4%) saturate(2863%) hue-rotate(296deg) brightness(88%) contrast(102%)",
+ group: "s8"
+ },
+ section_08_check_out_2: {
+ name: "06 partiell Diff",
+ variants: 4,
+ color: "#01D504",
+ filter: "invert(43%) sepia(74%) saturate(1175%) hue-rotate(89deg) brightness(106%) contrast(114%)",
+ group: "s8"
+ },
+ section_08_check_out_3: {
+ name: "7.03 Det 3x3 Folie 16",
+ variants: 4,
+ color: "#C6F237",
+ filter: "invert(96%) sepia(38%) saturate(4597%) hue-rotate(13deg) brightness(104%) contrast(89%)",
+ group: "s8"
+ },
+ section_09_check_in_1: {
+ name: "wann ver-x-facht sich K",
+ variants: 4,
+ color: "#B64537",
+ filter: "invert(36%) sepia(12%) saturate(4301%) hue-rotate(324deg) brightness(93%) contrast(92%)",
+ group: "s9"
+ },
+ section_09_check_in_2: {
+ name: "Zinssatz i berechnen",
+ variants: 4,
+ color: "#8C9BF5",
+ filter: "invert(64%) sepia(5%) saturate(3975%) hue-rotate(195deg) brightness(98%) contrast(96%)",
+ group: "s9"
+ },
+ section_09_check_in_modified2_6: {
+ name: "Barwert Zahlungsstrom (Duplikat Malte)(Kopiert aus Barwert Endwert Zahlungsstrom)",
+ variants: 4,
+ color: "#910602",
+ filter: "invert(11%) sepia(63%) saturate(4965%) hue-rotate(14deg) brightness(103%) contrast(124%)",
+ group: "s9"
+ },
+ section_09_check_in_modified2_7: {
+ name: "Endwert Zahlungsstrom (Duplikat Malte)(Kopiert aus Barwert Endwert Zahlungsstrom)",
+ variants: 4,
+ color: "#C8B210",
+ filter: "invert(72%) sepia(81%) saturate(1388%) hue-rotate(8deg) brightness(93%) contrast(87%)",
+ group: "s9"
+ },
+ section_09_check_in_4: {
+ name: "BW",
+ variants: 4,
+ color: "#9F6D55",
+ filter: "invert(49%) sepia(5%) saturate(4049%) hue-rotate(334deg) brightness(89%) contrast(72%)",
+ group: "s9"
+ },
+ section_09_check_in_5: {
+ name: "EW",
+ variants: 4,
+ color: "#65D794",
+ filter: "invert(80%) sepia(24%) saturate(818%) hue-rotate(88deg) brightness(91%) contrast(88%)",
+ group: "s9"
+ },
+ section_09_check_in_6: {
+ name: "Grundbegriffe",
+ variants: 4,
+ color: "#162095",
+ filter: "invert(18%) sepia(23%) saturate(6913%) hue-rotate(217deg) brightness(94%) contrast(98%)",
+ group: "s9"
+ },
+ section_09_check_out_1: {
+ name: "Äquivalenzprinzip",
+ variants: 4,
+ color: "#DD5BE4",
+ filter: "invert(46%) sepia(92%) saturate(1381%) hue-rotate(268deg) brightness(96%) contrast(85%)",
+ group: "s9"
+ },
+ section_09_check_out_2: {
+ name: "Effektivzins 1",
+ variants: 4,
+ color: "#A4FFDC",
+ filter: "invert(91%) sepia(24%) saturate(563%) hue-rotate(85deg) brightness(103%) contrast(103%)",
+ group: "s9"
+ },
+ section_09_check_out_3: {
+ name: "Impl. Terminzinss.",
+ variants: 4,
+ color: "#BA9DCC",
+ filter: "invert(70%) sepia(13%) saturate(705%) hue-rotate(233deg) brightness(94%) contrast(91%)",
+ group: "s9"
+ },
+ section_09_check_out_4: {
+ name: "Barwert und Endwert eines Zahlungsstroms",
+ variants: 4,
+ color: "#D34FDB",
+ filter: "invert(45%) sepia(84%) saturate(1892%) hue-rotate(259deg) brightness(88%) contrast(94%)",
+ group: "s9"
+ },
+ section_09_check_out_5: {
+ name: "Endwert berechnen",
+ variants: 4,
+ color: "#910602",
+ filter: "invert(11%) sepia(63%) saturate(4965%) hue-rotate(14deg) brightness(103%) contrast(124%)",
+ group: "s9"
+ },
+ section_09_check_out_6: {
+ name: "Kapitalwert bestimmen",
+ variants: 4,
+ color: "#C8B210",
+ filter: "invert(72%) sepia(81%) saturate(1388%) hue-rotate(8deg) brightness(93%) contrast(87%)",
+ group: "s9"
+ },
+ section_10_check_in_3: {
+ name: "Rentenbarwertfaktor",
+ variants: 4,
+ color: "#3BDBAA",
+ filter: "invert(92%) sepia(80%) saturate(1117%) hue-rotate(82deg) brightness(101%) contrast(69%)",
+ group: "s10"
+ },
+ section_10_check_in_4: {
+ name: "Rentenendwertfaktor",
+ variants: 4,
+ color: "#916F06",
+ filter: "invert(43%) sepia(44%) saturate(6440%) hue-rotate(38deg) brightness(93%) contrast(95%)",
+ group: "s10"
+ },
+ section_10_check_out_1: {
+ name: "Rente n berechnen",
+ variants: 4,
+ color: "#C5B6C7",
+ filter: "invert(80%) sepia(6%) saturate(490%) hue-rotate(246deg) brightness(91%) contrast(96%)",
+ group: "s10"
+ },
+ section_10_check_out_modified2_6: {
+ name: "Rentenbarwert, Rentenendwert (Duplikat Malte)",
+ variants: 4,
+ color: "#DA8376",
+ filter: "invert(76%) sepia(76%) saturate(1360%) hue-rotate(305deg) brightness(86%) contrast(86%)",
+ group: "s10"
+ },
+ section_10_check_out_3: {
+ name: "Annuität berechnen",
+ variants: 4,
+ color: "#88383B",
+ filter: "invert(27%) sepia(85%) saturate(439%) hue-rotate(308deg) brightness(84%) contrast(94%)",
+ group: "s10"
+ },
+ section_10_check_out_4: {
+ name: "Annutätentilgung, Tilgungsplan",
+ variants: 4,
+ color: "#71BC2E",
+ filter: "invert(61%) sepia(95%) saturate(366%) hue-rotate(48deg) brightness(91%) contrast(84%)",
+ group: "s10"
+ },
+ section_10_check_out_5: {
+ name: "Laufzeit eines Darlehens",
+ variants: 4,
+ color: "#B20EE3",
+ filter: "invert(22%) sepia(84%) saturate(4934%) hue-rotate(280deg) brightness(90%) contrast(116%)",
+ group: "s10"
+ },
+ section_10_check_out_6: {
+ name: "Restschuld eines Darlehens",
+ variants: 4,
+ color: "#C751FB",
+ filter: "invert(41%) sepia(23%) saturate(6695%) hue-rotate(255deg) brightness(101%) contrast(97%)",
+ group: "s10"
+ },
+ section_11_check_in_modified_7: {
+ name: "MatrixMultiplikation",
+ variants: 4,
+ color: "#496108",
+ filter: "invert(32%) sepia(17%) saturate(2438%) hue-rotate(36deg) brightness(96%) contrast(94%)",
+ group: "s11"
+ },
+ section_11_check_in_modified_8: {
+ name: "Transponieren",
+ variants: 4,
+ color: "#4DA97E",
+ filter: "invert(54%) sepia(42%) saturate(476%) hue-rotate(100deg) brightness(100%) contrast(84%)",
+ group: "s11"
+ },
+ section_11_check_in_modified_9: {
+ name: "8.12 LGS Matrix-Form Folie 11 (5.1 LGS) (Duplikat Malte)",
+ variants: 4,
+ color: "#F8C255",
+ filter: "invert(76%) sepia(85%) saturate(388%) hue-rotate(335deg) brightness(100%) contrast(95%)",
+ group: "s11"
+ },
+ section_11_check_out_1: {
+ name: "6.02 extern Matrizenrechnung",
+ variants: 4,
+ color: "#642E0E",
+ filter: "invert(18%) sepia(12%) saturate(6525%) hue-rotate(354deg) brightness(97%) contrast(92%)",
+ group: "s11"
+ },
+ section_11_check_out_2: {
+ name: "6.03 Matrix-Vektor-Produkt",
+ variants: 4,
+ color: "#16C9D7",
+ filter: "invert(67%) sepia(27%) saturate(3791%) hue-rotate(137deg) brightness(101%) contrast(83%)",
+ group: "s11"
+ },
+ section_11_check_out_3: {
+ name: "6.06 Addition von 2 Linearkombi",
+ variants: 4,
+ color: "#C768E5",
+ filter: "invert(51%) sepia(33%) saturate(1489%) hue-rotate(239deg) brightness(96%) contrast(86%)",
+ group: "s11"
+ },
+ section_11_check_out_4: {
+ name: "6.08 Folie S.18 Matrixprodukt",
+ variants: 4,
+ color: "#DA8376",
+ filter: "invert(76%) sepia(76%) saturate(1360%) hue-rotate(305deg) brightness(86%) contrast(86%)",
+ group: "s11"
+ },
+ section_11_check_out_5: {
+ name: "6.11 Operationen von 3 Matrizen",
+ variants: 4,
+ color: "#93916B",
+ filter: "invert(62%) sepia(7%) saturate(1282%) hue-rotate(19deg) brightness(91%) contrast(88%)",
+ group: "s11"
+ },
+ section_11_check_out_6: {
+ name: "8.05 LGS 2x2",
+ variants: 4,
+ color: "#A4AA17",
+ filter: "invert(57%) sepia(80%) saturate(463%) hue-rotate(23deg) brightness(95%) contrast(84%)",
+ group: "s11"
+ },
+ section_11_check_out_7: {
+ name: "8.06 LGS 3x3",
+ variants: 4,
+ color: "#62CB69",
+ filter: "invert(99%) sepia(33%) saturate(3140%) hue-rotate(51deg) brightness(87%) contrast(79%)",
+ group: "s11"
+ },
+ section_12_check_in_4: {
+ name: "Inverse 2x2",
+ variants: 4,
+ color: "#CD51BA",
+ filter: "invert(52%) sepia(46%) saturate(3109%) hue-rotate(280deg) brightness(85%) contrast(86%)",
+ group: "s12"
+ },
+ section_12_check_in_5: {
+ name: "Streichungsmatrix",
+ variants: 4,
+ color: "#877931",
+ filter: "invert(51%) sepia(15%) saturate(1482%) hue-rotate(13deg) brightness(88%) contrast(89%)",
+ group: "s12"
+ },
+ section_12_check_in_6: {
+ name: "7.01 Det 2x2",
+ variants: 4,
+ color: "#DDB76F",
+ filter: "invert(77%) sepia(47%) saturate(395%) hue-rotate(353deg) brightness(90%) contrast(91%)",
+ group: "s12"
+ },
+ section_12_check_out_modified_1: {
+ name: "7.03 Det 3x3 Folie 16",
+ variants: 4,
+ color: "#C14532",
+ filter: "invert(29%) sepia(72%) saturate(1119%) hue-rotate(334deg) brightness(100%) contrast(91%)",
+ group: "s12"
+ },
+ section_12_check_out_modified_2: {
+ name: "Inverse 3x3",
+ variants: 4,
+ color: "#70C3CA",
+ filter: "invert(72%) sepia(7%) saturate(2161%) hue-rotate(136deg) brightness(100%) contrast(88%)",
+ group: "s12"
+ },
+ section_12_check_out_modified_3: {
+ name: "Inverse singulär 3x3",
+ variants: 4,
+ color: "#6AC2E3",
+ filter: "invert(67%) sepia(76%) saturate(312%) hue-rotate(161deg) brightness(93%) contrast(90%)",
+ group: "s12"
+ },
+ section_12_check_out_modified_4: {
+ name: "Laplace 4x4 (TF) (Duplikat Malte)",
+ variants: 4,
+ color: "#8F822E",
+ filter: "invert(44%) sepia(53%) saturate(494%) hue-rotate(15deg) brightness(101%) contrast(89%)",
+ group: "s12"
+ },
+ section_13_check_out_modified_1: {
+ name: "Simplex Pivotelement Dualer Simplex",
+ variants: 4,
+ color: "#040237",
+ filter: "invert(5%) sepia(65%) saturate(6178%) hue-rotate(225deg) brightness(82%) contrast(117%)",
+ group: "s13"
+ },
+ section_13_check_out_modified_2: {
+ name: "Simplex Pivotelement+Neue Basis angeben",
+ variants: 4,
+ color: "#AEC069",
+ filter: "invert(74%) sepia(10%) saturate(1407%) hue-rotate(32deg) brightness(95%) contrast(97%)",
+ group: "s13"
+ },
+ section_13_check_out_modified_3: {
+ name: "Simplex dual",
+ variants: 4,
+ color: "#C6E2B2",
+ filter: "invert(99%) sepia(25%) saturate(1040%) hue-rotate(32deg) brightness(96%) contrast(83%)",
+ group: "s13"
+ },
+ section_13_check_out_modified_4: {
+ name: "Simplex Tableau aufstellen (Duplikat Malte)",
+ variants: 4,
+ color: "#0EE073",
+ filter: "invert(74%) sepia(55%) saturate(3187%) hue-rotate(95deg) brightness(100%) contrast(89%)",
+ group: "s13",
+ onsuccess: "_finish",
+ onfailure: "_finish"
+ }
+ }
+};
+
+/*Preparatory courses WiSe 2023-24*/
+let quizObjectAsString = '{"groups": {"start": "Start", "t0_syn_1": "Syntax", "t1_fra_1": "Bruchrechnung", "t3_frabin_1": "Binom. Formeln", "t4_pq_1": "pq-Formel", "t5_rul_1": "Potenzrechenregeln", "t7_der_1": "Ableitungen"}, "questions": {"start": {"name": "Start", "group": "start"}, "t0_syn_1_a": {"name": "Gleichung eingeben (Multiplikation)", "variants": 4, "color": "#573036", "filter": "invert(20%) sepia(11%) saturate(2292%) hue-rotate(301deg) brightness(88%) contrast(87%)"}, "t0_syn_1_b": {"name": "Gleichung eingeben (Division)", "variants": 4, "color": "#1BA1C7", "filter": "invert(46%) sepia(89%) saturate(419%) hue-rotate(147deg) brightness(97%) contrast(96%)"}, "t0_syn_1_c": {"name": "Potenzen", "variants": 4, "color": "#B38ABB", "filter": "invert(67%) sepia(28%) saturate(423%) hue-rotate(244deg) brightness(85%) contrast(89%)"}, "t0_syn_1_d": {"name": "Rationale Ausdr\u00fccke", "variants": 3, "color": "#D558A8", "filter": "invert(50%) sepia(90%) saturate(907%) hue-rotate(290deg) brightness(87%) contrast(90%)"}, "t0_syn_1_e": {"name": "Wurzelzeichen", "variants": 4, "color": "#1B5658", "filter": "invert(26%) sepia(12%) saturate(2407%) hue-rotate(133deg) brightness(95%) contrast(86%)"}, "t0_syn_1_f": {"name": "Mehrere L\u00f6sungen", "variants": 4, "color": "#810311", "filter": "invert(8%) sepia(64%) saturate(6140%) hue-rotate(346deg) brightness(93%) contrast(104%)"}, "t0_syn_1_g": {"name": "Gleichung mehrschrittig l\u00f6sen", "variants": 4, "color": "#74CD27", "filter": "invert(68%) sepia(76%) saturate(507%) hue-rotate(42deg) brightness(95%) contrast(83%)"}, "t0_syn_1_h": {"name": "Griechische Buchstaben", "variants": 4, "color": "#3CF48A", "filter": "invert(72%) sepia(40%) saturate(699%) hue-rotate(89deg) brightness(101%) contrast(98%)"}, "t0_syn_1_i": {"name": "Syntax-Endboss", "variants": 4, "color": "#77B211", "filter": "invert(64%) sepia(52%) saturate(5261%) hue-rotate(48deg) brightness(107%) contrast(87%)"}, "t1_fra_1_bi-a": {"name": "K\u00fcrzen zweier einfacher Br\u00fcche", "variants": 4, "color": "#FD9C80", "filter": "invert(84%) sepia(53%) saturate(4565%) hue-rotate(313deg) brightness(115%) contrast(108%)"}, "t1_fra_1_bi-b": {"name": "K\u00fcrzen zweier Br\u00fcche mit Variablen", "variants": 4, "color": "#E249B2", "filter": "invert(52%) sepia(64%) saturate(4425%) hue-rotate(292deg) brightness(93%) contrast(90%)"}, "t1_fra_1_bi-c": {"name": "K\u00fcrzen zweier Br\u00fcche mit Variablen und Zahlen", "variants": 4, "color": "#D57774", "filter": "invert(81%) sepia(50%) saturate(3032%) hue-rotate(305deg) brightness(86%) contrast(94%)"}, "t1_fra_1_bi-d": {"name": "K\u00fcrzen zweier Br\u00fcche mit Termen", "variants": 4, "color": "#944A6C", "filter": "invert(34%) sepia(25%) saturate(1028%) hue-rotate(280deg) brightness(96%) contrast(89%)"}, "t1_fra_1_bii-a": {"name": "Einfachen Bruch erweitern", "variants": 4, "color": "#9B49A2", "filter": "invert(35%) sepia(65%) saturate(573%) hue-rotate(248deg) brightness(92%) contrast(92%)"}, "t1_fra_1_bii-b": {"name": "Bruch mit Variablen erweitern", "variants": 4, "color": "#FA00D1", "filter": "invert(54%) sepia(100%) saturate(7435%) hue-rotate(298deg) brightness(97%) contrast(127%)"}, "t1_fra_1_bii-c": {"name": "Bruch mit Variablen und Zahlen erweitern", "variants": 4, "color": "#E2AFDA", "filter": "invert(96%) sepia(86%) saturate(2059%) hue-rotate(203deg) brightness(96%) contrast(83%)"}, "t1_fra_1_ca": {"name": "Einfache Addition von Br\u00fcchen", "variants": 4, "color": "#EB3E57", "filter": "invert(33%) sepia(19%) saturate(6570%) hue-rotate(328deg) brightness(97%) contrast(89%)"}, "t1_fra_1_cb": {"name": "Addition von Br\u00fcchen mit Variablen und gleichem Nenner", "variants": 4, "color": "#7E182C", "filter": "invert(14%) sepia(27%) saturate(5843%) hue-rotate(328deg) brightness(98%) contrast(98%)"}, "t1_fra_1_cc": {"name": "Addition von Br\u00fcchen mit Variablen und unterschiedlichen Nennern", "variants": 4, "color": "#3960A7", "filter": "invert(33%) sepia(56%) saturate(621%) hue-rotate(180deg) brightness(96%) contrast(95%)"}, "t1_fra_1_cd": {"name": "Addition von Br\u00fcchen mit einer Variablen und unterschiedlichen Nennern", "variants": 4, "color": "#E44FCD", "filter": "invert(76%) sepia(58%) saturate(7362%) hue-rotate(280deg) brightness(93%) contrast(93%)"}, "t1_fra_1_ce": {"name": "Addition von Br\u00fcchen mit Variablen und unterschiedlichen Nennern I", "variants": 4, "color": "#278495", "filter": "invert(40%) sepia(10%) saturate(2946%) hue-rotate(142deg) brightness(107%) contrast(86%)"}, "t1_fra_1_cf": {"name": "Addition von Br\u00fcchen mit Variablen und unterschiedlichen Nennern II", "variants": 4, "color": "#6D9D29", "filter": "invert(53%) sepia(90%) saturate(357%) hue-rotate(43deg) brightness(87%) contrast(88%)"}, "t1_fra_1_da": {"name": "Multiplikation zweier einfacher Br\u00fcche", "variants": 4, "color": "#302FFF", "filter": "invert(12%) sepia(96%) saturate(6720%) hue-rotate(247deg) brightness(102%) contrast(101%)"}, "t1_fra_1_db": {"name": "Multiplikation zweier Br\u00fcche mit Variablen", "variants": 4, "color": "#BBCBC4", "filter": "invert(93%) sepia(3%) saturate(752%) hue-rotate(102deg) brightness(89%) contrast(85%)"}, "t1_fra_1_dc": {"name": "Multiplikation Bruch mit Zahlen, Bruch mit Variablen, Ganzzahl", "variants": 4, "color": "#C5F99B", "filter": "invert(100%) sepia(16%) saturate(5613%) hue-rotate(328deg) brightness(109%) contrast(92%)"}, "t1_fra_1_dd": {"name": "Multiplikation zweier Br\u00fcche mit Termen", "variants": 4, "color": "#A3717F", "filter": "invert(51%) sepia(4%) saturate(3367%) hue-rotate(293deg) brightness(95%) contrast(75%)"}, "t1_fra_1_de": {"name": "Einfacher Doppelbruch", "variants": 4, "color": "#395C44", "filter": "invert(28%) sepia(21%) saturate(737%) hue-rotate(86deg) brightness(102%) contrast(87%)"}, "t1_fra_1_df": {"name": "Bruch und Geteilt-Rechnung", "variants": 4, "color": "#10F046", "filter": "invert(52%) sepia(95%) saturate(903%) hue-rotate(88deg) brightness(115%) contrast(90%)"}, "t1_fra_1_dg": {"name": "Doppelbruch mit Zahlen und Variablen", "variants": 4, "color": "#E39FB2", "filter": "invert(78%) sepia(4%) saturate(2863%) hue-rotate(296deg) brightness(88%) contrast(102%)"}, "t1_fra_1_dh": {"name": "Doppelbruch mit Termen", "variants": 4, "color": "#23F5CC", "filter": "invert(100%) sepia(72%) saturate(2181%) hue-rotate(84deg) brightness(106%) contrast(91%)"}, "t1_fra_1_ea": {"name": "Bruchrechnung Kombination I", "variants": 4, "color": "#01D504", "filter": "invert(43%) sepia(74%) saturate(1175%) hue-rotate(89deg) brightness(106%) contrast(114%)"}, "t1_fra_1_eb": {"name": "Bruchrechnung Kombination II", "variants": 4, "color": "#C6F237", "filter": "invert(96%) sepia(38%) saturate(4597%) hue-rotate(13deg) brightness(104%) contrast(89%)"}, "t1_fra_1_ec": {"name": "Bruchrechnung Kombination III", "variants": 4, "color": "#B64537", "filter": "invert(36%) sepia(12%) saturate(4301%) hue-rotate(324deg) brightness(93%) contrast(92%)"}, "t3_frabin_1_g": {"name": "Binomische Formeln Ia - Erste binomische Formel", "variants": 4, "color": "#8C9BF5", "filter": "invert(64%) sepia(5%) saturate(3975%) hue-rotate(195deg) brightness(98%) contrast(96%)"}, "t3_frabin_1_h": {"name": "Binomische Formeln Ib - Zweite binomische Formel", "variants": 4, "color": "#9F6D55", "filter": "invert(49%) sepia(5%) saturate(4049%) hue-rotate(334deg) brightness(89%) contrast(72%)"}, "t3_frabin_1_i": {"name": "Binomische Formeln Ic - Dritte binomische Formel", "variants": 4, "color": "#65D794", "filter": "invert(80%) sepia(24%) saturate(818%) hue-rotate(88deg) brightness(91%) contrast(88%)"}, "t3_frabin_1_j": {"name": "Binomische Formeln I - Anwendungsaufgabe", "variants": 4, "color": "#162095", "filter": "invert(18%) sepia(23%) saturate(6913%) hue-rotate(217deg) brightness(94%) contrast(98%)"}, "t3_frabin_1_k": {"name": "Bruchrechenregeln Ig2 - Bruch mit binomischem Term erweitern 2 (copy)", "variants": 3, "color": "#DD5BE4", "filter": "invert(46%) sepia(92%) saturate(1381%) hue-rotate(268deg) brightness(96%) contrast(85%)"}, "t4_pq_1_a": {"name": "p-q-Formal Ia - Termumformung", "variants": 4, "color": "#A4FFDC", "filter": "invert(91%) sepia(24%) saturate(563%) hue-rotate(85deg) brightness(103%) contrast(103%)"}, "t4_pq_1_b": {"name": "p-q-Formel Ib - pq-Formel", "variants": 4, "color": "#BA9DCC", "filter": "invert(70%) sepia(13%) saturate(705%) hue-rotate(233deg) brightness(94%) contrast(91%)"}, "t4_pq_1_c": {"name": "p-q-Formel I - Endboss", "variants": 4, "color": "#D34FDB", "filter": "invert(45%) sepia(84%) saturate(1892%) hue-rotate(259deg) brightness(88%) contrast(94%)"}, "t5_rul_1_a": {"name": "Potenzrechenregeln Ia \u2013 Exponenten addieren", "variants": 2, "color": "#910602", "filter": "invert(11%) sepia(63%) saturate(4965%) hue-rotate(14deg) brightness(103%) contrast(124%)"}, "t5_rul_1_b": {"name": "Potenzrechenregeln Ib \u2013 Exponenten subtrahieren", "variants": 2, "color": "#C8B210", "filter": "invert(72%) sepia(81%) saturate(1388%) hue-rotate(8deg) brightness(93%) contrast(87%)"}, "t5_rul_1_c": {"name": "Potenzrechenregeln Ic - Wurzel als Potenz darstellen", "variants": 4, "color": "#3BDBAA", "filter": "invert(92%) sepia(80%) saturate(1117%) hue-rotate(82deg) brightness(101%) contrast(69%)"}, "t5_rul_1_d": {"name": "Potenzrechenregeln Id \u2013 Exponenten multiplizieren", "variants": 2, "color": "#916F06", "filter": "invert(43%) sepia(44%) saturate(6440%) hue-rotate(38deg) brightness(93%) contrast(95%)"}, "t5_rul_1_e": {"name": "Potenzrechenregeln Ie - Potenzrechenregeln anwenden", "variants": 2, "color": "#C5B6C7", "filter": "invert(80%) sepia(6%) saturate(490%) hue-rotate(246deg) brightness(91%) contrast(96%)"}, "t5_rul_1_f": {"name": "Potenzrechenregeln I - Endboss", "variants": 2, "color": "#88383B", "filter": "invert(27%) sepia(85%) saturate(439%) hue-rotate(308deg) brightness(84%) contrast(94%)"}, "t7_der_1_a": {"name": "Ganzzahlige Summanden ableiten", "variants": 4, "color": "#71BC2E", "filter": "invert(61%) sepia(95%) saturate(366%) hue-rotate(48deg) brightness(91%) contrast(84%)"}, "t7_der_1_b": {"name": "Gebrochenrationale Summanden ableiten", "variants": 4, "color": "#B20EE3", "filter": "invert(22%) sepia(84%) saturate(4934%) hue-rotate(280deg) brightness(90%) contrast(116%)"}, "t7_der_1_c": {"name": "Produkte ableiten I", "variants": 4, "color": "#C751FB", "filter": "invert(41%) sepia(23%) saturate(6695%) hue-rotate(255deg) brightness(101%) contrast(97%)"}, "t7_der_1_d": {"name": "Produkte ableiten II", "variants": 4, "color": "#496108", "filter": "invert(32%) sepia(17%) saturate(2438%) hue-rotate(36deg) brightness(96%) contrast(94%)"}, "t7_der_1_e": {"name": "Division ableiten I", "variants": 4, "color": "#4DA97E", "filter": "invert(54%) sepia(42%) saturate(476%) hue-rotate(100deg) brightness(100%) contrast(84%)"}, "t7_der_1_f": {"name": "Division ableiten II", "variants": 4, "color": "#F8C255", "filter": "invert(76%) sepia(85%) saturate(388%) hue-rotate(335deg) brightness(100%) contrast(95%)"}, "t7_der_1_g": {"name": "Kettenregel I", "variants": 4, "color": "#642E0E", "filter": "invert(18%) sepia(12%) saturate(6525%) hue-rotate(354deg) brightness(97%) contrast(92%)"}, "t7_der_1_h": {"name": "Kettenregel II", "variants": 4, "color": "#16C9D7", "filter": "invert(67%) sepia(27%) saturate(3791%) hue-rotate(137deg) brightness(101%) contrast(83%)"}, "t7_der_1_i": {"name": "Gemischtes I", "variants": 4, "color": "#C768E5", "filter": "invert(51%) sepia(33%) saturate(1489%) hue-rotate(239deg) brightness(96%) contrast(86%)"}, "t7_der_1_j": {"name": "Gemischtes II", "variants": 4, "color": "#DA8376", "filter": "invert(76%) sepia(76%) saturate(1360%) hue-rotate(305deg) brightness(86%) contrast(86%)"}, "t7_der_1_k": {"name": "Gemischtes III", "variants": 4, "color": "#93916B", "filter": "invert(62%) sepia(7%) saturate(1282%) hue-rotate(19deg) brightness(91%) contrast(88%)"}, "t7_der_1_l": {"name": "Gemischtes IV", "variants": 4, "color": "#A4AA17", "filter": "invert(57%) sepia(80%) saturate(463%) hue-rotate(23deg) brightness(95%) contrast(84%)"}, "t7_der_1_m": {"name": "Gemischtes V", "variants": 4, "color": "#62CB69", "filter": "invert(99%) sepia(33%) saturate(3140%) hue-rotate(51deg) brightness(87%) contrast(79%)"}, "t7_der_1_n": {"name": "Gemischtes VI", "variants": 4, "color": "#CD51BA", "filter": "invert(52%) sepia(46%) saturate(3109%) hue-rotate(280deg) brightness(85%) contrast(86%)"}}}';
+quizObject = JSON.parse(quizObjectAsString);
+
+var processedAttempts = 0;
+var allAttempts = 0;
+//var CryptoObj =
+var fetches = {};
+var urls = {};
+
+//Paginate quiz objects
+let page = 0;
+for(let i in quizObject.questions) {
+ quizObject.questions[i].page = page;
+ let toAdd = quizObject.questions[i].variants == undefined ? 1 : quizObject.questions[i].variants;
+ page += toAdd;
+}
+
+let Encoder = new TextEncoder();
+//Hash functions to encrypt user id
+async function sha256(message) {
+ // encode as UTF-8
+ const msgBuffer = Encoder.encode(message);
+
+ // hash the message
+ const hashBuffer = await crypto.subtle.digest('SHA-256', msgBuffer);
+
+ // convert ArrayBuffer to Array
+ const hashArray = Array.from(new Uint8Array(hashBuffer));
+
+ // convert bytes to hex string
+ const hashHex = hashArray.map(b => ('00' + b.toString(16)).slice(-2)).join('');
+ return hashHex;
+}
+
+let monthTranslator = {
+ "Januar":0,
+ "Februar":1,
+ "März":2,
+ "März":2,
+ "April":3,
+ "Mai":4,
+ "Juni":5,
+ "Juli":6,
+ "August":7,
+ "September":8,
+ "Oktober":9,
+ "November":10,
+ "Dezember":11
+};
+//----------------CLASSES-------------------------
+class CQuestionAttempt {
+ constructor(timestampOrString, questionId, action, outcome, variant) {
+ this.variant = variant;
+ if(this.variant == undefined) {
+ this.variant = 1;
+ }
+ //Check timestampOrString
+ this.timestamp;
+ if(Number.isInteger(timestampOrString)) {
+ this.timestamp = timestampOrString;
+ }
+ else if(timestampOrString instanceof String || typeof timestampOrString === 'string') {
+ //German with full months written?
+ this.timestamp = this.getTimestampFromGermanTime(timestampOrString);
+ }
+ this.questionId = questionId;
+ this.action = action;
+ this.outcome = outcome;
+ if(!this.timestamp) {
+ console.log("timestring could not be converted");
+ this.timestamp = timestampOrString;
+ }
+ }
+
+ /*getTimestampFromGermanTime(timestring) {
+ let matchAllResult = timestring.matchAll(/(\d+)\. (.{4,}?) (\d{2,4}), (\d+):(\d+):(\d+)/g);
+ if(!matchAllResult) {
+ //probably not german
+ return false;
+ }
+
+ let matches = Array.from(matchAllResult)[0];
+ //1: day of month, 2: month in words, 3: year, 4: hours, 5: minutes, 6:seconds
+ if(monthTranslator[matches[2]] == undefined) {
+ //probably not german
+ return false;
+ }
+
+ let time = new Date(matches[3], monthTranslator[matches[2]], matches[1], matches[4], matches[5], matches[6]);
+ if(!time) {
+ return false;
+ }
+ return time.getTime();
+ }*/
+ getTimestampFromGermanTime(timestring) {
+ let hasAmPm = ((timestring.search(/ am/i) + timestring.search(/ pm/i)) > -2);
+ let time;
+ if(hasAmPm == true) {
+ console.log("special handling for AM / PM time string is neccessary");
+ return false;
+ }
+ //let matchAllResult = timestring.matchAll(/(\d+)\. (.{4,}?) (\d{2,4}), (\d+):(\d+):(\d+)/g);
+ let matchAllResult = timestring.matchAll(/(\d+)\.* (.{4,}?) (\d{2,4}),* (\d+):(\d+):*(\d*)/g);
+ let matches = Array.from(matchAllResult)[0];
+ if(!matches) {
+ //Give it another try, matching e. g. 18/09/23, 11:55:42
+ matchAllResult = timestring.matchAll(/(\d+)[\.\/-](\d+)[\.\/-](\d+),* (\d+):(\d+):*(\d*)/g);
+ matches = Array.from(matchAllResult)[0];
+
+ if(!matches) {
+ //probably not german, try Date
+ //console.log(timestring)
+ time = new Date(timestring);
+ }
+ else {
+ let year = matches[3]
+ if(matches[3].length == 2) {
+ year = "20"+year;
+ }
+ let month = parseInt(matches[2])-1;
+ time = new Date(year, month, matches[1], matches[4], matches[5], matches[6]);
+ }
+ }
+ else {
+ //1: day of month, 2: month in words, 3: year, 4: hours, 5: minutes, 6:seconds
+ if(monthTranslator[matches[2]] == undefined) {
+ //probably not german
+ return false;
+ }
+
+ time = new Date(matches[3], monthTranslator[matches[2]], matches[1], matches[4], matches[5], matches[6]);
+ }
+ if(isNaN(time)) {
+ return false;
+ }
+ return time.getTime();
+ }
+}
+
+class CUser {
+ constructor(idOrNode) {
+ let object = this;
+ this.Parser = new DOMParser();
+ this.QuestionAttempts = [];
+
+ if(idOrNode instanceof String || typeof idOrNode === 'string') {
+ this.id = idOrNode;
+ }
+ else if(idOrNode instanceof Element) {
+ if(idOrNode.tagName == "TR") {
+ let idNode = idOrNode.querySelector(".c3");
+ if(idNode == undefined) {
+ console.log("no id found for this row");
+ return;
+ }
+ this.id = idNode.innerHTML;
+
+ let reviewLink = idOrNode.querySelector(".reviewlink");
+ if(reviewLink == undefined) {
+ console.log("no review link found for this row");
+ return;
+ }
+ this.addAttempt(reviewLink.href);
+ }
+ }
+ else {
+ console.log("unknown type");
+ }
+ }
+
+ addAttempt(reviewUrl) {
+ let object = this;
+ if(reviewUrl == undefined) {
+ return;
+ }
+ fetch(reviewUrl)
+ .then(function(response) {
+ return response.text();
+ })
+ .then(function(htmlText) {
+ let fetchedPage = object.Parser.parseFromString(htmlText, "text/html");
+
+ let allQuestions = fetchedPage.querySelectorAll(".que");
+ if(allQuestions.length <= 1) {
+ //Sometimes, default is to show questions by pages. In this case, reload the page with all questions shown.
+ //Get url from .othernav or simply add "&showall=1" to the url.
+ return fetch(reviewUrl+"&showall=1").then(function(responseShowAll) {
+ return responseShowAll.text();
+ })
+ .then(function(htmlTextShowAll) {
+ let fetchedPageShowAll = object.Parser.parseFromString(htmlTextShowAll, "text/html");
+ //console.log(fetchedPageShowAll.querySelectorAll(".que"));
+ return fetchedPageShowAll;
+ });
+ }
+ else {
+ return fetchedPage;
+ }
+ })
+ .then(function(fetchedPageOrShowAll) {
+ //test = fetchedPageOrShowAll;
+ let allQuestions = fetchedPageOrShowAll.querySelectorAll(".que");
+ //console.log(allQuestions);
+ if(allQuestions.length < 1) {
+ throw new Error("bad amount of questions");
+ }
+
+ //Assume each question is shown, even the unattended. Then, allQuestions can be paginated as in quizObject.
+ //Loop through questions and variants in quiz object and append question information one by one.
+ let page = 0;
+ let questionIds = Object.keys(quizObject.questions);
+ let lastQuestionId = questionIds[questionIds.length-1];
+ let lastPage = quizObject.questions[lastQuestionId].page+quizObject.questions[lastQuestionId].variants-1;
+ for(let questionName in quizObject.questions) {
+ var variants = quizObject.questions[questionName].variants == undefined ? 1 : quizObject.questions[questionName].variants;
+
+ for(let i = 0;i<variants;i++) {
+ //console.log(page);
+ let relevantQuestionNode = allQuestions[page];
+ //fetch all question attempts from history
+ var previousQuestionAttemptUrls = relevantQuestionNode.querySelectorAll(".history a[id*='action_link']:not(.history tr a)");
+ if(previousQuestionAttemptUrls.length > 0) {
+ //console.log("but in "+questionName+" it's "+previousQuestionAttemptUrls.length);
+ for(var j=0;j<previousQuestionAttemptUrls.length;j++) {
+ let fetchId = Date.now().toString(36) + Math.random().toString(36).slice(2);
+ fetches[fetchId] = 0;
+ urls[fetchId] = previousQuestionAttemptUrls[j].href;
+ fetch(previousQuestionAttemptUrls[j].href)
+ .then(function(response) {
+ return response.text();
+ })
+ .then(function(htmlText) {
+ //console.log("and after fetch it's "+previousQuestionAttemptUrls.length);
+ let fetchedQuestionAttemptHistoryPage = object.Parser.parseFromString(htmlText, "text/html");
+ let infoTable = fetchedQuestionAttemptHistoryPage.querySelector(".que .history .generaltable");
+ if(infoTable == undefined) {
+ console.log(fetchedQuestionAttemptHistoryPage);
+ throw new Error("no table found error 2 for history number "+j);
+ }
+ let questionAttemptInfo = object.getQuestionAttemptInfoFromTable(infoTable);
+ object.QuestionAttempts.push(new CQuestionAttempt(questionAttemptInfo.timestring, questionName, questionAttemptInfo.action, questionAttemptInfo.status, i+1));
+
+ fetches[fetchId] = 1;
+ })
+ .catch(function(error) {
+ console.log("Error fetching question attempt from history.");
+ console.log(error);
+ });
+ }
+ }
+
+ //Fetch most recent question attempt. This one is found on the overview page without clicking.
+ let shownTable = allQuestions[page].querySelector(".generaltable");
+ if(shownTable == undefined) {
+ throw new Error("no table found error 1 for for question "+questionName);
+ }
+ let questionAttemptInfo = object.getQuestionAttemptInfoFromTable(shownTable);
+ object.QuestionAttempts.push(new CQuestionAttempt(questionAttemptInfo.timestring, questionName, questionAttemptInfo.action, questionAttemptInfo.status, i+1));
+
+ if(page == lastPage) {
+ processedAttempts++;
+ console.log("(Nearly) processed "+processedAttempts+" of "+allAttempts+ " attempts. (Fetch amount now at "+Object.keys(fetches).length+")");
+ }
+
+ page++;
+ }
+ }
+ })
+ .catch(function(error) {
+ console.log("error in promise chain");
+ console.log(error);
+ });
+ }
+
+ getQuestionAttemptInfoFromTable(tableNode) {
+ if(tableNode == undefined) {
+ return false;
+ }
+ let lastRow = tableNode.querySelector(".current.lastrow");
+ if(lastRow == undefined) {
+ return false;
+ }
+ //Assume c1 be the time, c2 be the action text and c3 be the status
+ let timestringNode = lastRow.querySelector(".c1");
+ let actionNode = lastRow.querySelector(".c2");
+ let statusNode = lastRow.querySelector(".c3");
+
+ if(timestringNode == undefined || statusNode == undefined) {
+ return false;
+ }
+
+ return {timestring:timestringNode.innerHTML, action:(actionNode.innerHTML == undefined ? "" : actionNode.innerHTML), status:statusNode.innerHTML};
+ }
+
+ simpleGetAttemptsAsCSV(addUserCol, addHeadingRow, encryptId, getRidOfInitializationAttempts) {
+ let csvString = "";
+ if(addUserCol == undefined) {
+ addUserCol = true;
+ }
+ if(addHeadingRow == undefined) {
+ addHeadingRow = false;
+ }
+ /*if(encryptId == undefined) {
+ encryptId = true;
+ }*/
+ encryptId = false;
+ let id = this.id;
+ i/*f(encryptId == true) {
+ //Because by default, Moodle's export results function returns Matrikelnummern as int, we encrypt the int too to ensure consistent results.
+ let toEncrypt = parseInt(id);
+ id = await sha256(""+toEncrypt);
+ }*/
+ if(getRidOfInitializationAttempts == undefined) {
+ getRidOfInitializationAttempts = true;
+ }
+
+
+ if(addHeadingRow == true) {
+ if(addUserCol == true) {
+ csvString += "user_id;";
+ }
+ csvString += "timestamp;question_id;variant;action;outcome;next_timestamp;next_question_id;next_variant\n";
+ }
+
+ //Sort attempts by time. To add next question attribute.
+ let SortedAttempts = this.getSanitizedAttempts(getRidOfInitializationAttempts);
+
+ for(let i=0;i<SortedAttempts.length;i++) {
+ let relevantVars = []
+ if(addUserCol == true) {
+ relevantVars.push(id);
+ }
+ relevantVars.push(SortedAttempts[i].timestamp, SortedAttempts[i].questionId, SortedAttempts[i].variant, SortedAttempts[i].action, SortedAttempts[i].outcome);
+ if(SortedAttempts[i+1] != undefined) {
+ relevantVars.push(SortedAttempts[i+1].timestamp, SortedAttempts[i+1].questionId, SortedAttempts[i+1].variant);
+ //relevantVars.push(SortedAttempts[i+1].questionId)
+ }
+ else {
+ relevantVars.push("", "_finish", "");
+ }
+ //csvString += "\""+relevantVars.join("\";\"")+"\"\n";
+ csvString += "'"+relevantVars.join("';'")+"'\n";
+ }
+
+ //csvString += "\n";
+ return csvString;
+ }
+
+ async getAttemptsAsCSV(addUserCol, addHeadingRow, encryptId, getRidOfInitializationAttempts) {
+ let csvString = "";
+ if(addUserCol == undefined) {
+ addUserCol = true;
+ }
+ if(addHeadingRow == undefined) {
+ addHeadingRow = false;
+ }
+ if(encryptId == undefined) {
+ encryptId = true;
+ }
+ let id = this.id;
+ if(encryptId == true) {
+ //Because by default, Moodle's export results function returns Matrikelnummern as int, we encrypt the int too to ensure consistent results.
+ let toEncrypt = parseInt(id);
+ if(!isNaN(toEncrypt)) {
+ id = await sha256(""+toEncrypt);
+ }
+ else {
+ //In case not the Matricel Id is listed, the e-mail-address will be hashed here to identify unique users.
+ id = await sha256(""+id);
+ }
+ }
+ if(getRidOfInitializationAttempts == undefined) {
+ getRidOfInitializationAttempts = true;
+ }
+
+
+ if(addHeadingRow == true) {
+ if(addUserCol == true) {
+ csvString += "user_id;";
+ }
+ csvString += "timestamp;question_id;variant;action;outcome;next_timestamp;next_question_id;next_variant\n";
+ }
+
+ //Sort attempts by time. To add next question attribute.
+ let SortedAttempts = this.getSanitizedAttempts(getRidOfInitializationAttempts);
+
+ for(let i=0;i<SortedAttempts.length;i++) {
+ let relevantVars = []
+ if(addUserCol == true) {
+ relevantVars.push(id);
+ }
+ relevantVars.push(SortedAttempts[i].timestamp, SortedAttempts[i].questionId, SortedAttempts[i].variant, SortedAttempts[i].action, SortedAttempts[i].outcome);
+ if(SortedAttempts[i+1] != undefined) {
+ relevantVars.push(SortedAttempts[i+1].timestamp, SortedAttempts[i+1].questionId, SortedAttempts[i+1].variant);
+ //relevantVars.push(SortedAttempts[i+1].questionId)
+ }
+ else {
+ relevantVars.push("", "_finish", "");
+ }
+ csvString += "'"+relevantVars.join("';'")+"'\n";
+ }
+
+ //csvString += "\n";
+ return csvString;
+ }
+
+ /*Leave the calculations up to python.
+ async getOverallInfoAsCSVRow(addHeadingRow, encryptId, getRidOfInitializationAttempts) {
+ let csvString = "";
+ if(addHeadingRow == undefined) {
+ addHeadingRow = false;
+ }
+ if(encryptId == undefined) {
+ encryptId = true;
+ }
+ let id = this.id;
+ if(encryptId == true) {
+ id = await sha256(this.id);
+
+ }
+ if(getRidOfInitializationAttempts == undefined) {
+ getRidOfInitializationAttempts = true;
+ }
+
+ if(addHeadingRow == true) {
+ if(addUserCol == true) {
+ csvString += "id,";
+ }
+ csvString += "started_working_amount,solved_amount,calls,first_action,last_action";
+ }
+
+ //Sort attempts by time. To add next question attribute.
+ let SortedAttempts = this.getSanitizedAttempts(getRidOfInitializationAttempts);
+
+ if(getRidOfInitializationAttempts == true) {
+ let initialTimestamp = SortedAttempts[0].timestamp;
+ let SortedAttemptsCopy = JSON.parse(JSON.stringify(SortedAttempts));
+ SortedAttempts = [];
+ for(let j=0;j<SortedAttemptsCopy.length;j++) {
+ if(SortedAttemptsCopy[j].timestamp != initialTimestamp) {
+ SortedAttempts.push(SortedAttemptsCopy[j]);
+ }
+ }
+ }
+
+ for(let i=0;i<SortedAttempts.length;i++) {
+ let relevantVars = []
+ if(addUserCol == true) {
+ relevantVars.push(id);
+ }
+ relevantVars.push(SortedAttempts[i].timestamp, SortedAttempts[i].questionId, SortedAttempts[i].variant, SortedAttempts[i].action, SortedAttempts[i].outcome);
+ if(SortedAttempts[i+1] != undefined) {
+ relevantVars.push(SortedAttempts[i+1].timestamp, SortedAttempts[i+1].questionId, SortedAttempts[i+1].variant);
+ //relevantVars.push(SortedAttempts[i+1].questionId)
+ }
+ else {
+ relevantVars.push("", "_finish", "");
+ }
+ csvString += "\""+relevantVars.join("\";\"")+"\"\n";
+ }
+
+ //csvString += "\n";
+ return csvString;
+ }*/
+
+ getSanitizedAttempts(getRidOfInitializationAttempts, getRidOfFinishedAttemptAttempts) {
+ //Will sort the question attempts and get rid of initialization attempts.
+ if(getRidOfInitializationAttempts == undefined) {
+ getRidOfInitializationAttempts = true;
+ }
+ if(getRidOfFinishedAttemptAttempts == undefined) {
+ getRidOfFinishedAttemptAttempts = true;
+ }
+
+ if(this.QuestionAttempts.length == 0) {
+ console.log("error: no attempts to sanitize");
+ return [];
+ }
+
+ let SanitizedAttempts = JSON.parse(JSON.stringify(this.QuestionAttempts));
+ SanitizedAttempts.sort(function(a, b) { return parseInt(a.timestamp) - parseInt(b.timestamp); });
+
+ if(getRidOfFinishedAttemptAttempts == true) {
+ let SanitizedAttemptsCopy = JSON.parse(JSON.stringify(SanitizedAttempts));
+ SanitizedAttempts = [];
+ for(let i=0;i<SanitizedAttemptsCopy.length;i++) {
+ if(SanitizedAttemptsCopy[i].action != "Versuch beendet" && SanitizedAttemptsCopy[i].action != "Attempt finished") {
+ SanitizedAttempts.push(SanitizedAttemptsCopy[i]);
+ }
+ }
+ }
+
+ if(!getRidOfInitializationAttempts) {
+ return SanitizedAttempts;
+ }
+
+ let initialTimestamp = SanitizedAttempts[0].timestamp;
+ let SanitizedAttemptsCopy = JSON.parse(JSON.stringify(SanitizedAttempts));
+ SanitizedAttempts = [];
+ for(let j=0;j<SanitizedAttemptsCopy.length;j++) {
+ if(SanitizedAttemptsCopy[j].timestamp != initialTimestamp) {
+ SanitizedAttempts.push(SanitizedAttemptsCopy[j]);
+ }
+ }
+ return SanitizedAttempts;
+ }
+}
+
+
+//----------------MAIN-------------------------
+//Classic theme?
+//let tableIdentifier = "#responses";
+//Alternative for HS BO Moodle Theme?
+
+let manualStart = false;
+
+let tableIdentifier = "#attempts";
+let allRows = document.querySelectorAll(tableIdentifier+" tbody tr:not(.emptyrow)");
+//Test group specific: Exclude those, who clicked through the questions as in control group design due to technically disappearing game design after re-initialization of the learning activity. This may not be neccessary any more as of 2023-09-19 due to fallback solutions.
+let i=0;
+allRows.forEach(function(row) {
+ let icons = row.querySelectorAll(".icon.fa");
+ if(icons.length > 1 /* Don't exclude those, who submitted their exercise and hence have one icon for each exercise. */ && row.classList.contains("gradedattempt") == false) {
+ console.log("Bad icon amount in row "+i+" ("+icons.length+"). Is excluded.");
+ row.classList.add("exclude");
+ }
+ i++;
+});
+//console.log(allRows);
+
+var rows = document.querySelectorAll(tableIdentifier+" tbody tr:not(.emptyrow):not(.exclude)");
+//console.log(rows);
+
+allAttempts = rows.length;
+var Users = {};
+
+console.log("There are "+allAttempts+" rows. Run 'loadUsers();' or 'loadUsers(from, to);' or 'loadUsersStepwise();' to start processing.");
+
+//for(let i=29;i<30;i++) {
+/*for(let i=0;i<rows.length;i++) {
+ let id;
+ let idNode = rows[i].querySelector(".c3");
+ if(idNode == undefined) {
+ console.log("no id found for row "+i);
+ continue;
+ }
+ id = idNode.innerHTML;
+ if(id == "") {
+ console.log("empty id in row "+i);
+ continue;
+ }
+
+ if(Users[id] == undefined) {
+ Users[id] = new CUser(rows[i]);
+ }
+ else {
+ //Get review link and add attempt to already existing user.
+ let reviewLink = rows[i].querySelector(".reviewlink");
+ if(reviewLink != undefined) {
+ Users[id].addAttempt(reviewLink.href);
+ }
+ else {
+ console.log("Found user row of already existing user, but didn't find review link ("+id+").");
+ }
+ }
+}*/
+
+function loadUsers(from, to) {
+ if(from == undefined) {
+ from = 0;
+ }
+ if(to == undefined) {
+ to = rows.length;
+ }
+
+ for(let i=from;i<to;i++) {
+ let id;
+ let idNode = rows[i].querySelector(".c3");
+ if(idNode == undefined) {
+ console.log("no id found for row "+i);
+ continue;
+ }
+ id = idNode.innerHTML;
+ if(id == "") {
+ console.log("empty id in row "+i);
+ continue;
+ }
+
+ if(Users[id] == undefined) {
+ Users[id] = new CUser(rows[i]);
+ }
+ else {
+ //Get review link and add attempt to already existing user.
+ let reviewLink = rows[i].querySelector(".reviewlink");
+ if(reviewLink != undefined) {
+ Users[id].addAttempt(reviewLink.href);
+ }
+ else {
+ console.log("Found user row of already existing user, but didn't find review link ("+id+").");
+ }
+ }
+ }
+}
+
+var csvText = "";
+
+function simpleLoadCSV(UsersObject) {
+ if(UsersObject == undefined) {
+ if(Users == undefined) {
+ return false;
+ }
+ UsersObject = Users;
+ }
+ csvText = "";
+ let first = true;
+ for(let i in UsersObject) {
+ csvText += UsersObject[i].getAttemptsAsCSV(true, first, false);
+ if(first == true) { first = false; }
+ }
+}
+
+async function loadCSV(UsersObject) {
+ if(UsersObject == undefined) {
+ if(Users == undefined) {
+ return false;
+ }
+ UsersObject = Users;
+ }
+ //let csvText = "";
+ csvText = "";
+ let first = true;
+ for(let i in UsersObject) {
+ csvText += await UsersObject[i].getAttemptsAsCSV(true, first);
+ if(first == true) { first = false; }
+ }
+ return csvText;
+ /*let c = document.createElement("a");
+ c.download = "alquiz-analysis-control.csv";
+ var t = new Blob([csvText], {
+ type: "text/plain"
+ });
+ c.href = window.URL.createObjectURL(t);
+ c.click();*/
+}
+
+function downloadCSV() {
+ let c = document.createElement("a");
+ c.download = "alquiz-analysis-test.csv";
+ var t = new Blob([csvText], {
+ type: "text/plain"
+ });
+ c.href = window.URL.createObjectURL(t);
+ c.click();
+}
+
+async function loadAndDownloadCSV() {
+ return await loadCSV().then(function(response) {
+ downloadCSV();
+ return response;
+ });
+}
+
+async function simpleDownloadCSV() {
+ if(UsersObject == undefined) {
+ if(Users == undefined) {
+ return false;
+ }
+ UsersObject = Users;
+ }
+ //let csvText = "";
+ csvText = "";
+ let first = true;
+ for(let i in UsersObject) {
+ csvText += await UsersObject[i].getAttemptsAsCSV(true, first, false);
+ if(first == true) { first = false; }
+ }
+ let c = document.createElement("a");
+ c.download = "alquiz-analysis-test-quick.csv";
+ var t = new Blob([csvText], {
+ type: "text/plain"
+ });
+ c.href = window.URL.createObjectURL(t);
+ c.click();
+}
+
+function getFetchState() {
+ /*let overallFetches = Object.keys(fetches).length;
+ let solvedFetches = 0;
+ for(let fetchId in fetches) {
+ if(fetches[fetchId] == 1) {
+ solvedFetches++;
+ }
+ }*/
+ infoObject = getFetchStateMachineReadable();
+ console.log("Fetched "+infoObject.solved+" of "+infoObject.overall+".");
+}
+
+function getFetchStateMachineReadable() {
+ let overallFetches = Object.keys(fetches).length;
+ let solvedFetches = 0;
+ for(let fetchId in fetches) {
+ if(fetches[fetchId] == 1) {
+ solvedFetches++;
+ }
+ }
+ return {"solved":solvedFetches, "overall":overallFetches};
+}
+
+//----------------TEST--------------------------
+function showAllAttemptsOf018345157(questionId) {
+ if(questionId == undefined) {
+ questionId = "start";
+ }
+ let OnlyStartAttempts = [];
+ if(Users["018345157"] != undefined) {
+ Users["018345157"].QuestionAttempts.forEach(function(QuestionAttempt) {
+ if(QuestionAttempt.questionId == questionId) {
+ OnlyStartAttempts.push(QuestionAttempt);
+ }
+ });
+ }
+ console.log(OnlyStartAttempts);
+}
+
+var processCount = 0;
+function processStepByStep() {
+ fetchInfoObject = getFetchStateMachineReadable();
+ if(fetchInfoObject.solved == fetchInfoObject.overall) {
+ if(processCount == allAttempts) {
+ console.log("Successfully processed all attempts.")
+ if(interval != undefined) {
+ clearInterval(interval);
+ }
+ return;
+ }
+ else {
+ loadUsers(processCount, processCount+1);
+ processCount++;
+ }
+ }
+}
+
+var interval;
+function loadUsersStepwise() {
+ interval = setInterval(processStepByStep, 5000);
+}
\ No newline at end of file
diff --git a/analysis/drawing.tex b/analysis/drawing.tex
new file mode 100644
index 0000000000000000000000000000000000000000..ccdd94ede9c142857b89caf8f8966278915cc60b
--- /dev/null
+++ b/analysis/drawing.tex
@@ -0,0 +1,51 @@
+\node [state] (start_instructions) at (0, 0) {};
+\node [state] (syn_instructions) at (1, 0) {};
+\node [state] (syn_a1) at (2, 0) {};
+\node [state] (syn_a2) at (3, 0) {};
+\node [state] (syn_b1) at (4, 0) {};
+\node [state] (syn_b2) at (5, 0) {};
+\node [state] (syn_c) at (6, 0) {};
+\node [state] (syn_d) at (7, 0) {};
+\node [state] (syn_e) at (8, 0) {};
+\node [state] (syn_f) at (9, 0) {};
+\node [state, boss] (syn_main) at (10, 0) {};
+\node [state] (fra_instructions) at (11, 0) {};
+\node [state] (fra_a) at (12, 0) {};
+\node [state] (fra_b) at (13, 0) {};
+\node [state] (fra_c) at (14, 0) {};
+\node [state] (fra_d) at (15, 0) {};
+\node [state] (fra_e) at (16, 0) {};
+\node [state] (fra_f) at (17, 0) {};
+\node [state] (bin_a) at (18, 0) {};
+\node [state] (bin_b) at (19, 0) {};
+\node [state] (bin_c) at (20, 0) {};
+\node [state] (bin_main) at (21, 0) {};
+\node [state, boss] (fra_main) at (22, 0) {};
+\node [state] (pq_instructions) at (23, 0) {};
+\node [state] (pq_a) at (24, 0) {};
+\node [state] (pq_b) at (25, 0) {};
+\node [state, boss] (pq_main) at (26, 0) {};
+\node [state] (rul_instructions) at (27, 0) {};
+\node [state] (rul_a) at (28, 0) {};
+\node [state] (rul_b) at (29, 0) {};
+\node [state] (rul_c) at (30, 0) {};
+\node [state] (rul_d) at (31, 0) {};
+\node [state] (rul_e) at (32, 0) {};
+\node [state, boss] (rul_main) at (33, 0) {};
+\node [state] (tri_instructions) at (34, 0) {};
+\node [state] (tri_a) at (35, 0) {};
+\node [state] (tri_b) at (36, 0) {};
+\node [state] (tri_c) at (37, 0) {};
+\node [state] (tri_d) at (38, 0) {};
+\node [state] (tri_e) at (39, 0) {};
+\node [state] (tri_f) at (40, 0) {};
+\node [state] (tri_g) at (41, 0) {};
+\node [state, boss] (tri_main) at (42, 0) {};
+\node [state] (sur_instructions) at (43, 0) {};
+\node [state] (survey) at (44, 0) {};
+\draw [category] (fra_instructions.west) -- (fra_main.east) node [midway, below=20pt+1.5em] {fractions\strut};
+\draw [category] (pq_instructions.west) -- (pq_main.east) node [midway, below=20pt+1.5em] {pq formula\strut};
+\draw [category] (rul_instructions.west) -- (rul_main.east) node [midway, below=20pt+1.5em] {power laws\strut};
+\draw [category] (syn_instructions.west) -- (syn_main.east) node [midway, below=20pt+1.5em] {syntax\strut};
+\draw [category] (tri_instructions.west) -- (tri_main.east) node [midway, below=20pt+1.5em] {trigonometry\strut};
+\draw [category] (sur_instructions.west) -- (survey.east) node [midway, below=20pt+1.5em] {survey\strut};
diff --git a/analysis/hops.csv b/analysis/hops.csv
new file mode 100644
index 0000000000000000000000000000000000000000..746d5dc16732cc0fd7505fe4479eff76da06e089
--- /dev/null
+++ b/analysis/hops.csv
@@ -0,0 +1,2503 @@
+question_id;next_question_id
+start_instructions;syn_instructions
+syn_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_b2
+syn_b2;syn_c
+syn_c;syn_c
+syn_c;syn_d
+syn_d;syn_e
+syn_e;syn_f
+syn_f;fra_instructions
+fra_instructions;syn_main
+syn_main;syn_e
+syn_e;fra_a
+fra_a;fra_b
+fra_b;fra_c
+fra_c;fra_c
+fra_c;fra_d
+fra_d;fra_e
+fra_e;fra_f
+fra_f;bin_a
+bin_a;bin_b
+bin_b;bin_c
+bin_c;bin_c
+bin_c;pq_a
+pq_a;pq_b
+pq_b;pq_main
+pq_main;rul_a
+rul_a;rul_a
+rul_a;rul_b
+rul_b;rul_c
+rul_c;rul_d
+rul_d;rul_e
+rul_e;tri_a
+tri_a;tri_b
+tri_b;tri_c
+tri_c;survey
+survey;tri_e
+start_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_c
+syn_c;syn_d
+syn_d;syn_e
+syn_e;syn_e
+syn_e;syn_e
+syn_e;syn_f
+syn_f;fra_a
+fra_a;fra_b
+fra_b;fra_b
+fra_b;fra_b
+fra_b;fra_c
+fra_c;fra_d
+fra_d;fra_e
+fra_e;fra_f
+fra_f;bin_a
+bin_a;bin_b
+bin_b;bin_b
+bin_b;bin_c
+bin_c;bin_c
+bin_c;bin_main
+bin_main;bin_main
+start_instructions;syn_instructions
+syn_instructions;start_instructions
+start_instructions;syn_main
+syn_main;fra_instructions
+fra_instructions;syn_main
+syn_main;fra_a
+fra_a;fra_b
+fra_b;pq_instructions
+pq_instructions;pq_a
+start_instructions;start_instructions
+start_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_c
+syn_c;syn_d
+syn_d;syn_e
+syn_e;syn_f
+syn_f;syn_main
+syn_main;syn_main
+syn_main;fra_a
+fra_a;survey
+start_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_c
+syn_c;syn_c
+syn_c;syn_d
+syn_d;syn_e
+syn_e;syn_f
+syn_f;syn_main
+syn_main;syn_main
+syn_main;fra_a
+fra_a;fra_b
+fra_b;fra_c
+fra_c;fra_d
+fra_d;fra_e
+fra_e;fra_f
+fra_f;bin_a
+bin_a;bin_b
+bin_b;bin_c
+bin_c;bin_main
+bin_main;fra_main
+fra_main;fra_main
+fra_main;pq_instructions
+pq_instructions;rul_instructions
+rul_instructions;tri_instructions
+tri_instructions;sur_instructions
+sur_instructions;survey
+start_instructions;syn_a1
+syn_a1;syn_d
+syn_d;syn_e
+syn_e;syn_f
+syn_f;syn_main
+syn_main;syn_main
+syn_main;fra_a
+fra_a;fra_b
+fra_b;fra_main
+start_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_c
+syn_c;syn_d
+syn_d;syn_e
+syn_e;syn_f
+syn_f;syn_main
+syn_main;syn_d
+syn_d;syn_main
+syn_main;bin_main
+bin_main;survey
+start_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_c
+syn_c;syn_d
+syn_d;syn_e
+syn_e;syn_f
+syn_f;syn_f
+syn_f;syn_main
+syn_main;syn_main
+syn_main;fra_a
+fra_a;fra_a
+fra_a;fra_b
+fra_b;fra_c
+fra_c;fra_c
+fra_c;fra_d
+fra_d;fra_e
+fra_e;fra_f
+fra_f;bin_a
+bin_a;bin_b
+bin_b;bin_c
+bin_c;bin_c
+bin_c;survey
+start_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_c
+syn_c;syn_d
+syn_d;syn_e
+syn_e;syn_f
+syn_f;syn_main
+syn_main;syn_d
+syn_d;syn_main
+syn_main;syn_main
+syn_main;syn_main
+syn_main;syn_main
+syn_main;bin_main
+bin_main;fra_instructions
+fra_instructions;pq_instructions
+pq_instructions;survey
+start_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b2
+syn_b2;syn_d
+syn_d;syn_e
+syn_e;syn_f
+syn_f;syn_main
+syn_main;fra_a
+fra_a;fra_b
+fra_b;fra_c
+fra_c;fra_d
+fra_d;fra_d
+fra_d;fra_e
+fra_e;fra_f
+fra_f;bin_a
+bin_a;bin_a
+bin_a;bin_main
+bin_main;fra_main
+start_instructions;syn_instructions
+syn_instructions;syn_b1
+syn_b1;syn_a2
+syn_a2;syn_a1
+syn_a1;syn_b2
+syn_b2;syn_c
+syn_c;syn_d
+syn_d;syn_e
+syn_e;syn_f
+syn_f;syn_main
+syn_main;fra_instructions
+fra_instructions;fra_a
+fra_a;fra_a
+fra_a;fra_b
+fra_b;fra_b
+fra_b;fra_c
+fra_c;fra_d
+fra_d;bin_main
+bin_main;fra_e
+fra_e;sur_instructions
+start_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_f
+syn_f;syn_main
+syn_main;syn_b2
+syn_b2;syn_c
+syn_c;syn_d
+syn_d;syn_e
+syn_e;syn_main
+syn_main;fra_a
+fra_a;fra_b
+fra_b;fra_c
+fra_c;survey
+start_instructions;syn_instructions
+syn_instructions;start_instructions
+start_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_c
+syn_c;syn_d
+syn_d;syn_d
+syn_d;syn_e
+syn_e;syn_f
+syn_f;syn_main
+syn_main;syn_main
+syn_main;syn_main
+syn_main;fra_a
+fra_a;fra_b
+fra_b;fra_c
+fra_c;fra_d
+fra_d;fra_e
+fra_e;bin_main
+bin_main;bin_main
+bin_main;survey
+survey;fra_f
+start_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_d
+syn_d;syn_d
+syn_d;syn_c
+syn_c;syn_d
+syn_d;syn_d
+syn_d;syn_d
+syn_d;syn_e
+syn_e;syn_f
+syn_f;syn_main
+syn_main;syn_main
+syn_main;fra_a
+fra_a;fra_b
+fra_b;fra_c
+fra_c;fra_c
+fra_c;fra_d
+fra_d;fra_e
+fra_e;fra_f
+fra_f;bin_a
+bin_a;bin_b
+bin_b;bin_c
+bin_c;bin_c
+bin_c;bin_main
+start_instructions;syn_instructions
+syn_instructions;syn_main
+syn_main;fra_main
+fra_main;fra_main
+fra_main;pq_main
+pq_main;bin_main
+start_instructions;syn_a1
+syn_a1;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_b2
+syn_b2;syn_b2
+syn_b2;syn_c
+syn_c;syn_d
+syn_d;syn_e
+syn_e;syn_f
+syn_f;bin_main
+bin_main;fra_a
+start_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_c
+syn_c;syn_d
+syn_d;syn_e
+syn_e;syn_f
+syn_f;syn_main
+syn_main;syn_main
+syn_main;fra_a
+fra_a;fra_b
+fra_b;fra_c
+fra_c;fra_d
+start_instructions;syn_a2
+syn_a2;syn_a1
+syn_a1;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_b2
+syn_b2;syn_c
+syn_c;syn_d
+syn_d;syn_e
+syn_e;syn_e
+syn_e;syn_f
+syn_f;syn_instructions
+syn_instructions;syn_main
+syn_main;fra_instructions
+fra_instructions;fra_a
+fra_a;fra_b
+fra_b;fra_c
+start_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_c
+syn_c;syn_d
+syn_d;syn_e
+syn_e;syn_f
+syn_f;start_instructions
+start_instructions;fra_instructions
+start_instructions;start_instructions
+start_instructions;syn_instructions
+syn_instructions;syn_a1
+syn_a1;syn_a2
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+pq_b;pq_main
+pq_main;rul_instructions
+rul_instructions;rul_a
+rul_a;rul_a
+rul_a;rul_c
+rul_c;rul_c
+rul_c;rul_d
+rul_d;tri_instructions
+tri_instructions;tri_a
+tri_a;tri_b
+tri_b;tri_c
+tri_c;sur_instructions
+sur_instructions;survey
+start_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_c
+syn_c;syn_d
+syn_d;syn_e
+syn_e;syn_f
+syn_f;syn_main
+syn_main;syn_main
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+fra_a;fra_b
+fra_b;fra_c
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+fra_c;fra_c
+fra_c;fra_c
+fra_c;fra_d
+fra_d;fra_d
+fra_d;fra_e
+fra_e;fra_f
+fra_f;bin_a
+bin_a;bin_b
+bin_b;bin_c
+bin_c;bin_main
+bin_main;fra_main
+fra_main;fra_main
+fra_main;pq_a
+pq_a;pq_b
+pq_b;pq_main
+pq_main;rul_instructions
+start_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_c
+syn_c;syn_d
+syn_d;syn_e
+syn_e;syn_f
+syn_f;fra_a
+fra_a;sur_instructions
+sur_instructions;fra_c
+fra_c;fra_instructions
+fra_instructions;pq_a
+pq_a;rul_a
+rul_a;rul_b
+rul_b;rul_c
+rul_c;rul_d
+rul_d;rul_e
+rul_e;rul_e
+rul_e;rul_main
+start_instructions;start_instructions
+start_instructions;syn_instructions
+syn_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_c
+syn_c;syn_d
+syn_d;syn_e
+syn_e;syn_f
+syn_f;syn_main
+syn_main;fra_instructions
+fra_instructions;fra_a
+fra_a;fra_b
+fra_b;fra_c
+fra_c;fra_c
+fra_c;fra_d
+fra_d;fra_e
+fra_e;fra_f
+fra_f;bin_a
+bin_a;bin_b
+bin_b;bin_c
+bin_c;bin_main
+bin_main;bin_main
+bin_main;fra_main
+fra_main;sur_instructions
+sur_instructions;survey
+survey;fra_main
+start_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_main
+syn_main;rul_a
+rul_a;rul_a
+rul_a;rul_b
+rul_b;fra_e
+fra_e;fra_f
+fra_f;bin_a
+bin_a;pq_b
+pq_b;pq_main
+pq_main;pq_instructions
+pq_instructions;survey
+survey;syn_e
+start_instructions;syn_instructions
+syn_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_a1
+syn_a1;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_c
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+syn_d;syn_d
+syn_d;syn_e
+syn_e;fra_a
+fra_a;fra_b
+fra_b;fra_c
+fra_c;fra_c
+fra_c;fra_c
+fra_c;fra_d
+fra_d;fra_e
+fra_e;fra_f
+fra_f;fra_f
+fra_f;bin_a
+bin_a;pq_a
+start_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_c
+syn_c;syn_c
+start_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_b2
+syn_b2;syn_c
+syn_c;syn_d
+syn_d;syn_e
+syn_e;syn_e
+syn_e;syn_e
+syn_e;syn_e
+syn_e;syn_e
+syn_e;syn_e
+syn_e;syn_f
+syn_f;syn_f
+syn_f;syn_main
+syn_main;fra_a
+fra_a;fra_a
+fra_a;fra_b
+fra_b;fra_b
+start_instructions;syn_instructions
+syn_instructions;fra_a
+fra_a;fra_instructions
+fra_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_c
+syn_c;fra_b
+fra_b;fra_c
+fra_c;fra_c
+fra_c;fra_d
+fra_d;fra_e
+fra_e;fra_f
+fra_f;bin_a
+bin_a;bin_b
+bin_b;bin_b
+bin_b;bin_c
+bin_c;bin_main
+bin_main;fra_main
+fra_main;pq_main
+pq_main;rul_main
+rul_main;rul_instructions
+rul_instructions;rul_main
+rul_main;tri_main
+tri_main;survey
+survey;syn_main
+start_instructions;syn_a1
+syn_a1;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_c
+syn_c;syn_d
+syn_d;syn_d
+syn_d;syn_e
+syn_e;syn_f
+syn_f;syn_f
+syn_f;syn_main
+syn_main;syn_main
+syn_main;fra_a
+fra_a;fra_b
+fra_b;fra_c
+fra_c;fra_c
+fra_c;fra_d
+fra_d;fra_e
+fra_e;fra_f
+fra_f;bin_a
+bin_a;bin_a
+bin_a;bin_b
+bin_b;bin_b
+bin_b;bin_c
+bin_c;bin_main
+bin_main;pq_instructions
+pq_instructions;pq_a
+pq_a;pq_a
+pq_a;sur_instructions
+start_instructions;syn_main
+syn_main;syn_main
+syn_main;fra_a
+fra_a;fra_b
+fra_b;fra_c
+fra_c;fra_d
+fra_d;fra_d
+fra_d;fra_e
+fra_e;fra_f
+fra_f;bin_a
+bin_a;bin_a
+bin_a;bin_b
+bin_b;bin_c
+bin_c;bin_main
+bin_main;bin_main
+bin_main;fra_main
+fra_main;pq_a
+pq_a;pq_b
+pq_b;pq_main
+pq_main;pq_main
+pq_main;rul_a
+rul_a;rul_a
+rul_a;rul_b
+rul_b;rul_c
+rul_c;rul_d
+rul_d;rul_e
+rul_e;rul_main
+start_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_c
+syn_c;syn_d
+syn_d;syn_e
+syn_e;syn_f
+syn_f;syn_main
+syn_main;syn_main
+syn_main;bin_a
+bin_a;bin_b
+bin_b;bin_c
+bin_c;bin_main
+bin_main;fra_main
+fra_main;pq_b
+pq_b;rul_instructions
+rul_instructions;rul_c
+rul_c;rul_d
+start_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_b2
+syn_b2;syn_c
+syn_c;syn_d
+syn_d;syn_e
+syn_e;syn_f
+syn_f;syn_f
+syn_f;syn_main
+syn_main;syn_instructions
+syn_instructions;syn_main
+syn_main;fra_a
+fra_a;fra_b
+fra_b;fra_b
+fra_b;fra_c
+fra_c;fra_d
+fra_d;fra_e
+fra_e;fra_f
+fra_f;bin_a
+bin_a;bin_a
+bin_a;bin_b
+bin_b;bin_c
+bin_c;bin_c
+bin_c;bin_main
+bin_main;fra_main
+fra_main;pq_a
+pq_a;pq_b
+pq_b;pq_main
+pq_main;rul_main
+rul_main;tri_main
+tri_main;survey
+start_instructions;syn_a1
+syn_a1;start_instructions
+start_instructions;syn_d
+syn_d;syn_e
+syn_e;syn_f
+syn_f;syn_main
+syn_main;syn_main
+syn_main;fra_a
+fra_a;fra_e
+fra_e;fra_f
+fra_f;bin_a
+bin_a;bin_b
+bin_b;bin_c
+bin_c;bin_c
+bin_c;bin_main
+bin_main;fra_main
+fra_main;pq_main
+pq_main;survey
+survey;syn_a1
+syn_a1;pq_main
+start_instructions;syn_main
+syn_main;syn_instructions
+syn_instructions;fra_instructions
+fra_instructions;fra_a
+fra_a;fra_b
+fra_b;fra_c
+fra_c;fra_c
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+fra_d;fra_e
+fra_e;fra_main
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+fra_f;fra_f
+fra_f;bin_a
+bin_a;bin_main
+bin_main;fra_main
+fra_main;pq_main
+pq_main;pq_main
+pq_main;rul_instructions
+rul_instructions;rul_a
+rul_a;rul_c
+rul_c;rul_d
+rul_d;rul_d
+rul_d;rul_e
+rul_e;rul_main
+rul_main;survey
+start_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_d
+syn_d;syn_d
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+syn_d;syn_d
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+fra_b;fra_b
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+fra_c;fra_c
+fra_c;fra_d
+fra_d;sur_instructions
+sur_instructions;fra_e
+fra_e;fra_e
+fra_e;rul_a
+rul_a;syn_c
+start_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
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+syn_b2;syn_c
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+syn_d;syn_e
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+syn_f;syn_main
+syn_main;fra_instructions
+fra_instructions;fra_a
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+fra_b;fra_a
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+fra_b;fra_d
+fra_d;pq_b
+pq_b;rul_a
+rul_a;rul_a
+rul_a;rul_a
+rul_a;rul_c
+rul_c;rul_c
+rul_c;rul_c
+rul_c;rul_d
+rul_d;rul_d
+rul_d;tri_instructions
+tri_instructions;tri_a
+tri_a;survey
+survey;pq_a
+pq_a;pq_b
+pq_b;pq_main
+pq_main;tri_a
+start_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
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+syn_d;syn_e
+syn_e;syn_e
+syn_e;syn_f
+syn_f;syn_main
+syn_main;fra_main
+fra_main;pq_main
+start_instructions;syn_instructions
+syn_instructions;start_instructions
+start_instructions;syn_b1
+syn_b1;syn_a2
+syn_a2;syn_a1
+syn_a1;syn_b2
+syn_b2;syn_c
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+fra_f;fra_f
+fra_f;bin_a
+bin_a;bin_a
+bin_a;bin_b
+bin_b;bin_c
+bin_c;bin_main
+bin_main;bin_main
+bin_main;fra_main
+fra_main;rul_a
+rul_a;rul_b
+rul_b;rul_b
+rul_b;rul_c
+rul_c;rul_d
+rul_d;rul_e
+rul_e;rul_main
+rul_main;tri_instructions
+tri_instructions;tri_a
+tri_a;tri_a
+tri_a;tri_b
+tri_b;tri_b
+tri_b;tri_c
+tri_c;tri_d
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+tri_d;tri_e
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+tri_e;tri_f
+tri_f;tri_g
+tri_g;tri_g
+tri_g;pq_b
+pq_b;pq_b
+pq_b;survey
+survey;pq_instructions
+pq_instructions;pq_a
+pq_a;pq_a
+pq_a;pq_a
+pq_a;pq_a
+pq_a;pq_a
+pq_a;pq_main
+start_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_c
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+fra_f;fra_f
+fra_f;bin_a
+bin_a;bin_b
+bin_b;bin_b
+bin_b;bin_c
+bin_c;bin_main
+bin_main;fra_f
+fra_f;fra_f
+fra_f;pq_instructions
+pq_instructions;pq_a
+pq_a;pq_a
+pq_a;pq_a
+pq_a;pq_b
+pq_b;survey
+survey;pq_b
+pq_b;pq_main
+start_instructions;syn_instructions
+syn_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_c
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+syn_main;syn_main
+syn_main;fra_instructions
+fra_instructions;fra_a
+fra_a;fra_b
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+fra_c;fra_d
+fra_d;fra_e
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+bin_main;bin_main
+bin_main;fra_main
+fra_main;fra_main
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+fra_main;fra_main
+fra_main;pq_instructions
+pq_instructions;survey
+survey;pq_main
+pq_main;pq_main
+start_instructions;syn_main
+syn_main;fra_instructions
+fra_instructions;pq_main
+pq_main;rul_main
+rul_main;rul_main
+rul_main;syn_main
+syn_main;tri_main
+tri_main;tri_main
+tri_main;fra_main
+fra_main;fra_main
+fra_main;survey
+start_instructions;syn_instructions
+syn_instructions;syn_main
+syn_main;syn_main
+syn_main;syn_a1
+syn_a1;syn_a2
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+fra_f;bin_a
+bin_a;bin_b
+bin_b;bin_c
+bin_c;bin_main
+bin_main;fra_main
+fra_main;rul_instructions
+rul_instructions;rul_a
+rul_a;rul_b
+rul_b;rul_c
+rul_c;rul_d
+rul_d;rul_e
+rul_e;rul_main
+rul_main;tri_a
+tri_a;tri_b
+tri_b;tri_c
+tri_c;tri_d
+tri_d;tri_e
+tri_e;tri_f
+tri_f;tri_g
+start_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
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+syn_b1;syn_main
+syn_main;syn_main
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+fra_b;fra_b
+fra_b;fra_b
+fra_b;syn_b2
+syn_b2;syn_c
+syn_c;syn_d
+syn_d;syn_d
+syn_d;syn_e
+syn_e;syn_f
+syn_f;syn_main
+syn_main;syn_main
+syn_main;fra_c
+fra_c;fra_c
+fra_c;fra_d
+fra_d;fra_d
+fra_d;fra_e
+fra_e;fra_e
+fra_e;fra_f
+fra_f;fra_f
+fra_f;fra_main
+fra_main;bin_a
+bin_a;bin_b
+bin_b;bin_c
+bin_c;bin_main
+bin_main;tri_main
+start_instructions;syn_instructions
+syn_instructions;syn_a1
+syn_a1;syn_a2
+syn_a2;syn_b1
+syn_b1;syn_b2
+syn_b2;syn_c
+syn_c;syn_d
+syn_d;syn_e
+syn_e;syn_f
+syn_f;syn_main
+syn_main;syn_main
+syn_main;fra_main
+fra_main;fra_main
+fra_main;pq_main
+pq_main;rul_instructions
+rul_instructions;survey
+start_instructions;syn_main
+syn_main;fra_c
+fra_c;bin_b
+bin_b;fra_main
+fra_main;fra_main
+fra_main;pq_main
+pq_main;survey
+survey;fra_a
diff --git a/analysis/tex/drawing-fractions.tex b/analysis/tex/drawing-fractions.tex
new file mode 100644
index 0000000000000000000000000000000000000000..7a70ef9aea6eef54c3c22c14dbd552936f496c6a
--- /dev/null
+++ b/analysis/tex/drawing-fractions.tex
@@ -0,0 +1,43 @@
+\node [state, info] (fra_instructions) at (0, 0) {};
+\node [state] (fra_a) at (1, 0) {};
+\node [state] (fra_b) at (2, 0) {};
+\node [state] (fra_c) at (3, 0) {};
+\node [state] (fra_d) at (4, 0) {};
+\node [state] (fra_e) at (5, 0) {};
+\node [state] (fra_f) at (6, 0) {};
+\node [state] (bin_a) at (7, 0) {};
+\node [state] (bin_b) at (8, 0) {};
+\node [state] (bin_c) at (9, 0) {};
+\node [state] (bin_main) at (10, 0) {};
+\node [state, boss] (fra_main) at (11, 0) {};
+\node [inout] (input) at (-1, 1) {};
+\node [inout] (output) at (12, 1) {};
+\path [line width=1.2pt, black!62] (input) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.222$} (fra_instructions);
+\path [line width=1.5pt, black!82] (input) edge [controls=+(80:2.0) and +(100:2.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.574$} (fra_a);
+\path [line width=1.4pt, black!81] (fra_instructions) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.548$} (fra_a);
+\path [line width=1.2pt, black!66] (fra_instructions) edge [controls=+(80:12.0) and +(100:12.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.290$} (output);
+\path [line width=1.1pt, black!58] (fra_a) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.147$} (fra_a);
+\path [line width=1.6pt, black!94] (fra_a) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.789$} (fra_b);
+\path [line width=1.2pt, black!66] (fra_b) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.278$} (fra_b);
+\path [line width=1.5pt, black!85] (fra_b) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.630$} (fra_c);
+\path [line width=1.2pt, black!67] (fra_c) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.307$} (fra_c);
+\path [line width=1.5pt, black!86] (fra_c) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.634$} (fra_d);
+\path [line width=1.1pt, black!58] (fra_d) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.137$} (fra_d);
+\path [line width=1.6pt, black!96] (fra_d) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.822$} (fra_e);
+\path [line width=1.6pt, black!91] (fra_e) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.729$} (fra_f);
+\path [line width=1.2pt, black!65] (fra_f) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.268$} (fra_f);
+\path [line width=1.5pt, black!86] (fra_f) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.634$} (bin_a);
+\path [line width=1.1pt, black!61] (bin_a) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.188$} (bin_a);
+\path [line width=1.6pt, black!90] (bin_a) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.719$} (bin_b);
+\path [line width=1.1pt, black!58] (bin_b) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.145$} (bin_b);
+\path [line width=1.6pt, black!94] (bin_b) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.782$} (bin_c);
+\path [line width=1.2pt, black!63] (bin_c) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.234$} (bin_c);
+\path [line width=1.5pt, black!82] (bin_c) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.578$} (bin_main);
+\path [line width=1.2pt, black!62] (bin_main) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.220$} (bin_main);
+\path [line width=1.4pt, black!79] (bin_main) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.525$} (fra_main);
+\path [line width=1.1pt, black!59] (bin_main) edge [controls=+(80:2.0) and +(100:2.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.153$} (output);
+\path [line width=1.3pt, black!70] (fra_main) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.350$} (fra_main);
+\path [line width=1.4pt, black!79] (fra_main) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.512$} (output);
+\path [line width=1.2pt, black!61] (output) edge [controls=+(260:11.0) and +(-80:11.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.200$} (fra_a);
+\path [line width=1.2pt, black!61] (output) edge [controls=+(260:7.0) and +(-80:7.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.200$} (fra_e);
+\path [line width=1.2pt, black!67] (output) edge [controls=+(260:1.0) and +(-80:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.300$} (fra_main);
diff --git a/analysis/tex/drawing-power laws.tex b/analysis/tex/drawing-power laws.tex
new file mode 100644
index 0000000000000000000000000000000000000000..d6af98e31c38977e56f9fefa5eb18ca1949af472
--- /dev/null
+++ b/analysis/tex/drawing-power laws.tex
@@ -0,0 +1,28 @@
+\node [state, info] (rul_instructions) at (0, 0) {};
+\node [state] (rul_a) at (1, 0) {};
+\node [state] (rul_b) at (2, 0) {};
+\node [state] (rul_c) at (3, 0) {};
+\node [state] (rul_d) at (4, 0) {};
+\node [state] (rul_e) at (5, 0) {};
+\node [state, boss] (rul_main) at (6, 0) {};
+\node [inout] (input) at (-1, 1) {};
+\node [inout] (output) at (7, 1) {};
+\path [line width=1.3pt, black!70] (input) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.360$} (rul_instructions);
+\path [line width=1.3pt, black!69] (input) edge [controls=+(80:2.0) and +(100:2.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.340$} (rul_a);
+\path [line width=1.2pt, black!65] (input) edge [controls=+(80:7.0) and +(100:7.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.260$} (rul_main);
+\path [line width=1.4pt, black!81] (rul_instructions) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.556$} (rul_a);
+\path [line width=1.1pt, black!56] (rul_instructions) edge [controls=+(80:6.0) and +(100:6.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.111$} (rul_main);
+\path [line width=1.2pt, black!62] (rul_instructions) edge [controls=+(80:7.0) and +(100:7.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.222$} (output);
+\path [line width=1.2pt, black!66] (rul_a) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.282$} (rul_a);
+\path [line width=1.5pt, black!84] (rul_a) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.615$} (rul_b);
+\path [line width=1.7pt, black!99] (rul_b) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.880$} (rul_c);
+\path [line width=1.7pt, black!99] (rul_c) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.871$} (rul_d);
+\path [line width=1.1pt, black!56] (rul_d) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.107$} (rul_d);
+\path [line width=1.6pt, black!90] (rul_d) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.714$} (rul_e);
+\path [line width=1.1pt, black!60] (rul_d) edge [controls=+(80:3.0) and +(100:3.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.179$} (output);
+\path [line width=1.1pt, black!59] (rul_e) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.154$} (rul_e);
+\path [line width=1.3pt, black!72] (rul_e) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.385$} (rul_main);
+\path [line width=1.4pt, black!76] (rul_e) edge [controls=+(80:2.0) and +(100:2.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.462$} (output);
+\path [line width=1.3pt, black!70] (rul_main) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.364$} (rul_main);
+\path [line width=1.4pt, black!81] (rul_main) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.545$} (output);
+\path [line width=1.8pt, black!100] (output) edge [controls=+(260:4.0) and +(-80:4.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$1.000$} (rul_c);
diff --git a/analysis/tex/drawing-pq formula.tex b/analysis/tex/drawing-pq formula.tex
new file mode 100644
index 0000000000000000000000000000000000000000..1a26c163a993acc7d5e26349356201caddb5b243
--- /dev/null
+++ b/analysis/tex/drawing-pq formula.tex
@@ -0,0 +1,22 @@
+\node [state, info] (pq_instructions) at (0, 0) {};
+\node [state] (pq_a) at (1, 0) {};
+\node [state] (pq_b) at (2, 0) {};
+\node [state, boss] (pq_main) at (3, 0) {};
+\node [inout] (input) at (-1, 1) {};
+\node [inout] (output) at (4, 1) {};
+\path [line width=1.2pt, black!62] (input) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.212$} (pq_instructions);
+\path [line width=1.3pt, black!70] (input) edge [controls=+(80:2.0) and +(100:2.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.364$} (pq_a);
+\path [line width=1.3pt, black!70] (input) edge [controls=+(80:4.0) and +(100:4.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.348$} (pq_main);
+\path [line width=1.3pt, black!74] (pq_instructions) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.429$} (pq_a);
+\path [line width=1.4pt, black!77] (pq_instructions) edge [controls=+(80:4.0) and +(100:4.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.476$} (output);
+\path [line width=1.2pt, black!67] (pq_a) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.306$} (pq_a);
+\path [line width=1.4pt, black!81] (pq_a) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.551$} (pq_b);
+\path [line width=1.1pt, black!60] (pq_b) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.184$} (pq_b);
+\path [line width=1.4pt, black!79] (pq_b) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.526$} (pq_main);
+\path [line width=1.2pt, black!66] (pq_b) edge [controls=+(80:2.0) and +(100:2.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.289$} (output);
+\path [line width=1.3pt, black!70] (pq_main) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.355$} (pq_main);
+\path [line width=1.4pt, black!80] (pq_main) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.532$} (output);
+\path [line width=1.1pt, black!56] (output) edge [controls=+(260:4.0) and +(-80:4.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.105$} (pq_instructions);
+\path [line width=1.4pt, black!79] (output) edge [controls=+(260:3.0) and +(-80:3.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.526$} (pq_a);
+\path [line width=1.1pt, black!59] (output) edge [controls=+(260:2.0) and +(-80:2.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.158$} (pq_b);
+\path [line width=1.2pt, black!62] (output) edge [controls=+(260:1.0) and +(-80:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.211$} (pq_main);
diff --git a/analysis/tex/drawing-survey.tex b/analysis/tex/drawing-survey.tex
new file mode 100644
index 0000000000000000000000000000000000000000..b0e8bc8c78afc67a19067293627c66bd98d1ae25
--- /dev/null
+++ b/analysis/tex/drawing-survey.tex
@@ -0,0 +1,9 @@
+\node [state] (sur_instructions) at (0, 0) {};
+\node [state] (survey) at (1, 0) {};
+\node [inout] (input) at (-1, 1) {};
+\node [inout] (output) at (2, 1) {};
+\path [line width=1.2pt, black!62] (input) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.213$} (sur_instructions);
+\path [line width=1.6pt, black!94] (input) edge [controls=+(80:2.0) and +(100:2.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.787$} (survey);
+\path [line width=1.5pt, black!84] (sur_instructions) edge [controls=+(260:1.0) and +(-80:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.600$} (input);
+\path [line width=1.3pt, black!72] (sur_instructions) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.400$} (survey);
+\path [line width=1.8pt, black!100] (survey) edge [controls=+(260:2.0) and +(-80:2.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$1.000$} (input);
diff --git a/analysis/tex/drawing-syntax.tex b/analysis/tex/drawing-syntax.tex
new file mode 100644
index 0000000000000000000000000000000000000000..67b23e749db7472a45341ca18f6c05f7c7bb018e
--- /dev/null
+++ b/analysis/tex/drawing-syntax.tex
@@ -0,0 +1,36 @@
+\node [state, info] (syn_instructions) at (0, 0) {};
+\node [state] (syn_a1) at (1, 0) {};
+\node [state] (syn_a2) at (2, 0) {};
+\node [state] (syn_b1) at (3, 0) {};
+\node [state] (syn_b2) at (4, 0) {};
+\node [state] (syn_c) at (5, 0) {};
+\node [state] (syn_d) at (6, 0) {};
+\node [state] (syn_e) at (7, 0) {};
+\node [state] (syn_f) at (8, 0) {};
+\node [state, boss] (syn_main) at (9, 0) {};
+\node [inout] (input) at (-1, 1) {};
+\node [inout] (output) at (10, 1) {};
+\path [line width=1.2pt, black!63] (input) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.228$} (syn_instructions);
+\path [line width=1.5pt, black!83] (input) edge [controls=+(80:2.0) and +(100:2.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.596$} (syn_a1);
+\path [line width=1.1pt, black!58] (syn_instructions) edge [controls=+(260:1.0) and +(-80:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.140$} (input);
+\path [line width=1.3pt, black!73] (syn_instructions) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.419$} (syn_a1);
+\path [line width=1.1pt, black!59] (syn_instructions) edge [controls=+(80:9.0) and +(100:9.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.163$} (syn_main);
+\path [line width=1.2pt, black!62] (syn_instructions) edge [controls=+(80:10.0) and +(100:10.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.209$} (output);
+\path [line width=1.6pt, black!95] (syn_a1) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.810$} (syn_a2);
+\path [line width=1.7pt, black!100] (syn_a2) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.892$} (syn_b1);
+\path [line width=1.7pt, black!98] (syn_b1) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.857$} (syn_b2);
+\path [line width=1.1pt, black!56] (syn_b2) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.112$} (syn_b2);
+\path [line width=1.6pt, black!94] (syn_b2) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.786$} (syn_c);
+\path [line width=1.7pt, black!97] (syn_c) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.848$} (syn_d);
+\path [line width=1.2pt, black!63] (syn_d) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.229$} (syn_d);
+\path [line width=1.5pt, black!89] (syn_d) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.695$} (syn_e);
+\path [line width=1.1pt, black!59] (syn_e) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.165$} (syn_e);
+\path [line width=1.6pt, black!91] (syn_e) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.738$} (syn_f);
+\path [line width=1.1pt, black!58] (syn_f) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.147$} (syn_f);
+\path [line width=1.5pt, black!86] (syn_f) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.642$} (syn_main);
+\path [line width=1.1pt, black!57] (syn_f) edge [controls=+(80:2.0) and +(100:2.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.126$} (output);
+\path [line width=1.3pt, black!68] (syn_main) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.320$} (syn_main);
+\path [line width=1.4pt, black!80] (syn_main) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.527$} (output);
+\path [line width=1.1pt, black!59] (output) edge [controls=+(260:9.0) and +(-80:9.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.167$} (syn_a1);
+\path [line width=1.1pt, black!56] (output) edge [controls=+(260:3.0) and +(-80:3.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.111$} (syn_e);
+\path [line width=1.3pt, black!75] (output) edge [controls=+(260:1.0) and +(-80:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.444$} (syn_main);
diff --git a/analysis/tex/drawing-trigonometry.tex b/analysis/tex/drawing-trigonometry.tex
new file mode 100644
index 0000000000000000000000000000000000000000..172c942f6771980e7b9df7fa48895784028d5c15
--- /dev/null
+++ b/analysis/tex/drawing-trigonometry.tex
@@ -0,0 +1,39 @@
+\node [state, info] (tri_instructions) at (0, 0) {};
+\node [state] (tri_a) at (1, 0) {};
+\node [state] (tri_b) at (2, 0) {};
+\node [state] (tri_c) at (3, 0) {};
+\node [state] (tri_d) at (4, 0) {};
+\node [state] (tri_e) at (5, 0) {};
+\node [state] (tri_f) at (6, 0) {};
+\node [state] (tri_g) at (7, 0) {};
+\node [state, boss] (tri_main) at (8, 0) {};
+\node [inout] (input) at (-1, 1) {};
+\node [inout] (output) at (9, 1) {};
+\path [line width=1.3pt, black!72] (input) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.385$} (tri_instructions);
+\path [line width=1.2pt, black!67] (input) edge [controls=+(80:2.0) and +(100:2.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.308$} (tri_a);
+\path [line width=1.2pt, black!64] (input) edge [controls=+(80:9.0) and +(100:9.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.256$} (tri_main);
+\path [line width=1.1pt, black!59] (tri_instructions) edge [controls=+(260:1.0) and +(-80:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.154$} (input);
+\path [line width=1.5pt, black!84] (tri_instructions) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.615$} (tri_a);
+\path [line width=1.2pt, black!63] (tri_instructions) edge [controls=+(80:9.0) and +(100:9.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.231$} (output);
+\path [line width=1.6pt, black!94] (tri_a) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.783$} (tri_b);
+\path [line width=1.6pt, black!92] (tri_b) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.750$} (tri_c);
+\path [line width=1.1pt, black!58] (tri_b) edge [controls=+(80:7.0) and +(100:7.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.150$} (output);
+\path [line width=1.3pt, black!72] (tri_c) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.400$} (tri_d);
+\path [line width=1.4pt, black!76] (tri_c) edge [controls=+(80:6.0) and +(100:6.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.467$} (output);
+\path [line width=1.1pt, black!56] (tri_d) edge [controls=+(260:5.0) and +(-80:5.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.111$} (input);
+\path [line width=1.2pt, black!62] (tri_d) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.222$} (tri_d);
+\path [line width=1.3pt, black!69] (tri_d) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.333$} (tri_e);
+\path [line width=1.3pt, black!69] (tri_d) edge [controls=+(80:5.0) and +(100:5.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.333$} (output);
+\path [line width=1.2pt, black!64] (tri_e) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.250$} (tri_e);
+\path [line width=1.6pt, black!92] (tri_e) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.750$} (tri_f);
+\path [line width=1.6pt, black!92] (tri_f) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.750$} (tri_g);
+\path [line width=1.2pt, black!64] (tri_f) edge [controls=+(80:3.0) and +(100:3.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.250$} (output);
+\path [line width=1.1pt, black!59] (tri_g) edge [controls=+(260:8.0) and +(-80:8.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.167$} (input);
+\path [line width=1.5pt, black!87] (tri_g) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.667$} (tri_g);
+\path [line width=1.1pt, black!59] (tri_g) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.167$} (tri_main);
+\path [line width=1.3pt, black!72] (tri_main) edge [loop above] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.400$} (tri_main);
+\path [line width=1.4pt, black!76] (tri_main) edge [controls=+(80:1.0) and +(100:1.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.467$} (output);
+\path [line width=1.3pt, black!72] (output) edge [controls=+(260:8.0) and +(-80:8.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.400$} (tri_a);
+\path [line width=1.2pt, black!61] (output) edge [controls=+(260:5.0) and +(-80:5.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.200$} (tri_d);
+\path [line width=1.2pt, black!61] (output) edge [controls=+(260:4.0) and +(-80:4.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.200$} (tri_e);
+\path [line width=1.2pt, black!61] (output) edge [controls=+(260:3.0) and +(-80:3.0)] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {$0.200$} (tri_f);
diff --git a/analysis/tex/overview.pdf b/analysis/tex/overview.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..e76ba472e17a39c14b8fff54d2bb8b4f7c0125a1
Binary files /dev/null and b/analysis/tex/overview.pdf differ
diff --git a/analysis/tex/overview.tex b/analysis/tex/overview.tex
new file mode 100644
index 0000000000000000000000000000000000000000..f8a311cd77a4127c80c5f25d6376a1ff3a68c2a7
--- /dev/null
+++ b/analysis/tex/overview.tex
@@ -0,0 +1,44 @@
+\documentclass[a4paper,twoside]{article}
+
+
+\usepackage{tikz}
+\usetikzlibrary{positioning}
+\usetikzlibrary{automata}
+\usetikzlibrary{arrows.meta}
+\usetikzlibrary{decorations.pathreplacing}
+
+\newcommand{\hopgraph}[2]{
+ %transform canvas={scale=0.75},
+ \begin{figure*}[!h]
+ \centering
+ \resizebox{\textwidth}{!}{%
+ \begin{tikzpicture}[scale=0.8,
+ x=2cm, auto, node distance=4cm, ->,
+ decoration={brace, mirror, amplitude=15pt, raise=20pt},
+ category/.style={-, blue!70, thick, decorate},
+ every state/.style={draw=blue!50,very thick,fill=blue!20},
+ boss/.style={draw=red!90!black!70, fill=red!40},
+ info/.style={draw=yellow!90!black!70, fill=yellow!40},
+ inout/.style={draw=green!80!black!60, fill=green!30, rectangle, minimum size=2em},
+ every edge/.style = {draw, -{Stealth[scale=1.2]}, bend angle=15}
+ ]
+ \input{drawing-#1.tex}
+ \end{tikzpicture}
+ }%
+ \caption{How users move along the #2 world.}
+ \label{fig:progress_#1}
+ \end{figure*}
+}
+
+\begin{document}
+
+\hopgraph{syntax}{syntax}
+\hopgraph{fractions}{fractions and binomial formulas}
+\hopgraph{pq formula}{pq forumla}
+\hopgraph{power laws}{power laws}
+\hopgraph{trigonometry}{trigonometry}
+
+
+
+\end{document}
+
diff --git a/analysis/visualize_hops.py b/analysis/visualize_hops.py
new file mode 100644
index 0000000000000000000000000000000000000000..cdf0856218b9b2fe88ed949ac6d23305576b838d
--- /dev/null
+++ b/analysis/visualize_hops.py
@@ -0,0 +1,224 @@
+# %% imports
+import numpy as np
+import pandas as pd
+
+# %% read data
+
+exercise_tokens = [
+ "syn_a1",
+ "syn_a2",
+ "syn_b1",
+ "syn_b2",
+ "syn_c",
+ "syn_d",
+ "syn_e",
+ "syn_f",
+ "syn_main",
+ "fra_a",
+ "fra_b",
+ "fra_c",
+ "fra_d",
+ "fra_e",
+ "fra_f",
+ "bin_a",
+ "bin_b",
+ "bin_c",
+ "bin_main",
+ "fra_main",
+ "pq_a",
+ "pq_b",
+ "pq_main",
+ "rul_a",
+ "rul_b",
+ "rul_c",
+ "rul_d",
+ "rul_e",
+ "rul_main",
+ "tri_a",
+ "tri_b",
+ "tri_c",
+ "tri_d",
+ "tri_e",
+ "tri_f",
+ "tri_g",
+ "tri_main"
+]
+
+exercise_tokens_df = pd.DataFrame(index=exercise_tokens)
+exercise_tokens_df[exercise_tokens_df.index.str.endswith('main')]
+
+# %% analyse
+endboss_questions_bool = exercise_tokens_df.index.str.endswith('main') \
+ & (exercise_tokens_df.index != 'bin_main') # bin_main is no endboss
+endboss_questions_names = exercise_tokens_df.index[endboss_questions_bool]
+
+info_questions_names = ["start_instructions", "syn_instructions", "fra_instructions", "pq_instructions", "rul_instructions", "tri_instructions"]
+
+
+# %% confusion matrix / hop graph
+
+#hops = pd.read_csv('../alquiz_history.csv')
+hops = pd.read_csv('hops.csv', delimiter=";")
+
+#Finish state is not of relevance here
+hops = hops.drop(hops[hops.next_question_id == "_finish"].index, axis=0)
+
+absolute_graph = pd.crosstab(hops['question_id'], hops['next_question_id'], normalize='index')
+absolute_graph = pd.crosstab(hops['question_id'], hops['next_question_id'])
+
+#graph *= 100
+
+graph = absolute_graph.copy(deep=True)
+
+for source in absolute_graph.index:
+ sumRow = np.sum(absolute_graph.loc[source,:])
+ for dest in absolute_graph.columns:
+ graph.loc[source,dest] = absolute_graph.loc[source,dest] / sumRow
+
+# %% complete question names
+all_questions = ['start_instructions'] + list(exercise_tokens_df.index) + ['sur_instructions', 'survey']
+add_questions = ['fra_instructions', 'pq_instructions', 'rul_instructions', 'syn_instructions', 'tri_instructions']
+for new_q in add_questions:
+ qtype = new_q[:new_q.index('_')+1] # e.g. 'fra_'
+ pos = [all_questions.index(q) for q in all_questions if q.startswith(qtype)][0]
+ all_questions.insert(pos, new_q)
+
+# sort graph in the order of the questions
+assert absolute_graph.shape[0] == len(all_questions)
+absolute_graph = absolute_graph[all_questions].loc[all_questions]
+
+assert graph.shape[0] == len(all_questions)
+graph = graph[all_questions].loc[all_questions]
+
+# %% make single large drawing
+qtypes = {'fra': 'fractions', 'pq': 'pq formula', 'rul': 'power laws', 'syn': 'syntax', 'tri': 'trigonometry', 'sur': 'survey'}
+
+bend_angle = 50
+biggestValue = graph.max().max()
+with open('drawing.tex', 'w') as f:
+ # place question nodes
+ for x, ex in enumerate(all_questions):
+ boss_style = ", boss" if ex in endboss_questions_names else ""
+ print(rf'\node [state{boss_style}] ({ex}) at ({x}, 0) {{}};', file=f)
+
+ # draw category braces
+ for qid, qname in qtypes.items():
+ qtype_questions = [q for q in all_questions if q.startswith(qid)]
+ first = qtype_questions[0]
+ last = qtype_questions[-1]
+ print(rf'\draw [category] ({first}.west) -- ({last}.east) node [midway, below=20pt+1.5em] {{{qname}\strut}};', file=f)
+
+ # draw hop arrows
+ for source in graph.index:
+ for dest in graph.columns:
+ val = graph.loc[source, dest]
+
+ strength = 1+val/biggestValue*0.7 if val > 1 else 0.7
+ opacity = round(50+val/biggestValue*50 if val > 1 else 10)
+
+ if val > 2: # ignore the minority! ;-) otherwise... too many arrows!
+ if source == dest:
+ bend_style = 'loop above'
+ else:
+ dist = all_questions.index(dest) - all_questions.index(source)
+ start_angle = bend_angle if dist > 0 else (180 + bend_angle)
+ end_angle = 180 - start_angle
+
+ stength = abs(dist / 2)
+ bend_style = f"controls=+({start_angle}:{stength}) and +({end_angle}:{stength})"
+
+ #print(rf'\path [line width={val/50:.1f}pt, black!{round(val / 2 + 50)}] ({source}) edge [{bend_style}] node {{${val:.1f}\%$}} ({dest});', file=f)
+ print(rf'\path [line width={strength:.1f}pt, black!{opacity}] ({source}) edge [{bend_style}] node {{${val}$}} ({dest});', file=f)
+
+
+# %% make multiple drawing, one for each question type
+qtypes = {'fra': 'fractions', 'pq': 'pq formula', 'rul': 'power laws', 'syn': 'syntax', 'tri': 'trigonometry', 'sur': 'survey'}
+
+
+#for qid, qname in qtypes.items():
+# print("continue here")
+
+bend_angle = 80
+biggestValue = graph.max().max()
+for qid, qname in qtypes.items():
+ qtype_questions = [q for q in all_questions if q.startswith(qid)]
+ if qid == "fra":
+ qtype_questions.pop()
+ qtype_questions.append("bin_a")
+ qtype_questions.append("bin_b")
+ qtype_questions.append("bin_c")
+ qtype_questions.append("bin_main")
+ qtype_questions.append("fra_main")
+ print(qtype_questions)
+ with open(f'./tex/drawing-{qname}.tex', 'w') as f:
+ # place question nodes
+ for x, ex in enumerate(qtype_questions):
+ if ex in endboss_questions_names:
+ boss_style = ", boss"
+ elif ex in info_questions_names:
+ boss_style = ", info"
+ else:
+ boss_style = ""
+ print(rf'\node [state{boss_style}] ({ex}) at ({x}, 0) {{}};', file=f)
+
+ # place input/output nodes
+ print(rf'\node [inout] (input) at (-1, 1) {{}};', file=f)
+ print(rf'\node [inout] (output) at ({x+1}, 1) {{}};', file=f)
+
+ # reduce graph
+ first_q_idx = all_questions.index(qtype_questions[0])
+ last_q_idx = all_questions.index(qtype_questions[-1])
+ input_row = absolute_graph.iloc[:first_q_idx].sum()[qtype_questions]
+ input_col = absolute_graph.iloc[:,:first_q_idx].sum(axis='columns')[qtype_questions]
+ output_row = absolute_graph.iloc[last_q_idx+1:].sum()[qtype_questions]
+ output_col = absolute_graph.iloc[:,last_q_idx+1:].sum(axis='columns')[qtype_questions]
+ input_col['input'] = 0
+ input_col['output'] = 0
+ output_col['input'] = 0
+ output_col['output'] = 0
+ qtype_index = ['input'] + qtype_questions + ['output']
+ qtype_graph = absolute_graph.loc[qtype_questions, qtype_questions]
+ qtype_graph.loc['input'] = input_row
+ qtype_graph.loc['output'] = output_row
+ qtype_graph.loc[:, 'input'] = input_col
+ qtype_graph.loc[:, 'output'] = output_col
+ qtype_graph = qtype_graph[qtype_index].loc[qtype_index]
+
+ for source in qtype_graph.index:
+ sumRow = np.sum(qtype_graph.loc[source,:])
+ for dest in qtype_graph.columns:
+ if sumRow==0:
+ qtype_graph.loc[source,dest] = 0
+ else:
+ qtype_graph.loc[source,dest] = qtype_graph.loc[source,dest] / sumRow
+ #print(qname)
+ #print(qtype_graph)
+
+
+
+ # draw arrows
+ for source in qtype_graph.index:
+ for dest in qtype_graph.columns:
+ val = qtype_graph.loc[source, dest]
+
+ strength = 1+val/biggestValue*0.7 if val > 0.1 else 0.7
+ opacity = round(50+val/biggestValue*50 if val > 0.1 else 10)
+ if opacity > 100:
+ opacity = 100
+
+ if val > 0.1: # ignore the minority! ;-) otherwise... too many arrows!
+ if source == dest:
+ bend_style = 'loop above'
+ else:
+ src_idx = qtype_index.index(source)
+ dst_idx = qtype_index.index(dest)
+ dist = dst_idx - src_idx
+ start_angle = bend_angle if dist > 0 else (180 + bend_angle)
+ end_angle = 180 - start_angle
+
+ stength = abs(dist / 1)
+ bend_style = f"controls=+({start_angle}:{stength}) and +({end_angle}:{stength})"
+
+ #print(rf'\path [line width={val/50:.1f}pt, black!{round(val / 2 + 50)}] ({source}) edge [{bend_style}] node {{${val:.1f}\%$}} ({dest});', file=f)
+ print(rf'\path [line width={strength:.1f}pt, black!{opacity}] ({source}) edge [{bend_style}] node[inner sep=1pt, fill=white, fill opacity=0.7, text opacity=1] {{${val:.3f}$}} ({dest});', file=f)
+
diff --git a/backup-files/backup-complete-course_ger.mbz b/backup-files/backup-complete-course_ger.mbz
new file mode 100644
index 0000000000000000000000000000000000000000..7c88c0915d2095df672bb7ea47cdaa47fa21db8f
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diff --git a/backup-files/backup-fantasy_ger.mbz b/backup-files/backup-fantasy_ger.mbz
new file mode 100644
index 0000000000000000000000000000000000000000..5668a7472f2e2bb05cb691b2db86c4bec357314c
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diff --git a/backup-moodle2-course-5780-training_area_dm-1-3_ger.mbz b/backup-files/backup-moodle2-course-5780-training_area_dm-1-3_ger.mbz
similarity index 100%
rename from backup-moodle2-course-5780-training_area_dm-1-3_ger.mbz
rename to backup-files/backup-moodle2-course-5780-training_area_dm-1-3_ger.mbz
diff --git a/backup-moodle2-course-5838-training_area_dm-1-3_en.mbz b/backup-files/backup-moodle2-course-5838-training_area_dm-1-3_en.mbz
similarity index 100%
rename from backup-moodle2-course-5838-training_area_dm-1-3_en.mbz
rename to backup-files/backup-moodle2-course-5838-training_area_dm-1-3_en.mbz
diff --git a/backup-files/backup-pa-instant-tutoring_ger.mbz b/backup-files/backup-pa-instant-tutoring_ger.mbz
new file mode 100644
index 0000000000000000000000000000000000000000..ead28c2cc5af8a30b5f3b0198a6aa0c6da9ad737
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diff --git a/backup-files/backup-pa-simple_en.mbz b/backup-files/backup-pa-simple_en.mbz
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index 0000000000000000000000000000000000000000..40031ef74aaf7af9b717b35ac8f69f397c6a2344
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diff --git a/backup-files/backup-pa-simple_ger.mbz b/backup-files/backup-pa-simple_ger.mbz
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index 0000000000000000000000000000000000000000..053459ab629a2912e50f109e2ab1db1b81031454
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diff --git a/backup-files/backup-quiz-normal_ger.mbz b/backup-files/backup-quiz-normal_ger.mbz
new file mode 100644
index 0000000000000000000000000000000000000000..227d7bac615919f813633c6b73697a1d0f74ac11
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diff --git a/exercise-generation/create_question_versions_from_csv.py b/exercise-generation/create_question_versions_from_csv.py
new file mode 100644
index 0000000000000000000000000000000000000000..f84617ab045c19bf1a64b01931df6e673d5f6c3d
--- /dev/null
+++ b/exercise-generation/create_question_versions_from_csv.py
@@ -0,0 +1,662 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Mon Jul 31 13:03:04 2023
+
+@author: malte
+"""
+#%%------------------------------------INIT----------------------------------
+from lxml import etree
+import copy
+import pandas as pd
+import json
+import re
+
+parser = etree.XMLParser(strip_cdata=False)
+
+#root = etree.Element("quiz")
+#tree = etree.ElementTree(root)
+
+class QuestionPool:
+ def __init__(self, Question_Ver, Raw_Questions):
+ self.Question_Ver = Question_Ver
+ self.Questions = []
+
+ self.root = etree.Element("quiz")
+ self.tree = etree.ElementTree(self.root)
+
+ self.first_elements = []
+ self.last_elements = []
+
+ for Question in Raw_Questions:
+ CopiedQuestion = copy.deepcopy(Question)
+
+ add_to_script_text = ""
+ if self.Question_Ver.callback_add_to_script != None:
+ add_to_script_text = self.Question_Ver.callback_add_to_script(Question=CopiedQuestion)
+
+ #Add script and hint (if desired) to exercise text.
+ exercise_hint_string = ""
+ if self.Question_Ver.show_hint == True:
+ exercise_hint_string = "" if pd.isna(Question.exercise_hint) else f'<p class="hint">{Question.exercise_hint}</p>'
+ for questiontext_element in CopiedQuestion.root.iterchildren("questiontext"):
+ for questiontext_text_element in questiontext_element.iterchildren("text"):
+ questiontext_text_element.text = etree.CDATA(f"{Question_Ver.script_on_init}{add_to_script_text}{questiontext_text_element.text}{exercise_hint_string}")
+
+
+ if self.Question_Ver.callback_change_before_clone != None:
+ self.Question_Ver.callback_change_before_clone(Question=CopiedQuestion)
+
+ if self.Question_Ver.variants_as_single == True:
+ print("special handling for variants as single")
+
+ seeds = []
+ for seed in CopiedQuestion.root.iterchildren("deployedseed"):
+ seeds.append(copy.deepcopy(seed))
+ CopiedQuestion.root.remove(seed)
+
+ if len(seeds) < 1:
+ print(f"No seed given for t{CopiedQuestion.topic_number}-{CopiedQuestion.exercise_number:02d}-{CopiedQuestion.exercise_part}.")
+ self.Questions.append(CopiedQuestion)
+ continue
+
+ question_clones = []
+
+ seed_amount = len(seeds) if (self.Question_Ver.fixed_seed_amount == 0 or len(seeds) < self.Question_Ver.fixed_seed_amount) else self.Question_Ver.fixed_seed_amount
+
+ for j in range(seed_amount):
+ question_clones.append(copy.deepcopy(CopiedQuestion))
+ question_clones[j].root.append(seeds[j])
+ j+=1
+
+ variant_count = 1
+ for question_variant in question_clones:
+ for name_element in question_variant.root.iterchildren("name"):
+ for nametext_element in name_element.iterchildren("text"):
+ nametext_element.text = f"{nametext_element.text} (Auto-Generation Variant {variant_count})"
+ self.Questions.append(question_variant)
+ variant_count+=1
+
+ else:
+ self.Questions.append(CopiedQuestion)
+
+ if self.Question_Ver.custom_first_elements_filepath != "":
+ custom_first_element_tree = etree.parse(self.Question_Ver.custom_first_elements_filepath, parser)
+ custom_first_element_root = custom_first_element_tree.getroot()
+ for question_element in custom_first_element_root.iterchildren("question"):
+ if question_element.attrib["type"] != "category":
+ self.first_elements.append(question_element)
+
+ if self.Question_Ver.custom_last_elements_filepath != "":
+ custom_last_element_tree = etree.parse(self.Question_Ver.custom_last_elements_filepath, parser)
+ custom_last_element_root = custom_last_element_tree.getroot()
+ for question_element in custom_last_element_root.iterchildren("question"):
+ if question_element.attrib["type"] != "category":
+ self.last_elements.append(question_element)
+
+ self.update_xml_tree();
+
+ def get_category_as_xml_element(self, category_name):
+ category_question = etree.Element("question", type="category")
+ category = etree.SubElement(category_question, "category")
+ category_text = etree.SubElement(category, "text")
+ info = etree.SubElement(category, "info")
+ info.append(etree.Element("text"))
+ category_question.append(etree.Element("idnumber"))
+ category_text.text = f"$course$/top/Question Pool Einstiegsakademie/{self.Question_Ver.name}/{category_name}"
+ return category_question
+
+ def update_xml_tree(self):
+ self.root = etree.Element("quiz")
+ self.tree = etree.ElementTree(self.root)
+
+ if self.first_elements != []:
+
+ if self.Question_Ver.callback_first_quiz_element_text != None:
+ text = self.Question_Ver.callback_first_quiz_element_text(**self.Question_Ver.callback_kwargs)
+ for questiontext_element in self.first_elements[0].iterchildren("questiontext"):
+ for questiontext_textelement in questiontext_element.iterchildren("text"):
+ questiontext_textelement.text = etree.CDATA(text)
+
+ self.root.append(self.get_category_as_xml_element("000 Start Elements"))
+ for starting_element in self.first_elements:
+ self.root.append(starting_element)
+
+
+
+ for Question in self.Questions:
+ last_category = ""
+ category_string = f"t{Question.topic_number}_{Question.topic_id} {Question.topic_label}"
+ if category_string != last_category:
+ self.root.append(self.get_category_as_xml_element(category_string))
+ last_category = category_string
+
+ self.root.append(Question.root)
+
+ if self.last_elements != []:
+ self.root.append(self.get_category_as_xml_element("zzz Config Elements"))
+ for finishing_element in self.last_elements:
+ self.root.append(finishing_element)
+
+ #change text in finishing element which shall contain the configuration
+ if self.Question_Ver.callback_last_quiz_element_text != None:
+ text = self.Question_Ver.callback_last_quiz_element_text(**self.Question_Ver.callback_kwargs)
+ questions = []
+ for question in self.root.iterchildren("question"):
+ questions.append(question)
+
+ last_question = questions[-1]
+ for questiontext_element in last_question.iterchildren("questiontext"):
+ for questiontext_text_element in questiontext_element.iterchildren("text"):
+ questiontext_text_element.text = etree.CDATA(text)
+
+ def write_to_file(self, filepath=""):
+ if filepath == "":
+ filepath = f"output-{self.Question_Ver.name}.xml"
+ self.tree.write(filepath, pretty_print=True)
+
+class QuestionVersion:
+ def __init__(self, name, variants_as_single=False, script_on_init="", custom_first_elements_filepath="", custom_last_elements_filepath="", fixed_seed_amount=0, show_hint=True, callback_first_quiz_element_text=None, callback_last_quiz_element_text=None, callback_add_to_script=None, callback_change_before_clone=None, **callback_kwargs):
+ self.name = name
+ self.variants_as_single = variants_as_single
+ self.script_on_init = script_on_init
+ self.custom_first_elements_filepath = custom_first_elements_filepath
+ self.callback_first_quiz_element_text = callback_first_quiz_element_text
+ self.custom_last_elements_filepath = custom_last_elements_filepath
+ self.fixed_seed_amount = fixed_seed_amount
+ self.show_hint = show_hint
+ self.callback_last_quiz_element_text = callback_last_quiz_element_text
+ self.callback_add_to_script = callback_add_to_script
+ self.callback_kwargs = callback_kwargs
+ self.callback_change_before_clone = callback_change_before_clone
+
+
+class MoodleQuestion:
+ def __init__(self, topic_number, topic_id, exercise_number, exercise_part, topic_label, exercise_description, exercise_variables, exercise_text, exercise_content, exercise_hint, custom_general_feedback, exercise_note, custom_prt, add_prt_node_on_not_correct, add_prt_node_wa, custom_input, custom_seed):
+ self.topic_number = topic_number
+ self.topic_id = topic_id
+ self.exercise_number = exercise_number
+ self.exercise_part = exercise_part
+ self.topic_label = topic_label
+ self.exercise_description = exercise_description
+ self.exercise_variables = exercise_variables
+ self.exercise_text = exercise_text
+ self.exercise_content = exercise_content
+ self.exercise_hint = exercise_hint
+ self.custom_general_feedback = custom_general_feedback
+ self.exercise_note = exercise_note
+ self.custom_prt = None if pd.isna(custom_prt) else etree.fromstring(custom_prt, parser)
+ self.add_prt_node_on_not_correct = add_prt_node_on_not_correct
+ self.add_prt_node_wa = None if type(add_prt_node_wa) is not list else [wa for wa in add_prt_node_wa if pd.isna(wa) == False]
+ self.custom_input = None if pd.isna(custom_input) else etree.fromstring(custom_input, parser)
+ self.custom_seed = None if pd.isna(custom_seed) else etree.fromstring(custom_seed, parser)
+
+ default_question_quiz_tree = etree.parse("default_question.xml", parser)
+ default_question_quiz_root = default_question_quiz_tree.getroot()
+
+ for question_element in default_question_quiz_root.iterchildren("question"):
+ if question_element.attrib["type"] == "stack":
+ self.root = question_element
+ break
+
+ for questionname_element in self.root.iterchildren("name"):
+ for questionname_text_element in questionname_element.iterchildren("text"):
+ questionname_text_element.text = f"t{self.topic_number}-{self.exercise_number:02d}-{self.exercise_part} {self.exercise_description}"
+
+ exercise_content_string = "" if pd.isna(self.exercise_content) else f"<p>{self.exercise_content}</p>"
+ for questiontext_element in self.root.iterchildren("questiontext"):
+ for questiontext_text_element in questiontext_element.iterchildren("text"):
+ questiontext_text_element.text = etree.CDATA(f"<p>{self.exercise_text}</p>\n{exercise_content_string}")
+
+ for questionvariables_element in self.root.iterchildren("questionvariables"):
+ for questionvariables_text_element in questionvariables_element.iterchildren("text"):
+ questionvariables_text_element.text = self.exercise_variables
+
+ if self.custom_general_feedback is not None and not pd.isna(self.custom_general_feedback):
+ for general_feedback_element in self.root.iterchildren("generalfeedback"):
+ for general_feedback_text_element in general_feedback_element.iterchildren("text"):
+ general_feedback_text_element.text = etree.CDATA(self.custom_general_feedback)
+
+ if self.exercise_note is not None and not pd.isna(self.exercise_note):
+ for questionnote_element in self.root.iterchildren("questionnote"):
+ for questionnote_text_element in questionnote_element.iterchildren("text"):
+ questionnote_text_element.text = self.exercise_note
+
+
+ if self.custom_prt is not None:
+ for prt_element in self.root.iterchildren("prt"):
+ self.root.remove(prt_element)
+ if self.custom_prt.tag == "prt":
+ self.root.append(self.custom_prt)
+ elif self.custom_prt.tag == "prt_fields":
+ for prt_element in self.custom_prt.iterchildren("prt"):
+ self.root.append(prt_element)
+
+ if self.custom_input is not None:
+ for old_input_element in self.root.iterchildren("input"):
+ self.root.remove(old_input_element)
+ if self.custom_input.tag == "input":
+ self.root.append(self.custom_input)
+ elif self.custom_input.tag == "input_fields":
+ for input_element in self.custom_input.iterchildren("input"):
+ self.root.append(input_element)
+
+ if self.custom_seed is not None:
+ for old_seed_element in self.root.iterchildren("deployedseed"):
+ self.root.remove(old_seed_element)
+ if self.custom_seed.tag == "deployedseed":
+ self.root.append(self.custom_seed)
+ elif self.custom_seed.tag == "seed_fields":
+ for seed_element in self.custom_seed.iterchildren("deployedseed"):
+ self.root.append(seed_element)
+
+ if self.add_prt_node_wa is not None:
+ i=1
+ for wa_text in self.add_prt_node_wa:
+ node_to_add_tree = etree.parse("default-prt-node.xml", parser)
+ node_to_add = node_to_add_tree.getroot()
+
+ for sans_element in node_to_add.iterchildren("sans"):
+ sans_element.text = "ans1"
+
+ for tans_element in node_to_add.iterchildren("tans"):
+ tans_element.text = f"wa{i}"
+
+ for truefeedback_element in node_to_add.iterchildren("truefeedback"):
+ for truefeedback_text_element in truefeedback_element.iterchildren("text"):
+ truefeedback_text_element.text = etree.CDATA(wa_text)
+
+
+ for prt in self.root.iterchildren("prt"):
+
+ all_nodes = []
+ node_amount = 0
+
+ prtname = ""
+ for prtname_element in prt.iterchildren("name"):
+ prtname = prtname_element.text
+
+ for node in prt.iterchildren("node"):
+ all_nodes.append(node)
+ node_amount+=1
+
+ if node_amount <= 0:
+ continue
+
+ #Assume that the last node in the tree is the last node in the flow chart. This code is problematic if e. g. the last node in the XML is one of the first nodes in the prt.
+ last_node = all_nodes[-1]
+ last_node_number = 0
+ for name_element in last_node.iterchildren("name"):
+ last_node_number = int(name_element.text)
+ new_node_name = f"{last_node_number+1}"
+ new_node_label = f"{last_node_number+2}"
+
+ for name_element in node_to_add.iterchildren("name"):
+ name_element.text = new_node_name
+
+ for trueanswernote_element in node_to_add.iterchildren("trueanswernote"):
+ trueanswernote_element.text = f"{prtname}-{new_node_label}-T"
+ for falseanswernote_element in node_to_add.iterchildren("falseanswernote"):
+ falseanswernote_element.text = f"{prtname}-{new_node_label}-F"
+
+ for falsenextnode_element in last_node.iterchildren("falsenextnode"):
+ if falsenextnode_element.text == "-1":
+ falsenextnode_element.text = new_node_name
+
+ #for truescore_element in last_node.iterchildren("truescore"):
+ # if truescore_element.text != "1":
+ # for truenextnode_element in node.iterchildren("truenextnode"):
+ # if truenextnode_element.text == "-1":
+ # truenextnode_element.text = new_node_name
+
+ prt.append(copy.deepcopy(node_to_add))
+
+ i+=1
+
+ if self.add_prt_node_on_not_correct is not None and not pd.isna(self.add_prt_node_on_not_correct):
+ node_to_add_tree = etree.parse("default-prt-node.xml", parser)
+ node_to_add = node_to_add_tree.getroot()
+ for truefeedback_element in node_to_add.iterchildren("truefeedback"):
+ for truefeedback_text_element in truefeedback_element.iterchildren("text"):
+ truefeedback_text_element.text = etree.CDATA(f"<p>{self.add_prt_node_on_not_correct}</p>")
+
+
+
+ for prt in self.root.iterchildren("prt"):
+ #node_amount = 0
+ #for node in prt.iterchildren("node"):
+ # node_amount+=1
+ for node in prt.iterchildren("node"):
+ for falsenextnode_element in node.iterchildren("falsenextnode"):
+ if falsenextnode_element.text == "-1":
+ falsenextnode_element.text = "999"
+ for truescore_element in node.iterchildren("truescore"):
+ if truescore_element.text != "1":
+ for truenextnode_element in node.iterchildren("truenextnode"):
+ if truenextnode_element.text == "-1":
+ truenextnode_element.text = "999"
+
+ prtname = ""
+ for prtname_element in prt.iterchildren("name"):
+ prtname = prtname_element.text
+
+ for trueanswernote_element in node_to_add.iterchildren("trueanswernote"):
+ trueanswernote_element.text = f"{prtname}-1000-T"
+ for falseanswernote_element in node_to_add.iterchildren("falseanswernote"):
+ falseanswernote_element.text = f"{prtname}-1000-F"
+
+ prt.append(copy.deepcopy(node_to_add))
+
+
+ def __str__(self):
+ return f"{etree.tostring(self.root, pretty_print=True)}"
+
+#%%-----------------------------------UPDATE----------------------------------
+df = pd.read_csv("exercises.csv", delimiter=";")
+
+last_category = ""
+to_parse = df[df.already_parsed == 0]
+#to_parse = df[df.note == 0]
+Exercises_To_Parse = []
+for data in to_parse.itertuples():
+ Exercise_To_Parse = MoodleQuestion(data.topic_number, data.topic_id, data.exercise_number, data.exercise_part, data.topic_label, data.exercise_description, data.exercise_variables, data.exercise_text, data.exercise_content, data.exercise_hint, data.custom_general_feedback, data.exercise_note, data.custom_prt, data.add_prt_node_on_not_correct, [data.add_prt_node_wa1, data.add_prt_node_wa2, data.add_prt_node_wa3], data.custom_input, data.custom_seed)
+ Exercises_To_Parse.append(Exercise_To_Parse)
+
+#%%------------------------------------TEST----------------------------------
+
+TestVersion = QuestionPool(QuestionVersion("test"), Exercises_To_Parse)
+TestVersion.write_to_file("output.xml")
+
+#%%------------------------------------PREVIEW---------------------------------
+def normal_version_config_text(**kwargs):
+ Exercises = kwargs.get("Exercises")
+ if Exercises == None:
+ print("no exercises found for config callback of instant tutoring version")
+ return ""
+
+ info_dict = {}
+ groups = []
+ groups.append({"id":"start", "name":"Start","questions":["i"]})
+
+ SortedExercises = sorted(Exercises, key=lambda x:f"t{x.topic_number}_{x.topic_id}_{x.exercise_number}_{x.exercise_part}")
+
+ previous_group = ""
+ for Exercise in SortedExercises:
+ group_identifier = f"t{Exercise.topic_number}_{Exercise.topic_id}_{Exercise.exercise_number}"
+ if previous_group == group_identifier:
+ groups[-1]["questions"].append(Exercise.exercise_part)
+ else:
+ groups.append({"id":group_identifier, "name":Exercise.topic_label , "questions":[Exercise.exercise_part]})
+ previous_group = group_identifier
+
+ info_dict["groups"] = groups
+ return json.dumps(info_dict)
+
+
+NormalVersion = QuestionPool(QuestionVersion("normal", False, '<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-normal.js"></script>', "start-normal.xml", "config-normal.xml", callback_last_quiz_element_text=normal_version_config_text, Exercises=Exercises_To_Parse), Exercises_To_Parse)
+NormalVersion.write_to_file()
+
+#%%------------------------------------ROLE-PLAY-GAME----------------------------------
+
+def rpg_version_insert_config_text(**kwargs):
+ random_colors = ["#573036","#1BA1C7","#B38ABB","#D558A8","#1B5658","#810311","#74CD27","#3CF48A","#77B211","#FD9C80","#E249B2","#D57774","#944A6C","#9B49A2","#FA00D1","#E2AFDA","#EB3E57","#7E182C","#3960A7","#E44FCD","#278495","#6D9D29","#302FFF","#BBCBC4","#C5F99B","#A3717F","#395C44","#10F046","#E39FB2","#23F5CC","#01D504","#C6F237","#B64537","#8C9BF5","#9F6D55","#65D794","#162095","#DD5BE4","#A4FFDC","#BA9DCC","#D34FDB","#910602","#C8B210","#3BDBAA","#916F06","#C5B6C7","#88383B","#71BC2E","#B20EE3","#C751FB","#496108","#4DA97E","#F8C255","#642E0E","#16C9D7","#C768E5","#DA8376","#93916B","#A4AA17","#62CB69","#CD51BA","#877931","#DDB76F","#C14532","#70C3CA","#6AC2E3","#8F822E","#040237","#AEC069","#C6E2B2","#0EE073","#E239C3","#D5C5B6","#167CFE","#7D9C92","#B138AC","#5E748B","#F31FE0","#A5F944","#58EF3F","#917DAB","#582BAF","#A7BB80","#FA570F","#E3C6EB","#CA2CB0","#914779","#27FE1F","#593E8B","#0DCB1E","#316E18","#D333EA","#ADB645","#1B303D","#DD089D","#5DB7C6","#B24D21","#CF7D35","#34BC98","#E9FCEE"]
+ random_filters = ["invert(20%) sepia(11%) saturate(2292%) hue-rotate(301deg) brightness(88%) contrast(87%)","invert(46%) sepia(89%) saturate(419%) hue-rotate(147deg) brightness(97%) contrast(96%)","invert(67%) sepia(28%) saturate(423%) hue-rotate(244deg) brightness(85%) contrast(89%)","invert(50%) sepia(90%) saturate(907%) hue-rotate(290deg) brightness(87%) contrast(90%)","invert(26%) sepia(12%) saturate(2407%) hue-rotate(133deg) brightness(95%) contrast(86%)","invert(8%) sepia(64%) saturate(6140%) hue-rotate(346deg) brightness(93%) contrast(104%)","invert(68%) sepia(76%) saturate(507%) hue-rotate(42deg) brightness(95%) contrast(83%)","invert(72%) sepia(40%) saturate(699%) hue-rotate(89deg) brightness(101%) contrast(98%)","invert(64%) sepia(52%) saturate(5261%) hue-rotate(48deg) brightness(107%) contrast(87%)","invert(84%) sepia(53%) saturate(4565%) hue-rotate(313deg) brightness(115%) contrast(108%)","invert(52%) sepia(64%) saturate(4425%) hue-rotate(292deg) brightness(93%) contrast(90%)","invert(81%) sepia(50%) saturate(3032%) hue-rotate(305deg) brightness(86%) contrast(94%)","invert(34%) sepia(25%) saturate(1028%) hue-rotate(280deg) brightness(96%) contrast(89%)","invert(35%) sepia(65%) saturate(573%) hue-rotate(248deg) brightness(92%) contrast(92%)","invert(54%) sepia(100%) saturate(7435%) hue-rotate(298deg) brightness(97%) contrast(127%)","invert(96%) sepia(86%) saturate(2059%) hue-rotate(203deg) brightness(96%) contrast(83%)","invert(33%) sepia(19%) saturate(6570%) hue-rotate(328deg) brightness(97%) contrast(89%)","invert(14%) sepia(27%) saturate(5843%) hue-rotate(328deg) brightness(98%) contrast(98%)","invert(33%) sepia(56%) saturate(621%) hue-rotate(180deg) brightness(96%) contrast(95%)","invert(76%) sepia(58%) saturate(7362%) hue-rotate(280deg) brightness(93%) contrast(93%)","invert(40%) sepia(10%) saturate(2946%) hue-rotate(142deg) brightness(107%) contrast(86%)","invert(53%) sepia(90%) saturate(357%) hue-rotate(43deg) brightness(87%) contrast(88%)","invert(12%) sepia(96%) saturate(6720%) hue-rotate(247deg) brightness(102%) contrast(101%)","invert(93%) sepia(3%) saturate(752%) hue-rotate(102deg) brightness(89%) contrast(85%)","invert(100%) sepia(16%) saturate(5613%) hue-rotate(328deg) brightness(109%) contrast(92%)","invert(51%) sepia(4%) saturate(3367%) hue-rotate(293deg) brightness(95%) contrast(75%)","invert(28%) sepia(21%) saturate(737%) hue-rotate(86deg) brightness(102%) contrast(87%)","invert(52%) sepia(95%) saturate(903%) hue-rotate(88deg) brightness(115%) contrast(90%)","invert(78%) sepia(4%) saturate(2863%) hue-rotate(296deg) brightness(88%) contrast(102%)","invert(100%) sepia(72%) saturate(2181%) hue-rotate(84deg) brightness(106%) contrast(91%)","invert(43%) sepia(74%) saturate(1175%) hue-rotate(89deg) brightness(106%) contrast(114%)","invert(96%) sepia(38%) saturate(4597%) hue-rotate(13deg) brightness(104%) contrast(89%)","invert(36%) sepia(12%) saturate(4301%) hue-rotate(324deg) brightness(93%) contrast(92%)","invert(64%) sepia(5%) saturate(3975%) hue-rotate(195deg) brightness(98%) contrast(96%)","invert(49%) sepia(5%) saturate(4049%) hue-rotate(334deg) brightness(89%) contrast(72%)","invert(80%) sepia(24%) saturate(818%) hue-rotate(88deg) brightness(91%) contrast(88%)","invert(18%) sepia(23%) saturate(6913%) hue-rotate(217deg) brightness(94%) contrast(98%)","invert(46%) sepia(92%) saturate(1381%) hue-rotate(268deg) brightness(96%) contrast(85%)","invert(91%) sepia(24%) saturate(563%) hue-rotate(85deg) brightness(103%) contrast(103%)","invert(70%) sepia(13%) saturate(705%) hue-rotate(233deg) brightness(94%) contrast(91%)","invert(45%) sepia(84%) saturate(1892%) hue-rotate(259deg) brightness(88%) contrast(94%)","invert(11%) sepia(63%) saturate(4965%) hue-rotate(14deg) brightness(103%) contrast(124%)","invert(72%) sepia(81%) saturate(1388%) hue-rotate(8deg) brightness(93%) contrast(87%)","invert(92%) sepia(80%) saturate(1117%) hue-rotate(82deg) brightness(101%) contrast(69%)","invert(43%) sepia(44%) saturate(6440%) hue-rotate(38deg) brightness(93%) contrast(95%)","invert(80%) sepia(6%) saturate(490%) hue-rotate(246deg) brightness(91%) contrast(96%)","invert(27%) sepia(85%) saturate(439%) hue-rotate(308deg) brightness(84%) contrast(94%)","invert(61%) sepia(95%) saturate(366%) hue-rotate(48deg) brightness(91%) contrast(84%)","invert(22%) sepia(84%) saturate(4934%) hue-rotate(280deg) brightness(90%) contrast(116%)","invert(41%) sepia(23%) saturate(6695%) hue-rotate(255deg) brightness(101%) contrast(97%)","invert(32%) sepia(17%) saturate(2438%) hue-rotate(36deg) brightness(96%) contrast(94%)","invert(54%) sepia(42%) saturate(476%) hue-rotate(100deg) brightness(100%) contrast(84%)","invert(76%) sepia(85%) saturate(388%) hue-rotate(335deg) brightness(100%) contrast(95%)","invert(18%) sepia(12%) saturate(6525%) hue-rotate(354deg) brightness(97%) contrast(92%)","invert(67%) sepia(27%) saturate(3791%) hue-rotate(137deg) brightness(101%) contrast(83%)","invert(51%) sepia(33%) saturate(1489%) hue-rotate(239deg) brightness(96%) contrast(86%)","invert(76%) sepia(76%) saturate(1360%) hue-rotate(305deg) brightness(86%) contrast(86%)","invert(62%) sepia(7%) saturate(1282%) hue-rotate(19deg) brightness(91%) contrast(88%)","invert(57%) sepia(80%) saturate(463%) hue-rotate(23deg) brightness(95%) contrast(84%)","invert(99%) sepia(33%) saturate(3140%) hue-rotate(51deg) brightness(87%) contrast(79%)","invert(52%) sepia(46%) saturate(3109%) hue-rotate(280deg) brightness(85%) contrast(86%)","invert(51%) sepia(15%) saturate(1482%) hue-rotate(13deg) brightness(88%) contrast(89%)","invert(77%) sepia(47%) saturate(395%) hue-rotate(353deg) brightness(90%) contrast(91%)","invert(29%) sepia(72%) saturate(1119%) hue-rotate(334deg) brightness(100%) contrast(91%)","invert(72%) sepia(7%) saturate(2161%) hue-rotate(136deg) brightness(100%) contrast(88%)","invert(67%) sepia(76%) saturate(312%) hue-rotate(161deg) brightness(93%) contrast(90%)","invert(44%) sepia(53%) saturate(494%) hue-rotate(15deg) brightness(101%) contrast(89%)","invert(5%) sepia(65%) saturate(6178%) hue-rotate(225deg) brightness(82%) contrast(117%)","invert(74%) sepia(10%) saturate(1407%) hue-rotate(32deg) brightness(95%) contrast(97%)","invert(99%) sepia(25%) saturate(1040%) hue-rotate(32deg) brightness(96%) contrast(83%)","invert(74%) sepia(55%) saturate(3187%) hue-rotate(95deg) brightness(100%) contrast(89%)","invert(36%) sepia(82%) saturate(2028%) hue-rotate(285deg) brightness(89%) contrast(99%)","invert(100%) sepia(14%) saturate(6473%) hue-rotate(297deg) brightness(96%) contrast(89%)","invert(32%) sepia(97%) saturate(1864%) hue-rotate(203deg) brightness(101%) contrast(102%)","invert(59%) sepia(17%) saturate(351%) hue-rotate(110deg) brightness(98%) contrast(88%)","invert(27%) sepia(54%) saturate(2411%) hue-rotate(277deg) brightness(97%) contrast(89%)","invert(44%) sepia(22%) saturate(502%) hue-rotate(170deg) brightness(94%) contrast(88%)","invert(29%) sepia(79%) saturate(5626%) hue-rotate(292deg) brightness(105%) contrast(102%)","invert(76%) sepia(95%) saturate(349%) hue-rotate(32deg) brightness(103%) contrast(95%)","invert(85%) sepia(39%) saturate(1594%) hue-rotate(52deg) brightness(105%) contrast(87%)","invert(63%) sepia(16%) saturate(751%) hue-rotate(224deg) brightness(80%) contrast(85%)","invert(21%) sepia(70%) saturate(2838%) hue-rotate(251deg) brightness(79%) contrast(98%)","invert(77%) sepia(8%) saturate(1333%) hue-rotate(39deg) brightness(92%) contrast(91%)","invert(63%) sepia(81%) saturate(6168%) hue-rotate(355deg) brightness(100%) contrast(97%)","invert(90%) sepia(93%) saturate(7327%) hue-rotate(187deg) brightness(95%) contrast(93%)","invert(22%) sepia(100%) saturate(1928%) hue-rotate(289deg) brightness(98%) contrast(93%)","invert(37%) sepia(6%) saturate(4740%) hue-rotate(267deg) brightness(86%) contrast(84%)","invert(88%) sepia(89%) saturate(7374%) hue-rotate(48deg) brightness(88%) contrast(133%)","invert(27%) sepia(17%) saturate(2095%) hue-rotate(219deg) brightness(96%) contrast(93%)","invert(62%) sepia(73%) saturate(2975%) hue-rotate(82deg) brightness(97%) contrast(103%)","invert(34%) sepia(11%) saturate(5321%) hue-rotate(66deg) brightness(88%) contrast(81%)","invert(39%) sepia(69%) saturate(5452%) hue-rotate(275deg) brightness(95%) contrast(99%)","invert(65%) sepia(95%) saturate(273%) hue-rotate(25deg) brightness(90%) contrast(87%)","invert(17%) sepia(41%) saturate(502%) hue-rotate(158deg) brightness(90%) contrast(97%)","invert(18%) sepia(80%) saturate(7083%) hue-rotate(309deg) brightness(92%) contrast(100%)","invert(88%) sepia(6%) saturate(5508%) hue-rotate(156deg) brightness(88%) contrast(72%)","invert(29%) sepia(18%) saturate(5200%) hue-rotate(352deg) brightness(103%) contrast(83%)","invert(61%) sepia(55%) saturate(1048%) hue-rotate(339deg) brightness(88%) contrast(83%)","invert(64%) sepia(14%) saturate(1723%) hue-rotate(114deg) brightness(94%) contrast(93%)","invert(100%) sepia(5%) saturate(4521%) hue-rotate(53deg) brightness(102%) contrast(96%)"]
+ text = ""
+ Exercises = kwargs.get("Exercises")
+ if Exercises == None:
+ print("no exercises found for config callback of role play game tutoring version")
+ return ""
+
+ seed_limit = kwargs.get("seed_limit")
+ if seed_limit == None:
+ seed_limit = 0
+ print("continue without seed limit in an role play game version")
+
+ text = """
+
+ """
+
+ info_dict = {}
+ groups = {}
+ groups["start"] = "Start"
+ questions = {}
+ questions["start"] = {"name":"Start", "group":"start"}
+ #In what order are the exercises parsed? They are implemented in Moodle alphabetically, but here: first come, first serves?
+
+ SortedExercises = sorted(Exercises, key=lambda x:f"t{x.topic_number}_{x.topic_id}_{x.exercise_number}_{x.exercise_part}")
+ color_count = 0
+ for Exercise in SortedExercises:
+ group_identifier = f"t{Exercise.topic_number}_{Exercise.topic_id}_{Exercise.exercise_number}"
+ group_check = groups.get(group_identifier)
+ if group_check == None:
+ groups[group_identifier] = Exercise.topic_label
+
+ #Check amount of possible variants
+ seed_amount = 0
+ for seed in Exercise.root.iterchildren("deployedseed"):
+ seed_amount+=1
+
+ if seed_amount < 1:
+ print(f"No seed given for t{Exercise.topic_number}-{Exercise.exercise_number}-{Exercise.exercise_part}.")
+ seed_amount = 1
+
+ variant_amount = seed_amount if (seed_limit == 0 or seed_amount < seed_limit) else seed_limit
+ question_identifier = f"{group_identifier}_{Exercise.exercise_part}"
+ #print(question_identifier)
+ #questions[question_identifier] = {"name":Exercise.exercise_description, "variants":variant_amount, "hint":Exercise.exercise_hint, "color":random_colors[color_count], "filter":random_filters[color_count]}
+ questions[question_identifier] = {"name":Exercise.exercise_description, "variants":variant_amount, "color":random_colors[color_count], "filter":random_filters[color_count]}
+
+ color_count+=1
+ #print(groups)
+ info_dict["groups"] = groups
+ info_dict["questions"] = questions
+ #print(info_dict)
+
+ #Necessary to escape " and ' here?
+ quiz_info_as_string = json.dumps(info_dict)
+
+ text = f"""
+<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-fantasy-bg-ver3.js"></script>
+<script>
+ let quizObjectAsString = '{quiz_info_as_string}';
+ let quizObject = JSON.parse(quizObjectAsString)
+ let ALQuiz = new FantasyQuiz(quizObject);
+ ALQuiz.setCurrentQuestionId("start");
+ document.addEventListener("DOMContentLoaded", function() {{
+ ALQuiz.init();
+ }});
+</script>
+<p dir="ltr" style="text-align: left;display:none;">Some formula to load Mathjax \(x=1\)<br></p>
+
+<p>[[input:ans1]] [[validation:ans1]]</p>
+<p>[[input:ans2]] [[validation:ans2]]<br></p>
+ """
+
+ return text
+
+def rpg_version_normalize_input_to_algebraic(**kwargs):
+ Question = kwargs.get("Question")
+ if Question == None:
+ print("no question found for input change")
+ return False
+
+ for input_element in Question.root.iterchildren("input"):
+ handling = False
+ for type_element in input_element.iterchildren("type"):
+ if type_element.text == "equiv":
+ handling = True
+ type_element.text = "algebraic"
+
+ if handling == False:
+ continue
+
+
+ for syntaxhint_element in input_element.iterchildren("syntaxhint"):
+ if "firstline" in syntaxhint_element.text:
+ sub_word_with_comma = re.compile("firstline[,\s]*(?=.*)")
+ syntaxhint_element.text = sub_word_with_comma.sub("", syntaxhint_element.text)
+
+ name = ""
+ for name_element in input_element.iterchildren("name"):
+ name = name_element.text
+
+ for input_options_element in input_element.iterchildren("options"):
+ if "hideequiv" in input_options_element.text:
+ sub_word_with_comma = re.compile("hideequiv[,\s]*(?=.*)")
+ input_options_element.text = sub_word_with_comma.sub("", input_options_element.text)
+ if "firstline" in input_options_element.text:
+ sub_word_with_comma = re.compile("firstline[,\s]*(?=.*)")
+ input_options_element.text = sub_word_with_comma.sub("", input_options_element.text)
+
+ name = ""
+ for input_name_element in input_element.iterchildren("name"):
+ name = input_name_element.text
+ if name == "":
+ continue
+
+ for input_tans_element in input_element.iterchildren("tans"):
+ input_tans_element.text = f"last({input_tans_element.text})"
+
+ for prt in Question.root.iterchildren("prt"):
+ for node in prt.iterchildren("node"):
+ for sans in node.iterchildren("sans"):
+ if name in sans.text:
+ regex = re.compile(f'{name}')
+ sans.text = regex.sub(f"[{name}]", sans.text)
+
+ return True
+
+
+
+
+rpg_fixed_seed_amount = 4
+RPGVersion = QuestionPool(QuestionVersion("rpg", True, script_on_init='<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>\n<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>\n', custom_first_elements_filepath="start-rpg.xml", fixed_seed_amount=rpg_fixed_seed_amount, show_hint=True, callback_first_quiz_element_text=rpg_version_insert_config_text, callback_change_before_clone=rpg_version_normalize_input_to_algebraic, Exercises=Exercises_To_Parse, seed_limit=rpg_fixed_seed_amount), Exercises_To_Parse)
+RPGVersion.write_to_file()
+
+#%%------------------------------------INTELLIGENT TUTORING SYSTEM----------------------------------
+
+def it_version_config_text(**kwargs):
+ text = ""
+ Exercises = kwargs.get("Exercises")
+ if Exercises == None:
+ print("no exercises found for config callback of instant tutoring version")
+ return ""
+
+ seed_limit = kwargs.get("seed_limit")
+ if seed_limit == None:
+ seed_limit = 0
+ print("continue without seed limit in an instant tutoring version")
+
+ info_dict = {}
+ groups = {}
+ groups["start"] = "Start"
+ questions = {}
+ questions["start"] = {"name":"Start", "group":"start"}
+ #, "type":"instruction"
+
+ SortedExercises = sorted(Exercises, key=lambda x:f"t{x.topic_number}_{x.topic_id}_{x.exercise_number}_{x.exercise_part}")
+
+
+ for Exercise in SortedExercises:
+ #Check amount of possible variants
+ seed_amount = 0
+ for seed in Exercise.root.iterchildren("deployedseed"):
+ seed_amount+=1
+ if seed_amount < 1:
+ print(f"No seed given for t{Exercise.topic_number}-{Exercise.exercise_number}-{Exercise.exercise_part}.")
+ seed_amount = 1
+
+ variant_amount = seed_amount if (seed_limit == 0 or seed_amount < seed_limit) else seed_limit
+
+ group_identifier = f"t{Exercise.topic_number}_{Exercise.topic_id}_{Exercise.exercise_number}"
+ group_check = groups.get(group_identifier)
+ if group_check == None:
+ groups[group_identifier] = Exercise.topic_label
+ question_identifier = f"{group_identifier}_{Exercise.exercise_part}"
+ questions[question_identifier] = {"name":Exercise.exercise_description, "variants":variant_amount}
+ text = f"{text}t{Exercise.topic_number}_{Exercise.exercise_number}_{Exercise.exercise_part}\n"
+ #print(groups)
+ info_dict["groups"] = groups
+ info_dict["questions"] = questions
+ #print(info_dict)
+ return f'<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href;</script>\n<p>Sie sind in der Konfigurationsdatei vom Digitalen Mentor gelandet. Klicken sie bitte auf eine der anderen Fragen in der Test-Navigation, um zurück zum Übungsraum zu gelangen.</p>\n{json.dumps(info_dict)}'
+
+def it_version_add_to_script_text(**kwargs):
+ text = ""
+ Question = kwargs.get("Question")
+ if Question == None:
+ print("no question found for callback of add to script text")
+ return "start"
+ text = f"<script>ALQuiz.setCurrentQuestionId('t{Question.topic_number}_{Question.topic_id}_{Question.exercise_number}_{Question.exercise_part}')</script>"
+ return text
+
+def it_version_change_text(**kwargs):
+ #Change inputs
+ Question = kwargs.get("Question")
+ if Question == None:
+ print("no question found for input change")
+ return False
+ #Turn algebraic input into equivalence reasoning
+ for input_element in Question.root.iterchildren("input"):
+ handling = False
+ for input_type_element in input_element.iterchildren("type"):
+ if(input_type_element.text == "algebraic"):
+ input_type_element.text = "equiv"
+ handling = True
+ if handling == False:
+ continue
+
+ for input_options_element in input_element.iterchildren("options"):
+ if input_options_element.text == "" or input_options_element.text == None:
+ input_options_element.text = "hideequiv"
+ elif not "hideequiv" in input_options_element.text:
+ input_options_element.text = f"{input_options_element.text}, hideequiv"
+ name = ""
+ for input_name_element in input_element.iterchildren("name"):
+ name = input_name_element.text
+ if name == "":
+ continue
+
+ for input_tans_element in input_element.iterchildren("tans"):
+ input_tans_element.text = f"[{input_tans_element.text}]"
+
+ for prt in Question.root.iterchildren("prt"):
+ for node in prt.iterchildren("node"):
+ for sans in node.iterchildren("sans"):
+ if name in sans.text:
+ regex = re.compile(f'{name}')
+ sans.text = regex.sub(f"last({name})", sans.text)
+ #else:
+ # print(f"{name} is not in {sans.text} ({Question.exercise_description})")
+
+ return True
+
+
+it_fixed_seed_amount = 4
+InstantTutoringVersion = QuestionPool(QuestionVersion("instant-tutoring", True, '<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-instant-tutoring.js"></script>', "start-instant-tutoring.xml", "config-instant-tutoring.xml", it_fixed_seed_amount, True, callback_last_quiz_element_text=it_version_config_text, callback_add_to_script=it_version_add_to_script_text, callback_change_before_clone=it_version_change_text, Exercises=Exercises_To_Parse, seed_limit=it_fixed_seed_amount), Exercises_To_Parse)
+InstantTutoringVersion.write_to_file()
+
+#%%------------------------------------PA AND ENDBOSS-----------------------
+def pa_version_add_to_script_text(**kwargs):
+ text = ""
+ Question = kwargs.get("Question")
+ if Question == None:
+ print("no question found for callback of add to script text")
+ return "start"
+ text = f"<script>ALQuiz.setCurrentQuestionId('t{Question.topic_number}_{Question.topic_id}_{Question.exercise_number}_{Question.exercise_part}')</script>"
+
+
+ hint_text = ""
+ if Question.exercise_hint != "" and not pd.isna(Question.exercise_hint):
+ hint_text = f'<div class="hint">{Question.exercise_hint}</div>'
+ else:
+ hint_text = "Viel Erfolg beim Lösen dieser Aufgabe!"
+
+ text = f'{text}<p class="bubble">{hint_text}</p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg">'
+
+ return text
+
+PAEndbossVersion = QuestionPool(QuestionVersion("pa", False, '<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script>', "start-instant-tutoring.xml", show_hint=False, custom_last_elements_filepath="config-instant-tutoring.xml", callback_add_to_script=pa_version_add_to_script_text, callback_last_quiz_element_text=it_version_config_text, Exercises=Exercises_To_Parse), Exercises_To_Parse)
+PAEndbossVersion.write_to_file()
+
+#%%
\ No newline at end of file
diff --git a/exercise-generation/exercises.csv b/exercise-generation/exercises.csv
new file mode 100644
index 0000000000000000000000000000000000000000..ea8272c2aaba323a218c118fa364145fb12a0b5d
--- /dev/null
+++ b/exercise-generation/exercises.csv
@@ -0,0 +1,5941 @@
+topic_number;topic_id;exercise_number;exercise_part;topic_label;exercise_description;exercise_variables;exercise_text;exercise_content;exercise_hint;exercise_note;already_parsed;custom_prt;add_prt_node_on_not_correct;add_prt_node_wa1;add_prt_node_wa2;add_prt_node_wa3;custom_input;custom_seed;custom_general_feedback;personal_note
+0;syn;1;a;Syntax;Gleichung eingeben (Multiplikation);"SYN_A:[[a1,y=3*x+5],[a2,y=4*x+3],[a3,y=2*x+1],[a4,y=2*x-5],[a5,y=5*x-3],[a6,y=4*x-6]];SYN_a:rand(SYN_A);ta1:SYN_a[2];";Geben Sie die Gleichung \({@ta1@}\) in das Eingabefeld ein.;[[input:ans1]] [[validation:ans1]][[feedback:prt1]];"Okay! Hier eine leichte Aufgabe zur Eingabe. Benutze für jede Multiplikation das Symbol * (Stern).
+ <!--<span class=""show-on-mobile-only""><br><br>Nutze die <a href=""javascript:;"" onclick=""let userFocusTop = document.createElement('div');userFocusTop.classList.add('user-focus', 'hide-top');let pageHeight = document.documentElement.scrollHeight;userFocusTop.style.height=Math.ceil(pageHeight+window.pageYOffset)+'px';userFocusTop.onclick = removeTutorialFocus;document.body.appendChild(userFocusTop);"">Buttons über deiner Tastatur</a>, um die wichtigsten Mathe-Operatoren schnell zu finden.</span>-->
+ <br><br>Falls du ohne Tastatur unterwegs bist, kannst du mithilfe des <a href=""javascript:;"" onclick=""tutorialFocusElement(document.querySelector('.mathsbutton'));"">Mathe-Operatoren-Buttons</a> zusätzliche Buttons aktivieren, um alle Mathe-Operatoren schnell zu finden.
+
+ <!--<br><br>Drücke jederzeit den ""Prüfen""-Button, um zu sehen, wie deine Eingabe interpretiert wurde.<br>Erst wenn du nach dem ""Prüfen""-Button deine Eingabe nicht änderst und
+ erneut ""Prüfen"" klickst, wird deine Eingabe als Antwort abgeschickt.-->
+<br><br>Neben dem Eingabefeld siehst du, wie deine Eingabe interpretiert wird.<br>Wenn du auf den ""Prüfen""-Button klickst, wird deine Eingabe als Antwort abgeschickt.
+";{@SYN_a[1]@};0;;;;;;;<seed_fields><deployedseed>480757020</deployedseed><deployedseed>585237317</deployedseed><deployedseed>1798333349</deployedseed><deployedseed>2118152732</deployedseed><deployedseed>1988707695</deployedseed></seed_fields>;;
+0;syn;1;b;Syntax;Gleichung eingeben (Division);"SYN_A:[[a1,y=5/3],[a2,y=4/7],[a3,y=1/3],[a4,y=2/5],[a5,y=3/10],[a6,y=1/4]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);TA:SYN_a[2];";Geben Sie die Gleichung \({@TA@}\) in das Eingabefeld ein.;[[input:ans1]] [[validation:ans1]][[feedback:prt1]];Okay! Divisionen werden mit / (Slash) dargestellt. Hier erscheinen Sie als Brüche.<br>;{@SYN_a[1]@};0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>TA</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Wir arbeiten hier nur wenn explizit danach gefragt wird mit Dezimalzahlen. Brüche stellen das Ergebnis in der Regel genauer dar.<br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";;;;;<input><name>ans1</name><type>algebraic</type><tans>TA</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint></syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords>3x</forbidwords><allowwords></allowwords><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options></options></input>;<seed_fields><deployedseed>2690042</deployedseed><deployedseed>300094393</deployedseed><deployedseed>765518486</deployedseed><deployedseed>17019212</deployedseed><deployedseed>1233892964</deployedseed><deployedseed>147932577</deployedseed></seed_fields>;;
+0;syn;1;c;Syntax;Potenzen;"SYN_A:[[a1,(4+b)^2],[a2,(5+b)^2],[a3,(3+b)^2],[a4,(2+b)^2],[a5,(3+2*b)^2],[a6,(4+2*b)^2]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:expand(SYN_a[2])=SYN_a[2];";Geben Sie die Gleichung \[{@ta@}\] in das Eingabefeld ein.;<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>;<p>Mit dem Zeichen ^ (Caret) kannst du Potenzen darstellen.</p><div> <ul> <li>\(x^2\) wird so eingegeben: <code>x^2</code></li> <li>\(x^{-2}\) wird so eingegeben: <code>x^(-2)</code></li> <li>\(x^{1/3}\) wird so eingegeben: <code>x^(1/3)</code></li> </ul></div>;{@SYN_a[1]@};0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format=""html""><text><![CDATA[Sehr gut. Hier wurde übrigens eine binomische Formel angewendet, um einen Term zu faktorisieren.<br><p dir=""ltr"" style=""text-align: left;"" <br=""""></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Deine Antwort ist zwar äquivalent mit der dargestellten Gleichung, aber du hast nicht genau die gleiche Gleichung dargestellt.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";;;;;<input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint></syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords></forbidwords><allowwords></allowwords><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options></options></input>;<seed_fields><deployedseed>93323135</deployedseed><deployedseed>1032837775</deployedseed><deployedseed>680315517</deployedseed><deployedseed>838329017</deployedseed><deployedseed>162866526</deployedseed></seed_fields>;;
+0;syn;1;d;Syntax;Rationale Ausdrücke;"a:x^2;b:(x+1);c:(x-5);SYN_A:[[a1,a,b,c],[a2,b,a,c],[a3,c,a,b]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:SYN_a[2]/(SYN_a[3]*SYN_a[4]);wa:SYN_a[2]/SYN_a[3]*SYN_a[4];";Geben Sie die Gleichung \[{@ta@}\] in das Eingabefeld ein.;[[input:ans1]] [[validation:ans1]][[feedback:prt1]];Okay! Machen wir es etwas komplizierter. Um Terme in Brüchen darzustellen, musst du besonders auf die Klammersetzung achten.<br>;{@SYN_a[1]@};0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"" <br=""""></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Bitte beachte, dass du um den Nenner zusätzliche Klammern setzen musst, damit er als zusammenhängender Divisor interpretiert wird.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";;;;;<input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint></syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords></forbidwords><allowwords></allowwords><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options></options></input>;<seed_fields><deployedseed>82298515</deployedseed><deployedseed>1458249622</deployedseed><deployedseed>1731794639</deployedseed></seed_fields>;;
+0;syn;1;e;Syntax;Wurzelzeichen;"SYN_A:[[a1,3],[a2,5],[a3,7],[a4,11],[a5,13],[a6,19]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta1:sqrt(SYN_a[2]);";Geben Sie \[{@ta1@}\] in das Eingabefeld ein.;[[input:ans1]] [[validation:ans1]][[feedback:prt1]];"Gut. Um eine Wurzel darzustellen nutze <code>sqrt(x)</code> für \(\sqrt{x}\;\).";{@SYN_a[1]@};0;;;;;;;<seed_fields><deployedseed>1136692395</deployedseed><deployedseed>659595513</deployedseed><deployedseed>2040368424</deployedseed><deployedseed>262860513</deployedseed><deployedseed>592365331</deployedseed><deployedseed>1218846808</deployedseed></seed_fields>;;Erklärung, wie man Wurzeln eingibt, fehlt.
+0;syn;1;f;Syntax;Mehrere Lösungen;"SYN_A:[[a1,4],[a2,9],[a3,16],[a4,25],[a5,36]];/*SYN_a:SYN_A[1];*/SYN_a:rand(SYN_A);ta:x=sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);taalt:x=+sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);task:x^2=SYN_a[2];wa1:x=sqrt(SYN_a[2]);wa2:x=-sqrt(SYN_a[2]);wa3:x=sqrt(SYN_a[2]) nounand x=-sqrt(SYN_a[2]);";Lösen Sie nach \(x\) auf. Geben Sie die Lösung in der Form \(x=? \mbox{ or } x=?\) ein.;<p>\[{@task@}\]<br></p><p>[[input:ans]] [[validation:ans]][[feedback:prt1]]</p><p><em>Achtung: Bitte setzen Sie kein zusätzliches +-Symbol vor positive Zahlen.<br></em></p>;Gelegentlich müssen Ausdrücke mit logischen Verbindungen verknüpft werden. Nutze dafür <code>and</code> oder <code>or</code>. <br>;{@SYN_a[1]@};0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans</sans><tans>ta</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>ta</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty></truepenalty><truenextnode>4</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa2</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty></truepenalty><truenextnode>4</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>5</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>4</name><answertest>AlgEquiv</answertest><sans>1</sans><tans>1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-5-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"">Du hast nur eine von zwei richtigen Lösungen eingegeben.<br>Beispiel: \(5 \cdot 5 = 25\) und \(-5 \cdot -5 = 25\) (Minus Mal Minus ergibt Plus).<br>Für \(x^2 = 25\) gilt deshalb \(x = 5\) oder \(x = -5\), was hier in der Form <code>x=5 or x=-5</code> aufgeschrieben wird.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-5-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>5</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa3</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-6-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du hast alle richtigen Lösungen angegeben, allerdings hast du sie mit <code>and</code> verknüpft. Korrekt ist, sie mit <code>or</code> zu verknüpfen. Man schreibt</p><ul><li>entweder \(x=?\; oder \;x=?\)</li><li>oder \(x_1=?\; und \;x_2 = ?\;\).</li></ul>Hier benutzen wir ausschließlich die erste Form, die mit <code>x=? or x=?</code> dargestellt wird.<br>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-6-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";;;;;<input><name>ans</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint></syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords>4x</forbidwords><allowwords></allowwords><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options></options></input>;<seed_fields><deployedseed>1032259226</deployedseed><deployedseed>2071301041</deployedseed><deployedseed>668615301</deployedseed><deployedseed>1810103727</deployedseed><deployedseed>2047586646</deployedseed></seed_fields>;;
+0;syn;1;g;Syntax;Gleichung mehrschrittig lösen;"a:2;b:3;c:4;SYN_A:[[a1,a,b,c],[a2,b,a,c],[a3,c,a,b],[a4,a,c,b],[a5,b,c,a],[a6,c,b,a]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:[SYN_a[2]*(SYN_a[3]+x)=SYN_a[4],SYN_a[2]*SYN_a[3]+SYN_a[2]*x=SYN_a[4],SYN_a[2]*x=SYN_a[4]-SYN_a[2]*SYN_a[3],x=(SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]];/*ta:[2*(3+x)=-3,2*x+6=-3,2*x=-9,x=-9/2];*/p:first(ta);/*p:""\\(2 \\cdot (3 + x) = -3\\)"";*/wa1:x=-((SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]);wa2:x=SYN_a[4]-SYN_a[2]*SYN_a[3];";"<p>Lösen Sie \(\;\){@p@}\(\;\) nach x auf.</p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.</p><p>Sie brauchen kein Äquivalenz-Zeichen eingeben.<br></p>";[[input:ans1]] [[validation:ans1]][[feedback:prt1]];Um einen Rechenweg darzustellen, tippe jeden Schritt deiner Rechnung in eine neue Zeile in das Eingabefeld ein.;{@SYN_a[1]@};0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last(ans1)</sans><tans>last(ta)</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>wa1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Aber fast richtig. Du hast dich offenbar mit dem Vorzeichen vertan.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>wa2</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Offenbar ist dir ein Fehler beim Lösen der Klammer unterlaufen. Um die Klammer aufzulösen, musst du beide beide Summanden in der Klammer mit dem Faktor vor der Klammer multiplizieren.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>last(ta)</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Weiter so. Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";;;;;<input><name>ans1</name><type>equiv</type><tans>ta</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint>firstline</syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords></forbidwords><allowwords></allowwords><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options>hideequiv</options></input>;<seed_fields><deployedseed>668615301</deployedseed><deployedseed>1810103727</deployedseed><deployedseed>2047586646</deployedseed><deployedseed>1032259226</deployedseed><deployedseed>2071301041</deployedseed></seed_fields>;;
+0;syn;1;h;Syntax;Griechische Buchstaben;"a:beta;b:pi;c:alpha;SYN_A:[[a1,a,b],[a2,b,a],[a3,a,c],[a4,c,a],[a5,b,c],[a6,c,b]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:SYN_a[2]*z^(SYN_a[3]*x)wa1:SYN_a[2]*z^SYN_a[3]*x";Geben Sie \[{@ta@}\] in das Eingebefeld ein.;"<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p><em>Achtung: Bitte kopieren Sie keine Unicode-Zeichen, sondern benutzen Sie einfach Ihre Tastatur. <br></em></p>";Wenn griechische Buchstaben einzugeben sind, schreibe sie einfach aus. Beispiel: \(\alpha=\) <code>alpha</code> , \(\beta=\) <code>beta</code><code></code> ,\(\pi=\) <code>pi </code><code></code>.<br>;{@SYN_a[1]@};0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du hast offenbar vergessen, eine Klammer um die Potenz zu schreiben. Schreibe Potenzen in Klammern, wenn sie aus mehr als einer Zahl bestehen. Beispiel: \(x^{-2a}\) wird so eingegeben: <code>x^(-2*a)</code>.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";;;;;<input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint></syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords></forbidwords><allowwords></allowwords><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options></options></input>;<seed_fields><deployedseed>1516837293</deployedseed><deployedseed>911975771</deployedseed><deployedseed>742782033</deployedseed><deployedseed>1709130663</deployedseed><deployedseed>648468622</deployedseed><deployedseed>272609913</deployedseed></seed_fields>;;
+0;syn;1;i;Syntax;Syntax-Endboss;"a:2;b:3;c:4;d:2;e:3;SYN_A:[[a1,a,d],[a2,b,d],[a3,c,d],[a4,a,e],[a5,b,e],[a6,c,e]];SYN_a:rand(SYN_A);pifactor:ev(SYN_a[2]*(SYN_a[3]^2),simp);ta:[/*(SYN_a[2]*x^2)/(pifactor*pi)=1,*/SYN_a[2]*x^2=pifactor*pi,x^2=(SYN_a[3]^2)*pi,x=SYN_a[3]*sqrt(pi) nounor x=-SYN_a[3]*sqrt(pi)];p:first(ta);wa1:x=SYN_a[3]*sqrt(pi);wa2:x=-SYN_a[3]*sqrt(pi);";<p>Lösen Sie {@p@} nach \(x\) auf.<br></p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.<br></p>;[[input:ans1]] [[validation:ans1]][[feedback:prt1]]<p></p><p><em>Zur Erinnerung: Das Kommando für</em> \(\sqrt{x}\)<em> lautet </em><code>sqrt(x)</code><em>. Nutzen Sie </em><code>or</code><em> um mehrere Lösungen anzugeben.</em></p>;Willkommen zum Endgegner dieser Mathe-Welt. Mit dem Lösen dieser Aufgabe hast du die erste Mathe-Welt bereits abgeschlossen. Viel Erfolg!<br>;{@SYN_a[1]@};0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last(ans1)</sans><tans>last(ta)</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format=""html""><text><![CDATA[]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>4</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>wa1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty></truepenalty><truenextnode>3</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>wa2</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty></truepenalty><truenextnode>3</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>1</sans><tans>1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du hast nur eine von zwei richtigen Lösungen eingegeben.<br>Beispiel: \(5\,\sqrt{\pi} \cdot 5\,\sqrt{\pi} = 25\,\pi\) und \(-5\,\sqrt{\pi} \cdot -5\,\sqrt{\pi} = 25\,\pi\) (Minus Mal Minus ergibt Plus).<br>Für \(x^2 = 25\pi\) gilt deshalb \(x = 5\,\sqrt{\pi}\) oder \(x = -5\,\sqrt{\pi}\), was hier in der Form <code>x=5*sqrt(pi) or x=-5*sqrt(pi)</code> aufgeschrieben wird.</p><p dir=""ltr"" style=""text-align: left;""></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>4</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>last(ta)</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-5-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>1</falsenextnode><falseanswernote>prt1-5-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";;;;;<input><name>ans1</name><type>equiv</type><tans>ta</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint>firstline</syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords></forbidwords><allowwords></allowwords><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options>hideequiv</options></input>;<seed_fields><deployedseed>1169120426</deployedseed><deployedseed>1624332195</deployedseed><deployedseed>1578649438</deployedseed><deployedseed>1629124203</deployedseed><deployedseed>2120835467</deployedseed></seed_fields>;;
+1;fra;1;a;Bruchrechnung;Welcher Bruch ist größer?;"a:rand_with_step(0,2,1); b:rand_with_step(0,3,1);c:rand_with_prohib(0,2,[a]);d:rand_with_prohib(0,3,[b]);e:ev((a+2)/(b*2+5),simp);f:ev((c+2)/(d*2+5),simp);ta1:lmax([e,f]);";Was ist größer {@e@} oder {@f@}?;[[input:ans1]][[validation:ans1]][[feedback:prt1]];;{@e@}, {@f@};1;;;;;;;<seed_fields><deployedseed>1150152566</deployedseed><deployedseed>1493154809</deployedseed><deployedseed>213116642</deployedseed><deployedseed>1642637086</deployedseed><deployedseed>2013023483</deployedseed></seed_fields>;;Visualize circles
+1;fra;1;b;Bruchrechnung;Gib einen kleineren Bruch an!;"a:rand_with_step(2,9,1); b:1/a; ta1:1/(a+1);";Gib einen Bruch an, der kleiner als {@b@} ist.;[[input:ans1]][[validation:ans1]][[feedback:prt1]];;{@b@};1;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text><![CDATA[if(ans1<a) then test:true else test:false;]]></text></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>test</sans><tans>true</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";;;;;;<seed_fields><deployedseed>1259684802</deployedseed><deployedseed>472488446</deployedseed><deployedseed>1739952511</deployedseed><deployedseed>1878391608</deployedseed><deployedseed>1361264400</deployedseed><deployedseed>147214256</deployedseed></seed_fields>;;"Visualize circles, add to feedback variables and adapt prt: if(ans1<a) then test:true else test:false; [EqualComAss sans:test tans:true]"
+1;fra;1;c;Bruchrechnung;Ist das ein Bruch?;"a:rand_with_step(2,8,1); b:2*a; simp:false; c:b/a; ta1:c;";Ist {@c@} ein Bruch?;[[input:ans1]][[validation:ans1]][[feedback:prt1]];;{@c@};1;;;;;;;<seed_fields><deployedseed>909516242</deployedseed><deployedseed>1570539735</deployedseed><deployedseed>1316494823</deployedseed><deployedseed>472858503</deployedseed><deployedseed>836690145</deployedseed><deployedseed>177164078</deployedseed></seed_fields>;;
+1;fra;1;d;Bruchrechnung;Pizza aufteilen;"a:rand_with_step(3,6,1);b:a+1; ta1:a/b;";Teile {@a@} Pizzen gerecht auf {@b@} Personen auf. Wie viele Pizzen bekommt jeder?;[[input:ans1]][[validation:ans1]][[feedback:prt1]];;{@a/b@};1;;;;;;;<seed_fields><deployedseed>1585319522</deployedseed><deployedseed>1444115849</deployedseed><deployedseed>1404326029</deployedseed><deployedseed>207515686</deployedseed></seed_fields>;;
+1;fra;1;bi-a;Bruchrechnung;Kürzen zweier einfacher Brüche;"a:rand_with_step(2,8,1); b:rand_with_step(20,40,10); c:a*b; d:b/5; e:a*b/10; ta1:1/a; simp:false; f:5/e; g:d/10; wa1:(5+d)/(e+10);";Kürze und fasse so weit wie möglich zusammen.;\({@f@} \cdot {@g@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];Tipp: Gekürzt wird, indem man Zähler & Nenner durch dieselbe Zahl teilt.;\({@f@} \cdot {@g@} = {@ta1@}\);0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir=""ltr"" style=""text-align: left;"">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";;;;;;<seed_fields><deployedseed>423191525</deployedseed><deployedseed>1756629135</deployedseed><deployedseed>505485688</deployedseed><deployedseed>813830513</deployedseed><deployedseed>1619258121</deployedseed></seed_fields>;;
+1;fra;1;bi-b;Bruchrechnung;Kürzen zweier Brüche mit Variablen;"varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); powers:makelist(rand(5)+1, 6); myvar1: mya^powers[1]; myvar2: myb^powers[2]; myvar3: myc^powers[3]; myvar4: mya^powers[4]; myvar5: myb^powers[5]; myvar6: myc^powers[6]; d:(myvar1*myvar2*myvar3)/(myvar4*myvar5*myvar6); ta1:d;";Kürze und fasse so weit wie möglich zusammen.;\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];Tipp: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\,a\,a\,b\,b\,c}{a\,a\,a\,a\,a\,b\,c\,c\,c}\);\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} = {@ta1@}\);0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";Beispiel: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,b\,b\mkern-5mu/\,c\mkern-5mu/}{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,a\,a\,b\mkern-5mu/\,c\mkern-5mu/\,c\,c} = \frac{b}{a^2\,c^2}\);;;;;<seed_fields><deployedseed>194802941</deployedseed><deployedseed>1917875187</deployedseed><deployedseed>1931041228</deployedseed><deployedseed>928137609</deployedseed><deployedseed>264598581</deployedseed><deployedseed>1633750828</deployedseed><deployedseed>1318198792</deployedseed></seed_fields>;;
+1;fra;1;bi-c;Bruchrechnung;Kürzen zweier Brüche mit Variablen und Zahlen;"num1:rand_with_step(5,8,1); varlist:[a,b,c,u,v,w,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1], varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); num2:rand_with_step(3,7,1); num3:rand_with_step(3,7,1); nom1:num1*num2*myvars[1]; denom1:num1*myvars[2]; nom2:num1*num3*myvars[1]*myvars[2]; denom2:num1*myvars[1]*myvars[3]; ta1:(nom1/denom1)*(nom2/denom2); /*Alle Variablen in den Zählern mit einer Variable im Nenner gekürzt.*/wa1:((nom1/myvars[1])*(nom2/myvars[1]))/((denom1*denom2)/myvars[1]);";Kürze und fasse so weit wie möglich zusammen.;\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];Tipp: Erst auf einen Bruchstrich sortieren. Beispiel: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} = \frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c}\);\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} = {@ta1@}\);0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du hast offensichtlich die Variable {@myvars[1]@} im Nenner gegen beide Variablen in den Zählern gekürzt. Bei der Multiplikation von Brüchen kannst du immer nur einen Faktor gegen den anderen kürzen. Beispiel: \(\frac{36}{6} = \frac{6\cdot6}{6} = \frac{6\mkern-5mu/\cdot6}{6\mkern-5mu/} = \frac{6}{1} = 6\) und nicht \(\frac{36}{6} = \frac{6\cdot6}{6} \ne \frac{6\mkern-5mu/\cdot6\mkern-5mu/}{6\mkern-5mu/} = 1\;\).<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";"So lassen sich Produkte auf einem Bruchstrich sortieren und kürzen: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} =\frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c} =\frac{49^7\mkern-14mu\large/ \small \; \cdot 21^3\mkern-14mu\large/\small \; \cdot a\mkern-5mu/ \cdot a \cdot b\mkern-5mu/}{7\mkern-5.5mu/ \cdot7\mkern-5.5mu/ \cdot a\mkern-5mu/\cdot b\mkern-5mu/\cdot c} =\frac{21\,a}{c}\)";;;;;<seed_fields><deployedseed>1842189518</deployedseed><deployedseed>1601667602</deployedseed><deployedseed>2136766316</deployedseed><deployedseed>1542661342</deployedseed><deployedseed>2072145258</deployedseed><deployedseed>328965971</deployedseed></seed_fields>;;
+1;fra;1;bi-d;Bruchrechnung;Kürzen zweier Brüche mit Termen;"myvar:rand([x,y,z]); term_summand1:rand_with_prohib(-3,3,[0]); term_summand2:rand_with_prohib(-3,3,[0,term_summand1]); term1:myvar+term_summand1; term2:myvar+term_summand2; ta1:term1/myvar*(myvar^2/(term1*term2*myvar)); /*wa1 means: naive shortened fraction*/ wa1:(term1-myvar)/1*(myvar^2/(term1*term2*myvar));";Kürze und fasse so weit wie möglich zusammen.;\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];Tipp: Kennst du noch den Ausspruch „Aus Summen kürzen nur die Dummen“?!;\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}={@ta1@}\);0;; Nur ganze Faktoren dürfen gekürzt werden. Zum Beispiel: \(\frac{\boldsymbol{(x-1)}\cdot 2}{x \cdot \boldsymbol{(x-1)}} = \frac{2}{x}\);"Offensichtlich hast du beim ersten Bruch die Variable {@myvar@} im Nenner gegen die Variable {@myvar@} im Zähler gekürzt. Das geht aber nicht, weil die Variable {@myvar@} im Zähler mit einem anderen Summanden eine Summe bildet. Beispiel: \(3 = \frac{6}{2} = \frac{4+2}{2} \ne \frac{4 + 2\mkern-5.5mu/}{2\mkern-5.5mu/} = \frac{4}{1} = 4\;\).";;;;<seed_fields><deployedseed>837792651</deployedseed><deployedseed>528135820</deployedseed><deployedseed>879656886</deployedseed><deployedseed>1917537516</deployedseed><deployedseed>1617668401</deployedseed><deployedseed>159039633</deployedseed><deployedseed>1131743594</deployedseed></seed_fields>;;
+1;fra;1;bii-a;Bruchrechnung;Einfachen Bruch erweitern;"a:rand_with_step(4,9,1); b:a-1; c:a/b; d:a*5; e:b*5; simp:false; ta1:d/e;";Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.;\({@c@} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]];;\({@c@} = {@ta1@}\);0;;;;;;;<seed_fields><deployedseed>437845679</deployedseed><deployedseed>2092409135</deployedseed><deployedseed>1712748750</deployedseed><deployedseed>182980498</deployedseed><deployedseed>388683995</deployedseed><deployedseed>1561500176</deployedseed></seed_fields>;;Instead of „Du kannst noch weiter vereinfachen“ write something else.
+1;fra;1;bii-b;Bruchrechnung;Bruch mit Variablen erweitern;"varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,4); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[1]^powers[3]; fac4:myvars[2]^powers[4]; numerator:fac1*fac2; denominator:fac3*fac4; d:numerator/denominator; tanumerator:5*num(d); tadenominator:5*denom(d); simp:false; ta1:tanumerator/tadenominator;";Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.;\(\frac{{@numerator@}}{{@denominator@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]];;\(\frac{{@numerator@}}{{@denominator@}} = {@ta1@}\);0;;;;;;;<seed_fields><deployedseed>36209422</deployedseed><deployedseed>1000344719</deployedseed><deployedseed>1827440244</deployedseed><deployedseed>1291739138</deployedseed><deployedseed>825866743</deployedseed></seed_fields>;;Instead of „Du kannst noch weiter vereinfachen“ write something else.
+1;fra;1;bii-c;Bruchrechnung;Bruch mit Variablen und Zahlen erweitern;"varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,3); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[2]^powers[3]; rand1:rand(4); rand2:rand_with_prohib(0,3,[rand1]); number1:rand1*2+3; number2:rand2*2+3; number3:rand_with_step(2,8,2); numerator:fac1*fac2; denominator:fac3; d:numerator/denominator; tanumerator:5*number1*number2*num(d); tadenominator:5*number3*denom(d); simp:false; ta1:tanumerator/tadenominator;";Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.;\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]];;\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = {@ta1@}\);0;;;;;;;<seed_fields><deployedseed>1516326427</deployedseed><deployedseed>1341581403</deployedseed><deployedseed>79491835</deployedseed><deployedseed>1422333316</deployedseed><deployedseed>1757641065</deployedseed></seed_fields>;;What exactly here is the correct solution? Shorten variables but don’t shorten numbers? Furthermore: Instead of „Du kannst noch weiter vereinfachen“ write something else.
+1;fra;1;ca;Bruchrechnung;Einfache Addition von Brüchen;"a:rand_with_step(1,4,1)*2+1; fac1:rand_with_step(1,4,1); fac2:rand_with_prohib(1,4,[fac1]); denoms:[a, a*fac1,a*fac2]; nums:makelist(rand_with_step(1,denoms[i]-1,2),i,3); signs:makelist(rand_with_prohib(-1,1,[0]),3); fractions:makelist(signs[i]*nums[i]/denoms[i],i,3); fractions:random_permutation(fractions); ta1:fractions[1]+fractions[2]+fractions[3]; simp:false; exercise:fractions[1]+fractions[2]+fractions[3]; /*wa1 means: naive addition*/ wa1:(num(fractions[1])+num(fractions[2])+num(fractions[3]))/(denom(fractions[1])+denom(fractions[2])+denom(fractions[3]));";Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.;\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];Tipp: Beim Addieren und Subtrahieren müssen die Nenner der Brüche gleich sein. Kannst du dich noch an das kleinste gemeinsame Vielfache erinnern?;\({@exercise@} = {@ta1@}\);0;;<p>Um die Nenner gleich zu machen, musst du sie so erweitern, dass sie den gleichen Nenner haben. Dann können die Zähler addiert werden. Das kleinste gemeinsame Vielfache von 5, 10 und 15 lässt sich zum Beispiel finden, indem man die jeweiligen Reihen notiert und die kleinste gemeinsame Zahl sucht.</p><table><tr><th>5er-Reihe</th><th>10er-Reihe</th><th>15er-Reihe</th></tr><tr><td>5</td><td>10</td><td>15</td></tr><tr><td>10</td><td>20</td><td><strong>30</strong></td></tr><tr><td>15</td><td><strong>30</strong></td><td>...</td></tr><tr><td>20</td><td>...</td><td>...</td></tr><tr><td>25</td><td>...</td><td>...</td></tr><tr><td><strong>30</strong></td><td>...</td><td>...</td></tr><tr><td>...</td><td>...</td><td>...</td></tr></table>;"Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir=""ltr"" style=""text-align: left;"">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>";;;;<seed_fields><deployedseed>311233457</deployedseed><deployedseed>584289189</deployedseed><deployedseed>1338253474</deployedseed><deployedseed>933392702</deployedseed><deployedseed>236951333</deployedseed></seed_fields>;;
+1;fra;1;cb;Bruchrechnung;Addition von Brüchen mit Variablen und gleichem Nenner;"myvar:rand([a,b,c]); fractions_correct_and_wa1:[[(myvar+1)/myvar, -myvar+1], [(myvar-1)/myvar, -myvar-1], [(1-myvar)/myvar, -1-myvar]]; fractions_correct_and_wa1:random_permutation(fractions_correct_and_wa1); fractions:makelist(fractions_correct_and_wa1[i][1],i,3); terms_wa1:makelist(fractions_correct_and_wa1[i][2],i,3); exercise:fractions[1]-fractions[2]-fractions[3]; ta1:combine(exercise); wa1:(num(fractions[1])+terms_wa1[2]+terms_wa1[3])/myvar;";Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.;\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];Tipp: Überlege genau, was ein Minus vor einem Bruch bedeutet.;\({@fractions[1]@}-{@fractions[2]@}-{@fractions[3]@} = {@ta1@}\);0;;<p>Tipp: Ein Minus vor dem Bruch gehört zum ganzen Bruch: gilt also für den ganzen Zähler oder ganzen Nenner (häufig nimmt man den Zähler).</p><p>\(\Rightarrow -\frac{a-1}{a} = \frac{-\boldsymbol{(a-1)}}{a} = \frac{-a+1}{a}\)</p><p>Wichtig bei Summen im Zähler!!!</p>;Du hast offenbar die Minuszeichen nicht korrekt aufgelöst.;;;;<seed_fields><deployedseed>471812117</deployedseed><deployedseed>416709956</deployedseed><deployedseed>743127794</deployedseed><deployedseed>2005900637</deployedseed><deployedseed>634867927</deployedseed></seed_fields>;;Not all hints/error patterns could be considered.
+1;fra;1;cc;Bruchrechnung;Addition von Brüchen mit Variablen und unterschiedlichen Nennern;"varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); fractions:[(1+myvars[1])/myvars[1], rand_with_step(2,5,1)/myvars[2], myvars[1]/myvars[3]]; fractions:random_permutation(fractions); exercise:fractions[1]+fractions[2]+fractions[3]; common_denom:denom(fractions[1])*denom(fractions[2])*denom(fractions[3]); ta1:((num(fractions[1])*denom(fractions[2])*denom(fractions[3]))+(num(fractions[2])*denom(fractions[1])*denom(fractions[3]))+(num(fractions[3])*denom(fractions[1])*denom(fractions[2])))/common_denom; ta1alt:(expand((num(fractions[1])*denom(fractions[2])*denom(fractions[3])))+expand((num(fractions[2])*denom(fractions[1])*denom(fractions[3])))+expand((num(fractions[3])*denom(fractions[1])*denom(fractions[2]))))/common_denom;";Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.;\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];Tipp: Jeder Teilnenner (hier: {@myvars[1]@}, {@myvars[2]@}, {@myvars[3]@}) muss als Faktor im gemeinsamen Nenner vorkommen.;\({@exercise@} = {@ta1@}\);0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>2</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>2</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";<p>Um einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{1+a}{a}+\frac{2}{b}+\frac{a}{c}\) ist der gemeinsame Nenner \(a \cdot b \cdot c\). So muss erweitert werden, damit die Zähler addiert werden können:</p><p>\(\frac{(1+a) \boldsymbol{\cdot b \cdot c} }{a \boldsymbol{\cdot b \cdot c}}+\frac{2 \boldsymbol{\cdot a \cdot c}}{\boldsymbol{a} \cdot b \boldsymbol{\cdot c}}+\frac{a \boldsymbol{\cdot a \cdot b}}{\boldsymbol{a \cdot b} \cdot c}\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(1+a\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p>;;;;;<seed_fields><deployedseed>638235066</deployedseed><deployedseed>1053964038</deployedseed><deployedseed>625975426</deployedseed><deployedseed>1098133316</deployedseed><deployedseed>1880026849</deployedseed><deployedseed>1344755034</deployedseed></seed_fields>;;
+1;fra;1;cd;Bruchrechnung;Addition von Brüchen mit einer Variablen und unterschiedlichen Nennern;"myvar:rand([x,y,z]); nums:makelist(rand_with_step(2,5,1),2); fractions:[(nums[1]+myvar)/myvar^2,(nums[2]-myvar^2)/myvar]; common_denom:myvar^2; ta1:(num(fractions[1])-num(fractions[2])*myvar)/common_denom; ta1alt:(num(fractions[1])-expand(num(fractions[2])*myvar))/common_denom; exercise:fractions[1]-fractions[2]; /*wa1 means: didn't consider minus sign before bracket*/ wa1:(num(fractions[1])+(-nums[2]-myvar^2)*myvar)/common_denom;";Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.;\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];;\({@exercise@} = {@ta1@}\);0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";<p>Um immer einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{3+x}{x^2}-\frac{5-x}{x}\) ist ein gemeinsame Nenner \(x^2 \cdot x = x^3\). Betrachtet man die Teilnenner \(x^2\) und \(x\) genauer, fällt auf, dass \(x\) bereits als Faktor in \(x^2\) vorkommt. Denn \(x^2 = x \cdot x\). Deswegen kann hier auch \(x^2\) als Hauptnenner gewählt werden.</p><p>Dazu muss so erweitert werden:</p><p>\(\frac{(3+x)}{x^{2}}-\frac{(5-x^2) \boldsymbol{ \cdot x}}{x \boldsymbol{\cdot x}} = \frac{3+x}{x^{2}}-\frac{5x-x^3}{x^{\boldsymbol{2}}} = \frac{3+x-(5x-x^3)}{x^2} = \dots\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(5-x^2\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p>;Du hast offenbar die Minuszeichen nicht korrekt aufgelöst (siehe Tipp unten).;;;;<seed_fields><deployedseed>669633138</deployedseed><deployedseed>2093071884</deployedseed><deployedseed>1766326583</deployedseed><deployedseed>488830876</deployedseed><deployedseed>1210423031</deployedseed><deployedseed>158072256</deployedseed></seed_fields>;;Add to prt: Don’t just add ^2 to num and denom. It’s not equivalent. Not all hints/error patterns could be considered.
+1;fra;1;ce;Bruchrechnung;Addition von Brüchen mit Variablen und unterschiedlichen Nennern I (Update1);"varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); numbers:makelist(rand_with_step(2,5,1), 5); factors:random_permutation([1,2,4]); /*only +*/ signs:makelist(rand_with_prohib(1,1,[0]),2); fractions:[(numbers[1]*myvars[1]-numbers[2]*myvars[2])/(factors[1]*5*myvars[1]*myvars[2]), (numbers[3]*myvars[3]-numbers[4]*myvars[1])/(factors[2]*5*myvars[1]*myvars[3]), (myvars[3]^2-numbers[5])/(factors[3]*5*myvars[2]*myvars[3])]; tanum:(num(fractions[1])*(4/factors[1])*myvars[3]+num(fractions[2])*(4/factors[2])*myvars[2]+num(fractions[3])*(4/factors[3])*myvars[1]); tanumalt:expand(tanum); tadenom:(5*4*myvars[1]*myvars[2]*myvars[3]); ta1:tanum/tadenom; /*fractions_to_show:random_permutation(fractions);*/ fractions_to_show:fractions; ta1alt:tanumalt/tadenom; fractions_to_show[2]:fractions_to_show[2]*signs[1]; fractions_to_show[3]:fractions_to_show[3]*signs[2]; exercise:fractions_to_show[1]+fractions_to_show[2]+fractions_to_show[3];";Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.;\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];Tipp: Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.;\({@exercise@} = {@ta1@}\);0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>2</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>2</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";"<p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{5\,z-4\,x}{10\,x\,z}+\frac{7\,y-3\,z}{20\,y\,z}+\frac{y^2-2}{5\,x\,y}\) ist \(20\) das kleinste gemeinsame Vielfache (kgV) von \(10\), \(20\) und \(5\) und \(x \cdot y \cdot z\) ist das kgV von \(x \cdot z\), \(y \cdot z\) und \(x \cdot y\). Der Hauptnenner ist demnach \(20 \cdot x \cdot y \cdot z\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(20 \cdot x \cdot y \cdot z\;\) steht. \(\frac{5\,z-4\,x}{10\,x\,z}\) wird mit \(2 \cdot y\) erweitert, \(\frac{7\,y-3\,z}{20\,y\,z}\) wird mit \(x\) erweitert und \(\frac{y^2-2}{5\,x\,y}\) wird mit \(4 \cdot z\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(5\,z-4\,x)\boldsymbol{ \cdot 2\,y}}{10\,x\,z \boldsymbol{ \cdot 2\,y}}+\frac{(7\,y-3\,z) \boldsymbol{ \cdot x}}{20\,y\,z \boldsymbol{ \cdot x}}+\frac{(y^2-2) \boldsymbol{ \cdot 4\,z}}{5\,x\,y \boldsymbol{ \cdot 4\,z}}\)</p><p>\(= \frac{10\,y\,z-8\,x\,y}{20\,x\,y\,z}+\frac{7\,x\,y-3\,x\,z}{20\,x\,y\,z}+\frac{4\,y^2\,z-8\,z}{20\,x\,y\,z} = \dots\)</p>";;;;;<seed_fields><deployedseed>1330316881</deployedseed><deployedseed>2007639052</deployedseed><deployedseed>846124380</deployedseed><deployedseed>520216901</deployedseed><deployedseed>1618486590</deployedseed></seed_fields>;;
+1;fra;1;cf;Bruchrechnung;Addition von Brüchen mit Variablen und unterschiedlichen Nennern II;"varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); numbers:rand_selection(makelist(i,i,5),2); denom_nums_origin:rand_selection([18,12,6],1)[1]; denom_nums:[denom_nums_origin, denom_nums_origin/2, denom_nums_origin/3]; main_fraction:(numbers[1]-myvars[1])/(denom_nums[1]*myvars[1]^2); fractions:[(myvars[2])/(denom_nums[2]*myvars[1]), (myvars[2]+numbers[2])/(denom_nums[3]*myvars[1]*myvars[2])]; tanum:num(main_fraction)*myvars[2]-num(fractions[1])*2*myvars[1]*myvars[2]-num(fractions[2])*3*myvars[1]; tanumalt:expand(tanum); tadenom:denom_nums_origin*myvars[1]^2*myvars[2]; ta1:tanum/tadenom; ta1alt:tanumalt/tadenom; fractions:random_permutation(fractions); simp:false; exercise:main_fraction-fractions[1]-fractions[2];";Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.;\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];Tipp: 1) Überlege genau, was ein Minus vor einem Bruch bedeutet. 2) Jeder Teilnenner (hier: {@denom(main_fraction)@}, {@denom(fractions[1])@}, {@denom(fractions[2])@}) muss als Faktor im gemeinsamen Nenner vorkommen. 3) Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.;\({@exercise@} = {@ta1@}\);0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;""></p><p dir=""ltr"">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";"<p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{1-x}{18\,x^2}-\frac{y}{9\,x}-\frac{x+3}{6\,x\,y}\) ist \(18\) das kleinste gemeinsame Vielfache (kgV) von \(18\), \(9\) und \(6\) und \(x^2 \cdot y\) ist das kgV von \(x^2\), \(x\) und \(x \cdot y\). Der Hauptnenner ist demnach \(18 \cdot x^2 \cdot y\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(18 \cdot x^2 \cdot y\;\) steht. \(\frac{1-x}{18\,x^2}\) wird mit \(y\) erweitert, \(\frac{y}{9\,x}\) wird mit \(2\,x\,y\) erweitert und \(\frac{x+3}{6\,x\,y}\) wird mit \(3 \cdot x\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(1-x) \boldsymbol{\cdot y}}{18\,x^2 \boldsymbol{\cdot y}}-\frac{y \boldsymbol{\cdot 2\,x\,y}}{9\,x \boldsymbol{\cdot 2\,x\,y}}-\frac{(x+3) \boldsymbol{\cdot 3\,x}}{6\,x\,y \boldsymbol{\cdot 3\,x}}\)</p><p>\(= \frac{y-x\,y}{18\,x^2\,y}-\frac{2\,x\,y^2}{18\,x^2\,y}-\frac{3\,x^2+9\,x}{18\,x^2\,y} = \dots\)</p>";;;;;<seed_fields><deployedseed>527686404</deployedseed><deployedseed>1918490776</deployedseed><deployedseed>2103547991</deployedseed><deployedseed>1091135158</deployedseed><deployedseed>1696865873</deployedseed></seed_fields>;;Skipped g, h and i
+1;fra;1;da;Bruchrechnung;Multiplikation zweier einfacher Brüche;"nums:rand_selection(makelist(i+1,i,8),4); fractions:[nums[1]/nums[2], nums[3]/nums[4]]; ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions*/ wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied*/ wa2:fractions[1]+fractions[2];";Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.;\({@fractions[1]@}\cdot{@fractions[2]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.;\({@fractions[1]@}\cdot{@fractions[2]@} = {@ta1@}\);0;;<p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{2}{3} \cdot \frac{6}{5} = \frac{2 \cdot 6}{3 \cdot 5} = \frac{12}{15} = \frac{4}{5}\)</p>;Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.;Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.;;;<seed_fields><deployedseed>1088212423</deployedseed><deployedseed>1553109555</deployedseed><deployedseed>777390971</deployedseed><deployedseed>1688656099</deployedseed><deployedseed>1485690277</deployedseed></seed_fields>;;Added some error patterns. A link to addition of fractions here could be helpful.
+1;fra;1;db;Bruchrechnung;Multiplikation zweier Brüche mit Variablen;"varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); fractions:[mya/myb, mya^2/(mya*myb)]; fractions:random_permutation(fractions); ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions with previously shortened the larger fraction*/ wa1:(2*mya)/(2*myb); /*wa2 means: naively summed fractions without previously shortening the larger fraction*/ wa2:(mya+myb^2)/(mya+myb*mya); /*wa3 means: correctly summed fractions instead of multiplied*/ wa3:fractions[1]+fractions[2]; /*wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied wa2:fractions[1]+fractions[2];*/";Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.;\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.;\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} = {@ta1@}\);0;;<p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{a}{b} \cdot \frac{a^2}{a\,b} = \frac{a}{b} \cdot \frac{a \cdot a}{a\,b} = \frac{a \cdot a \cdot a}{a \cdot b \cdot b} = \frac{a^3}{a\,b^2}\)</p>;Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.;Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden. Du hast außerdem den Bruch \({@mya@}^2/({@mya@}*{@myb@})\) nicht ausreichend vereinfacht. Er kann zu \({@mya@}/{@myb@}\) gekürzt werden.;Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.;;<seed_fields><deployedseed>545658671</deployedseed><deployedseed>1228864607</deployedseed><deployedseed>806993602</deployedseed><deployedseed>1501016569</deployedseed><deployedseed>710282177</deployedseed></seed_fields>;;Added some error patterns. A link to addition of fractions here could be helpful.
+1;fra;1;dc;Bruchrechnung;Multiplikation Bruch mit Zahlen, Bruch mit Variablen, Ganzzahl;"nums:rand_selection(makelist(i+1,i,8),3); nums:sort(nums); varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); factors:[nums[1], (mya*myb)/myc, nums[2]/nums[3]]; factors:random_permutation(factors); ta1:factors[1]*factors[2]*factors[3]; simp:false; exercise:factors[1]*factors[2]*factors[3];";Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.;\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];Tipp: Wie kann man eine ganze Zahl als Bruch schreiben?;\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} = {@ta1@}\);0;;<p>Tipp: Jede ganze Zahl kann als Bruch geschrieben werden, indem man sie durch 1 teilt. Beispiel: \(3 \cdot \frac{a\,b}{c} \cdot \frac{5}{6} = \frac{3}{1} \cdot \frac{a\,b}{c} \cdot \frac{5}{6}\)</p><p>\( = \frac{3 \cdot a \cdot b \cdot 5}{1 \cdot c \cdot 6} = \frac{15\,a\,b}{6\,c} = \frac{5\,a\,b}{2\,c}\)</p><p>Hinweis: Generellt gilt \(\cdot 1\) und \(:\,1\) geht immer.</p>;;;;;<seed_fields><deployedseed>1569886884</deployedseed><deployedseed>1980675582</deployedseed><deployedseed>1601683210</deployedseed><deployedseed>51348788</deployedseed><deployedseed>726919830</deployedseed></seed_fields>;;
+1;fra;1;dd;Bruchrechnung;Multiplikation zweier Brüche mit Termen;"varlist:[a,b,c,x,y,z]; myvars:rand_selection(varlist, 2); nums:rand_selection(makelist(i+1,i,9), 6); fractions:[(nums[1]*myvars[1]+nums[2]*myvars[2])/(nums[3]*myvars[2]+nums[4]*myvars[1]), (-nums[5]*myvars[1])/(nums[6]+myvars[1])]; ta1:fractions[1]*fractions[2]; taalt:combine(expand(ta1)); /*wa1 means: the multiplication of the numerator was done with only one summand of the first fraction’s numerator (the second one)*/ wa1:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(denom(fractions[1])*denom(fractions[2])); /*old_wa2 means the same as wa1 but with the first fraction numerator’s second summand*/ /*old_wa2: (nums[1]*myvars[1]*num(fractions[2])+nums[2]*myvars[2])/(denom(fractions[1])*denom(fractions[2]));*/ /*wa2 means the same as wa1 but with the denominators, so no brackets: first summand of second fraction is multiplied with last summand of first fraction*/ wa2:(num(fractions[1])*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]); /*wa3 is the combination of wa1 and wa2*/ wa3:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]);";Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.;\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];Tipp: Achtung: Summanden & Faktoren => Klammer!;\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}= {@ta1@}\);0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;""></p><p dir=""ltr"">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";<p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{4\,x+10\,y}{5\,y+2\,x} \cdot \frac{-4\,x}{3+x} = \)\(\frac{\boldsymbol{(4\,x+10\,y)} \cdot -4\,x}{\boldsymbol{(5\,y+2\,x)} \cdot \boldsymbol{(3+x)}} = \dots\)</p>;Du hast die Nenner richtig multipliziert, doch du hast den Faktor im Zähler des zweiten Bruches nur mit dem zweiten Summanden des Zählers im ersten Bruch multipliziert. Das heißt bei der Multiplikation der Zähler musst du Klammern um die Summe setzen und jeden Summanden des ersten Zählers mit dem Faktor des anderen Zählers multiplizieren.;Du hast die Zähler richtig multipliziert, hast jedoch im Nenner nicht beachtet, dass Summen als Ganzes multipliziert werden. Das heißt bei der Multiplikation der Nenner musst du Klammern um die Summen setzen und jeden Summanden des einen Nenners mit jedem Summanden des anderen Nenners multiplizieren.;Du hast die Summen nicht als Ganzes multipliziert. Das betrifft eine Summe im Zähler und die Summen im Nenner. Du musst jeweils Klammern setzen, damit jeder Summand mit jedem anderen Summanden multipliziert wird. ;;<seed_fields><deployedseed>783029466</deployedseed><deployedseed>1177445020</deployedseed><deployedseed>1009895582</deployedseed><deployedseed>1167689465</deployedseed><deployedseed>1922827729</deployedseed></seed_fields>;;
+1;fra;1;de;Bruchrechnung;Einfacher Doppelbruch;"nums:rand_selection(makelist(i+1,i,8), 4); nums:sort(nums); ta1:((nums[1])/(nums[4]))/((nums[2])/(nums[3])); /*wa1 means: multiplied fractions instead of division*/ wa1:((nums[1])/(nums[4]))*((nums[2])/(nums[3])); /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:((nums[4])/(nums[1]))*((nums[2])/(nums[3]));";Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.;\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];Tipp: Achtung: Doppelbruch;\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} = {@ta1@}\);0;;<p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p>;Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.;Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.;;;<seed_fields><deployedseed>352990161</deployedseed><deployedseed>467670994</deployedseed><deployedseed>1747402747</deployedseed><deployedseed>2135608811</deployedseed><deployedseed>460810681</deployedseed></seed_fields>;;
+1;fra;1;df;Bruchrechnung;Bruch und Geteilt-Rechnung;"power:rand_with_step(2,4,1); myvars:rand_selection([a,b,c,x,y,z],2); dividend:myvars[1]/myvars[2]; num:rand_with_step(1,5,1); divisor:(num-myvars[1])/(myvars[2]^power); ta1: dividend/divisor; /*wa1 means: multiplied fractions instead of division*/ wa1:dividend*divisor; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:dividend^(-1)*divisor; /*wa3 means: didn’t consider to multiply the denominator of the first fraction with the sum of the second fraction’s numerator as a whole*/ wa3:(num(dividend)*denom(divisor))/(myvars[2]*num-myvars[1]);";Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.;\({@dividend@}:{@divisor@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];"Achtung: Auch ein Doppelbruch ;)";\({@dividend@}:{@divisor@} = {@ta1@}\);0;;<p>Tipp: \(\boldsymbol{:}\) ist dasselbe wir ein Doppelbruchstrich.</p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p>;Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.;Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.;<p>Du hast den richtigen Kehrwert gebildet um die Brüche dann zu multiplizieren, jedoch hast du dann die Klammersetzung bei der Mutliplikation nicht beachtet.</p><p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{x}{a} : \frac{1-x}{a^2} = \frac{x}{a} \cdot \frac{a^2}{1-x}\)\(= \frac{x \cdot a^2}{a \cdot \boldsymbol{(1-x)}} = \dots\)</p>;;<seed_fields><deployedseed>68495326</deployedseed><deployedseed>83279259</deployedseed><deployedseed>1848999895</deployedseed><deployedseed>1656521999</deployedseed><deployedseed>333378154</deployedseed></seed_fields>;;
+1;fra;1;dg;Bruchrechnung;Doppelbruch mit Zahlen und Variablen;"powers:rand_selection(makelist(i+1,i,3),2); nums:rand_selection(makelist(i+1,i,4),2); myvars:rand_selection([a,b,c,x,y,z],2); fractions:[nums[1]/myvars[1]^powers[1], (nums[2]*myvars[2]^powers[2])/myvars[1]]; fractions:random_permutation(fractions); ta1:fractions[1]/fractions[2]; /*wa1 means: multiplied fractions instead of division*/ wa1:fractions[1]*fractions[2]; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:fractions[1]^(-1)*fractions[2];";Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.;\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];Tipp: Achtung: Doppelbruch;\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} = {@ta1@}\);0;;<p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{2}{a^2}}{\frac{3\,b^2}{a}} = \frac{2}{a^2} \cdot \frac{a}{3\,b^2} = \frac{2\,a}{3\,a^2\,b^2}\)</p>;Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.;Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.;;;<seed_fields><deployedseed>1783639635</deployedseed><deployedseed>863915904</deployedseed><deployedseed>446314797</deployedseed><deployedseed>1562297660</deployedseed><deployedseed>1172377010</deployedseed></seed_fields>;;
+1;fra;1;dh;Bruchrechnung;Doppelbruch mit Termen;"nums:rand_selection(makelist(i+1,i,8), 3); nums:sort(nums); myvars:rand_selection([a,b,c,x,y,z],2); terms:[nums[1]*((1-myvars[1])/myvars[2]), (nums[2]/nums[3])*(myvars[2]^2/myvars[1])]; /*terms:random_permutation(terms);*/ ta1:terms[1]/terms[2]; taalt:combine(expand(ta1)); /*wa1 means: didn't consider to multiple first factor in the numerator with both summands of the fraction's numerator*/ wa1:((nums[1]*1-myvars[1])/myvars[2])/terms[2]; wa2:terms[1]*terms[2]; wa3:terms[1]^(-1)*terms[2];";Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.;\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];Tipp: Achtung: Doppelbruch;\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} = {@ta1@}\);0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;""></p><p dir=""ltr"">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";<p>Lösungsweg für eine Beispielaufgabe:</p><p>\(\large\frac{5 \cdot \frac{1-a}{b}}{\frac{1}{3} \cdot \frac{b^2}{a}}\)\(\large = \frac{\frac{5 \cdot \boldsymbol{(1-a)}}{b}}{\frac{b^2}{3\,a}} = \frac{5 - 5\,a}{b} \cdot \frac{3\,a}{b^2}\)</p><p>\(\large = \frac{3\,a \cdot \boldsymbol{(5-5\,a)}}{b \cdot b^2} = \frac{15\,a - 15\,a^2}{b^3}\)</p>;<p>Beim Multiplizieren des Faktors {@nums[1]@} und des Bruchs \(\frac{1-{@myvars[1]@}}{{@myvars[2]@}}\) im Zähler des Doppelbruchs musst du beachten, dass Summen als Ganzes multipliziert werden.</p><p>Beispiel: \(5 \cdot \frac{1-a}{b} = \frac{5 \cdot \boldsymbol{(1-a)}}{b} = \dots\)</p>;Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.;Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.;;<seed_fields><deployedseed>611281053</deployedseed><deployedseed>439766047</deployedseed><deployedseed>725695831</deployedseed><deployedseed>1029360039</deployedseed><deployedseed>1825759080</deployedseed></seed_fields>;;
+1;fra;1;ea;Bruchrechnung;Bruchrechnung Kombination I;"int:rand_with_step(2,4,1); nums_real_frac:sort(rand_selection(makelist(i,i,9),4)); nums_unreal_frac:sort(rand_selection(makelist(i+3,i,7),6)); main_summand:((nums_real_frac[1])/(nums_real_frac[4]))/((nums_real_frac[2])/(nums_real_frac[3])); summands:[int*(nums_unreal_frac[6]/nums_unreal_frac[1]), ((nums_unreal_frac[5])/(nums_unreal_frac[2]))/((nums_unreal_frac[4])/(nums_unreal_frac[3]))]; ta1:main_summand+summands[1]-summands[2]; wa1:(main_summand+int)*summands[1]/int-summands[2];";Berechne und fasse soweit wie möglich zusammen.;\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];Tipp: Achtung: Doppelbrüche und Summanden => Punkt-vor-Strich-Rechnung;\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} = {@ta1@}\);0;;<p>Tipp: Jeden Summanden einzeln betrachten und ausrechnen: Doppelbrüche auflösen und zusammenfassen.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6}-\frac{\frac{13}{4}}{\frac{6}{5}} = \frac{5}{6} \cdot \frac{3}{1}+\frac{2}{1} \cdot \frac{9}{6}-\frac{13}{5} \cdot \frac{5}{6}\)</p><p>\(= (\frac{5}{6\mkern-5mu/^2} \cdot \frac{3\mkern-5mu/^1}{1})+(\frac{2\mkern-5mu/^1}{1} \cdot \frac{9}{6\mkern-5mu/^2})-(\frac{13}{5\mkern-5mu/^1} \cdot \frac{5\mkern-5mu/^1}{6})\)</p><p>\(= \frac{5}{2} + \frac{9}{2} - \frac{13}{6} = \frac{5 \cdot 3}{2 \cdot 3} + \frac{9 \cdot 3}{2 \cdot 3} - \frac{13}{6} = \frac{15}{6} + \frac{27}{6} - \frac{13}{6}\)</p><p>\(= \frac{15+27+13}{6} = \frac{55}{6}\)<\p>;<p>Du hast offensichtlich die Punkt-vor-Strich-Regel nicht beachtet.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6} = \frac{\frac{5}{6}}{\frac{1}{3}}+(2 \cdot \frac{9}{6}) \ne (\frac{\frac{5}{6}}{\frac{1}{3}}+2) \cdot \frac{9}{6}\)</p>;;;;<seed_fields><deployedseed>2022519868</deployedseed><deployedseed>2007714528</deployedseed><deployedseed>1652468809</deployedseed><deployedseed>1890021691</deployedseed><deployedseed>1160555762</deployedseed></seed_fields>;;
+1;fra;1;eb;Bruchrechnung;Bruchrechnung Kombination II;"int:rand_with_step(3,7,1); nums:sort(rand_selection(makelist(i,i,9),6)); factors:[int, (nums[1]/nums[6]+nums[2]/nums[5]), (1-nums[3]/nums[4])]; ta1:factors[1]*factors[2]*factors[3];";Berechne und fasse soweit wie möglich zusammen.;\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];Tipp: Sorgfältig ausmultiplizieren;\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})= {@ta1@}\);0;;<p>Hier hast du zwei Möglichkeiten: Alles sauber ausmultiplizieren oder vor dem Multiplizieren die Klammern ausrechnen (Empfehlung!)</p><p>Beispiel: \(6 \cdot (\frac{3}{4}+\frac{1}{8}) \cdot (1-\frac{1}{4}) = 6 \cdot (\frac{3 \cdot 2}{4 \cdot 2}+\frac{1}{8}) \cdot (\frac{1 \cdot 4}{1 \cdot 4}-\frac{1}{4})\) </p><p>\(= 6 \cdot (\frac{6}{8}+\frac{1}{8}) \cdot (\frac{4}{4}-\frac{1}{4}) = 6 \cdot (\frac{7}{8}) \cdot (\frac{3}{4})\)</p><p>\( = \frac{6}{1} \cdot \frac{7}{8} \cdot \frac{3}{4} = \frac{6\mkern-5mu/^3 \cdot 7 \cdot 3}{1 \cdot 8\mkern-5mu/^4 \cdot 4} = \frac{63}{16}\)</p>;;;;;<seed_fields><deployedseed>382901616</deployedseed><deployedseed>1683089904</deployedseed><deployedseed>724792720</deployedseed><deployedseed>857106597</deployedseed><deployedseed>2126061360</deployedseed></seed_fields>;;
+1;fra;1;ec;Bruchrechnung;Bruchrechnung Kombination III;"int:rand_with_step(2,4,1); myvar:rand_selection([a,b,c,x,y,z],1)[1]; nums:sort(rand_selection(makelist(i,i,9),6)); summands:[(int+(nums[1]/nums[4]))*(myvar/nums[5]),1-((nums[6]-myvar)/((nums[4])/(nums[3])))]; ta1:combine(expand(summands[1]+summands[2])); wa1:(int*(nums[1]/nums[4]))*(myvar/nums[5])+summands[2];";Berechne und fasse soweit wie möglich zusammen.;\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];Tipp: Achtung: Doppelbruch und gemischter Bruch vs. unechter Bruch;\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} = {@ta1@}\);0;;"<p>Tipp: \(\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}}\) ist auch ein Doppelbruch.</p><p>Achte darauf, dann die Klammer richtig zu setzen.</p><p>Beispiel: \(\frac{2-a}{\frac{7}{8}} = \boldsymbol{(}2-a\boldsymbol{)} \cdot \frac{8}{7}\)</p><p>Beachte: 1) Ganze Zahlen zum Bruch umschreiben. 2) Doppelbrüche umschreiben (Beispiel oben). 3) Gemischte Brüche umschreiben (Beispiel \(2\frac{1}{6}\) sind \(\frac{13}{6}\;\)). 4) Punkt-vor-Strich-Regel.";<p>Du hast offenbar den gemischten Bruch \({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\) als Multiplikation \({@int@} \cdot \frac{{@nums[1]@}}{{@nums[4]@}}\) interpretiert. Allerdings meint der gemischte Bruch hier \({@int@}\) Ganze und \(\frac{{@nums[1]@}}{{@nums[4]@}}\) Anteil. Empfehlung: Gemischte Brüche als unechte Brüche umschreiben. Beispiel:\(2\frac{1}{6} = 2+\frac{1}{6} = \frac{2 \cdot 6}{1 \cdot 6} + \frac{1}{6} = \frac{12}{6}+\frac{1}{6} = \frac{13}{6}\);;;;<seed_fields><deployedseed>2024587341</deployedseed><deployedseed>1597148134</deployedseed><deployedseed>899831950</deployedseed><deployedseed>29495097</deployedseed><deployedseed>97014366</deployedseed></seed_fields>;;
+1;fra;1;fa;Bruchrechnung;Textaufgabe Minussi;"ta1:9; ta2:6; ta3:2;";"Die drei Söhne des verstorbenen Scheichs Minussi erben eine Kamelherde, die aus 17 Tieren besteht. Im Testament heißt es: ""Mein erstgeborener Sohn Ali soll die Hälfte der Tiere, Abdulla ein Drittel und Arif ein Neuntel der Kamelherde bekommen. Kein Kamel darf geschlachtet werden."" Die Söhne sind ratlos. Sie tragen ihr Problem einem Nachbarn vor, der als weiser Mann bekannt ist. Er überlegt nicht lange und gibt ihnen den folgenden Rat: ""Ich besitze selbst Kamele. Davon leihe ich euch eines. Vollzieht damit die Teilung, wie es das Testament verlangt."" Wie viele Kamele bekommt jeder der Söhne?";<p>Ali: [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p>Abdulla: [[input:ans2]][[validation:ans2]][[feedback:prt2]]</p><p>Arif: [[input:ans3]][[validation:ans3]][[feedback:prt3]]</p>;;18-1 = 9+6+2;1;"<prt_fields><prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt><prt><name>prt2</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans2</sans><tans>ta2</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt2-1-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>1</falsenextnode><falseanswernote>prt2-1-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans2</sans><tans>ta2</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt2-2-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt2-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt><prt><name>prt3</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans3</sans><tans>ta3</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt3-1-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>1</falsenextnode><falseanswernote>prt3-1-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans3</sans><tans>ta3</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt3-2-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt3-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt></prt_fields>";;;;;<input_fields><input><name>ans1</name><type>algebraic</type><tans>ta1</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint></syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords></forbidwords><allowwords></allowwords><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>0</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options></options></input><input><name>ans2</name><type>algebraic</type><tans>ta2</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint></syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords></forbidwords><allowwords></allowwords><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>0</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options></options></input><input><name>ans3</name><type>algebraic</type><tans>ta3</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint></syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords></forbidwords><allowwords></allowwords><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>0</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options></options></input></input_fields>;;;
+2;ter;2;a;Termumformungen;Klammern auflösen;"nums:rand_selection(makelist(i+1,i,40),4); myvars:rand_selection([a,b,c,x,y,z],2); main_term:(nums[3]*myvars[2]-nums[4]*myvars[1]); terms:[nums[1]*myvars[1], nums[2]]; terms:random_permutation(terms); ta1:terms[1]+terms[2]+main_term;";Berechne und fasse soweit wie möglich zusammen.;\({@terms[1]@}+{@terms[2]@}+({@main_term@}) =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];;\({@terms[1]@}+{@terms[2]@}+({@main_term@}) = {@ta1@}\);1;;;;;;;<seed_fields><deployedseed>98123780</deployedseed><deployedseed>2097055857</deployedseed><deployedseed>1849331272</deployedseed><deployedseed>548041107</deployedseed><deployedseed>1447017568</deployedseed><deployedseed>779140534</deployedseed></seed_fields>;;
+2;ter;2;b;Termumformungen;Minusklammer auflösen;"nums:rand_selection(makelist(i+1,i,40),3); myvars:rand_selection([a,b,c,x,y,z],1); terms::[nums[1]*myvars[1], (nums[2]*myvars[1]+nums[3])]; ta1:terms[1]-terms[2];";Berechne und fasse soweit wie möglich zusammen.;\({@terms[1]@}-({@terms[2]@}) =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];;\({@terms[1]@}-({@terms[2]@}) = {@ta1@}\);1;;;;;;;<seed_fields><deployedseed>1245029422</deployedseed><deployedseed>281996518</deployedseed><deployedseed>1135651070</deployedseed><deployedseed>1589986238</deployedseed><deployedseed>148824344</deployedseed></seed_fields>;;
+2;ter;2;c;Termumformungen;Minusklammer mit Zahl auflösen;"nums:rand_selection(makelist(i+1,i,40),3); factor:rand_with_step(2,4,1); myvars:rand_selection([a,b,c,x,y,z],1); terms:[nums[1]*myvars[1], factor*(nums[2]-nums[3]*myvars[1])]; ta1:expand(terms[1]-terms[2]);";Berechne und fasse soweit wie möglich zusammen.;\({@terms[1]@}-{@terms[2]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];;\({@terms[1]@}-{@terms[2]@} = {@ta1@}\);1;;;;;;;<seed_fields><deployedseed>1881228523</deployedseed><deployedseed>339721357</deployedseed><deployedseed>212322978</deployedseed><deployedseed>1447139271</deployedseed><deployedseed>674745126</deployedseed></seed_fields>;;
+2;ter;2;d;Termumformungen;Klammer in Klammer auflösen;"nums:rand_selection(makelist(i+1,i,10),2); myvars:rand_selection([a,b,c,x,y,z],5); exercise:myvars[1]-(nums[1]*myvars[2]-nums[2]*(myvars[3]+myvars[4]-myvars[5])); ta1:expand(exercise);";Berechne und fasse soweit wie möglich zusammen.;\({@myvars[1]@}-({@nums[1]@}\cdot{@myvars[2]@}-{@nums[2]@}\cdot({@myvars[3]@}+{@myvars[4]@}-{@myvars[5]@})) =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];;\({@myvars[1]@}-({@nums[1]@}\cdot{@myvars[2]@}-{@nums[2]@}\cdot({@myvars[3]@}+{@myvars[4]@}-{@myvars[5]@})) = {@ta1@}\);1;;;;;;;<seed_fields><deployedseed>229444725</deployedseed><deployedseed>1633729054</deployedseed><deployedseed>354272089</deployedseed><deployedseed>1060620449</deployedseed><deployedseed>105804302</deployedseed><deployedseed>539622500</deployedseed></seed_fields>;;
+2;ter;2;e;Termumformungen;Addition und Multiplikation von Klammern;"nums:rand_selection(makelist(i+1,i,40),7); myvars:rand_selection([a,b,c,x,y,z],2); exercise:nums[1]*myvars[1]-(nums[2]*myvars[2]-nums[3]*myvars[1])+(nums[4]-nums[5]*myvars[1])*(nums[6]*myvars[1]+nums[7]*myvars[2]); ta1:expand(exercise);";Berechne und fasse soweit wie möglich zusammen.;\({@nums[1]@}\cdot{@myvars[1]@}-({@nums[2]@}\cdot{@myvars[2]@}-{@nums[3]@}\cdot{@myvars[1]@})+({@nums[4]@}-{@nums[5]@}\cdot{@myvars[1]@})\cdot({@nums[6]@}\cdot{@myvars[1]@}+{@nums[7]@}\cdot{@myvars[2]@}) =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];;\({@nums[1]@}\cdot{@myvars[1]@}-({@nums[2]@}\cdot{@myvars[2]@}-{@nums[3]@}\cdot{@myvars[1]@})+({@nums[4]@}-{@nums[5]@}\cdot{@myvars[1]@})\cdot({@nums[6]@}\cdot{@myvars[1]@}+{@nums[7]@}\cdot{@myvars[2]@}) = {@ta1@}\);1;;;;;;;<seed_fields><deployedseed>1031059893</deployedseed><deployedseed>129199253</deployedseed><deployedseed>2087016460</deployedseed><deployedseed>1339318725</deployedseed><deployedseed>1002421408</deployedseed><deployedseed>452770538</deployedseed></seed_fields>;;
+2;ter;2;f;Termumformungen;(Minus-)Klammern in (Minus-)Klammern;"nums:rand_selection(makelist(i+1,i,10),6); myvars:rand_selection([a,b,c,x,y,z],3); exercise:nums[1]*myvars[1]-nums[2]*myvars[2]-(nums[3]*myvars[3]-(nums[4]*myvars[3]+(nums[5]*myvars[3]-nums[6]*myvars[1]))); ta1:expand(exercise);";Berechne und fasse soweit wie möglich zusammen.;\({@nums[1]@}\cdot{@myvars[1]@}-{@nums[2]@}\cdot{@myvars[2]@}-({@nums[3]@}\cdot{@myvars[3]@}-({@nums[4]@}\cdot{@myvars[3]@}+({@nums[5]@}\cdot{@myvars[3]@}-{@nums[6]@}\cdot{@myvars[1]@}))) =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];;\({@nums[1]@}\cdot{@myvars[1]@}-{@nums[2]@}\cdot{@myvars[2]@}-({@nums[3]@}\cdot{@myvars[3]@}-({@nums[4]@}\cdot{@myvars[3]@}+({@nums[5]@}\cdot{@myvars[3]@}-{@nums[6]@}\cdot{@myvars[1]@}))) = {@ta1@}\);1;;;;;;;<seed_fields><deployedseed>444907455</deployedseed><deployedseed>1815012079</deployedseed><deployedseed>199161685</deployedseed><deployedseed>79630960</deployedseed><deployedseed>385302520</deployedseed><deployedseed>599350252</deployedseed></seed_fields>;;
+2;ter;2;g;Termumformungen;Doppel(minus-)klammern;"nums:rand_selection(makelist(i+1,i,40),6); myvars:rand_selection([a,b,c,x,y,z],3); exercise:(nums[1]*myvars[1]-(nums[2]*myvars[2]-nums[3]*myvars[3]))-((nums[4]*myvars[2]+nums[5]*myvars[3])-nums[6]*myvars[1]); ta1:expand(exercise);";Berechne und fasse soweit wie möglich zusammen.;\(({@nums[1]@}\cdot{@myvars[1]@}-({@nums[2]@}\cdot{@myvars[2]@}-{@nums[3]@}\cdot{@myvars[3]@}))-(({@nums[4]@}\cdot{@myvars[2]@}+{@nums[5]@}\cdot{@myvars[3]@})-{@nums[6]@}\cdot{@myvars[1]@}) =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];;\(({@nums[1]@}\cdot{@myvars[1]@}-({@nums[2]@}\cdot{@myvars[2]@}-{@nums[3]@}\cdot{@myvars[3]@}))-(({@nums[4]@}\cdot{@myvars[2]@}+{@nums[5]@}\cdot{@myvars[3]@})-{@nums[6]@}\cdot{@myvars[1]@}) = {@ta1@}\);1;;;;;;;<seed_fields><deployedseed>592919465</deployedseed><deployedseed>248931898</deployedseed><deployedseed>607632140</deployedseed><deployedseed>1514629483</deployedseed><deployedseed>1327743583</deployedseed><deployedseed>243351828</deployedseed></seed_fields>;;
+2;ter;2;h;Termumformungen;Kombinationen mit Minusklammern;"myvars:rand_selection([a,b,c,x,y,z],3); terms:[myvars[2]+myvars[3], myvars[1]-myvars[3], myvars[2]-myvars[3], myvars[1]+myvars[2]]; terms:random_permutation(terms); exercise:-(myvars[1]-(terms[1]))-((terms[2])+(terms[3])-(terms[4])); ta1:expand(exercise);";Berechne und fasse soweit wie möglich zusammen.;\(-({@myvars[1]@}-({@terms[1]@}))-(({@terms[2]@})+({@terms[3]@})-({@terms[4]@})) =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];;\(-({@myvars[1]@}-({@terms[1]@}))-(({@terms[2]@})+({@terms[3]@})-({@terms[4]@})) = {@ta1@}\);1;;;;;;;<seed_fields><deployedseed>1417988214</deployedseed><deployedseed>1168898649</deployedseed><deployedseed>1282250123</deployedseed><deployedseed>830978426</deployedseed><deployedseed>2049694143</deployedseed><deployedseed>685589828</deployedseed></seed_fields>;;
+2;ter;2;i;Termumformungen;Klammern auflösen mit Potenzen II;"nums:rand_selection(makelist(i+1,i,5),4); myvars:rand_selection([a,b,c,x,y,z],2); exercise:(nums[1]*myvars[1]^2-myvars[2]+nums[2])*nums[3]-(myvars[1]*myvars[2]+nums[4]); ta1:expand(exercise);";Berechne und fasse soweit wie möglich zusammen.;\(({@nums[1]@}\cdot{@myvars[1]@}^2-{@myvars[2]@}+{@nums[2]@})\cdot{@nums[3]@}-({@myvars[1]@}\cdot{@myvars[2]@}+{@nums[4]@}) =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];;\(({@nums[1]@}\cdot{@myvars[1]@}^2-{@myvars[2]@}+{@nums[2]@})\cdot{@nums[3]@}-({@myvars[1]@}\cdot{@myvars[2]@}+{@nums[4]@}) = {@ta1@}\);1;;;;;;;<seed_fields><deployedseed>830630785</deployedseed><deployedseed>1777159907</deployedseed><deployedseed>668589773</deployedseed><deployedseed>2134597486</deployedseed><deployedseed>1465804945</deployedseed></seed_fields>;;
+2;ter;2;j;Termumformungen;Klammern auflösen mit Potenzen II;"nums:rand_selection(makelist(i+1,i,5),5); myvars:rand_selection([a,b,c,x,y,z],2); exercise:-(myvars[1]^2*myvars[2]+nums[1]*myvars[2]*myvars[1]^2)-(nums[2]*myvars[2]+nums[3]*myvars[1])*(nums[4]*myvars[1]*myvars[2]^2+nums[5]*myvars[2]); ta1:expand(exercise);";Berechne und fasse soweit wie möglich zusammen.;\(-({@myvars[1]@}^2\cdot{@myvars[2]@}+{@nums[1]@}\cdot{@myvars[2]@}\cdot{@myvars[1]@}^2)-({@nums[2]@}\cdot{@myvars[2]@}+{@nums[3]@}\cdot{@myvars[1]@})\cdot({@nums[4]@}\cdot{@myvars[1]@}\cdot{@myvars[2]@}^2+{@nums[5]@}\cdot{@myvars[2]@}) =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];;\(-({@myvars[1]@}^2\cdot{@myvars[2]@}+{@nums[1]@}\cdot{@myvars[2]@}\cdot{@myvars[1]@}^2)-({@nums[2]@}\cdot{@myvars[2]@}+{@nums[3]@}\cdot{@myvars[1]@})\cdot({@nums[4]@}\cdot{@myvars[1]@}\cdot{@myvars[2]@}^2+{@nums[5]@}\cdot{@myvars[2]@}) = {@ta1@}\);1;;;;;;;<seed_fields><deployedseed>1656097513</deployedseed><deployedseed>2111060878</deployedseed><deployedseed>2120070394</deployedseed><deployedseed>1964891640</deployedseed><deployedseed>20522672</deployedseed></seed_fields>;;
+2;ter;2;k;Termumformungen;Klammern auflösen mit Potenzen III;"nums:rand_selection(makelist(i+1,i,6),6); myvars:rand_selection([a,b,c,x,y,z],1); exercise:nums[1]*myvars[1]^2+(nums[2]+nums[3]*myvars[1])-(-nums[4]*myvars[1]^2+nums[5]-nums[6]*myvars[1]); ta1:expand(exercise);";Berechne und fasse soweit wie möglich zusammen.;\({@nums[1]@}\cdot{@myvars[1]@}^2+({@nums[2]@}+{@nums[3]@}\cdot{@myvars[1]@})-(-{@nums[4]@}\cdot{@myvars[1]@}^2+{@nums[5]@}-{@nums[6]@}\cdot{@myvars[1]@}) =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];;\({@nums[1]@}\cdot{@myvars[1]@}^2+({@nums[2]@}+{@nums[3]@}\cdot{@myvars[1]@})-(-{@nums[4]@}\cdot{@myvars[1]@}^2+{@nums[5]@}-{@nums[6]@}\cdot{@myvars[1]@}) = {@ta1@}\);1;;;;;;;<seed_fields><deployedseed>1451685547</deployedseed><deployedseed>301933220</deployedseed><deployedseed>1285342340</deployedseed><deployedseed>1483690535</deployedseed><deployedseed>2056687528</deployedseed></seed_fields>;;
+2;ter;2;l;Termumformungen;Klammern auflösen mit Potenzen IV;"nums:rand_selection(makelist(i+1,i,6),6); myvars:rand_selection([a,b,c,x,y,z],2); exercise:-(nums[1]*myvars[1]*myvars[2]+nums[2]*myvars[1]^2*myvars[2]^2)-nums[3]*(nums[4]*myvars[2]*myvars[1]-(nums[5]*myvars[1]^2+nums[6]*myvars[2])); ta1:expand(exercise);";Berechne und fasse soweit wie möglich zusammen.;\(-({@nums[1]@}\cdot{@myvars[1]@}\cdot{@myvars[2]@}+{@nums[2]@}\cdot{@myvars[1]@}^2\cdot{@myvars[2]@}^2)-{@nums[3]@}\cdot({@nums[4]@}\cdot{@myvars[2]@}\cdot{@myvars[1]@}-({@nums[5]@}\cdot{@myvars[1]@}^2+{@nums[6]@}\cdot{@myvars[2]@})) =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];;\(-({@nums[1]@}\cdot{@myvars[1]@}\cdot{@myvars[2]@}+{@nums[2]@}\cdot{@myvars[1]@}^2\cdot{@myvars[2]@}^2)-{@nums[3]@}\cdot({@nums[4]@}\cdot{@myvars[2]@}\cdot{@myvars[1]@}-({@nums[5]@}\cdot{@myvars[1]@}^2+{@nums[6]@}\cdot{@myvars[2]@})) = {@ta1@}\);1;;;;;;;<seed_fields><deployedseed>1751070217</deployedseed><deployedseed>242675702</deployedseed><deployedseed>37263267</deployedseed><deployedseed>1925740365</deployedseed><deployedseed>47116969</deployedseed></seed_fields>;;
+2;ter;2;m;Termumformungen;Klammern auflösen mit Potenzen V;"nums:rand_selection(makelist(i+1,i,5),4); myvars:rand_selection([a,b,c,x,y,z],2); exercise:nums[1]*myvars[1]^2*myvars[2]-((nums[2]*myvars[1]*myvars[2]+nums[3]*myvars[1]*myvars[2]^2)-nums[4]*myvars[1]*myvars[2]); ta1:expand(exercise);";Berechne und fasse soweit wie möglich zusammen.;\({@nums[1]@}\cdot{@myvars[1]@}^2\cdot{@myvars[2]@}-(({@nums[2]@}\cdot{@myvars[1]@}\cdot{@myvars[2]@}+{@nums[3]@}\cdot{@myvars[1]@}\cdot{@myvars[2]@}^2)-{@nums[4]@}\cdot{@myvars[1]@}\cdot{@myvars[2]@}) =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];;\({@nums[1]@}\cdot{@myvars[1]@}^2\cdot{@myvars[2]@}-(({@nums[2]@}\cdot{@myvars[1]@}\cdot{@myvars[2]@}+{@nums[3]@}\cdot{@myvars[1]@}\cdot{@myvars[2]@}^2)-{@nums[4]@}\cdot{@myvars[1]@}\cdot{@myvars[2]@}) = {@ta1@}\);1;;;;;;;<seed_fields><deployedseed>1719644762</deployedseed><deployedseed>972584707</deployedseed><deployedseed>379455589</deployedseed><deployedseed>1397741703</deployedseed><deployedseed>1109275415</deployedseed><deployedseed>45305082</deployedseed></seed_fields>;;
+2;ter;2;n;Termumformungen;Klammern auflösen mit Potenzen VI;"nums:rand_selection(makelist(i+1,i,5),3); myvars:rand_selection([a,b,c,x,y,z],2); exercise:(-nums[1]*myvars[1]-nums[2]*myvars[2])-((myvars[1]^2*myvars[2]+nums[3]*myvars[1]*myvars[2]^2)-(myvars[2]^2+myvars[1]^2)); ta1:expand(exercise);";Berechne und fasse soweit wie möglich zusammen.;\((-{@nums[1]@}\cdot{@myvars[1]@}-{@nums[2]@}\cdot{@myvars[2]@})-(({@myvars[1]@}^2\cdot{@myvars[2]@}+{@nums[3]@}\cdot{@myvars[1]@}\cdot{@myvars[2]@}^2)-({@myvars[2]@}^2+{@myvars[1]@}^2)) =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]];;\((-{@nums[1]@}\cdot{@myvars[1]@}-{@nums[2]@}\cdot{@myvars[2]@})-(({@myvars[1]@}^2\cdot{@myvars[2]@}+{@nums[3]@}\cdot{@myvars[1]@}\cdot{@myvars[2]@}^2)-({@myvars[2]@}^2+{@myvars[1]@}^2)) = {@ta1@}\);1;;;;;;;<seed_fields><deployedseed>1077680438</deployedseed><deployedseed>831477889</deployedseed><deployedseed>204570994</deployedseed><deployedseed>541084006</deployedseed><deployedseed>1670415546</deployedseed><deployedseed>506584933</deployedseed></seed_fields>;;
+3;frabin;1;j;Binom. Formeln;Binomische Formeln I - Anwendungsaufgabe;"aa:4;
+bb:5;
+c:3;
+d:2;
+
+u:(c*a-d*b)^2;
+ualt:(d*b-c*a)^2;
+v:(aa*a+d*b)^2;
+w:(bb*a-c*b)*(bb*a+c*b);
+
+x:(aa*a-d*b)^2;
+xalt:(d*b-aa*a)^2;
+y:(bb*a+c*b)^2;
+z:(c*a+d*b)*(c*a-d*b);
+
+/*BIN_A:[
+[a1,(2*a+5*b)^2,""\\(\\frac{4\\,a^2+20\\,a\\,b+25\\,b^2}{16\\,a^2-9\\,b^2}\\cdot(4\\,a-3\\,b)\\cdot(4\\,a+3\\,b)\\)""]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];*/
+
+BIN_A:[
+[a1,u,v,ualt],
+[a2,v,w,v],
+[a3,w,u,w],
+[a4,x,y,xalt],
+[a5,y,z,y],
+[a6,z,y,z]
+];
+BIN_a:rand(BIN_A);
+
+ta:BIN_a[2];
+taalt:BIN_a[4];
+
+";"
+
+
+<p></p>
+<div>
+ <div>Vereinfachen und faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.</div>
+</div>
+<p></p>
+<p>\(\frac{{@expand(BIN_a[2])@}}{{@expand(BIN_a[3])@}} \cdot {@BIN_a[3]@}\)\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p><br></p>
+<p><br></p>";;Um diese Aufgabe zu lösen, musst du mehrere binomische Formeln anwenden.<br>;{@BIN_a[1]@};0;"<prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;""></p><p dir=""ltr"">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ ";;;;;"<input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ ";<seed_fields><deployedseed>534740616</deployedseed> <deployedseed>47766652</deployedseed> <deployedseed>1657775726</deployedseed> <deployedseed>931829986</deployedseed> <deployedseed>1703936373</deployedseed> <deployedseed>151644710</deployedseed> </seed_fields>;;
+3;frabin;1;g;Binom. Formeln;Binomische Formeln Ia - Erste binomische Formel;"BIN_A:[
+[a1,(4+b)^2],
+[a2,(5+b)^2],
+[a3,(3+b)^2],
+[a4,(2+b)^2],
+[a5,(3+2*b)^2],
+[a6,(4+2*b)^2]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];
+task:expand(BIN_a[2]);";"
+
+
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p>";;"Um den Bruch aus der Endgegner-Aufgabe zu vereinfachen, musst du binomische Formeln anwenden. Deshalb kommen wir nun zu den binomischen Formeln. Die erste binomische Formel besagt: \((a + b)^2 = a^2 + 2\,a\,b + b^2\;\).";{@BIN_a[1]@};0;"<prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;"">Du hast die erste binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ ";;;;;"<input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ ";<seed_fields><deployedseed>1994312303</deployedseed> <deployedseed>1744518788</deployedseed> <deployedseed>1627526666</deployedseed> <deployedseed>1566276649</deployedseed> <deployedseed>1138479794</deployedseed> <deployedseed>806677520</deployedseed> </seed_fields>;;
+3;frabin;1;h;Binom. Formeln;Binomische Formeln Ib - Zweite binomische Formel;"a:4;
+b:5;
+c:3;
+d:2;
+
+e:1;
+f:2;
+
+BIN_A:[
+[a1,a,e],
+[a2,b,e],
+[a3,c,e],
+[a4,d,e],
+[a5,a,f],
+[a6,c,f]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]-BIN_a[3]*y)^2;
+taalt:(BIN_a[3]*y-BIN_a[2])^2;
+task:expand(ta);";"
+
+
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p>";;"Die zweite binomische Formel besagt:\((a - b)^2 = a^2 - 2\,a\,b + b^2\;\).<!--Diesmal musst du den Term erst umformen, damit er in der richtigen Form erscheint.--><br>";{@BIN_a[1]@};0;"<prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;"">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;"">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ ";;;;;"<input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ ";<seed_fields><deployedseed>893674818</deployedseed> <deployedseed>675538571</deployedseed> <deployedseed>985713485</deployedseed> <deployedseed>1039647874</deployedseed> <deployedseed>1781202861</deployedseed> <deployedseed>824682247</deployedseed> </seed_fields>;;
+3;frabin;1;i;Binom. Formeln;Binomische Formeln Ic - Dritte binomische Formel;"aa:4;
+bb:5;
+c:3;
+d:2;
+
+
+BIN_A:[
+[a1,aa,bb],
+[a2,c,d],
+[a3,d,aa],
+[a4,d,bb],
+[a5,d,c],
+[a6,aa,c]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]*x-BIN_a[3]*y)*(BIN_a[2]*x+BIN_a[3]*y);
+task:expand(ta);
+wa:(BIN_a[2]^2*x-BIN_a[3]^2*y)*(BIN_a[2]^2*x+BIN_a[3]^2*y);";"
+
+
+<p></p>
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p>";;"Die dritte binomische Formel besagt: \((a + b)\,(a - b) = a^2 - b^2\;\).<br>";{@BIN_a[1]@};0;"<prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;"">Du hast die dritte binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du hast zwar die Unbekannten x und y korrekt faktorisiert, aber die sie begleitenden Faktoren unverändert in die Klammern geschrieben. Um diese korrekt zu faktorisieren, musst du ihre Wurzeln berechnen. Richtig wäre {@ta@}.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ ";;;;;"<input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ ";<seed_fields><deployedseed>455750255</deployedseed> <deployedseed>970764179</deployedseed> <deployedseed>1971560923</deployedseed> <deployedseed>987956614</deployedseed> <deployedseed>533447380</deployedseed> <deployedseed>299284489</deployedseed> </seed_fields>;;
+3;frabin;1;a;Brüche & binom. Formeln;Bruchrechenregeln Ia - Brüche kürzen;"FRA_A:[
+[a1,1/4,""\\(\\frac{4}{16}\\)""],
+[a2,1/4,""\\(\\frac{20}{80}\\)""],
+[a3,2/5,""\\(\\frac{4}{10}\\)""],
+[a4,3/8,""\\(\\frac{6}{16}\\)""],
+[a5,2/3,""\\(\\frac{12}{18}\\)""],
+[a6,1/3,""\\(\\frac{7}{21}\\)""]
+];
+FRA_a:rand(FRA_A);
+ta:FRA_a[2];";"
+
+
+<p></p>
+<div>
+ <div>Kürzen Sie folgenden Bruch so weit wie möglich.<br></div>
+</div>
+<p></p>
+<p>{@FRA_a[3]@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p>";;Um Brüche zu vereinfachen, kannst du Zähler (oben) und Nenner (unten) durch die gleiche Zahl dividieren.<br>;{@FRA_a[1]@};1;"<prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ ";;;;;"<input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ ";<seed_fields><deployedseed>720161921</deployedseed> <deployedseed>1139524153</deployedseed> <deployedseed>1554597896</deployedseed> <deployedseed>881244059</deployedseed> <deployedseed>1636805254</deployedseed></seed_fields>;;
+3;frabin;1;b;Brüche & binom. Formeln;Bruchrechenregeln Ib - Brüche erweitern und addieren;"simp:true;
+b:rand([3,5,7,9]);
+a:b-rand(b-2)-1;
+d:b+1+2*rand(3);
+c:d+rand(3)+1;
+ta:(a/b)+(c/d);
+lcm:lcm(b,d);
+simp:false;
+
+/*inspired by [{""DOMAINUID"":""03BF991""}]*/";"
+
+
+<p>Berechnen Sie und kürzen Sie die Antwort soweit wie möglich:</p>
+<p>\(\displaystyle\frac{{@a@}}{{@b@}}+\displaystyle\frac{{@c@}}{{@d@}}\,=\,\) [[input:ans]] [[validation:ans]] [[feedback:prt1]]</p>";;Um Brüche zu addieren, musst du sie zunächst auf den gleichen Nenner bringen, indem du sie erweiterst. Erweitern heißt: Zähler und Nenner mit der gleichen Zahl multiplizieren.<br>;\[{@a/b@}+{@c/d@} = {@ta@}\];1;"<prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>0</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty>0</truepenalty>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>1-0-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty>0</falsepenalty>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>1-0-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans</sans>
+ <tans>(a+c)/(b+d)</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty>0</truepenalty>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>1-1-T (naive adding of fractions)</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p>Achte darauf, dass bei der Addition von Brüchen zuerst die Brüche so erweitert werden müssen, dass die beiden Brüche den gleichen Nenner haben.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty>0</falsepenalty>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>1-1-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text><![CDATA[<p>Um Brüche zu addieren oder zu subtrahieren, müssen diese zunächst auf einen gemeinsamen Hauptnenner gebracht werden.</p>
+<p>Zuerst muss man das kleinste gemeinsame Vielfache von den Nennern suchen. Dann erweitert man die Brüche auf den gemeinsamen Nenner. Danach kann man die Zähler der beiden Brüche addieren.</p>]]></text>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty>0</truepenalty>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>1-2-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p>Du musst die Brüche noch weiter zusammenfassen und kürzen.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty>0</falsepenalty>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>1-2-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ ";;;;;"<input>
+ <name>ans</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>40</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ ";<seed_fields><deployedseed>1415883509</deployedseed> <deployedseed>792880578</deployedseed> <deployedseed>100612339</deployedseed> <deployedseed>1175078867</deployedseed> </seed_fields>;;
+3;frabin;1;c;Brüche & binom. Formeln;Bruchrechenregeln Ic - Brüche multiplizieren;"FRA_A:[
+[a1,3/8*4/5*8/12,""\\(\\frac{3}{8} \\cdot \\frac{4}{5} \\cdot \\frac{8}{12}\\)""],
+[a2,5/6*2/3*9/12,""\\(\\frac{5}{6} \\cdot \\frac{2}{3} \\cdot \\frac{9}{12}\\)""],
+[a3,1/4*3/5*5/12,""\\(\\frac{1}{4} \\cdot \\frac{3}{5} \\cdot \\frac{5}{12}\\)""],
+[a4,10/11*22/5*1/5,""\\(\\frac{10}{11} \\cdot \\frac{22}{5} \\cdot \\frac{1}{5}\\)""],
+[a5,6/7*14/5*2/3,""\\(\\frac{6}{7} \\cdot \\frac{14}{5} \\cdot \\frac{2}{3}\\)""],
+[a6,3/7*4/8*8/12,""\\(\\frac{3}{7} \\cdot \\frac{4}{8} \\cdot \\frac{8}{12}\\)""]
+];
+FRA_a:rand(FRA_A);
+ta:FRA_a[2];";"
+
+
+<p></p>
+<div>
+ <div>Berechnen und vereinfachen Sie den folgenden Bruch so weit wie möglich.<br></div>
+</div>
+<p></p>
+<p>{@FRA_a[3]@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p>";;"Bei der Multiplikation von Brüchengilt: Nenner Mal Nenner und Zähler Mal Zähler.
+ Dabei kannst du schon vor der Multiplikation Zahlen, die sowohl im
+ Zähler als auch im Nenner erscheinen (und umgekehrt) gegeneinander
+ wegkürzen.<br>";{@FRA_a[1]@};1;"<prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ ";;;;;"<input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ ";<seed_fields><deployedseed>1013621353</deployedseed> <deployedseed>1466832460</deployedseed> <deployedseed>1838669736</deployedseed> <deployedseed>415342648</deployedseed> <deployedseed>2094810781</deployedseed> <deployedseed>637567417</deployedseed> </seed_fields>;;
+3;frabin;1;d;Brüche & binom. Formeln;Bruchrechenregeln Id - Brüche dividieren;"a:ev(rand(7)+1,simp);
+b:ev(a+rand(5)+1,simp);
+c:ev(rand(7)+1,simp);
+d:ev(c+rand(5)+1,simp);
+ta:ev((a/b)/(c/d),simp);
+fa:ev((a/b)*(c/d),simp);
+
+/*inspired by [{""DOMAINUID"":""665C3F9""}]*/";"
+
+
+<p>Berechnen Sie und kürzen Sie die Antwort soweit wie möglich:</p>
+<p>\(\large{@ev(a/b,simp)@}\div{@ev(c/d,simp)@}\,=\,\) [[input:ans]] [[validation:ans]] [[feedback:prt1]]</p>";;Um Brüche zu dividieren kannst du Zähler und Nenner des Divisors (rechter Teil der Divsion) tauschen und stattdessen multiplizieren.<br>;\[{@ev(a/b,simp)@}\div{@ev(c/d,simp)@} = {@ta@}\];1;"<prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>0</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty>0</truepenalty>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>1-0-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty>0</falsepenalty>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>1-0-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans</sans>
+ <tans>fa</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty>0</truepenalty>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>1-1-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p>Du hast die Brüche multipliziert statt dividiert.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty>0</falsepenalty>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>1-1-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty>0</truepenalty>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>1-2-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p>Du kannst die Antwort noch weiter kürzen.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty>0</falsepenalty>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>1-2-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text><![CDATA[<p>Um zwei Brüche zu dividieren muss man den ersten Bruch mit dem Kehrbruch des zweiten multiplizieren. \[\displaystyle\frac{a}{b} \div \displaystyle\frac{c}{d}=\displaystyle\frac{a}{b} \cdot \displaystyle\frac{d}{c}\]</p>]]></text>
+ </falsefeedback>
+ </node>
+ </prt>
+ ";;;;;"<input>
+ <name>ans</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>40</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ ";<seed_fields><deployedseed>1151437541</deployedseed> <deployedseed>1537112035</deployedseed> <deployedseed>1191227729</deployedseed> <deployedseed>1808373935</deployedseed> </seed_fields>;;
+3;frabin;1;e;Brüche & binom. Formeln;Bruchrechenregeln Ie - Doppelbrüche;"a:ev(rand(7)+1,simp);
+b:ev(a+rand(5)+1,simp);
+c:ev(rand(7)+1,simp);
+d:ev(c+rand(5)+1,simp);
+ta:ev((a/b)/(c/d),simp);
+fa:ev((a/b)*(c/d),simp);
+
+/*inspired by [{""DOMAINUID"":""665C3F9""}]*/";"
+
+
+<p>Berechnen Sie und kürzen Sie die Antwort soweit wie möglich:</p>
+<p>\(\large{\frac{{@ev(a/b,simp)@}}{{@ev(c/d,simp)@}}}\,=\,\) [[input:ans]] [[validation:ans]] [[feedback:prt1]]</p>";;Der Bruchstrich markiert letztendlich eine Division. Deshalb gilt für Doppelbrüche das Gleiche wie für die Divison von Brüchen: Zähler und Nenner des Divisors tauschen und multiplizieren.<br>;\[{@ev(a/b,simp)@}\div{@ev(c/d,simp)@} = {@ta@}\];1;"<prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>0</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty>0</truepenalty>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>1-0-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty>0</falsepenalty>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>1-0-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans</sans>
+ <tans>fa</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty>0</truepenalty>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>1-1-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p>Sie haben die Brüche multipliziert statt dividiert.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty>0</falsepenalty>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>1-1-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty>0</truepenalty>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>1-2-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p>Sie können die Antwort noch weiter kürzen.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty>0</falsepenalty>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>1-2-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text><![CDATA[<p>Um zwei Brüche zu dividieren muss man den ersten Bruch mit dem Kehrbruch des zweiten multiplizieren. \[\displaystyle\frac{a}{b} \div \displaystyle\frac{c}{d}=\displaystyle\frac{a}{b} \cdot \displaystyle\frac{d}{c}\]</p>]]></text>
+ </falsefeedback>
+ </node>
+ </prt>
+ ";;;;;"<input>
+ <name>ans</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>40</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ ";<seed_fields><deployedseed>2061062839</deployedseed> <deployedseed>1434533090</deployedseed> <deployedseed>1381553652</deployedseed> <deployedseed>654582760</deployedseed> <deployedseed>272702008</deployedseed> </seed_fields>;;
+3;frabin;1;f;Brüche & binom. Formeln;Bruchrechenregeln If - Brüche Zwischenfazit;"a:-1/6;
+b:-7/4;
+c:3/4;
+d:2/3;
+e:1/5;
+f:-3/2;
+k:6/8;
+g:5/4;
+l:7/10;
+h:2/3;
+m:6/8;
+i:3/12;
+n:4/5;
+j:3/4;
+o:2/3;
+
+FRA_A:[
+[a1,a,b,c,d,""\\(-\\frac{1}{6}-\\frac{7}{4}+\\frac{3}{4} \\cdot \\frac{2}{3}\\)""],
+[a2,e,a,f,k,""\\(\\frac{1}{5}-\\frac{1}{6}-\\frac{3}{2} \\cdot \\frac{6}{8}\\)""],
+[a3,a,c,g,l,""\\(-\\frac{1}{6}+\\frac{3}{4}+\\frac{5}{4} \\cdot \\frac{7}{10}\\)""],
+[a4,b,d,h,m,""\\(-\\frac{7}{4}+\\frac{2}{3}+\\frac{2}{3} \\cdot \\frac{6}{8}\\)""],
+[a5,c,b,i,n,""\\(\\frac{3}{4}-\\frac{7}{4}+\\frac{3}{12} \\cdot \\frac{4}{5}\\)""],
+[a6,a,d,j,o,""\\(-\\frac{1}{6}+\\frac{2}{3}+\\frac{3}{4} \\cdot \\frac{2}{3}\\)""]
+];
+FRA_a:rand(FRA_A);
+ta:FRA_a[2]+FRA_a[3]+FRA_a[4]*FRA_a[5];
+wa1:(FRA_a[2]+FRA_a[3]+FRA_a[4])*FRA_a[5];
+";"
+
+
+<p></p>
+<p></p>
+<p>Vereinfachen Sie folgenden Bruch so weit wie möglich.<br></p>
+<p>{@FRA_a[6]@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p>
+<div class=""bubble in-modal no-arrow"">
+ <div>
+ <div>
+ <ul>
+ </ul>Hier zur Erinnerung die wichtigsten Bruchrechenregeln:<br>
+ <div>
+ </div>
+ <ul>
+ <li>
+ <div>
+ <div>Erweitern: \(\frac a c \cdot 1 = \frac a c \cdot \frac d d = \frac{a\,d}{c\,d}\)<span class="""" style=""font-size: small;""><br></span><div style=""text-align: center;""><span class="""" style=""font-size: x-small;"">Beispiel: </span><span class="""" style=""font-size: x-small;"">\(\frac 3 4 = \frac 6 8\)</span></div></div>
+ </div>
+ </li>
+ <li>
+ <div>
+ <div>Addition: \(\frac a c + \frac b d = \frac{a\,d + b\,c}{c\,d}\)<br><div style=""text-align: center;""><span class="""" style=""font-size: x-small;"">Beispiel: </span><span class="""" style=""font-size: x-small;"">\(\frac 1 2 + \frac 1 4 = \frac 2 4 + \frac 1 4 = \frac 3 4\)</span></div></div>
+ </div>
+ </li>
+ <li>
+ <div>
+ <div>Kürzen: \(\frac{a\,d}{b\,d} = \frac a b \cdot \frac d d = \frac a b \cdot 1\)<span class="""" style=""font-size: small;""><br></span><div style=""text-align: center;""><span class="""" style=""font-size: x-small;"">Beispiel: </span><span class="""" style=""font-size: x-small;"">\(\frac{10}{15} = \frac{2\cdot5}{3\cdot5} = \frac 2 3\)</span></div></div>
+ </div>
+ </li>
+ <li>Aber keine Summanden kürzen: \(\frac{a}{b + c}\)<span class="""" style=""font-size: small;""><br></span><div style=""text-align: center;""><span class="""" style=""font-size: x-small;"">Beispiel: </span><span class="""" style=""font-size: x-small;"">\(\frac{10}{10 + 5} = \frac 2 3\)</span><br></div></li>
+ </ul>
+ </div>
+ </div>
+</div>";;Kombiniere die Bruchrechenregeln, um die folgende Aufgabe zu lösen.<br>;{@FRA_a[1]@};1;"<prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Beachte die Punkt-vor-Strich-Rechnung: Du musst erst die Produkte berechnen und dann addieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ ";;;;;"<input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ ";<seed_fields><deployedseed>107427398</deployedseed> <deployedseed>1784987913</deployedseed> <deployedseed>1007469958</deployedseed> <deployedseed>1114721015</deployedseed> <deployedseed>1287281907</deployedseed> <deployedseed>1726212908</deployedseed> </seed_fields>;;
+3;frabin;1;k;Binom. Formeln;Bruchrechenregeln Ig2 - Bruch mit binomischem Term erweitern 2 (copy);"a:2;
+b:3;
+c:4;
+
+aa:x-a;
+bb:x-b;
+cc:x-c;
+
+/*FRA_A:[
+[a1,(x^2-3)/(x^2-4),""\\(\\frac{x + 3}{x^2 - 4} + \\frac{x - 3}{x - 2}\\)"",(x^2-3)/((x+2)*(x-2))]
+];*/
+
+FRA_A:[
+[a1,aa, a],
+[a2,bb, b],
+[a3,cc, c]
+];
+FRA_a:rand(FRA_A);
+task:(3*FRA_a[3]*x+FRA_a[3]^2)/expand(FRA_a[2]^2)+x/FRA_a[2];
+ta:(x+FRA_a[3])^2/(FRA_a[2])^2;
+
+simp:false;
+taalt:((x+FRA_a[3])/(FRA_a[2]))^2;
+simp:true;
+
+wa1:expand((x+FRA_a[3])^2)/(FRA_a[2])^2;
+wa2:(x+FRA_a[3])^2/expand((FRA_a[2])^2);
+wa3:expand((x+FRA_a[3])^2)/expand(FRA_a[2]^2);
+wa4:(3*FRA_a[3]*x+FRA_a[3]^2)/expand(FRA_a[2]^2)+x^2/FRA_a[2]^2; /*naively expanded fraction by squaring numerator and denominator*/
+wa5:(3*FRA_a[3]*x+FRA_a[3]^2+x)/(expand(FRA_a[2]^2)+FRA_a[2]); /*naively summed fractions, keeping the denominators*/";"
+
+
+<p></p>
+<div>
+ <div>Vereinfachen und faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p>";;Dies ist der Endgegner zur Mathe-Welt <strong>Bruchrechenregeln und binomische Formeln</strong>. Wenn du diese Aufgabe schaffst, hast du diese Welt schon gemeistert. Wende zuerst die binomischen Formeln an, um die Nenner zu vereinfachen. Um die Brüche dann zu addieren, musst du mit einem Term erweitern.<br>;{@FRA_a[1]@};0;"<prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>2</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Wende die erste binomische Formel an, um den Zähler zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa2</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Wende die zweite binomische Formel an, um den Nenner zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>4</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa3</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Wende die erste binomische Formel an, um den Zähler zu faktorisieren und
+ wende die zweite binomische Formel an, um den Nenner zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa4</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du hast offensichtlich den zweiten Summanden mit sich selbst multipliziert (quadriert), damit die Nenner gleich sind. Allerdings wird ein Bruch so nicht erweitert. Der quadrierte Bruch ist nicht mehr äquivalent mit dem vorherigen Bruch. Beispiel: \((\frac{2}{5})^2 = \frac{4}{25} \ne \frac{2}{5}\;\) wohingegen \(\frac{2}{5} = \frac{2 \cdot 5}{5 \cdot 5} = \frac{10}{25}\;\). Bitte überlege erneut, womit der zweite Summand erweitert werden muss, damit die Nenner gleich sind.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa5</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du hast offensichtlich die beiden Brüche addiert, indem du Zähler plus Zähler (oben) und Nenner plus Nenner (unten) gerechnet hast. So können Brüche nicht addiert werden. Beispiel: \( \frac{1}{2} + \frac{1}{4} \ne \frac{1+1}{2+4}\;\) . Brüche müssen so erweitert werden, dass sie den gleichen Nenner haben. Dann können die Zähler addiert werden: \(\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}\).</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ ";;;;;"<input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ ";<seed_fields><deployedseed>2099085786</deployedseed> <deployedseed>245667775</deployedseed> <deployedseed>1806806387</deployedseed></seed_fields>;;Has only three variants
+4;pq;1;a;pq-Formel;p-q-Formal Ia - Termumformung;"BIN_A:[
+[a1,[6*x+3*x^2-2=10,x^2+2*x-4=0],6*x+3*x^2-2=10],
+[a2,[15*x+5*x^2=20,x^2+3*x-4=0],15*x+5*x^2=20],
+[a3,[8*x+2*x^2-2=12,x^2+4*x-7=0],8*x+2*x^2-2=12],
+[a4,[20*x+4*x^2=-16,x^2+5*x+4=0],20*x+4*x^2=-16]
+];
+
+BIN_a:rand(BIN_A);";"
+
+
+<p>Formen Sie den Term so um, dass er in der Form \(x^2+px+q = 0\) erscheint. Sie können dies Zeile für Zeile tun.<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>";;Um die p-q-Formel anzuwenden, müssen wir zunächst den Term in die richtige Form bringen. Um den folgenden Term wie gewünscht umzuformen, subtrahiere und dividiere auf beiden Seiten der Gleichung.<br>;{@BIN_a[1]@};0;"<prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text></text>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions></testoptions>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty></truepenalty>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;"">Gut gemacht! Wenn ein Term auf diese Weise umgeformt ist, kannst du mit der p-q-Formel die möglichen Werte für \(x\) bestimmen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty></falsepenalty>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text></text>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions></testoptions>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty></truepenalty>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Weiter so! Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty></falsepenalty>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text></text>
+ </falsefeedback>
+ </node>
+ </prt>";;;;;"<input>
+ <name>ans1</name>
+ <type>equiv</type>
+ <tans>BIN_a[2]</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint>firstline</syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options>firstline</options>
+ </input>
+ ";<seed_fields><deployedseed>1126686893</deployedseed> <deployedseed>1832581792</deployedseed> <deployedseed>1406889611</deployedseed> <deployedseed>511391873</deployedseed></seed_fields>;;
+4;pq;1;c;pq-Formel;p-q-Formel I - Endboss;"BIN_A:[
+[a1,[-2*y^2+6*y=4, -2*y^2+6*y-4=0,y^2-3*y-2=0,stackeq(y=3/2+sqrt(9/4-2) nounor y=3/2-sqrt(9/4-2)),y=1 nounor y=2],-2*y^2+6*y=4,y,1,2,y=3/2+sqrt(9/4+2),y=3/2-sqrt(9/4+2)],
+[a2,[2*y^2-16=-4*y,2*y^2+4*y-16=0,y^2+2*y-8=0,stackeq(y=-1+sqrt((1)^2+8) nounor y=-1-sqrt((1)^2+8)),y=-4 nounor y=2],2*y^2-16=-4*y,y,-4,2,y=-1+sqrt((1)^2-8),y=-1-sqrt((1)^2-8)],
+[a3,[-2*d^2+2*d=-24,-2*d^2+2*d+24=0,d^2-d-12=0,d=1/2+sqrt((1/2)^2+12) nounor d=1/2-sqrt((1/2)^2+12),d=-3 nounor d=4],-2*d^2+2*d=-24,d,-3,4,d=1/2+sqrt((1/2)^2-12),d=1/2-sqrt((1/2)^2-12)],
+[a4,[-2*u^2-14*u=24,-2*u^2-14*u-24=0,u^2+7*u+12=0,u=-7/2+sqrt((7/2)^2-12) nounor u=-7/2-sqrt((7/2)^2-12),u=-4 nounor u=-3],-2*u^2-14*u=24,u,-4,-3,u=-7/2+sqrt((7/2)^2+12), u=-7/2-sqrt((7/2)^2+12)]
+];
+
+BIN_a:rand(BIN_A);";"
+
+
+<p>Bestimmen Sie alle reellen Lösungen der quadratischen Gleichung in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\(= ?\;\). Sie können Ihren Rechenweg angeben.<br></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>";;Forme den Term um und wende dann die p-q-Formel an, um diese Endgegner-Aufgabe zu lösen. Dann bist du mit dieser Mathe-Welt fertig.<br>;{@BIN_a[1]@};0;"<prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;""></p><p dir=""ltr"">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir=""ltr"">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.</p><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;""></p><p dir=""ltr"">Fast!
+ Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel
+in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2}
+\boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir=""ltr"">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir=""ltr"">Versuche es erneut und gib beide Lösungen an.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;""></p><p dir=""ltr"">Fast! Offenbar hast du dich beim
+\(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet
+ \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil
+ am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du
+das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;""></p><p dir=""ltr"">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir=""ltr"">Außerdem
+ hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel
+ bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+}
+\sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-}
+\sqrt{...}\) gibt.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;""></p><p dir=""ltr"">Fast!
+ Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ ";;;;;"<input>
+ <name>ans1</name>
+ <type>equiv</type>
+ <tans>BIN_a[2]</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint>firstline</syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options>firstline</options>
+ </input>
+ ";<seed_fields><deployedseed>1183308849</deployedseed> <deployedseed>1817300183</deployedseed> <deployedseed>1556042756</deployedseed> <deployedseed>493079990</deployedseed> </seed_fields>;;
+4;pq;1;b;pq-Formel;p-q-Formel Ib - pq-Formel;"BIN_A:[
+[a1,[h^2+3*h-4=0,h=-3/2+sqrt((3/2)^2+4) nounor h=-3/2-sqrt((3/2)^2+4),h=-3/2+sqrt(25/4) nounor h=-3/2-sqrt(25/4),h=-3/2+5/2 nounor h=-3/2-5/2,h=-4 nounor h=1],""\\(h^2+3\\,h-4=0\\)"",h,1,-4,h=-3/2+sqrt(9/4-4),h=-3/2-sqrt(9/4-4)],
+[a2,[y^2-2*y-8=0,y=1+sqrt((-1)^2+8) nounor y=1-sqrt((-1)^2+8),y=-2 nounor y=4],""\\(y^2-2\\,y-8=0\\)"",y,-2,4,y=1-sqrt(1-8),y=1+sqrt(1-8)],
+[a3,[z^2-4*z-5=0,z=2+sqrt((-2)^2+5) nounor z=2-sqrt((-2)^2+5),z=5 nounor z=-1],""\\(z^2-4\\,z-5=0\\)"",z,5,-1,z=2+sqrt(4-5),z=2-sqrt(4-5)],
+[a4,[a^2-10*a+9=0,a=5+sqrt((-5)^2-9) nounor a=5-sqrt((-5)^2-9),a=9 nounor a=1],""\\(a^2-10\\,a+9=0\\)"",a,9,1,a=5+sqrt(25+9),a=5-sqrt(25+9)]
+];
+
+BIN_a:rand(BIN_A);";"
+
+
+<p>Bestimmen Sie den Wert der Variable in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\( = ?\;\).<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>";;"Erinnerst du dich noch an die pq-Formel? Für \(\;x^2 + p\,x + q = 0\;\) gilt \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\).<br>";{@BIN_a[1]@};0;"<prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir=""ltr"" style=""text-align: left;"">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Fast! Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2} \boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir=""ltr"" style=""text-align: left;"">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir=""ltr"" style=""text-align: left;"">Versuche es erneut und gib beide Lösungen an.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Fast! Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir=""ltr"" style=""text-align: left;"">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Fast! Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\) gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ ";;;;;"<input>
+ <name>ans1</name>
+ <type>equiv</type>
+ <tans>BIN_a[2]</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint>firstline</syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options>firstline</options>
+ </input>
+ ";<seed_fields><deployedseed>1183616185</deployedseed> <deployedseed>1771539896</deployedseed> <deployedseed>1420701792</deployedseed> <deployedseed>1009534997</deployedseed></seed_fields>;;
+5;rul;1;f;Potenzrechenregeln;Potenzrechenregeln I - Endboss;"RUL_A:[
+[a1,stackeq(y^(-1/6)),""\\(\\frac{1}{\\sqrt[3]{y \\, \\sqrt x}} \\, \\sqrt[6]{x \\, y}\\)""],
+[a2,a^20*x^8,""\\(\\left( \\frac{a^3 x^5}{a^{-2} x^3} \\right)^4\\)""]
+];
+RUL_a:rand(RUL_A);
+
+/*ans1 is evaluated by ev(ans1,simp) to accept e. g. 1/(y^(1/6)) and y^(-1/6) and y^(-(1/6))*/";"
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie folgenden Ausdruck; hierbei sind \(x,y \in \mathbb{R_{> 0}}\).</div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>";;Dies ist die Endgegner-Aufgabe dieser Mathe-Welt <strong>Potenzrechenrelgen</strong>. Wenn du diese Aufgabe schaffst, hast du diese Mathe-Welt gemeistert. Viel Erfolg!;{@RUL_a[1]@};0;"<prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ev(ans1,simp)</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ ";;;;;"<input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ ";<seed_fields><deployedseed>1167231517</deployedseed> <deployedseed>1313491755</deployedseed></seed_fields>;;
+5;rul;1;a;Potenzrechenregeln;Potenzrechenregeln Ia – Exponenten addieren;"RUL_A:[
+[a1,c^a*c^b,""\\(c^{\\,a}\\cdot c^{\\,b}\\)""],
+[a2,x^a*x^b,""\\(x^{\\,a}\\cdot x^{\\,b}\\)""]
+];
+RUL_a:rand(RUL_A);
+";"
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>";;Fangen wir damit an, die Exponenten zu addieren, wenn die Basis gleich ist und multipliziert wird.<br>;{@RUL_a[1]@};0;"<prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ ";;;;;"<input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ ";<seed_fields><deployedseed>1724483596</deployedseed> <deployedseed>337440314</deployedseed></seed_fields>;;
+5;rul;1;b;Potenzrechenregeln;Potenzrechenregeln Ib – Exponenten subtrahieren;"RUL_A:[
+[a1,c^a/c^b,""\\(\\frac{c^{\\,a}}{c^{\\,b}}\\)""],
+[a2,x^a/x^b,""\\(\\frac{x^{\\,a}}{x^{\\,b}}\\)""]
+];
+RUL_a:rand(RUL_A);
+";"
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>";;Das funktioniert auch in die andere Richtung.<br>;{@RUL_a[1]@};0;"<prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ ";;;;;"<input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ ";<seed_fields><deployedseed>29351489</deployedseed> <deployedseed>1996084793</deployedseed></seed_fields>;;
+5;rul;1;c;Potenzrechenregeln;Potenzrechenregeln Ic - Wurzel als Potenz darstellen;"RUL_A:[
+[a1,c^(1/6),""\\(\\sqrt[6]{c}\\)""],
+[a2,c^(1/5),""\\(\\sqrt[5]{c}\\)""],
+[a3,c^(1/4),""\\(\\sqrt[4]{c}\\)""],
+[a4,c^(1/3),""\\(\\sqrt[3]{c}\\)""],
+[a5,c^(1/7),""\\(\\sqrt[7]{c}\\)""],
+[a6,c^(1/8),""\\(\\sqrt[8]{c}\\)""]
+];
+RUL_a:rand(RUL_A);
+";"
+
+
+<p></p>
+<div>
+ <div>Stellen Sie den Ausdruck in der Form \(c^{\frac{1}{n}}\) dar.<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>";;"Mithilfe von Potenzen der Form \(c^{\frac{1}{n}}\) lässt sich die n-te Wurzel von \(c\), also \(\;\sqrt[n]{c}\;\), darstellen.";{@RUL_a[1]@};0;"<prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Sie können noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ ";;;;;"<input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ ";<seed_fields><deployedseed>1074873352</deployedseed> <deployedseed>460473552</deployedseed> <deployedseed>771365681</deployedseed> <deployedseed>1250006169</deployedseed> <deployedseed>259744359</deployedseed></seed_fields>;;
+5;rul;1;d;Potenzrechenregeln;Potenzrechenregeln Id – Exponenten multiplizieren;"RUL_A:[
+[a1,c^(a*b),""\\((c^a)^b\\)"",c^a*b],
+[a2,x^(a*b),""\\((x^a)^b\\)"",x^a*b]
+];
+RUL_a:rand(RUL_A);
+wa:RUL_a[4];
+";"
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>";;Wird ein Ausdruck, der eine Potenz enthält, potenziert, lassen sich die Exponenten miteinander multiplizieren.<br>;{@RUL_a[1]@};0;"<prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du hast die Klammer falsch gesetzt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ ";;;;;"<input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ ";<seed_fields><deployedseed>1495340815</deployedseed> <deployedseed>1196787611</deployedseed></seed_fields>;;
+5;rul;1;e;Potenzrechenregeln;Potenzrechenregeln Ie - Potenzrechenregeln anwenden;"RUL_A:[
+[a1,c^(13/6),""\\(\\sqrt[6]{c} \\cdot c^2\\)""],
+[a2,x^10,""\\(\\frac{x^5}{x^{-5}}\\)""]
+];
+RUL_a:rand(RUL_A);
+";"
+
+
+<p></p>
+<div>Nutzen Sie die Potenzrechenregeln, um folgenden Ausdruck zu vereinfachen.<br></div>
+<p>
+</p>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p>
+<div class=""bubble in-modal no-arrow"">
+ <div>Hier zur Erinnerung die wichtigsten Potenzrechenregeln. Für \(x, y \neq 0\) und \(n, m \in \mathbb{Z}\) gilt:</div>
+<div>
+ <div>
+ <div>
+ <ul>
+ <li>\(x^{n+m} = x^n\,x^m\;\)<br><div style=""text-align: center;""><span class="""" style=""font-size: x-small;"">Beispiel: \(2^5 = 2^{2+3} = 2^2 \cdot 2^3 = 4 \cdot 8 = 32\)</span></div></li></ul><ul>
+ <li>
+ <div>
+ <div>\(\left( x^n \right)^m = x^{n\,m}\;\)<br><div style=""text-align: center;""><span class="""" style=""font-size: x-small;"">Beispiel: \(\left( 2^2 \right)^3 = 2^6 = 64\)</span></div></div>
+ </div>
+ </li>
+ <li>
+ <div>
+ <div>
+ <div>
+ <div>\((x\,y)^n = x^n\,y^n\;\)<br><div style=""text-align: center;""><span class="""" style=""font-size: x-small;"">Beispiel: \(6^2 = (2 \cdot 3)^2 = 2^2 \cdot 3^2 = 4 \cdot 9 = 36\)</span></div></div>
+ </div>
+ </div>
+ </div>
+ </li>
+ <li>\(\frac{1}{x^n} = x^{-n}\)<br><div style=""text-align: center;""><span class="""" style=""font-size: x-small;"">Beispiel: \( \frac{1}{x^2} \cdot x^2 = x^{-2} \cdot x^2 = x^{-2+2} = x^0 = 1\)</span><br></div></li>
+ <li>\(\sqrt[n]{x} = x^{\frac{1}{n}}\)<br><div style=""text-align: center;""><span class="""" style=""font-size: x-small;"">Beispiel: \( \sqrt[3]{x} \cdot x^3 = x^{\frac{1}{3}} \cdot x^3 = x^{\frac{1}{3}+3} = x^1 = x\)</span></div></li>
+ </ul>
+ </div>
+ </div>
+</div>
+<p></p>
+<div>
+ <div>
+ <div>
+ <ul></ul>
+ </div>
+ </div>
+</div>
+</div>";;Um diese Aufgabe zu lösen, kannst du mehrere der gerade erläuterten Regeln kombinieren. ;{@RUL_a[1]@};0;"<prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Richtig, aber du kannst noch weiter vereinfachen.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ ";;;;;"<input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ ";<seed_fields><deployedseed>1602709371</deployedseed> <deployedseed>547016054</deployedseed></seed_fields>;;
+6;tri;1;a;Trigonometrie;Trigonometrie Ia - Begriffsklärungen;"TRI_A:[
+[a1,[[1,true,""Hypothenuse""],[2,false,""Katheten""],[3,false,""Ankathete""],[4,false,""Gegenkathete""]],[[4,false,""Hypothenuse""],[2,false,""Katheten""],[3,false,""Ankathete""],[1,true,""Gegenkathete""]],[[3,false,""Hypothenuse""],[2,false,""Katheten""],[1,true,""Ankathete""],[4,false,""Gegenkathete""]],[""Richtig wäre: Hypothenuse. Die Hypothenuse bezeichnet die dem rechten Winkel gegenüberliegende Seite. Es ist die längste Seite des rechtwinkligen Dreiecks."", ""Richtig wäre: Gegenkathete. Die dem Winkel gegenüberliegende Seite wird als Gegenkathete bezeichnet."", ""Richtig wäre: Ankathete. Die dem Winkel anliegende Seite, die nicht die Hypothenuse ist, wird als Ankathete bezeichnet.""],[""\\(c\\) beschreibt die Länge der "",""."", ""Nennen wir den Winkel zwischen \\(c\\) und \\(b\\)\\(\\;\\alpha\\;\\). Dann beschreibt \\(a\\) die Länge der "","" von \\(\\alpha\\)"", ""und \\(b\\) die Länge der "","" von \\(\\alpha\\).""]],
+[a2,[[1,true,""Hypothenuse""],[2,false,""Katheten""],[3,false,""Ankathete""],[4,false,""Gegenkathete""]],[[3,false,""Hypothenuse""],[2,false,""Katheten""],[1,true,""Ankathete""],[4,false,""Gegenkathete""]],[[4,false,""Hypothenuse""],[2,false,""Katheten""],[3,false,""Ankathete""],[1,true,""Gegenkathete""]],[""Richtig wäre: Hypothenuse. Die Hypothenuse bezeichnet die dem rechten Winkel gegenüberliegende Seite. Es ist die längste Seite des rechtwinkligen Dreiecks."", ""Richtig wäre: Ankathete. Die dem Winkel anliegende Seite, die nicht die Hypothenuse ist, wird als Ankathete bezeichnet."", ""Richtig wäre: Gegenkathete. Die dem Winkel gegenüberliegende Seite wird als Gegenkathete bezeichnet.""],[""\\(c\\) beschreibt die Länge der "",""."", ""Nennen wir den Winkel zwischen \\(c\\) und \\(a\\)\\(\\;\\alpha\\;\\). Dann beschreibt \\(a\\) die Länge der "","" von \\(\\alpha\\)"", ""und \\(b\\) die Länge der "","" von \\(\\alpha\\).""]],
+[a3,[[3,false,""Hypothenuse""],[2,false,""Katheten""],[1,true,""Ankathete""],[4,false,""Gegenkathete""]],[[4,false,""Hypothenuse""],[2,false,""Katheten""],[3,false,""Ankathete""],[1,true,""Gegenkathete""]],[[1,true,""Hypothenuse""],[2,false,""Katheten""],[3,false,""Ankathete""],[4,false,""Gegenkathete""]],[""Richtig wäre: Ankathete. Die dem Winkel anliegende Seite, die nicht die Hypothenuse ist, wird als Ankathete bezeichnet."", ""Richtig wäre: Gegenkathete. Die dem Winkel gegenüberliegende Seite wird als Gegenkathete bezeichnet."",""Richtig wäre: Hypothenuse. Die Hypothenuse bezeichnet die dem rechten Winkel gegenüberliegende Seite. Es ist die längste Seite des rechtwinkligen Dreiecks.""],[""Nennen wir den Winkel zwischen \\(c\\) und \\(a\\)\\(\\;\\alpha\\;\\). Dann beschreibt \\(a\\) die Länge der "","" von \\(\\alpha\\)"", ""und \\(b\\) die Länge der "","" von \\(\\alpha\\)."",""\\(c\\) beschreibt die Länge der "","".""]]
+];
+TRI_a:rand(TRI_A);
+List_a:random_permutation(TRI_a[2]);
+List_b:random_permutation(TRI_a[3]);
+List_c:random_permutation(TRI_a[4]);";"
+
+
+<p></p>
+<p>Füllen Sie die Lücken aus.</p>
+<p><img src=""https://marvin.hs-bochum.de/~mneugebauer/Right_triangle_abc.svg"" alt=""Rechwinkliges Dreieck mit a,b,c"" class=""img-fluid atto_image_button_text-bottom"" style=""width:25em;"" width=""454"" height=""227""><br></p>
+
+
+<p></p>
+<p>{@TRI_a[6][1]@}[[input:ans1]][[validation:ans1]]{@TRI_a[6][2]@}[[feedback:prt1]]</p>
+<p>{@TRI_a[6][3]@}[[input:ans2]] [[validation:ans2]]{@TRI_a[6][4]@}[[feedback:prt2]]<br></p>
+<p>{@TRI_a[6][5]@}[[input:ans3]] [[validation:ans3]]{@TRI_a[6][6]@}[[feedback:prt3]]</p>";;Klären wir zunächst die Begriffe im rechtwinkligen Dreieck.;{@TRI_a[1]@};1;"<prt_fields><prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">{@TRI_a[5][1]@}<br></p>]]></text>
+ </falsefeedback>
+ </node>
+ </prt>
+ <prt>
+ <name>prt2</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans2</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt2-1-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt2-1-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">{@TRI_a[5][2]@}<br></p>]]></text>
+ </falsefeedback>
+ </node>
+ </prt>
+ <prt>
+ <name>prt3</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans3</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt3-1-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt3-1-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">{@TRI_a[5][3]@}<br></p>]]></text>
+ </falsefeedback>
+ </node>
+ </prt>
+ </prt_fields>";;;;;"<input_fields><input>
+ <name>ans1</name>
+ <type>dropdown</type>
+ <tans>List_a</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>0</mustverify>
+ <showvalidation>0</showvalidation>
+ <options/>
+ </input>
+ <input>
+ <name>ans2</name>
+ <type>dropdown</type>
+ <tans>List_b</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>0</mustverify>
+ <showvalidation>0</showvalidation>
+ <options/>
+ </input>
+ <input>
+ <name>ans3</name>
+ <type>dropdown</type>
+ <tans>List_c</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>0</mustverify>
+ <showvalidation>0</showvalidation>
+ <options/>
+ </input>
+ </input_fields>";<seed_fields><deployedseed>1158166345</deployedseed> <deployedseed>1869227289</deployedseed> <deployedseed>646925243</deployedseed></seed_fields>;;
+6;tri;1;b;Trigonometrie;Trigonometrie Ib - Satz des Pythagoras 1;"TRI_A:[
+[a1,""c"",""b"",""a"",""50"", a,b,c],
+[a2,""p"",""q"",""r"",""90"", r,p,q],
+[a3,""y"",""z"",""x"",""30"", x,y,z],
+[a4,""b"",""c"",""a"",""160"",a,b,c]
+];
+TRI_a:rand(TRI_A);
+ta1:TRI_a[6];
+wa1_1:TRI_a[7];
+wa1_2:TRI_a[8];
+ta2:TRI_a[7]^2+TRI_a[8]^2=TRI_a[6]^2;";"
+
+<br>
+
+<p>1. Welche Seite ist in diesem Dreieck die Hypothenuse?</p>
+<p><br></p>
+<p><br></p>
+<svg style=""transform:rotate({@TRI_a[5]@}deg);width:20em;"" viewBox=""40 30 520 270"">
+ <g font-style=""italic"" font-size=""24"" font-family=""Times"" id=""g3011"">
+ <!--<text text-anchor=""end"" x=""440"" y=""170"" id=""text3013"">h</text>-->
+ <!--<text text-anchor=""middle"" x=""250"" y=""240"" id=""text3015"">q</text>-->
+ <!--<text text-anchor=""middle"" x=""500"" y=""240"" id=""text3017"">p</text>-->
+ <text text-anchor=""middle"" rotate=""-{@TRI_a[5]@}"" x=""350"" y=""275"" id=""text3019"" style=""font-size:30px;"">{@TRI_a[4]@}</text>
+ <text text-anchor=""start"" rotate=""-{@TRI_a[5]@}"" x=""510"" y=""150"" id=""text3021"" style=""font-size:30px;"">
+ {@TRI_a[2]@}
+ </text>
+ <text text-anchor=""end"" rotate=""-{@TRI_a[5]@}"" x=""240"" y=""150"" id=""text3023"" style=""font-size:30px;"">{@TRI_a[3]@}</text>
+ </g>
+ <path d=""M 450,50 L 50,250 550,250 450,50"" fill=""none"" stroke=""black"" stroke-width=""1"" id=""path3025""></path>
+ <path transform=""matrix(0.50145999,-0.01568658,-0.01833095,0.4410847,293.36534,-135.37245)"" sodipodi:type=""arc"" style=""fill:none;stroke:#000000;stroke-width:2.85345483;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none;display:inline"" id=""path5323"" sodipodi:cx=""329"" sodipodi:cy=""433"" sodipodi:rx=""63"" sodipodi:ry=""77"" d=""M 360.09564,499.96686 A 63,77 0 0 1 271.21076,463.66302"" sodipodi:start=""1.0545931"" sodipodi:end=""2.732016"" sodipodi:open=""true""></path>
+ <path sodipodi:type=""arc"" style=""opacity:0.98999999;fill:#000000;fill-opacity:1;stroke:#000000;stroke-width:0.3052347;stroke-linejoin:round;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none"" id=""path3006"" sodipodi:cx=""326.28125"" sodipodi:cy=""29.410919"" sodipodi:rx=""0.46875"" sodipodi:ry=""0.4375"" d=""m 326.75,29.410919 a 0.46875,0.4375 0 1 1 -0.9375,0 0.46875,0.4375 0 1 1 0.9375,0 z"" transform=""matrix(4.5036224,0,0,4.2865266,-1026.6105,-59.086052)""></path>
+</svg>
+<p><br></p>
+
+
+<p></p>
+<p><br></p>
+<p><br></p>
+<p>[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p>
+<p>2. Formulieren Sie die Formel gemäß des Satzes von Pythagoras für das gegebene Beispiel in der Form \(a^2+b^2 = c^2\;\).</p>
+<p>[[input:ans2]][[validation:ans2]][[feedback:prt2]]<br></p>";;Erinnerst du dich noch an den Satz des Pythagoras?;{@TRI_a[1]@};1;"<prt_fields><prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa1_1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>3</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa1_2</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>3</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du hast eine der Katheten angegeben. Die Hypothenuse ist die dem rechten Winkel gegenüberliegende Seite und die längste Seite des rechtwinkligen Dreiecks.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <prt>
+ <name>prt2</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans2</sans>
+ <tans>ta2</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt2-1-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt2-1-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans2</sans>
+ <tans>ta2</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>2</truenextnode>
+ <trueanswernote>prt2-2-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[Du hast die Formel nicht in der Form \(a^2+b^2=c^2\) notiert, sondern bereits umgestellt.<br>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt2-2-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans2</sans>
+ <tans>TRI_a[6]=sqrt(TRI_a[7]^2+TRI_a[8]^2)</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt2-3-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""></p>
+<p dir=""ltr"">Du
+ hast schon zur unbekannten aufgelöst, was eigentlich sehr gut ist Allerdings war danach
+ gefragt, den Satz des Pythagoras in der Form \(a^2+b^2=c^2\)
+ darzustellen.<br></p><br>
+<p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt2-3-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt2-4-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>4</falsenextnode>
+ <falseanswernote>prt2-4-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>TRI_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>5</truenextnode>
+ <trueanswernote>prt2-5-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt2-5-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans2</sans>
+ <tans>TRI_a[7]^2=TRI_a[6]^2+TRI_a[8]^2</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt2-6-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Wenn {@ans1@} die Hypothenuse wäre, hättest du den Satz des Pythagoras richtig angewendet. Doch da du die Hypothenuse im vorhergehenden Schritt falsch bestimmt hast, passt diese Antwort nicht mit dem oben gezeigten Dreieck überein.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt2-6-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>TRI_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>7</truenextnode>
+ <trueanswernote>prt2-7-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt2-7-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans2</sans>
+ <tans>TRI_a[8]^2=TRI_a[6]^2+TRI_a[7]^2</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt2-8-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;""></p><p dir=""ltr"">Wenn
+ {@ans1@} die Hypothenuse wäre, hättest du den Satz des Pythagoras
+richtig angewendet. Doch da du die Hypothenuse im vorhergehenden Schritt
+ falsch bestimmt hast, passt diese Antwort nicht mit dem oben gezeigten
+Dreieck überein.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt2-8-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">8<br></p>]]></text>
+ </falsefeedback>
+ </node>
+ </prt>
+ </prt_fields>";;;;;"<input_fields><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <input>
+ <name>ans2</name>
+ <type>algebraic</type>
+ <tans>ta2</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ </input_fields>";<seed_fields><deployedseed>1090853240</deployedseed> <deployedseed>556370179</deployedseed> <deployedseed>101332667</deployedseed> <deployedseed>1321080434</deployedseed></seed_fields>;;
+6;tri;1;c;Trigonometrie;Trigonometrie Ic - Satz des Pythagoras 2;"TRI_A:[
+[a1,5,a,""https://marvin.hs-bochum.de/~mneugebauer/trigonometry_question_56_a.png"",""Ein dunkelblaues, rechtwinkliges Dreieck gesucht ist die Hypothenuse und die Katheten haben die Längen 3 und 4"",a,3,4],
+[a2,3,a,""https://marvin.hs-bochum.de/~mneugebauer/trigonometry_question_56_b.png"",""Ein rotes, rechtwinkliges Dreieck mit einer Hypothenuse der Länge 4 und einer Kathete mit Länge Wurzel 7 gesucht ist die andere Kathete"",4,a,sqrt(7)]
+];
+TRI_a:rand(TRI_A);
+ta1:TRI_a[7]^2+TRI_a[8]^2=TRI_a[6]^2;
+wa1_1:TRI_a[7]^2+TRI_a[8]^2=TRI_a[6];
+wa1_2:TRI_a[7]+TRI_a[8]^2=TRI_a[6]^2;
+wa1_3:TRI_a[7]^2+TRI_a[8]=TRI_a[6]^2;
+ta2:TRI_a[2];
+wa2_1:TRI_a[2]^2;";"
+
+
+<p></p>
+<div>
+ <div>Finden Sie die gesuchte Größe mit Hilfe des Satzes von Pythagoras.</div>
+ <div><br></div>
+ <div><img id=""alplot1"" src=""{@TRI_a[4]@}"" alt=""{@TRI_a[5]@}"" style=""width:15em;"" class=""img-fluid atto_image_button_text-bottom""><br></div>
+</div>
+<p></p>
+<p>1. Formulieren Sie den Satz des Pythagoras für das gegebene Beispiel in der Form \(a^2+b^2 = c^2\;\).<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>
+<p>2. Berechnen Sie die unbekannte Variable.<br></p>
+<p>{@TRI_a[3]@}\(\,=\,\) [[input:ans2]] [[validation:ans2]][[feedback:prt2]]</p>";;Jetzt kannst du den Satz des Pythagoras anwenden, um folgende Aufgabe zu lösen.<br>;{@TRI_a[1]@};1;"<prt_fields><prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>TRI_a[6]=sqrt(TRI_a[8]^2+TRI_a[7]^2)</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;"">Du hast schon zur unbekannten aufgelöst. Sehr gut. Allerdings war danach gefragt, den Satz des Pythagoras in der Form \(a^2+b^2=c^2\) darzustellen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa1_1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Deine Gleichung ist äquivalent mit \(a^2+b^2=c\;\). Offenbar hast du vergessen, auch die Hypothenuse zu quadrieren. Richtig wäre \(a^2+b^2=c\mathbf{^2}\;\).<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa1_2</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>5</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>4</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa1_3</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>5</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Deine Gleichung ist äquivalent mit \(a^2+b=c^2\;\). Offenbar hast du
+vergessen, eine der Katheten zu quadrieren. Richtig wäre
+\(a^2+b\mathbf{^2}=c^2\;\).<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <prt>
+ <name>prt2</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans2</sans>
+ <tans>ta2</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt2-1-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt2-1-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans2</sans>
+ <tans>wa2_1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt2-2-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du hast offenbar vergessen, die Wurzel zu ziehen. Beispiel: Wenn \(a^2+b^2=c^2\) dann gilt \(a=\sqrt(c^2-b^2)\;\).<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falseanswernote>prt2-2-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ </prt_fields>";;;;;"<input_fields><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <input>
+ <name>ans2</name>
+ <type>algebraic</type>
+ <tans>ta2</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ </input_fields>";<seed_fields><deployedseed>1852221206</deployedseed> <deployedseed>1423232892</deployedseed> </seed_fields>;;
+6;tri;1;d;Trigonometrie;Trigonometrie Id - Begriffsklärungen trigonometrischer Funktionen;"TRI_A:[
+[a1,
+[[1,true,""Gegenkathete von α""],[2,false,""Hypothenuse""],[3,false,""Ankathete von α""]],
+[[2,false,""Gegenkathete von α""],[1,true,""Hypothenuse""],[3,false,""Ankathete von α""]],
+""Der Sinus beschreibt das Verhältnis der Gegenkathete zur Hypothenuse. Richtig wäre also: Gegenkathete von \\(\\alpha / \\) Hypothenuse \\(= \\frac{a}{c}\\;\\)"",
+a/c,
+[[3,false,""Gegenkathete von α""],[2,false,""Hypothenuse""],[1,true,""Ankathete von α""]],
+[[2,false,""Gegenkathete von α""],[1,true,""Hypothenuse""],[3,false,""Ankathete von α""]],
+""Der Cosinus beschreibt das Verhältnis der Ankathete zur Hypothenuse. Richtig wäre also: Ankathete von \\(\\alpha / \\) Hypothenuse \\(= \\frac{b}{c}\\;\\)"",
+b/c,
+[[1,true,""Gegenkathete von α""],[2,false,""Hypothenuse""],[3,false,""Ankathete von α""]],
+[[2,false,""Gegenkathete von α""],[3,false,""Hypothenuse""],[1,true,""Ankathete von α""]],
+""Der Tangens beschreibt das Verhältnis der Gegenkathete zur Ankathete. Richtig wäre also: Gegenkathete von \\(\\alpha / \\) Ankathete von \\(\\alpha = \\frac{a}{b}\\;\\)"",
+a/b,
+[""\\(\\sin \\alpha \\) \\(=\\) "",""\\(\\cos \\alpha \\) \\(=\\) "",""\\(\\tan \\alpha \\) \\(=\\)""]
+],
+
+[a2,
+[[1,true,""Gegenkathete von α""],[2,false,""Hypothenuse""],[3,false,""Ankathete von α""]],
+[[2,false,""Gegenkathete von α""],[3,false,""Hypothenuse""],[1,true,""Ankathete von α""]],
+""Der Tangens beschreibt das Verhältnis der Gegenkathete zur Ankathete. Richtig wäre also: Gegenkathete von \\(\\alpha / \\) Ankathete von \\(\\alpha = \\frac{a}{b}\\;\\)"",
+a/b,
+[[1,true,""Gegenkathete von α""],[2,false,""Hypothenuse""],[3,false,""Ankathete von α""]],
+[[2,false,""Gegenkathete von α""],[1,true,""Hypothenuse""],[3,false,""Ankathete von α""]],
+""Der Sinus beschreibt das Verhältnis der Gegenkathete zur Hypothenuse. Richtig wäre also: Gegenkathete von \\(\\alpha / \\) Hypothenuse \\(= \\frac{a}{c}\\;\\)"",
+a/c,
+[[3,false,""Gegenkathete von α""],[2,false,""Hypothenuse""],[1,true,""Ankathete von α""]],
+[[2,false,""Gegenkathete von α""],[1,true,""Hypothenuse""],[3,false,""Ankathete von α""]],
+""Der Cosinus beschreibt das Verhältnis der Ankathete zur Hypothenuse. Richtig wäre also: Ankathete von \\(\\alpha / \\) Hypothenuse \\(= \\frac{b}{c}\\;\\)"",
+b/c,
+[""\\(\\tan \\alpha \\) \\(=\\)"", ""\\(\\sin \\alpha \\) \\(=\\) "",""\\(\\cos \\alpha \\) \\(=\\) ""]
+],
+
+[a3,
+[[1,true,""Gegenkathete von α""],[2,false,""Hypothenuse""],[3,false,""Ankathete von α""]],
+[[2,false,""Gegenkathete von α""],[1,true,""Hypothenuse""],[3,false,""Ankathete von α""]],
+""Der Sinus beschreibt das Verhältnis der Gegenkathete zur Hypothenuse. Richtig wäre also: Gegenkathete von \\(\\alpha / \\) Hypothenuse \\(= \\frac{a}{c}\\;\\)"",
+a/c,
+[[1,true,""Gegenkathete von α""],[2,false,""Hypothenuse""],[3,false,""Ankathete von α""]],
+[[2,false,""Gegenkathete von α""],[3,false,""Hypothenuse""],[1,true,""Ankathete von α""]],
+""Der Tangens beschreibt das Verhältnis der Gegenkathete zur Ankathete. Richtig wäre also: Gegenkathete von \\(\\alpha / \\) Ankathete von \\(\\alpha = \\frac{a}{b}\\;\\)"",
+a/b,
+[[3,false,""Gegenkathete von α""],[2,false,""Hypothenuse""],[1,true,""Ankathete von α""]],
+[[2,false,""Gegenkathete von α""],[1,true,""Hypothenuse""],[3,false,""Ankathete von α""]],
+""Der Cosinus beschreibt das Verhältnis der Ankathete zur Hypothenuse. Richtig wäre also: Ankathete von \\(\\alpha / \\) Hypothenuse \\(= \\frac{b}{c}\\;\\)"",
+b/c,
+[""\\(\\sin \\alpha \\) \\(=\\) "",""\\(\\tan \\alpha \\) \\(=\\)"",""\\(\\cos \\alpha \\) \\(=\\) ""]
+]
+];
+TRI_a:rand(TRI_A);
+ta3:TRI_a[5];
+ta6:TRI_a[9]
+ta9:TRI_a[13]
+List_a:random_permutation(TRI_a[2]);
+List_b:random_permutation(TRI_a[3]);
+List_c:random_permutation(TRI_a[6]);
+List_d:random_permutation(TRI_a[7]);
+List_e:random_permutation(TRI_a[10]);
+List_f:random_permutation(TRI_a[11]);";"
+
+
+<p></p>
+<p>Füllen Sie die Lücken aus und geben Sie für die Ausdrücke eine Gleichung in der Form von \(\;\frac{a}{b}\;\) an.<br></p>
+<p><img src=""https://marvin.hs-bochum.de/~mneugebauer/RechtwinkligesDreieck.svg"" alt=""Rechtwinkliges Dreieck mit Seitenvariablen und Begriffen"" class=""img-fluid atto_image_button_text-bottom"" width=""442"" height=""238""><br></p>
+
+
+
+<p></p>
+<p style=""display:inline;"">{@TRI_a[14][1]@}[[input:ans1]][[validation:ans1]][[feedback:prt1]] \( / \) [[input:ans2]][[validation:ans2]][[feedback:prt2]] \( = \)
+ [[input:ans3]][[validation:ans3]][[feedback:prt3]]</p><p>{@TRI_a[14][2]@}[[input:ans4]][[validation:ans4]][[feedback:prt4]] \( / \) [[input:ans5]][[validation:ans5]][[feedback:prt5]] \( = \)
+ [[input:ans6]][[validation:ans6]][[feedback:prt6]]
+</p><p style=""display:inline;"">{@TRI_a[14][3]@}[[input:ans7]][[validation:ans7]][[feedback:prt7]] \( / \) [[input:ans8]][[validation:ans8]][[feedback:prt8]] \( = \)
+ [[input:ans9]][[validation:ans9]][[feedback:prt9]]</p>";;Klären wir nun die Begriffe zu den trigonometrischen Funktionen.;{@TRI_a[1]@};1;"<prt_fields><prt>
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+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">{@TRI_a[5][1]@}<br></p>]]></text>
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+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
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+ <falsefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">{@TRI_a[5][2]@}<br></p>]]></text>
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+ <sans>ans3</sans>
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+ <trueanswernote>prt3-1-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text/>
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+ <falseanswernote>prt3-1-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
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+ <trueanswernote>prt3-2-T</trueanswernote>
+ <truefeedback format=""html"">
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+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
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+ <falseanswernote>prt3-2-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
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+ <sans>ans2</sans>
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+ <trueanswernote>prt3-3-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
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+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
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+ <truescoremode>+</truescoremode>
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+ <trueanswernote>prt3-4-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">{@TRI_a[4]@}<br></p>]]></text>
+ </truefeedback>
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+ <falseanswernote>prt3-4-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <prt>
+ <name>prt4</name>
+ <value>1.0000000</value>
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+ </truefeedback>
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+ <text/>
+ </falsefeedback>
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+ <prt>
+ <name>prt5</name>
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+ <sans>ans5</sans>
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+ <truefeedback format=""html"">
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+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <prt>
+ <name>prt6</name>
+ <value>1.0000000</value>
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+ <node>
+ <name>0</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans6</sans>
+ <tans>ta6</tans>
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+ <falseanswernote>prt6-1-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans4</sans>
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+ <falsefeedback format=""html"">
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+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans5</sans>
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+ <trueanswernote>prt6-3-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsefeedback format=""html"">
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+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
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+ <tans>1</tans>
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+ <truescoremode>+</truescoremode>
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+ <trueanswernote>prt6-4-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">{@TRI_a[8]@}<br></p>]]></text>
+ </truefeedback>
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+ </prt_fields>";;;;;"<input_fields><input>
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+ </input_fields>";<seed_fields><deployedseed>1235785111</deployedseed> <deployedseed>402058525</deployedseed> <deployedseed>289804370</deployedseed></seed_fields>;;
+6;tri;1;f;Trigonometrie;Trigonometrie If - Trigonometrische Umkehrfunktionen 1;"TRI_A:[
+[a1,atan(a/b),""\\(\\alpha\\)"",a,b, ""Weil \\(a\\) (Gegenkathete von \\(\\alpha\\)) und \\(b\\) (Ankathete von \\(alpha\\)) gegeben sind, wäre der Arkustangens hier die richtige Wahl gewesen. \\(\\alpha=\\arctan(\\frac{a}{b})\\)""],
+[a2,atan(b/a),""\\(\\beta\\)"",a,b,""Weil \\(b\\) (Gegenkathete von \\(\\beta\\)) und \\(a\\) (Ankathete von \\(beta\\)) gegeben sind, wäre der Arkustangens hier die richtige Wahl gewesen. \\(\\beta=\\arctan(\\frac{b}{a})\\)""],
+[a3,asin(a/c),""\\(\\alpha\\)"",a,c, ""Weil \\(a\\) (Gegenkathete von \\(\\alpha\\)) und die Hypothenuse \\(c\\) gegeben sind, wäre der Arkussinus hier die richtige Wahl gewesen. \\(\\alpha=\\arcsin(\\frac{a}{c})\\)""],
+[a4,asin(b/c),""\\(\\beta\\)"",b,c, ""Weil \\(b\\) (Gegenkathete von \\(\\beta\\)) und die Hypothenuse \\(c\\) gegeben sind, wäre der Arkussinus hier die richtige Wahl gewesen. \\(\\beta=\\arcsin(\\frac{b}{c})\\)""],
+[a5,acos(b/c),""\\(\\alpha\\)"",b,c, ""Weil \\(b\\) (Ankathete von \\(\\alpha\\)) und die Hypothenuse \\(c\\) gegeben sind, wäre der Arkuscosinus hier die richtige Wahl gewesen. \\(\\alpha=\\arccos(\\frac{b}{c})\\)""],
+[a6,acos(a/c),""\\(\\beta\\)"",a,c, ""Weil \\(a\\) (Ankathete von \\(\\beta\\)) und die Hypothenuse \\(c\\) gegeben sind, wäre der Arkuscosinus hier die richtige Wahl gewesen. \\(\\beta=\\arccos(\\frac{a}{c})\\)""]
+];
+TRI_a:rand(TRI_A);
+ta1:TRI_a[2];";"
+
+<br>
+
+<p>Gegeben sei ein Dreieck mit \(\gamma = 90^\circ\;\). Mit welcher Funktion lässt sich der Winkel {@TRI_a[3]@} berechnen, wenn {@TRI_a[4]@} und {@TRI_a[5]@} gegeben sind. Geben Sie Ihre Rechnung in folgender Form ein: <code>asin(a/b) </code> . (Dies wird interpretiert als \(\sin^{-1}\frac{a}{b}\;\), was gleichbedeutend ist mit \(\arcsin{\frac{a}{b}}\;\)).<br></p>
+
+<p><img src=""https://marvin.hs-bochum.de/~mneugebauer/right-triangle-mathematics-geometry-triangle.png"" alt=""Rechtwinkliges Dreieck mit Variablen und Winkeln"" class=""img-fluid atto_image_button_text-bottom"" style=""width:35em;"" width=""1280"" height=""768""><br></p>
+
+
+<p></p>
+
+<p>{@TRI_a[3]@} \( = \) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>";;Mit den Umkehrfunktionen der trigonometrischen Funktionen (Arkussinus, Arkuskosinus und Arkustangens), kann man mithilfe der Seitenlängen einen gesuchten Winkel berechnen.<br>;{@TRI_a[1]@};1;"<prt>
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+ <falsefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">{@TRI_a[6]@}<br></p>]]></text>
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+ ";;;;;"<input>
+ <name>ans1</name>
+ <type>algebraic</type>
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+6;tri;1;h;Trigonometrie;Trigonometrie I - Endboss (new trig table);"TRI_A:[
+[a1,14,a,""https://marvin.hs-bochum.de/~mneugebauer/trigonometry_question_56_g.png"",""Ein nicht-rechtwinkliges Dreieck mit einem Winkel von 30 Grad zwischen einer Seite mit Länge 10 Mal Wurzel 3 und einer Seite mit Länge 4 und gesucht ist die Länge der dritten Seite a und zwischen der Seite mit Länge a und der Seite mit Länge 4 liegt ein stumpfer Winkel"",""https://marvin.hs-bochum.de/~mneugebauer/trigonometry_question_56_g_solution.png"",10,4],
+[a2,7,a,""https://marvin.hs-bochum.de/~mneugebauer/trigonometry_question_added_j.png"",""Ein nicht-rechtwinkliges Dreieck mit einem Winkel von 30 Grad zwischen einer Seite mit Länge 5 Mal Wurzel 3 und einer Seite mit Länge 2 und gesucht ist die Länge der dritten Seite a und zwischen der Seite mit Länge a und der Seite mit Länge 2 liegt ein stumpfer Winkel"",""https://marvin.hs-bochum.de/~mneugebauer/trigonometry_question_added_j_solution.png"",5,2],
+[a3,21,a,""https://marvin.hs-bochum.de/~mneugebauer/trigonometry_question_added_k.png"",""Ein nicht-rechtwinkliges Dreieck mit einem Winkel von 30 Grad zwischen einer Seite mit Länge 15 Mal Wurzel 3 und einer Seite mit Länge 6 und gesucht ist die Länge der dritten Seite a und zwischen der Seite mit Länge a und der Seite mit Länge 6 liegt ein stumpfer Winkel"",""https://marvin.hs-bochum.de/~mneugebauer/trigonometry_question_added_k_solution.png"",15,6]
+];
+TRI_a:rand(TRI_A);
+ta1:TRI_a[2];";"
+
+
+<p></p>
+<div>
+ <div>Finden Sie die gesuchten Größe mit Hilfe des Satzes von Pythagoras und ggf. mit dem Sinus,<br>Cosinus und Tangens für rechtwinklige Dreiecke.<br><br></div>
+ <div><br></div>
+ <div><img id=""alplot1"" src=""{@TRI_a[4]@}"" alt=""{@TRI_a[5]@}"" style=""width:35em;"" class=""img-fluid atto_image_button_text-bottom""><br></div>
+</div>
+<p></p><br>
+<p>{@TRI_a[3]@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p></p>
+<table style=""border:1px solid black;width:100%;"">
+ <tbody>
+ <tr>
+ <th style=""border:1px solid black;text-align:center;"">\(\alpha\)</th>
+ <th style=""border:1px solid black;text-align:center;"">\(\sin{\alpha}\)</th>
+ <th style=""border:1px solid black;text-align:center;"">\(\cos{\alpha}\) </th>
+ <th style=""border:1px solid black;text-align:center;"">\(\tan{\alpha}\)</th>
+ </tr>
+ <tr>
+ <th style=""border:1px solid black;text-align:center;"">\(0^\circ\)</th>
+ <td style=""border:1px solid black;text-align:center;"">\(0\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(1\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(0\)</td>
+ </tr>
+ <tr>
+ <th style=""border:1px solid black;text-align:center;"">\(30^\circ\)</th>
+ <td style=""border:1px solid black;text-align:center;"">\(\frac{1}{2}\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(\frac{1}{2}\,\sqrt{3}\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(\frac{1}{3}\,\sqrt{3}\)</td>
+ </tr>
+ <tr>
+ <th style=""border:1px solid black;text-align:center;"">\(45^\circ\)</th>
+ <td style=""border:1px solid black;text-align:center;"">\(\frac{1}{2}\,\sqrt{2}\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(\frac{1}{2}\,\sqrt{2}\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(1\)</td>
+ </tr>
+ <tr>
+ <th style=""border:1px solid black;text-align:center;"">\(60^\circ\)</th>
+ <td style=""border:1px solid black;text-align:center;"">\(\frac{1}{2}\,\sqrt{3}\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(\frac{1}{2}\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(\sqrt{3}\)</td>
+ </tr>
+ <tr>
+ <th style=""border:1px solid black;text-align:center;"">\(90^\circ\)</th>
+ <td style=""border:1px solid black;text-align:center;"">\(1\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(0\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(\pm\,\infty \)</td>
+ </tr>
+ </tbody>
+</table>";;Teile dieses nicht-rechtwinklige Dreieck in zwei rechtwinklige Dreieck auf, um dir mithilfe des Satzes von Pythagoras und den trigonometrischen (Umkehr-)Funktionen die Lösung zu erarbeiten. Dies ist die Endgegner-Aufgabe zur Trigonometrie-Welt. Wenn du sie meisterst, bist du hier fertig.<br>;{@TRI_a[1]@};1;"<prt>
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+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
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+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
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+ </falsefeedback>
+ </node>
+ </prt>
+ ";;;;;"<input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
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+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ ";<seed_fields><deployedseed>1459126498</deployedseed><deployedseed>473477096</deployedseed><deployedseed>1107908827</deployedseed></seed_fields>;;
+6;tri;1;e;Trigonometrie;Trigonometrie Ie - Trigonometrie 2 (new trig table);"TRI_A:[
+[a1,5,a,""https://marvin.hs-bochum.de/~mneugebauer/trigonometry_question_56_c.png"",""Ein grünes, rechtwinkliges Dreieck mit einem Winkel von 30 Grad zwischen der Hypothenuse mit Länge 10 und gesucht ist die Länge der Gegenkathete a""],
+[a2,5*sqrt(2),a,""https://marvin.hs-bochum.de/~mneugebauer/trigonometry_question_56_d.png"",""Ein lilanes, rechtwinkliges Dreieck mit einem Winkel von 45 Grad zwischen der Hypothenuse a und Ankathete mit Länge 5 und gesucht ist a""],
+[a3,6,a,""https://marvin.hs-bochum.de/~mneugebauer/trigonometry_question_56_e.png"",""Ein oranges, rechtwinkliges Dreieck mit eine Winkel von 60 Grad zwischen der Hypothenuse und der Ankathete mit Länge 2 Mal Wurzel 3 und gesucht ist die Gegenkathete a""]
+];
+TRI_a:rand(TRI_A);
+ta1:TRI_a[2];";"
+
+
+<p></p>
+<div>
+ <div>Finden Sie die gesuchte Größe mit dem Sinus, Cosinus und Tangens für rechtwinklige Dreiecke. Nutzen Sie die untenstehende Tabelle, um ohne Taschenrechner zu rechnen.<br></div>
+ <div><br></div>
+ <div><img id=""alplot1"" src=""{@TRI_a[4]@}"" alt=""{@TRI_a[5]@}"" style=""width:15em;"" class=""img-fluid atto_image_button_text-bottom""><br></div>
+</div>
+<p></p><br>
+<p>{@TRI_a[3]@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p>
+<p></p><table style=""border:1px solid black;width:100%;"">
+ <tbody>
+ <tr>
+ <th style=""border:1px solid black;text-align:center;"">\(\alpha\)</th>
+ <th style=""border:1px solid black;text-align:center;"">\(\sin{\alpha}\)</th>
+ <th style=""border:1px solid black;text-align:center;"">\(\cos{\alpha}\) </th>
+ <th style=""border:1px solid black;text-align:center;"">\(\tan{\alpha}\)</th>
+ </tr>
+ <tr>
+ <th style=""border:1px solid black;text-align:center;"">\(0^\circ\)</th>
+ <td style=""border:1px solid black;text-align:center;"">\(0\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(1\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(0\)</td>
+ </tr>
+ <tr>
+ <th style=""border:1px solid black;text-align:center;"">\(30^\circ\)</th>
+ <td style=""border:1px solid black;text-align:center;"">\(\frac{1}{2}\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(\frac{1}{2}\,\sqrt{3}\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(\frac{1}{3}\,\sqrt{3}\)</td>
+ </tr>
+ <tr>
+ <th style=""border:1px solid black;text-align:center;"">\(45^\circ\)</th>
+ <td style=""border:1px solid black;text-align:center;"">\(\frac{1}{2}\,\sqrt{2}\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(\frac{1}{2}\,\sqrt{2}\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(1\)</td>
+ </tr>
+ <tr>
+ <th style=""border:1px solid black;text-align:center;"">\(60^\circ\)</th>
+ <td style=""border:1px solid black;text-align:center;"">\(\frac{1}{2}\,\sqrt{3}\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(\frac{1}{2}\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(\sqrt{3}\)</td>
+ </tr>
+ <tr>
+ <th style=""border:1px solid black;text-align:center;"">\(90^\circ\)</th>
+ <td style=""border:1px solid black;text-align:center;"">\(1\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(0\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(\pm\,\infty \)</td>
+ </tr>
+ </tbody>
+</table>
+<p></p>";;Jetzt kannst du die trigonometrischen Funktionen anwenden, um die folgende Aufgabe zu lösen.<br>;{@TRI_a[1]@};1;"<prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
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+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
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+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ ";;;;;"<input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
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+ <options/>
+ </input>
+ ";<seed_fields><deployedseed>1802148976</deployedseed><deployedseed>524685442</deployedseed><deployedseed>1311829765</deployedseed></seed_fields>;;
+6;tri;1;g;Trigonometrie;Trigonometrie Ig - Trigonometrische Umkehrfunktion 2 (new trig table);"TRI_A:[
+[a1,60,alpha,""https://marvin.hs-bochum.de/~mneugebauer/trigonometry_question_56_f.png"",""Ein hellblaues, rechtwinkliges Dreieck gesucht ist alpha, was zwischen der Hypothenuse mit Länge 6 und der Ankathete mit Länge 3 liegt"", ""Weil die Ankathete von \\(\\alpha\\) und die Hypothenuse gegeben sind, wäre der Arkuscosinus hier die richtige Wahl gewesen. \\(\\alpha=\\arccos(\\frac{3}{6}) = \\arccos(\\frac{1}{2}) = 60^\\circ\\)""],
+[a2,45,alpha,""https://marvin.hs-bochum.de/~mneugebauer/trigonometry_question_added_g.png"",""Ein braunes, rechtwinkliges Dreieck gesucht ist alpha, was zwischen der Hypothenuse mit Länge 6 und der unbekannten Seite liegt und die gegenüberliegende Seite hat eine Länge von 3 Mal Wurzel 2"", ""Weil die Gegenkathete von \\(\\alpha\\) und die Hypothenuse gegeben sind, wäre der Arkussinus hier die richtige Wahl gewesen. \\(\\alpha=\\arcsin(\\frac{3\\,\\sqrt{2}}{6}) = \\arcsin(\\frac{1}{2}\\,\\sqrt{2}) = 45^\\circ\\)""],
+[a3,60,alpha,""https://marvin.hs-bochum.de/~mneugebauer/trigonometry_question_added_h.png"",""Ein pinkes, rechtwinkliges Dreieck gesucht ist alpha, was zwischen der Hypothenuse mit unbekannter Länge und einer Seite mit Länge 5 liegt und die gegenüberliegende Seite hat die Länge 5 Mal Wurzel 3"",""Weil die Gegenkathete von \\(\\alpha\\) und die Ankathete von \\(\\alpha\\) gegeben sind, wäre der Arkustangens hier die richtige Wahl gewesen. \\(\\alpha=\\arctan(\\frac{5\\,\\sqrt{3}}{5}) = \\arctan(\\sqrt{3}) = 60^\\circ\\)""]
+];
+TRI_a:rand(TRI_A);
+ta:TRI_a[2];";"
+
+
+<p></p>
+<div>
+ <div>Finden Sie die gesuchte Größe mit Hilfe des Arcussinus, des Arcuscosinus oder des Arcustangens und geben Sie sie im Gradmaß an. Nutzen Sie die untenstehende Tabelle, um ohne Taschenrechner zu rechnen.<br></div>
+ <div><br></div>
+ <div><img id=""alplot1"" src=""{@TRI_a[4]@}"" alt=""{@TRI_a[5]@}"" style=""width:15em;"" class=""img-fluid atto_image_button_text-bottom""><br></div>
+</div>
+<p></p><br>
+<p>{@TRI_a[3]@}\(\,=\,\) [[input:ans1]]\(^\circ\)[[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p>
+<table style=""border:1px solid black;width:100%;"">
+ <tbody>
+ <tr>
+ <th style=""border:1px solid black;text-align:center;"">\(\alpha\)</th>
+ <th style=""border:1px solid black;text-align:center;"">\(\sin{\alpha}\)</th>
+ <th style=""border:1px solid black;text-align:center;"">\(\cos{\alpha}\) </th>
+ <th style=""border:1px solid black;text-align:center;"">\(\tan{\alpha}\)</th>
+ </tr>
+ <tr>
+ <th style=""border:1px solid black;text-align:center;"">\(0^\circ\)</th>
+ <td style=""border:1px solid black;text-align:center;"">\(0\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(1\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(0\)</td>
+ </tr>
+ <tr>
+ <th style=""border:1px solid black;text-align:center;"">\(30^\circ\)</th>
+ <td style=""border:1px solid black;text-align:center;"">\(\frac{1}{2}\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(\frac{1}{2}\,\sqrt{3}\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(\frac{1}{3}\,\sqrt{3}\)</td>
+ </tr>
+ <tr>
+ <th style=""border:1px solid black;text-align:center;"">\(45^\circ\)</th>
+ <td style=""border:1px solid black;text-align:center;"">\(\frac{1}{2}\,\sqrt{2}\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(\frac{1}{2}\,\sqrt{2}\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(1\)</td>
+ </tr>
+ <tr>
+ <th style=""border:1px solid black;text-align:center;"">\(60^\circ\)</th>
+ <td style=""border:1px solid black;text-align:center;"">\(\frac{1}{2}\,\sqrt{3}\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(\frac{1}{2}\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(\sqrt{3}\)</td>
+ </tr>
+ <tr>
+ <th style=""border:1px solid black;text-align:center;"">\(90^\circ\)</th>
+ <td style=""border:1px solid black;text-align:center;"">\(1\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(0\)</td>
+ <td style=""border:1px solid black;text-align:center;"">\(\pm\,\infty \)</td>
+ </tr>
+ </tbody>
+</table>";;Jetzt kannst du die trigonometrischen Umkehrfunktionen anwenden, um folgende Aufgabe zu lösen.<br>;{@TRI_a[1]@};1;"<prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
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+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir=""ltr"" style=""text-align: left;""><br></p>]]></text>
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+ <falsefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">{@TRI_a[6]@}<br></p>]]></text>
+ </falsefeedback>
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+ ";;;;;"<input>
+ <name>ans1</name>
+ <type>algebraic</type>
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+ ";<seed_fields><deployedseed>1254109099</deployedseed><deployedseed>1900357917</deployedseed><deployedseed>909199558</deployedseed></seed_fields>;;
+8;sur;1;a;Umfrage;Umfrage I - Fragen gesammelt;"/*ta1:[[1,true,""1 - Stimme überhaupt nicht zu""],[2,true,""2""],[3,true,""3""],[4,true,""4""],[5,true,""5""],[6,true,""6""],[7,true,""7""],[8,true,""8""],[9,true,""9""],[10,true,""10 - Stimme voll zu""]];*/
+ta1:[[1,true,""1 - Stimme überhaupt nicht zu""],[2,true,""2""],[3,true,""3""],[4,true,""4""],[5,true,""5 - Stimme voll zu""]];
+ta2:"""";
+ta3:[[1,true,""Zuhause""],[2,true,""unterwegs (z. B. Bus, Bahn)""],[3,true,""in der Hochschule""],[4,true,""woanders, nämlich""]];
+ta4:[[1,true,""Smartphone""],[2,true,""Tablet""],[3,true,""Laptop""],[4,true,""anderes, nämlich""]];";"
+<p></p>
+<p>[[input:ans6]] [[validation:ans6]][[feedback:prt6]]<br></p>
+<p>1. Verglichen mit dem Lösen von Aufgaben in der Schule, war ich motivierter, die Aufgaben im gerade durchlaufenen Übungsraum zu lösen.<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p>
+<p><br></p>
+<p></p>
+<div>
+ <p xml:lang=""DE-DE"" lang=""DE-DE""><span data-contrast=""auto"" xml:lang=""DE-DE"" lang=""DE-DE"">2. Die Hilfestellungen im gerade durchlaufenen Übungsraum haben mir beim Lösen der Aufgaben weitergeholfen.</span></p>
+</div>
+<p></p>
+<p></p>
+<p>[[input:ans2]] [[validation:ans2]][[feedback:prt2]]</p>
+<p><br></p>
+<p><br></p>
+<p></p>
+<div>
+ <p xml:lang=""DE-DE"" lang=""DE-DE""><span data-contrast=""auto"" xml:lang=""DE-DE"" lang=""DE-DE"">3. Der ansteigende Schwierigkeitsgrad zusammen mit dem Aufgabendesign haben mich motiviert, am Ball zu bleiben.</span> <br></p>
+</div>[[input:ans11]] [[validation:ans11]][[feedback:prt11]]<br>
+<p></p>
+<p><br></p>
+<p><br></p>
+<p>4. Ich hätte es besser gefunden, wenn die Aufgaben in absteigender Schwierigkeit gestellt worden wären. Also von schwer nach leicht, statt von leicht nach schwer.<br></p>
+<p>[[input:ans14]] [[validation:ans14]][[feedback:prt14]]<br>
+</p>
+<p></p>
+<p><br></p>
+<p><br></p>5. Ich kann mir gut vorstellen, Übungsräume wie diese als studienbegleitendes Training zu nutzen.<br>
+<p></p>
+<p>[[input:ans3]] [[validation:ans3]][[feedback:prt3]]</p>
+<p><br></p>
+<p><br></p>
+<p>6. Den Einsatz spielerischer Elemente (Level, Welten, Endgegner) im Übungsraum empfand ich als passend.<br></p>
+<p></p>
+<p>[[input:ans4]] [[validation:ans4]][[feedback:prt4]]</p>
+<p><br></p>
+<p><br></p>
+<p></p>
+<p>7. Welches
+ Feedback haben Sie noch grundsätzlich zu den spielerischen Elementen (Level, Welten, Endgegner)
+ des Übungsraums?<br></p>
+<p></p>
+<p>[[input:ans7]] [[validation:ans7]][[feedback:prt7]]</p>
+<p></p>
+<p><br></p>
+<p></p>
+<p><br></p>
+<p></p>
+<p></p>
+<div>
+ <p xml:lang=""DE-DE"" lang=""DE-DE""><span data-contrast=""auto"" xml:lang=""DE-DE"" lang=""DE-DE"">8. Dass die Unterstützung durch ein Icon dargestellt wurde finde ich grundsätzlich gut.</span> <br></p>
+</div>
+<p></p>
+<img style=""border:2px solid black; border-radius:50%; width: 7.5em;"" src=""https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"">
+<p></p>
+<p>[[input:ans8]] [[validation:ans8]][[feedback:prt8]]</p><br>
+<p></p>
+<p><br></p>
+
+<p><span data-contrast=""auto"" xml:lang=""DE-DE"" lang=""DE-DE"">9. Ich möchte in Zukunft selber auswählen können, welches Icon die Unterstützung darstellt. Beispiele:<br></span></p>
+
+<p style=""display:flex;flex-wrap:wrap;"">
+ <img style=""border:2px solid black; border-radius:50%; width: 7.5em;margin:0.1em 0.5em;"" src=""https://marvin.hs-bochum.de/~mneugebauer/avatar_alt/avatar_2.svg"">
+ <img style=""border:2px solid black; border-radius:50%; width: 7.5em;margin:0.1em 0.5em;"" src=""https://marvin.hs-bochum.de/~mneugebauer/avatar_alt/avatar_3.svg"">
+ <img style=""border:2px solid black; border-radius:50%; width: 7.5em;margin:0.1em 0.5em;"" src=""https://marvin.hs-bochum.de/~mneugebauer/avatar_alt/avatar_4.svg"">
+ <img style=""border:2px solid black; border-radius:50%; width: 7.5em;margin:0.1em 0.5em;"" src=""https://marvin.hs-bochum.de/~mneugebauer/avatar_alt/avatar_5.svg"">
+ <img style=""border:2px solid black; border-radius:50%; width: 7.5em;margin:0.1em 0.5em;"" src=""https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"">
+</p>
+
+<p></p>
+<p>[[input:ans12]] [[validation:ans12]][[feedback:prt12]]</p>
+<p><br></p>
+<p><br></p>
+<p></p>
+<div>
+ <p xml:lang=""DE-DE"" lang=""DE-DE""><span data-contrast=""auto"" xml:lang=""DE-DE"" lang=""DE-DE"">10. Ich habe den Übungsraum heute an folgendem Gerät gemacht.</span></p>
+ <p class=""move-next-input-field-here"" xml:lang=""DE-DE"" lang=""DE-DE""><span data-contrast=""auto"" xml:lang=""DE-DE"" lang=""DE-DE"">[[input:ans15]] [[validation:ans15]][[feedback:prt15]]<br>[[input:ans16]] [[validation:ans16]][[feedback:prt16]]<br></span></p>
+</div>
+<div>
+ <p xml:lang=""DE-DE"" lang=""DE-DE""><span data-contrast=""auto"" xml:lang=""DE-DE"" lang=""DE-DE""><br></span></p><p xml:lang=""DE-DE"" lang=""DE-DE""><span data-contrast=""auto"" xml:lang=""DE-DE"" lang=""DE-DE""><br></span></p>
+ <p xml:lang=""DE-DE"" lang=""DE-DE""><span data-contrast=""auto"" xml:lang=""DE-DE"" lang=""DE-DE"">11. Der Ort, an dem ich in Zukunft am ehesten solche Übungsräume benutzen würde, wäre</span></p>
+ <p xml:lang=""DE-DE"" class=""move-next-input-field-here"" lang=""DE-DE"">[[input:ans9]] [[validation:ans9]][[feedback:prt9]]<br>
+ [[input:ans13]] [[validation:ans13]][[feedback:prt13]]
+ </p>
+</div><br>
+<p></p>
+<p>12. Welches Feedback haben Sie noch grundsätzlich zur Bedienung des Übungsraumes?<br></p>
+<p></p>
+<p>[[input:ans5]] [[validation:ans5]][[feedback:prt5]]</p>
+<p></p>
+<p><br></p>
+<p><br></p><br>
+<p></p><br>
+<p></p>
+<p></p>
+<p></p>
+<p><br></p><br>
+<p></p>";;;;1;"<prt_fields><prt>
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+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Danke! Ihre Eingabe wurde gespeichert.<br></p>]]></text>
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+ <truefeedback format=""html"">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt13-1-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <prt>
+ <name>prt14</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>2</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt14-1-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Danke! Ihre Eingabe wurde gespeichert.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt14-1-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <prt>
+ <name>prt15</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>2</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt15-1-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Danke! Ihre Eingabe wurde gespeichert.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt15-1-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <prt>
+ <name>prt16</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt16-1-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt16-1-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <prt>
+ <name>prt2</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>2</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt2-1-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Danke! Ihre Eingabe wurde gespeichert.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt2-1-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <prt>
+ <name>prt3</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>2</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt3-1-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Danke! Ihre Eingabe wurde gespeichert.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt3-1-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <prt>
+ <name>prt4</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>2</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt4-1-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Danke! Ihre Eingabe wurde gespeichert.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt4-1-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <prt>
+ <name>prt5</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>2</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt5-1-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Danke! Ihre Eingabe wurde gespeichert.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt5-1-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <prt>
+ <name>prt6</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt6-1-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt6-1-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <prt>
+ <name>prt7</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>2</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt7-1-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Danke! Ihre Eingabe wurde gespeichert.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt7-1-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <prt>
+ <name>prt8</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>2</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt8-1-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Danke! Ihre Eingabe wurde gespeichert.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt8-1-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <prt>
+ <name>prt9</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>2</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt9-1-T</trueanswernote>
+ <truefeedback format=""html"">
+ <text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Danke! Ihre Eingabe wurde gespeichert.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt9-1-F</falseanswernote>
+ <falsefeedback format=""html"">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ </prt_fields>";;;;;"<input_fields><input>
+ <name>ans1</name>
+ <type>radio</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>0</mustverify>
+ <showvalidation>0</showvalidation>
+ <options>nonotanswered</options>
+ </input>
+ <input>
+ <name>ans11</name>
+ <type>radio</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>0</mustverify>
+ <showvalidation>0</showvalidation>
+ <options>nonotanswered</options>
+ </input>
+ <input>
+ <name>ans12</name>
+ <type>radio</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>0</mustverify>
+ <showvalidation>0</showvalidation>
+ <options>nonotanswered</options>
+ </input>
+ <input>
+ <name>ans13</name>
+ <type>string</type>
+ <tans>ta2</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>0</mustverify>
+ <showvalidation>0</showvalidation>
+ <options>hideanswer</options>
+ </input>
+ <input>
+ <name>ans14</name>
+ <type>radio</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>0</mustverify>
+ <showvalidation>0</showvalidation>
+ <options>nonotanswered</options>
+ </input>
+ <input>
+ <name>ans15</name>
+ <type>radio</type>
+ <tans>ta4</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>0</mustverify>
+ <showvalidation>0</showvalidation>
+ <options>nonotanswered</options>
+ </input>
+ <input>
+ <name>ans16</name>
+ <type>string</type>
+ <tans>ta2</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>0</mustverify>
+ <showvalidation>0</showvalidation>
+ <options>hideanswer</options>
+ </input>
+ <input>
+ <name>ans2</name>
+ <type>radio</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>0</mustverify>
+ <showvalidation>0</showvalidation>
+ <options>nonotanswered</options>
+ </input>
+ <input>
+ <name>ans3</name>
+ <type>radio</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>0</mustverify>
+ <showvalidation>0</showvalidation>
+ <options>nonotanswered</options>
+ </input>
+ <input>
+ <name>ans4</name>
+ <type>radio</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>0</mustverify>
+ <showvalidation>0</showvalidation>
+ <options>nonotanswered</options>
+ </input>
+ <input>
+ <name>ans5</name>
+ <type>notes</type>
+ <tans>ta2</tans>
+ <boxsize>30</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>0</mustverify>
+ <showvalidation>0</showvalidation>
+ <options/>
+ </input>
+ <input>
+ <name>ans6</name>
+ <type>string</type>
+ <tans><![CDATA[""Filled by Javascript""]]></tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>0</mustverify>
+ <showvalidation>0</showvalidation>
+ <options>hideanswer</options>
+ </input>
+ <input>
+ <name>ans7</name>
+ <type>notes</type>
+ <tans>ta2</tans>
+ <boxsize>30</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>0</mustverify>
+ <showvalidation>0</showvalidation>
+ <options/>
+ </input>
+ <input>
+ <name>ans8</name>
+ <type>radio</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>0</mustverify>
+ <showvalidation>0</showvalidation>
+ <options>nonotanswered</options>
+ </input>
+ <input>
+ <name>ans9</name>
+ <type>radio</type>
+ <tans>ta3</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>0</mustverify>
+ <showvalidation>0</showvalidation>
+ <options>nonotanswered</options>
+ </input>
+ </input_fields>";;;
+7;der;1;a;Ableitungen;Ganzzahlige Summanden ableiten;"nums:rand_selection(makelist(i,i,10),4); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; exercise:nums[1]*myvar^powers[1]+nums[2]*myvar^powers[2]+nums[3]*myvar+nums[4]; ta1:diff(exercise,myvar);";"Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).";\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]];Tipp: Leite jeden Summanden einzeln ab.;"\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)";0;;;;;;;<seed_fields><deployedseed>351097132</deployedseed> <deployedseed>1047509677</deployedseed> <deployedseed>442872926</deployedseed> <deployedseed>286970886</deployedseed> <deployedseed>999400432</deployedseed></seed_fields>;;
+7;der;1;b;Ableitungen;Gebrochenrationale Summanden ableiten;"myint:rand_with_step(1,10,1); numerators:rand_selection(makelist(i+2,i,6),3); denominators:makelist(rand_with_step(numerators[i]+1,numerators[i]+5,1),i,3); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; fractions:makelist(numerators[i]/denominators[i],i,3); exercise:fractions[1]*myvar^powers[1]+fractions[2]*myvar^powers[2]+fractions[3]*myvar+myint; ta1:diff(exercise,myvar);";"Bestimme die Ableitung von \(f({@myvar@})={@fractions[1]@} \cdot {@myvar@}^{@powers[1]@}+{@fractions[2]@} \cdot {@myvar@}^{@powers[2]@}+{@fractions[3]@} \cdot {@myvar@}+{@myint@}\;\).";\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]];Tipp: Leite jeden Summanden einzeln ab.;"\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)";0;;;;;;;<seed_fields><deployedseed>857840145</deployedseed> <deployedseed>1543126498</deployedseed> <deployedseed>1871228756</deployedseed> <deployedseed>318121367</deployedseed> <deployedseed>2127933990</deployedseed> <deployedseed>484803571</deployedseed> <deployedseed>1056868370</deployedseed></seed_fields>;;
+7;der;1;c;Ableitungen;Produkte ableiten I;"powers:rand_selection(makelist(i+1,i,4),2); myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,4),2); exercise:(myvar^powers[1]+nums[1])*(myvar^powers[2]-nums[2]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);";"Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).";\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]];<p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p>;"\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)";0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";;;;;;<seed_fields><deployedseed>1213180404</deployedseed> <deployedseed>1876101711</deployedseed> <deployedseed>1520468669</deployedseed> <deployedseed>1233734487</deployedseed> <deployedseed>1329784126</deployedseed></seed_fields>;;
+7;der;1;d;Ableitungen;Produkte ableiten II;"num:rand_with_step(1,5,2); denom:rand_with_step(num+2, num+5,2); fraction:num/denom; nums:rand_selection(append(makelist(i-7,i,6),makelist(i,i,6)),4); myvar:rand([a,b,c,x,y,z]); power:rand([3,4]); exercise:(fraction*myvar+nums[1])*(nums[2]*myvar^power+nums[3]*myvar+nums[4]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);";"Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).";\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]];<p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p>;"\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)";0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";;;;;;<seed_fields><deployedseed>290055394</deployedseed> <deployedseed>1877259825</deployedseed> <deployedseed>1027269811</deployedseed> <deployedseed>1906880472</deployedseed> <deployedseed>1551769121</deployedseed></seed_fields>;;
+7;der;1;e;Ableitungen;Division ableiten I;"powers:[rand_with_step(3,4,1), 2]; nums:rand_selection(makelist(i,i,12),5); myvar:rand([a,b,c,x,y,z]); exercise:(myvar^powers[1]+nums[1]*myvar^powers[2]+myvar)/(nums[2]*myvar^2+nums[3]*myvar+nums[4]); ta1:diff(exercise, myvar); ta1alt:expand(ta1);";"Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).";\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]];<p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p>;"\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)";0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";;;;;;<seed_fields><deployedseed>1439694172</deployedseed> <deployedseed>1028579078</deployedseed> <deployedseed>1454088108</deployedseed> <deployedseed>1063999325</deployedseed> <deployedseed>1974598074</deployedseed></seed_fields>;;
+7;der;1;f;Ableitungen;Division ableiten II;"nums:[rand([3,5,7,11]), rand_with_step(2,5,1)]; myvar:rand([a,b,c,x,y,z]); terms:[sqrt(nums[1])*myvar-nums[2], nums[1]*myvar^2-nums[2]]; terms:random_permutation(terms); exercise:terms[1]/terms[2]; ta1:diff(exercise, myvar); ta1alt:expand(ta1);";"Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).";\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]];<p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p>;"\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)";0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format=""html""><text><![CDATA[<p dir=""ltr"" style=""text-align: left;"">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";;;;;;<seed_fields><deployedseed>525681144</deployedseed> <deployedseed>1447367624</deployedseed> <deployedseed>435810786</deployedseed> <deployedseed>1421496847</deployedseed> <deployedseed>918279888</deployedseed></seed_fields>;;
+7;der;1;g;Ableitungen;Kettenregel I;"myvar:rand([a,b,c,x,y,z]); root:rand([3,5]); num:rand_with_step(3,9,1); exercise:(myvar^2-num)^(1/root); ta1:diff(exercise,myvar);";"Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root@}]{{@myvar@}^2-{@num@}}\;\).";\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]];<p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p>;"\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)";0;;;;;;;<seed_fields><deployedseed>1079586531</deployedseed> <deployedseed>1754291070</deployedseed> <deployedseed>1751932072</deployedseed> <deployedseed>1089076165</deployedseed> <deployedseed>215450400</deployedseed> <deployedseed>766534514</deployedseed></seed_fields>;;
+7;der;1;h;Ableitungen;Kettenregel II;"myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,5),3); power:rand_with_step(3,7,2); signs:makelist(rand([-1,1]),2); exercise:(nums[1]*myvar^2+signs[1]*nums[2]*myvar+signs[2]*nums[3])^power; ta1:diff(exercise,myvar);";"Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).";\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]];<p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p>;"\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)";0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";;;;;;<seed_fields><deployedseed>1676415387</deployedseed> <deployedseed>146672542</deployedseed> <deployedseed>1726255949</deployedseed> <deployedseed>1628089061</deployedseed> <deployedseed>633210403</deployedseed> <deployedseed>1850144475</deployedseed></seed_fields>;;Custom PRT consists of one node: Algebraic Equivalence with ta1 is correct.
+7;der;1;i;Ableitungen;Gemischtes I;"myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,5),2); nums:rand_selection(makelist(i+1,i,58),2); exercise:(myvar^powers[1]+nums[1])^powers[2]*nums[2]*myvar; ta1:diff(exercise, myvar);";"Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).";\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]];;"\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)";0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";;;;;;<seed_fields><deployedseed>603470063</deployedseed> <deployedseed>1387533043</deployedseed> <deployedseed>820026169</deployedseed> <deployedseed>1884036955</deployedseed> <deployedseed>562165609</deployedseed> <deployedseed>931146921</deployedseed></seed_fields>;;Custom PRT consists of one node: Algebraic Equivalence with ta1 is correct.
+7;der;1;j;Ableitungen;Gemischtes II;"myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,3),3); nums:rand_selection(makelist(i,i,5),2); exercise:(myvar^powers[1]-nums[1])^powers[2]*(myvar+nums[2])^powers[3]; ta1:diff(exercise,myvar);";"Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).";\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]];;"\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)";0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";;;;;;<seed_fields><deployedseed>949540891</deployedseed> <deployedseed>2032277992</deployedseed> <deployedseed>504654950</deployedseed> <deployedseed>906697601</deployedseed> <deployedseed>1241320418</deployedseed> <deployedseed>891184866</deployedseed></seed_fields>;;Custom PRT consists of one node: Algebraic Equivalence with ta1 is correct.
+7;der;1;k;Ableitungen;Gemischtes III;"myvar:rand([a,b,c,x,y,z]); terms:[rand_with_step(1,4,1)+myvar, myvar]; terms:random_permutation(terms); power:rand_with_step(3,7,1); exercise:(terms[1]/terms[2])^power; ta1:diff(exercise,myvar);";"Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).";\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]];;"\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)";0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";;;;;;<seed_fields><deployedseed>1060600269</deployedseed> <deployedseed>1317786455</deployedseed> <deployedseed>2016195942</deployedseed> <deployedseed>79640143</deployedseed> <deployedseed>1481526612</deployedseed></seed_fields>;;Custom PRT consists of one node: Algebraic Equivalence with ta1 is correct.
+7;der;1;l;Ableitungen;Gemischtes IV;"myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),2); power:rand_with_step(2,6,1); exercise:nums[1]*sqrt(nums[2]*myvar+myvar^power); ta1:diff(exercise,myvar);";"Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).";\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]];;"\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)";0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";;;;;;<seed_fields><deployedseed>63010318</deployedseed> <deployedseed>2022252790</deployedseed> <deployedseed>2032269463</deployedseed> <deployedseed>1301956355</deployedseed> <deployedseed>1085730060</deployedseed></seed_fields>;;Custom PRT consists of one node: Algebraic Equivalence with ta1 is correct.
+7;der;1;m;Ableitungen;Gemischtes V;"myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),4); power:rand_with_step(2,5,1); terms:[(nums[1]*myvar+nums[2]), (nums[3]*myvar^power-nums[4])]; terms:random_permutation(terms); exercise:(terms[1]*terms[2])/myvar; ta1:diff(exercise,myvar);";"Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).";\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]];;"\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)";0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";;;;;;<seed_fields><deployedseed>1627444094</deployedseed> <deployedseed>570947981</deployedseed> <deployedseed>1123631251</deployedseed> <deployedseed>566895213</deployedseed> <deployedseed>265672538</deployedseed></seed_fields>;;Custom PRT consists of one node: Algebraic Equivalence with ta1 is correct.
+7;der;1;n;Ableitungen;Gemischtes VI;"myvar:rand([a,b,c,x,y,z]); root_power:rand_with_step(3,6,1); power:rand_with_prohib(2,5,[root_power]); nums:rand_selection(makelist(i+2,i,6),2);exercise:(nums[1]*myvar-nums[2])^(power/root_power); ta1:diff(exercise,myvar);";"Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;\).";\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]];;"\(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;f’(x)={@ta1@}\)";0;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";;;;;;<seed_fields><deployedseed>466316231</deployedseed> <deployedseed>73259082</deployedseed> <deployedseed>253364053</deployedseed> <deployedseed>1197047345</deployedseed> <deployedseed>873528357</deployedseed> <deployedseed>10923026</deployedseed> <deployedseed>1464509121</deployedseed></seed_fields>;;Custom PRT consists of one node: Algebraic Equivalence with ta1 is correct.
+7;der;1;o;Ableitungen;Gemischtes VII;"myvar:rand([a,b,c,x,y,z]);";"Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).";\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]];;"\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)";1;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";;;;;;<seed_fields></seed_fields>;;Custom PRT consists of one node: Algebraic Equivalence with ta1 is correct.
+7;der;1;p;Ableitungen;Gemischtes VIII;"myvar:rand([a,b,c,x,y,z]);";"Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).";\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]];;"\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)";1;"<prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text></text></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions></testoptions><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty></truepenalty><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format=""html""><text></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty></falsepenalty><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format=""html""><text></text></falsefeedback></node></prt>";;;;;;<seed_fields></seed_fields>;;Custom PRT consists of one node: Algebraic Equivalence with ta1 is correct.
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diff --git a/question-files/questions-all_ger.xml b/question-files/questions-all_ger.xml
new file mode 100644
index 0000000000000000000000000000000000000000..442a38acab01674c18a1d358c1ed85d598cb6432
--- /dev/null
+++ b/question-files/questions-all_ger.xml
@@ -0,0 +1,46920 @@
+<quiz><question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-a Gleichung eingeben (Multiplikation)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Geben Sie die Gleichung \({@ta1@}\) in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Hier eine leichte Aufgabe zur Eingabe. Benutze für jede Multiplikation das Symbol * (Stern).
+ <!--<span class="show-on-mobile-only"><br><br>Nutze die <a href="javascript:;" onclick="let userFocusTop = document.createElement('div');userFocusTop.classList.add('user-focus', 'hide-top');let pageHeight = document.documentElement.scrollHeight;userFocusTop.style.height=Math.ceil(pageHeight+window.pageYOffset)+'px';userFocusTop.onclick = removeTutorialFocus;document.body.appendChild(userFocusTop);">Buttons über deiner Tastatur</a>, um die wichtigsten Mathe-Operatoren schnell zu finden.</span>-->
+ <br><br>Falls du ohne Tastatur unterwegs bist, kannst du mithilfe des <a href="javascript:;" onclick="tutorialFocusElement(document.querySelector('.mathsbutton'));">Mathe-Operatoren-Buttons</a> zusätzliche Buttons aktivieren, um alle Mathe-Operatoren schnell zu finden.
+
+ <!--<br><br>Drücke jederzeit den "Prüfen"-Button, um zu sehen, wie deine Eingabe interpretiert wurde.<br>Erst wenn du nach dem "Prüfen"-Button deine Eingabe nicht änderst und
+ erneut "Prüfen" klickst, wird deine Eingabe als Antwort abgeschickt.-->
+<br><br>Neben dem Eingabefeld siehst du, wie deine Eingabe interpretiert wird.<br>Wenn du auf den "Prüfen"-Button klickst, wird deine Eingabe als Antwort abgeschickt.
+</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,y=3*x+5],[a2,y=4*x+3],[a3,y=2*x+1],[a4,y=2*x-5],[a5,y=5*x-3],[a6,y=4*x-6]];SYN_a:rand(SYN_A);ta1:SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>480757020</deployedseed><deployedseed>585237317</deployedseed><deployedseed>1798333349</deployedseed><deployedseed>2118152732</deployedseed><deployedseed>1988707695</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-b Gleichung eingeben (Division)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Geben Sie die Gleichung \({@TA@}\) in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Divisionen werden mit / (Slash) dargestellt. Hier erscheinen Sie als Brüche.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,y=5/3],[a2,y=4/7],[a3,y=1/3],[a4,y=2/5],[a5,y=3/10],[a6,y=1/4]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);TA:SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>TA</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Wir arbeiten hier nur wenn explizit danach gefragt wird mit Dezimalzahlen. Brüche stellen das Ergebnis in der Regel genauer dar.<br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>TA</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords>3x</forbidwords><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>2690042</deployedseed><deployedseed>300094393</deployedseed><deployedseed>765518486</deployedseed><deployedseed>17019212</deployedseed><deployedseed>1233892964</deployedseed><deployedseed>147932577</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-c Potenzen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Geben Sie die Gleichung \[{@ta@}\] in das Eingabefeld ein.</p>
+<p><p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p><p class="hint"><p>Mit dem Zeichen ^ (Caret) kannst du Potenzen darstellen.</p><div> <ul> <li>\(x^2\) wird so eingegeben: <code>x^2</code></li> <li>\(x^{-2}\) wird so eingegeben: <code>x^(-2)</code></li> <li>\(x^{1/3}\) wird so eingegeben: <code>x^(1/3)</code></li> </ul></div></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,(4+b)^2],[a2,(5+b)^2],[a3,(3+b)^2],[a4,(2+b)^2],[a5,(3+2*b)^2],[a6,(4+2*b)^2]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:expand(SYN_a[2])=SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[Sehr gut. Hier wurde übrigens eine binomische Formel angewendet, um einen Term zu faktorisieren.<br><p dir="ltr" style="text-align: left;" <br=""></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Deine Antwort ist zwar äquivalent mit der dargestellten Gleichung, aber du hast nicht genau die gleiche Gleichung dargestellt.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>93323135</deployedseed><deployedseed>1032837775</deployedseed><deployedseed>680315517</deployedseed><deployedseed>838329017</deployedseed><deployedseed>162866526</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-d Rationale Ausdrücke</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Geben Sie die Gleichung \[{@ta@}\] in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Machen wir es etwas komplizierter. Um Terme in Brüchen darzustellen, musst du besonders auf die Klammersetzung achten.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:x^2;b:(x+1);c:(x-5);SYN_A:[[a1,a,b,c],[a2,b,a,c],[a3,c,a,b]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:SYN_a[2]/(SYN_a[3]*SYN_a[4]);wa:SYN_a[2]/SYN_a[3]*SYN_a[4];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;" <br=""></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Bitte beachte, dass du um den Nenner zusätzliche Klammern setzen musst, damit er als zusammenhängender Divisor interpretiert wird.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>82298515</deployedseed><deployedseed>1458249622</deployedseed><deployedseed>1731794639</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-e Wurzelzeichen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Geben Sie \[{@ta1@}\] in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Gut. Um eine Wurzel darzustellen nutze <code>sqrt(x)</code> für \(\sqrt{x}\;\).</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,3],[a2,5],[a3,7],[a4,11],[a5,13],[a6,19]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta1:sqrt(SYN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1136692395</deployedseed><deployedseed>659595513</deployedseed><deployedseed>2040368424</deployedseed><deployedseed>262860513</deployedseed><deployedseed>592365331</deployedseed><deployedseed>1218846808</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-f Mehrere Lösungen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Lösen Sie nach \(x\) auf. Geben Sie die Lösung in der Form \(x=? \mbox{ or } x=?\) ein.</p>
+<p><p>\[{@task@}\]<br></p><p>[[input:ans]] [[validation:ans]][[feedback:prt1]]</p><p><em>Achtung: Bitte setzen Sie kein zusätzliches +-Symbol vor positive Zahlen.<br></em></p></p><p class="hint">Gelegentlich müssen Ausdrücke mit logischen Verbindungen verknüpft werden. Nutze dafür <code>and</code> oder <code>or</code>. <br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,4],[a2,9],[a3,16],[a4,25],[a5,36]];/*SYN_a:SYN_A[1];*/SYN_a:rand(SYN_A);ta:x=sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);taalt:x=+sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);task:x^2=SYN_a[2];wa1:x=sqrt(SYN_a[2]);wa2:x=-sqrt(SYN_a[2]);wa3:x=sqrt(SYN_a[2]) nounand x=-sqrt(SYN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>4</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>4</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>5</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>4</name><answertest>AlgEquiv</answertest><sans>1</sans><tans>1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-5-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr">Du hast nur eine von zwei richtigen Lösungen eingegeben.<br>Beispiel: \(5 \cdot 5 = 25\) und \(-5 \cdot -5 = 25\) (Minus Mal Minus ergibt Plus).<br>Für \(x^2 = 25\) gilt deshalb \(x = 5\) oder \(x = -5\), was hier in der Form <code>x=5 or x=-5</code> aufgeschrieben wird.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-5-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>5</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa3</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-6-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast alle richtigen Lösungen angegeben, allerdings hast du sie mit <code>and</code> verknüpft. Korrekt ist, sie mit <code>or</code> zu verknüpfen. Man schreibt</p><ul><li>entweder \(x=?\; oder \;x=?\)</li><li>oder \(x_1=?\; und \;x_2 = ?\;\).</li></ul>Hier benutzen wir ausschließlich die erste Form, die mit <code>x=? or x=?</code> dargestellt wird.<br>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-6-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords>4x</forbidwords><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>1032259226</deployedseed><deployedseed>2071301041</deployedseed><deployedseed>668615301</deployedseed><deployedseed>1810103727</deployedseed><deployedseed>2047586646</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-g Gleichung mehrschrittig lösen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p><p>Lösen Sie \(\;\){@p@}\(\;\) nach x auf.</p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.</p><p>Sie brauchen kein Äquivalenz-Zeichen eingeben.<br></p></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Um einen Rechenweg darzustellen, tippe jeden Schritt deiner Rechnung in eine neue Zeile in das Eingabefeld ein.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;b:3;c:4;SYN_A:[[a1,a,b,c],[a2,b,a,c],[a3,c,a,b],[a4,a,c,b],[a5,b,c,a],[a6,c,b,a]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:[SYN_a[2]*(SYN_a[3]+x)=SYN_a[4],SYN_a[2]*SYN_a[3]+SYN_a[2]*x=SYN_a[4],SYN_a[2]*x=SYN_a[4]-SYN_a[2]*SYN_a[3],x=(SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]];/*ta:[2*(3+x)=-3,2*x+6=-3,2*x=-9,x=-9/2];*/p:first(ta);/*p:"\\(2 \\cdot (3 + x) = -3\\)";*/wa1:x=-((SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]);wa2:x=SYN_a[4]-SYN_a[2]*SYN_a[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last(ans1)</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Aber fast richtig. Du hast dich offenbar mit dem Vorzeichen vertan.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar ist dir ein Fehler beim Lösen der Klammer unterlaufen. Um die Klammer aufzulösen, musst du beide beide Summanden in der Klammer mit dem Faktor vor der Klammer multiplizieren.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Weiter so. Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>equiv</type><tans>ta</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint>firstline</syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options>hideequiv</options></input><deployedseed>668615301</deployedseed><deployedseed>1810103727</deployedseed><deployedseed>2047586646</deployedseed><deployedseed>1032259226</deployedseed><deployedseed>2071301041</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-h Griechische Buchstaben</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Geben Sie \[{@ta@}\] in das Eingebefeld ein.</p>
+<p><p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p><em>Achtung: Bitte kopieren Sie keine Unicode-Zeichen, sondern benutzen Sie einfach Ihre Tastatur. <br></em></p></p><p class="hint">Wenn griechische Buchstaben einzugeben sind, schreibe sie einfach aus. Beispiel: \(\alpha=\) <code>alpha</code> , \(\beta=\) <code>beta</code><code></code> ,\(\pi=\) <code>pi </code><code></code>.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:beta;b:pi;c:alpha;SYN_A:[[a1,a,b],[a2,b,a],[a3,a,c],[a4,c,a],[a5,b,c],[a6,c,b]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:SYN_a[2]*z^(SYN_a[3]*x)wa1:SYN_a[2]*z^SYN_a[3]*x</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offenbar vergessen, eine Klammer um die Potenz zu schreiben. Schreibe Potenzen in Klammern, wenn sie aus mehr als einer Zahl bestehen. Beispiel: \(x^{-2a}\) wird so eingegeben: <code>x^(-2*a)</code>.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>1516837293</deployedseed><deployedseed>911975771</deployedseed><deployedseed>742782033</deployedseed><deployedseed>1709130663</deployedseed><deployedseed>648468622</deployedseed><deployedseed>272609913</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-i Syntax-Endboss</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p><p>Lösen Sie {@p@} nach \(x\) auf.<br></p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.<br></p></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]<p></p><p><em>Zur Erinnerung: Das Kommando für</em> \(\sqrt{x}\)<em> lautet </em><code>sqrt(x)</code><em>. Nutzen Sie </em><code>or</code><em> um mehrere Lösungen anzugeben.</em></p></p><p class="hint">Willkommen zum Endgegner dieser Mathe-Welt. Mit dem Lösen dieser Aufgabe hast du die erste Mathe-Welt bereits abgeschlossen. Viel Erfolg!<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;b:3;c:4;d:2;e:3;SYN_A:[[a1,a,d],[a2,b,d],[a3,c,d],[a4,a,e],[a5,b,e],[a6,c,e]];SYN_a:rand(SYN_A);pifactor:ev(SYN_a[2]*(SYN_a[3]^2),simp);ta:[/*(SYN_a[2]*x^2)/(pifactor*pi)=1,*/SYN_a[2]*x^2=pifactor*pi,x^2=(SYN_a[3]^2)*pi,x=SYN_a[3]*sqrt(pi) nounor x=-SYN_a[3]*sqrt(pi)];p:first(ta);wa1:x=SYN_a[3]*sqrt(pi);wa2:x=-SYN_a[3]*sqrt(pi);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last(ans1)</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text><![CDATA[]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>4</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>3</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>3</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>1</sans><tans>1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast nur eine von zwei richtigen Lösungen eingegeben.<br>Beispiel: \(5\,\sqrt{\pi} \cdot 5\,\sqrt{\pi} = 25\,\pi\) und \(-5\,\sqrt{\pi} \cdot -5\,\sqrt{\pi} = 25\,\pi\) (Minus Mal Minus ergibt Plus).<br>Für \(x^2 = 25\pi\) gilt deshalb \(x = 5\,\sqrt{\pi}\) oder \(x = -5\,\sqrt{\pi}\), was hier in der Form <code>x=5*sqrt(pi) or x=-5*sqrt(pi)</code> aufgeschrieben wird.</p><p dir="ltr" style="text-align: left;"></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>4</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-5-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-5-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>equiv</type><tans>ta</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint>firstline</syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options>hideequiv</options></input><deployedseed>1169120426</deployedseed><deployedseed>1624332195</deployedseed><deployedseed>1578649438</deployedseed><deployedseed>1629124203</deployedseed><deployedseed>2120835467</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-a Kürzen zweier einfacher Brüche</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\({@f@} \cdot {@g@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Gekürzt wird, indem man Zähler & Nenner durch dieselbe Zahl teilt.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(2,8,1); b:rand_with_step(20,40,10); c:a*b; d:b/5; e:a*b/10; ta1:1/a; simp:false; f:5/e; g:d/10; wa1:(5+d)/(e+10);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@f@} \cdot {@g@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir="ltr" style="text-align: left;">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>423191525</deployedseed><deployedseed>1756629135</deployedseed><deployedseed>505485688</deployedseed><deployedseed>813830513</deployedseed><deployedseed>1619258121</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-b Kürzen zweier Brüche mit Variablen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\,a\,a\,b\,b\,c}{a\,a\,a\,a\,a\,b\,c\,c\,c}\)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); powers:makelist(rand(5)+1, 6); myvar1: mya^powers[1]; myvar2: myb^powers[2]; myvar3: myc^powers[3]; myvar4: mya^powers[4]; myvar5: myb^powers[5]; myvar6: myc^powers[6]; d:(myvar1*myvar2*myvar3)/(myvar4*myvar5*myvar6); ta1:d;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Beispiel: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,b\,b\mkern-5mu/\,c\mkern-5mu/}{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,a\,a\,b\mkern-5mu/\,c\mkern-5mu/\,c\,c} = \frac{b}{a^2\,c^2}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>194802941</deployedseed><deployedseed>1917875187</deployedseed><deployedseed>1931041228</deployedseed><deployedseed>928137609</deployedseed><deployedseed>264598581</deployedseed><deployedseed>1633750828</deployedseed><deployedseed>1318198792</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-c Kürzen zweier Brüche mit Variablen und Zahlen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Erst auf einen Bruchstrich sortieren. Beispiel: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} = \frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c}\)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>num1:rand_with_step(5,8,1); varlist:[a,b,c,u,v,w,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1], varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); num2:rand_with_step(3,7,1); num3:rand_with_step(3,7,1); nom1:num1*num2*myvars[1]; denom1:num1*myvars[2]; nom2:num1*num3*myvars[1]*myvars[2]; denom2:num1*myvars[1]*myvars[3]; ta1:(nom1/denom1)*(nom2/denom2); /*Alle Variablen in den Zählern mit einer Variable im Nenner gekürzt.*/wa1:((nom1/myvars[1])*(nom2/myvars[1]))/((denom1*denom2)/myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich die Variable {@myvars[1]@} im Nenner gegen beide Variablen in den Zählern gekürzt. Bei der Multiplikation von Brüchen kannst du immer nur einen Faktor gegen den anderen kürzen. Beispiel: \(\frac{36}{6} = \frac{6\cdot6}{6} = \frac{6\mkern-5mu/\cdot6}{6\mkern-5mu/} = \frac{6}{1} = 6\) und nicht \(\frac{36}{6} = \frac{6\cdot6}{6} \ne \frac{6\mkern-5mu/\cdot6\mkern-5mu/}{6\mkern-5mu/} = 1\;\).<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>So lassen sich Produkte auf einem Bruchstrich sortieren und kürzen: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} =\frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c} =\frac{49^7\mkern-14mu\large/ \small \; \cdot 21^3\mkern-14mu\large/\small \; \cdot a\mkern-5mu/ \cdot a \cdot b\mkern-5mu/}{7\mkern-5.5mu/ \cdot7\mkern-5.5mu/ \cdot a\mkern-5mu/\cdot b\mkern-5mu/\cdot c} =\frac{21\,a}{c}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1842189518</deployedseed><deployedseed>1601667602</deployedseed><deployedseed>2136766316</deployedseed><deployedseed>1542661342</deployedseed><deployedseed>2072145258</deployedseed><deployedseed>328965971</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-d Kürzen zweier Brüche mit Termen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Kennst du noch den Ausspruch „Aus Summen kürzen nur die Dummen“?!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([x,y,z]); term_summand1:rand_with_prohib(-3,3,[0]); term_summand2:rand_with_prohib(-3,3,[0,term_summand1]); term1:myvar+term_summand1; term2:myvar+term_summand2; ta1:term1/myvar*(myvar^2/(term1*term2*myvar)); /*wa1 means: naive shortened fraction*/ wa1:(term1-myvar)/1*(myvar^2/(term1*term2*myvar));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Offensichtlich hast du beim ersten Bruch die Variable {@myvar@} im Nenner gegen die Variable {@myvar@} im Zähler gekürzt. Das geht aber nicht, weil die Variable {@myvar@} im Zähler mit einem anderen Summanden eine Summe bildet. Beispiel: \(3 = \frac{6}{2} = \frac{4+2}{2} \ne \frac{4 + 2\mkern-5.5mu/}{2\mkern-5.5mu/} = \frac{4}{1} = 4\;\).]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p> Nur ganze Faktoren dürfen gekürzt werden. Zum Beispiel: \(\frac{\boldsymbol{(x-1)}\cdot 2}{x \cdot \boldsymbol{(x-1)}} = \frac{2}{x}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>837792651</deployedseed><deployedseed>528135820</deployedseed><deployedseed>879656886</deployedseed><deployedseed>1917537516</deployedseed><deployedseed>1617668401</deployedseed><deployedseed>159039633</deployedseed><deployedseed>1131743594</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-a Einfachen Bruch erweitern</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\({@c@} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(4,9,1); b:a-1; c:a/b; d:a*5; e:b*5; simp:false; ta1:d/e;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@c@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>437845679</deployedseed><deployedseed>2092409135</deployedseed><deployedseed>1712748750</deployedseed><deployedseed>182980498</deployedseed><deployedseed>388683995</deployedseed><deployedseed>1561500176</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-b Bruch mit Variablen erweitern</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@numerator@}}{{@denominator@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,4); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[1]^powers[3]; fac4:myvars[2]^powers[4]; numerator:fac1*fac2; denominator:fac3*fac4; d:numerator/denominator; tanumerator:5*num(d); tadenominator:5*denom(d); simp:false; ta1:tanumerator/tadenominator;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@numerator@}}{{@denominator@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>36209422</deployedseed><deployedseed>1000344719</deployedseed><deployedseed>1827440244</deployedseed><deployedseed>1291739138</deployedseed><deployedseed>825866743</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-c Bruch mit Variablen und Zahlen erweitern</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,3); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[2]^powers[3]; rand1:rand(4); rand2:rand_with_prohib(0,3,[rand1]); number1:rand1*2+3; number2:rand2*2+3; number3:rand_with_step(2,8,2); numerator:fac1*fac2; denominator:fac3; d:numerator/denominator; tanumerator:5*number1*number2*num(d); tadenominator:5*number3*denom(d); simp:false; ta1:tanumerator/tadenominator;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
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+ <truepenalty/>
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+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
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+ <falsescore>0</falsescore>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
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+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
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+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
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+ <name>
+ <text>t1-01-ca Einfache Addition von Brüchen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Addieren und Subtrahieren müssen die Nenner der Brüche gleich sein. Kannst du dich noch an das kleinste gemeinsame Vielfache erinnern?</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
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+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(1,4,1)*2+1; fac1:rand_with_step(1,4,1); fac2:rand_with_prohib(1,4,[fac1]); denoms:[a, a*fac1,a*fac2]; nums:makelist(rand_with_step(1,denoms[i]-1,2),i,3); signs:makelist(rand_with_prohib(-1,1,[0]),3); fractions:makelist(signs[i]*nums[i]/denoms[i],i,3); fractions:random_permutation(fractions); ta1:fractions[1]+fractions[2]+fractions[3]; simp:false; exercise:fractions[1]+fractions[2]+fractions[3]; /*wa1 means: naive addition*/ wa1:(num(fractions[1])+num(fractions[2])+num(fractions[3]))/(denom(fractions[1])+denom(fractions[2])+denom(fractions[3]));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
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+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
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+ <value>1.0000000</value>
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+ <node>
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+ <truepenalty/>
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+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
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+ <falsescore>0</falsescore>
+ <falsepenalty/>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir="ltr" style="text-align: left;">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>]]></text>
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+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
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+<truepenalty/>
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+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um die Nenner gleich zu machen, musst du sie so erweitern, dass sie den gleichen Nenner haben. Dann können die Zähler addiert werden. Das kleinste gemeinsame Vielfache von 5, 10 und 15 lässt sich zum Beispiel finden, indem man die jeweiligen Reihen notiert und die kleinste gemeinsame Zahl sucht.</p><table><tr><th>5er-Reihe</th><th>10er-Reihe</th><th>15er-Reihe</th></tr><tr><td>5</td><td>10</td><td>15</td></tr><tr><td>10</td><td>20</td><td><strong>30</strong></td></tr><tr><td>15</td><td><strong>30</strong></td><td>...</td></tr><tr><td>20</td><td>...</td><td>...</td></tr><tr><td>25</td><td>...</td><td>...</td></tr><tr><td><strong>30</strong></td><td>...</td><td>...</td></tr><tr><td>...</td><td>...</td><td>...</td></tr></table></p>]]></text>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
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+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cb Addition von Brüchen mit Variablen und gleichem Nenner</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Überlege genau, was ein Minus vor einem Bruch bedeutet.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c]); fractions_correct_and_wa1:[[(myvar+1)/myvar, -myvar+1], [(myvar-1)/myvar, -myvar-1], [(1-myvar)/myvar, -1-myvar]]; fractions_correct_and_wa1:random_permutation(fractions_correct_and_wa1); fractions:makelist(fractions_correct_and_wa1[i][1],i,3); terms_wa1:makelist(fractions_correct_and_wa1[i][2],i,3); exercise:fractions[1]-fractions[2]-fractions[3]; ta1:combine(exercise); wa1:(num(fractions[1])+terms_wa1[2]+terms_wa1[3])/myvar;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@}-{@fractions[2]@}-{@fractions[3]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
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+ <sqrtsign>1</sqrtsign>
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+ <type>algebraic</type>
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+ <boxsize>15</boxsize>
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+ <insertstars>5</insertstars>
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+ <options/>
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+ <value>1.0000000</value>
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+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
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+ <falsescore>0</falsescore>
+ <falsepenalty/>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
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+ <answertest>AlgEquiv</answertest>
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+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
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+ <node>
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+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast offenbar die Minuszeichen nicht korrekt aufgelöst.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
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+<falseanswernote>prt1-3-F</falseanswernote>
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+ <text/>
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+<name>999</name>
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+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Ein Minus vor dem Bruch gehört zum ganzen Bruch: gilt also für den ganzen Zähler oder ganzen Nenner (häufig nimmt man den Zähler).</p><p>\(\Rightarrow -\frac{a-1}{a} = \frac{-\boldsymbol{(a-1)}}{a} = \frac{-a+1}{a}\)</p><p>Wichtig bei Summen im Zähler!!!</p></p>]]></text>
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+<falsepenalty/>
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+<falseanswernote>prt1-1000-F</falseanswernote>
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+ <text/>
+</falsefeedback>
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+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cc Addition von Brüchen mit Variablen und unterschiedlichen Nennern</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Jeder Teilnenner (hier: {@myvars[1]@}, {@myvars[2]@}, {@myvars[3]@}) muss als Faktor im gemeinsamen Nenner vorkommen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); fractions:[(1+myvars[1])/myvars[1], rand_with_step(2,5,1)/myvars[2], myvars[1]/myvars[3]]; fractions:random_permutation(fractions); exercise:fractions[1]+fractions[2]+fractions[3]; common_denom:denom(fractions[1])*denom(fractions[2])*denom(fractions[3]); ta1:((num(fractions[1])*denom(fractions[2])*denom(fractions[3]))+(num(fractions[2])*denom(fractions[1])*denom(fractions[3]))+(num(fractions[3])*denom(fractions[1])*denom(fractions[2])))/common_denom; ta1alt:(expand((num(fractions[1])*denom(fractions[2])*denom(fractions[3])))+expand((num(fractions[2])*denom(fractions[1])*denom(fractions[3])))+expand((num(fractions[3])*denom(fractions[1])*denom(fractions[2]))))/common_denom;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
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+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
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+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
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+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{1+a}{a}+\frac{2}{b}+\frac{a}{c}\) ist der gemeinsame Nenner \(a \cdot b \cdot c\). So muss erweitert werden, damit die Zähler addiert werden können:</p><p>\(\frac{(1+a) \boldsymbol{\cdot b \cdot c} }{a \boldsymbol{\cdot b \cdot c}}+\frac{2 \boldsymbol{\cdot a \cdot c}}{\boldsymbol{a} \cdot b \boldsymbol{\cdot c}}+\frac{a \boldsymbol{\cdot a \cdot b}}{\boldsymbol{a \cdot b} \cdot c}\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(1+a\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>638235066</deployedseed><deployedseed>1053964038</deployedseed><deployedseed>625975426</deployedseed><deployedseed>1098133316</deployedseed><deployedseed>1880026849</deployedseed><deployedseed>1344755034</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cd Addition von Brüchen mit einer Variablen und unterschiedlichen Nennern</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([x,y,z]); nums:makelist(rand_with_step(2,5,1),2); fractions:[(nums[1]+myvar)/myvar^2,(nums[2]-myvar^2)/myvar]; common_denom:myvar^2; ta1:(num(fractions[1])-num(fractions[2])*myvar)/common_denom; ta1alt:(num(fractions[1])-expand(num(fractions[2])*myvar))/common_denom; exercise:fractions[1]-fractions[2]; /*wa1 means: didn't consider minus sign before bracket*/ wa1:(num(fractions[1])+(-nums[2]-myvar^2)*myvar)/common_denom;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast offenbar die Minuszeichen nicht korrekt aufgelöst (siehe Tipp unten).]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um immer einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{3+x}{x^2}-\frac{5-x}{x}\) ist ein gemeinsame Nenner \(x^2 \cdot x = x^3\). Betrachtet man die Teilnenner \(x^2\) und \(x\) genauer, fällt auf, dass \(x\) bereits als Faktor in \(x^2\) vorkommt. Denn \(x^2 = x \cdot x\). Deswegen kann hier auch \(x^2\) als Hauptnenner gewählt werden.</p><p>Dazu muss so erweitert werden:</p><p>\(\frac{(3+x)}{x^{2}}-\frac{(5-x^2) \boldsymbol{ \cdot x}}{x \boldsymbol{\cdot x}} = \frac{3+x}{x^{2}}-\frac{5x-x^3}{x^{\boldsymbol{2}}} = \frac{3+x-(5x-x^3)}{x^2} = \dots\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(5-x^2\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>669633138</deployedseed><deployedseed>2093071884</deployedseed><deployedseed>1766326583</deployedseed><deployedseed>488830876</deployedseed><deployedseed>1210423031</deployedseed><deployedseed>158072256</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ce Addition von Brüchen mit Variablen und unterschiedlichen Nennern I (Update1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); numbers:makelist(rand_with_step(2,5,1), 5); factors:random_permutation([1,2,4]); /*only +*/ signs:makelist(rand_with_prohib(1,1,[0]),2); fractions:[(numbers[1]*myvars[1]-numbers[2]*myvars[2])/(factors[1]*5*myvars[1]*myvars[2]), (numbers[3]*myvars[3]-numbers[4]*myvars[1])/(factors[2]*5*myvars[1]*myvars[3]), (myvars[3]^2-numbers[5])/(factors[3]*5*myvars[2]*myvars[3])]; tanum:(num(fractions[1])*(4/factors[1])*myvars[3]+num(fractions[2])*(4/factors[2])*myvars[2]+num(fractions[3])*(4/factors[3])*myvars[1]); tanumalt:expand(tanum); tadenom:(5*4*myvars[1]*myvars[2]*myvars[3]); ta1:tanum/tadenom; /*fractions_to_show:random_permutation(fractions);*/ fractions_to_show:fractions; ta1alt:tanumalt/tadenom; fractions_to_show[2]:fractions_to_show[2]*signs[1]; fractions_to_show[3]:fractions_to_show[3]*signs[2]; exercise:fractions_to_show[1]+fractions_to_show[2]+fractions_to_show[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{5\,z-4\,x}{10\,x\,z}+\frac{7\,y-3\,z}{20\,y\,z}+\frac{y^2-2}{5\,x\,y}\) ist \(20\) das kleinste gemeinsame Vielfache (kgV) von \(10\), \(20\) und \(5\) und \(x \cdot y \cdot z\) ist das kgV von \(x \cdot z\), \(y \cdot z\) und \(x \cdot y\). Der Hauptnenner ist demnach \(20 \cdot x \cdot y \cdot z\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(20 \cdot x \cdot y \cdot z\;\) steht. \(\frac{5\,z-4\,x}{10\,x\,z}\) wird mit \(2 \cdot y\) erweitert, \(\frac{7\,y-3\,z}{20\,y\,z}\) wird mit \(x\) erweitert und \(\frac{y^2-2}{5\,x\,y}\) wird mit \(4 \cdot z\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(5\,z-4\,x)\boldsymbol{ \cdot 2\,y}}{10\,x\,z \boldsymbol{ \cdot 2\,y}}+\frac{(7\,y-3\,z) \boldsymbol{ \cdot x}}{20\,y\,z \boldsymbol{ \cdot x}}+\frac{(y^2-2) \boldsymbol{ \cdot 4\,z}}{5\,x\,y \boldsymbol{ \cdot 4\,z}}\)</p><p>\(= \frac{10\,y\,z-8\,x\,y}{20\,x\,y\,z}+\frac{7\,x\,y-3\,x\,z}{20\,x\,y\,z}+\frac{4\,y^2\,z-8\,z}{20\,x\,y\,z} = \dots\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1330316881</deployedseed><deployedseed>2007639052</deployedseed><deployedseed>846124380</deployedseed><deployedseed>520216901</deployedseed><deployedseed>1618486590</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cf Addition von Brüchen mit Variablen und unterschiedlichen Nennern II</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: 1) Überlege genau, was ein Minus vor einem Bruch bedeutet. 2) Jeder Teilnenner (hier: {@denom(main_fraction)@}, {@denom(fractions[1])@}, {@denom(fractions[2])@}) muss als Faktor im gemeinsamen Nenner vorkommen. 3) Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); numbers:rand_selection(makelist(i,i,5),2); denom_nums_origin:rand_selection([18,12,6],1)[1]; denom_nums:[denom_nums_origin, denom_nums_origin/2, denom_nums_origin/3]; main_fraction:(numbers[1]-myvars[1])/(denom_nums[1]*myvars[1]^2); fractions:[(myvars[2])/(denom_nums[2]*myvars[1]), (myvars[2]+numbers[2])/(denom_nums[3]*myvars[1]*myvars[2])]; tanum:num(main_fraction)*myvars[2]-num(fractions[1])*2*myvars[1]*myvars[2]-num(fractions[2])*3*myvars[1]; tanumalt:expand(tanum); tadenom:denom_nums_origin*myvars[1]^2*myvars[2]; ta1:tanum/tadenom; ta1alt:tanumalt/tadenom; fractions:random_permutation(fractions); simp:false; exercise:main_fraction-fractions[1]-fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
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+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{1-x}{18\,x^2}-\frac{y}{9\,x}-\frac{x+3}{6\,x\,y}\) ist \(18\) das kleinste gemeinsame Vielfache (kgV) von \(18\), \(9\) und \(6\) und \(x^2 \cdot y\) ist das kgV von \(x^2\), \(x\) und \(x \cdot y\). Der Hauptnenner ist demnach \(18 \cdot x^2 \cdot y\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(18 \cdot x^2 \cdot y\;\) steht. \(\frac{1-x}{18\,x^2}\) wird mit \(y\) erweitert, \(\frac{y}{9\,x}\) wird mit \(2\,x\,y\) erweitert und \(\frac{x+3}{6\,x\,y}\) wird mit \(3 \cdot x\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(1-x) \boldsymbol{\cdot y}}{18\,x^2 \boldsymbol{\cdot y}}-\frac{y \boldsymbol{\cdot 2\,x\,y}}{9\,x \boldsymbol{\cdot 2\,x\,y}}-\frac{(x+3) \boldsymbol{\cdot 3\,x}}{6\,x\,y \boldsymbol{\cdot 3\,x}}\)</p><p>\(= \frac{y-x\,y}{18\,x^2\,y}-\frac{2\,x\,y^2}{18\,x^2\,y}-\frac{3\,x^2+9\,x}{18\,x^2\,y} = \dots\)</p></p>]]></text>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>527686404</deployedseed><deployedseed>1918490776</deployedseed><deployedseed>2103547991</deployedseed><deployedseed>1091135158</deployedseed><deployedseed>1696865873</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-da Multiplikation zweier einfacher Brüche</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@}\cdot{@fractions[2]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8),4); fractions:[nums[1]/nums[2], nums[3]/nums[4]]; ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions*/ wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied*/ wa2:fractions[1]+fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@}\cdot{@fractions[2]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
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+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{2}{3} \cdot \frac{6}{5} = \frac{2 \cdot 6}{3 \cdot 5} = \frac{12}{15} = \frac{4}{5}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1088212423</deployedseed><deployedseed>1553109555</deployedseed><deployedseed>777390971</deployedseed><deployedseed>1688656099</deployedseed><deployedseed>1485690277</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-db Multiplikation zweier Brüche mit Variablen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); fractions:[mya/myb, mya^2/(mya*myb)]; fractions:random_permutation(fractions); ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions with previously shortened the larger fraction*/ wa1:(2*mya)/(2*myb); /*wa2 means: naively summed fractions without previously shortening the larger fraction*/ wa2:(mya+myb^2)/(mya+myb*mya); /*wa3 means: correctly summed fractions instead of multiplied*/ wa3:fractions[1]+fractions[2]; /*wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied wa2:fractions[1]+fractions[2];*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden. Du hast außerdem den Bruch \({@mya@}^2/({@mya@}*{@myb@})\) nicht ausreichend vereinfacht. Er kann zu \({@mya@}/{@myb@}\) gekürzt werden.]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{a}{b} \cdot \frac{a^2}{a\,b} = \frac{a}{b} \cdot \frac{a \cdot a}{a\,b} = \frac{a \cdot a \cdot a}{a \cdot b \cdot b} = \frac{a^3}{a\,b^2}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>545658671</deployedseed><deployedseed>1228864607</deployedseed><deployedseed>806993602</deployedseed><deployedseed>1501016569</deployedseed><deployedseed>710282177</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dc Multiplikation Bruch mit Zahlen, Bruch mit Variablen, Ganzzahl</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Wie kann man eine ganze Zahl als Bruch schreiben?</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8),3); nums:sort(nums); varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); factors:[nums[1], (mya*myb)/myc, nums[2]/nums[3]]; factors:random_permutation(factors); ta1:factors[1]*factors[2]*factors[3]; simp:false; exercise:factors[1]*factors[2]*factors[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>999</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Jede ganze Zahl kann als Bruch geschrieben werden, indem man sie durch 1 teilt. Beispiel: \(3 \cdot \frac{a\,b}{c} \cdot \frac{5}{6} = \frac{3}{1} \cdot \frac{a\,b}{c} \cdot \frac{5}{6}\)</p><p>\( = \frac{3 \cdot a \cdot b \cdot 5}{1 \cdot c \cdot 6} = \frac{15\,a\,b}{6\,c} = \frac{5\,a\,b}{2\,c}\)</p><p>Hinweis: Generellt gilt \(\cdot 1\) und \(:\,1\) geht immer.</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1569886884</deployedseed><deployedseed>1980675582</deployedseed><deployedseed>1601683210</deployedseed><deployedseed>51348788</deployedseed><deployedseed>726919830</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dd Multiplikation zweier Brüche mit Termen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Summanden & Faktoren => Klammer!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:rand_selection(varlist, 2); nums:rand_selection(makelist(i+1,i,9), 6); fractions:[(nums[1]*myvars[1]+nums[2]*myvars[2])/(nums[3]*myvars[2]+nums[4]*myvars[1]), (-nums[5]*myvars[1])/(nums[6]+myvars[1])]; ta1:fractions[1]*fractions[2]; taalt:combine(expand(ta1)); /*wa1 means: the multiplication of the numerator was done with only one summand of the first fraction’s numerator (the second one)*/ wa1:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(denom(fractions[1])*denom(fractions[2])); /*old_wa2 means the same as wa1 but with the first fraction numerator’s second summand*/ /*old_wa2: (nums[1]*myvars[1]*num(fractions[2])+nums[2]*myvars[2])/(denom(fractions[1])*denom(fractions[2]));*/ /*wa2 means the same as wa1 but with the denominators, so no brackets: first summand of second fraction is multiplied with last summand of first fraction*/ wa2:(num(fractions[1])*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]); /*wa3 is the combination of wa1 and wa2*/ wa3:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}= {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Nenner richtig multipliziert, doch du hast den Faktor im Zähler des zweiten Bruches nur mit dem zweiten Summanden des Zählers im ersten Bruch multipliziert. Das heißt bei der Multiplikation der Zähler musst du Klammern um die Summe setzen und jeden Summanden des ersten Zählers mit dem Faktor des anderen Zählers multiplizieren.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Zähler richtig multipliziert, hast jedoch im Nenner nicht beachtet, dass Summen als Ganzes multipliziert werden. Das heißt bei der Multiplikation der Nenner musst du Klammern um die Summen setzen und jeden Summanden des einen Nenners mit jedem Summanden des anderen Nenners multiplizieren.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>5</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>5</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-6-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Summen nicht als Ganzes multipliziert. Das betrifft eine Summe im Zähler und die Summen im Nenner. Du musst jeweils Klammern setzen, damit jeder Summand mit jedem anderen Summanden multipliziert wird. ]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-6-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{4\,x+10\,y}{5\,y+2\,x} \cdot \frac{-4\,x}{3+x} = \)\(\frac{\boldsymbol{(4\,x+10\,y)} \cdot -4\,x}{\boldsymbol{(5\,y+2\,x)} \cdot \boldsymbol{(3+x)}} = \dots\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>783029466</deployedseed><deployedseed>1177445020</deployedseed><deployedseed>1009895582</deployedseed><deployedseed>1167689465</deployedseed><deployedseed>1922827729</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-de Einfacher Doppelbruch</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8), 4); nums:sort(nums); ta1:((nums[1])/(nums[4]))/((nums[2])/(nums[3])); /*wa1 means: multiplied fractions instead of division*/ wa1:((nums[1])/(nums[4]))*((nums[2])/(nums[3])); /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:((nums[4])/(nums[1]))*((nums[2])/(nums[3]));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
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+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>352990161</deployedseed><deployedseed>467670994</deployedseed><deployedseed>1747402747</deployedseed><deployedseed>2135608811</deployedseed><deployedseed>460810681</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-df Bruch und Geteilt-Rechnung</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@dividend@}:{@divisor@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Achtung: Auch ein Doppelbruch ;)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>power:rand_with_step(2,4,1); myvars:rand_selection([a,b,c,x,y,z],2); dividend:myvars[1]/myvars[2]; num:rand_with_step(1,5,1); divisor:(num-myvars[1])/(myvars[2]^power); ta1: dividend/divisor; /*wa1 means: multiplied fractions instead of division*/ wa1:dividend*divisor; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:dividend^(-1)*divisor; /*wa3 means: didn’t consider to multiply the denominator of the first fraction with the sum of the second fraction’s numerator as a whole*/ wa3:(num(dividend)*denom(divisor))/(myvars[2]*num-myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@dividend@}:{@divisor@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast den richtigen Kehrwert gebildet um die Brüche dann zu multiplizieren, jedoch hast du dann die Klammersetzung bei der Mutliplikation nicht beachtet.</p><p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{x}{a} : \frac{1-x}{a^2} = \frac{x}{a} \cdot \frac{a^2}{1-x}\)\(= \frac{x \cdot a^2}{a \cdot \boldsymbol{(1-x)}} = \dots\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: \(\boldsymbol{:}\) ist dasselbe wir ein Doppelbruchstrich.</p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>68495326</deployedseed><deployedseed>83279259</deployedseed><deployedseed>1848999895</deployedseed><deployedseed>1656521999</deployedseed><deployedseed>333378154</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dg Doppelbruch mit Zahlen und Variablen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:rand_selection(makelist(i+1,i,3),2); nums:rand_selection(makelist(i+1,i,4),2); myvars:rand_selection([a,b,c,x,y,z],2); fractions:[nums[1]/myvars[1]^powers[1], (nums[2]*myvars[2]^powers[2])/myvars[1]]; fractions:random_permutation(fractions); ta1:fractions[1]/fractions[2]; /*wa1 means: multiplied fractions instead of division*/ wa1:fractions[1]*fractions[2]; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:fractions[1]^(-1)*fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{2}{a^2}}{\frac{3\,b^2}{a}} = \frac{2}{a^2} \cdot \frac{a}{3\,b^2} = \frac{2\,a}{3\,a^2\,b^2}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1783639635</deployedseed><deployedseed>863915904</deployedseed><deployedseed>446314797</deployedseed><deployedseed>1562297660</deployedseed><deployedseed>1172377010</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dh Doppelbruch mit Termen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8), 3); nums:sort(nums); myvars:rand_selection([a,b,c,x,y,z],2); terms:[nums[1]*((1-myvars[1])/myvars[2]), (nums[2]/nums[3])*(myvars[2]^2/myvars[1])]; /*terms:random_permutation(terms);*/ ta1:terms[1]/terms[2]; taalt:combine(expand(ta1)); /*wa1 means: didn't consider to multiple first factor in the numerator with both summands of the fraction's numerator*/ wa1:((nums[1]*1-myvars[1])/myvars[2])/terms[2]; wa2:terms[1]*terms[2]; wa3:terms[1]^(-1)*terms[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Beim Multiplizieren des Faktors {@nums[1]@} und des Bruchs \(\frac{1-{@myvars[1]@}}{{@myvars[2]@}}\) im Zähler des Doppelbruchs musst du beachten, dass Summen als Ganzes multipliziert werden.</p><p>Beispiel: \(5 \cdot \frac{1-a}{b} = \frac{5 \cdot \boldsymbol{(1-a)}}{b} = \dots\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>5</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>5</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-6-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-6-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Lösungsweg für eine Beispielaufgabe:</p><p>\(\large\frac{5 \cdot \frac{1-a}{b}}{\frac{1}{3} \cdot \frac{b^2}{a}}\)\(\large = \frac{\frac{5 \cdot \boldsymbol{(1-a)}}{b}}{\frac{b^2}{3\,a}} = \frac{5 - 5\,a}{b} \cdot \frac{3\,a}{b^2}\)</p><p>\(\large = \frac{3\,a \cdot \boldsymbol{(5-5\,a)}}{b \cdot b^2} = \frac{15\,a - 15\,a^2}{b^3}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>611281053</deployedseed><deployedseed>439766047</deployedseed><deployedseed>725695831</deployedseed><deployedseed>1029360039</deployedseed><deployedseed>1825759080</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ea Bruchrechnung Kombination I</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbrüche und Summanden => Punkt-vor-Strich-Rechnung</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(2,4,1); nums_real_frac:sort(rand_selection(makelist(i,i,9),4)); nums_unreal_frac:sort(rand_selection(makelist(i+3,i,7),6)); main_summand:((nums_real_frac[1])/(nums_real_frac[4]))/((nums_real_frac[2])/(nums_real_frac[3])); summands:[int*(nums_unreal_frac[6]/nums_unreal_frac[1]), ((nums_unreal_frac[5])/(nums_unreal_frac[2]))/((nums_unreal_frac[4])/(nums_unreal_frac[3]))]; ta1:main_summand+summands[1]-summands[2]; wa1:(main_summand+int)*summands[1]/int-summands[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast offensichtlich die Punkt-vor-Strich-Regel nicht beachtet.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6} = \frac{\frac{5}{6}}{\frac{1}{3}}+(2 \cdot \frac{9}{6}) \ne (\frac{\frac{5}{6}}{\frac{1}{3}}+2) \cdot \frac{9}{6}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Jeden Summanden einzeln betrachten und ausrechnen: Doppelbrüche auflösen und zusammenfassen.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6}-\frac{\frac{13}{4}}{\frac{6}{5}} = \frac{5}{6} \cdot \frac{3}{1}+\frac{2}{1} \cdot \frac{9}{6}-\frac{13}{5} \cdot \frac{5}{6}\)</p><p>\(= (\frac{5}{6\mkern-5mu/^2} \cdot \frac{3\mkern-5mu/^1}{1})+(\frac{2\mkern-5mu/^1}{1} \cdot \frac{9}{6\mkern-5mu/^2})-(\frac{13}{5\mkern-5mu/^1} \cdot \frac{5\mkern-5mu/^1}{6})\)</p><p>\(= \frac{5}{2} + \frac{9}{2} - \frac{13}{6} = \frac{5 \cdot 3}{2 \cdot 3} + \frac{9 \cdot 3}{2 \cdot 3} - \frac{13}{6} = \frac{15}{6} + \frac{27}{6} - \frac{13}{6}\)</p><p>\(= \frac{15+27+13}{6} = \frac{55}{6}\)<\p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>2022519868</deployedseed><deployedseed>2007714528</deployedseed><deployedseed>1652468809</deployedseed><deployedseed>1890021691</deployedseed><deployedseed>1160555762</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-eb Bruchrechnung Kombination II</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Sorgfältig ausmultiplizieren</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(3,7,1); nums:sort(rand_selection(makelist(i,i,9),6)); factors:[int, (nums[1]/nums[6]+nums[2]/nums[5]), (1-nums[3]/nums[4])]; ta1:factors[1]*factors[2]*factors[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})= {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>999</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Hier hast du zwei Möglichkeiten: Alles sauber ausmultiplizieren oder vor dem Multiplizieren die Klammern ausrechnen (Empfehlung!)</p><p>Beispiel: \(6 \cdot (\frac{3}{4}+\frac{1}{8}) \cdot (1-\frac{1}{4}) = 6 \cdot (\frac{3 \cdot 2}{4 \cdot 2}+\frac{1}{8}) \cdot (\frac{1 \cdot 4}{1 \cdot 4}-\frac{1}{4})\) </p><p>\(= 6 \cdot (\frac{6}{8}+\frac{1}{8}) \cdot (\frac{4}{4}-\frac{1}{4}) = 6 \cdot (\frac{7}{8}) \cdot (\frac{3}{4})\)</p><p>\( = \frac{6}{1} \cdot \frac{7}{8} \cdot \frac{3}{4} = \frac{6\mkern-5mu/^3 \cdot 7 \cdot 3}{1 \cdot 8\mkern-5mu/^4 \cdot 4} = \frac{63}{16}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>382901616</deployedseed><deployedseed>1683089904</deployedseed><deployedseed>724792720</deployedseed><deployedseed>857106597</deployedseed><deployedseed>2126061360</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ec Bruchrechnung Kombination III</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch und gemischter Bruch vs. unechter Bruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(2,4,1); myvar:rand_selection([a,b,c,x,y,z],1)[1]; nums:sort(rand_selection(makelist(i,i,9),6)); summands:[(int+(nums[1]/nums[4]))*(myvar/nums[5]),1-((nums[6]-myvar)/((nums[4])/(nums[3])))]; ta1:combine(expand(summands[1]+summands[2])); wa1:(int*(nums[1]/nums[4]))*(myvar/nums[5])+summands[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast offenbar den gemischten Bruch \({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\) als Multiplikation \({@int@} \cdot \frac{{@nums[1]@}}{{@nums[4]@}}\) interpretiert. Allerdings meint der gemischte Bruch hier \({@int@}\) Ganze und \(\frac{{@nums[1]@}}{{@nums[4]@}}\) Anteil. Empfehlung: Gemischte Brüche als unechte Brüche umschreiben. Beispiel:\(2\frac{1}{6} = 2+\frac{1}{6} = \frac{2 \cdot 6}{1 \cdot 6} + \frac{1}{6} = \frac{12}{6}+\frac{1}{6} = \frac{13}{6}\)]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: \(\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}}\) ist auch ein Doppelbruch.</p><p>Achte darauf, dann die Klammer richtig zu setzen.</p><p>Beispiel: \(\frac{2-a}{\frac{7}{8}} = \boldsymbol{(}2-a\boldsymbol{)} \cdot \frac{8}{7}\)</p><p>Beachte: 1) Ganze Zahlen zum Bruch umschreiben. 2) Doppelbrüche umschreiben (Beispiel oben). 3) Gemischte Brüche umschreiben (Beispiel \(2\frac{1}{6}\) sind \(\frac{13}{6}\;\)). 4) Punkt-vor-Strich-Regel.</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>2024587341</deployedseed><deployedseed>1597148134</deployedseed><deployedseed>899831950</deployedseed><deployedseed>29495097</deployedseed><deployedseed>97014366</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-j Binomische Formeln I - Anwendungsaufgabe</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen und faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.</div>
+</div>
+<p></p>
+<p>\(\frac{{@expand(BIN_a[2])@}}{{@expand(BIN_a[3])@}} \cdot {@BIN_a[3]@}\)\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p><br></p>
+<p><br></p></p>
+<p class="hint">Um diese Aufgabe zu lösen, musst du mehrere binomische Formeln anwenden.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>aa:4;
+bb:5;
+c:3;
+d:2;
+
+u:(c*a-d*b)^2;
+ualt:(d*b-c*a)^2;
+v:(aa*a+d*b)^2;
+w:(bb*a-c*b)*(bb*a+c*b);
+
+x:(aa*a-d*b)^2;
+xalt:(d*b-aa*a)^2;
+y:(bb*a+c*b)^2;
+z:(c*a+d*b)*(c*a-d*b);
+
+/*BIN_A:[
+[a1,(2*a+5*b)^2,"\\(\\frac{4\\,a^2+20\\,a\\,b+25\\,b^2}{16\\,a^2-9\\,b^2}\\cdot(4\\,a-3\\,b)\\cdot(4\\,a+3\\,b)\\)"]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];*/
+
+BIN_A:[
+[a1,u,v,ualt],
+[a2,v,w,v],
+[a3,w,u,w],
+[a4,x,y,xalt],
+[a5,y,z,y],
+[a6,z,y,z]
+];
+BIN_a:rand(BIN_A);
+
+ta:BIN_a[2];
+taalt:BIN_a[4];
+
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>534740616</deployedseed> <deployedseed>47766652</deployedseed> <deployedseed>1657775726</deployedseed> <deployedseed>931829986</deployedseed> <deployedseed>1703936373</deployedseed> <deployedseed>151644710</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-g Binomische Formeln Ia - Erste binomische Formel</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Um den Bruch aus der Endgegner-Aufgabe zu vereinfachen, musst du binomische Formeln anwenden. Deshalb kommen wir nun zu den binomischen Formeln. Die erste binomische Formel besagt: \((a + b)^2 = a^2 + 2\,a\,b + b^2\;\).</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,(4+b)^2],
+[a2,(5+b)^2],
+[a3,(3+b)^2],
+[a4,(2+b)^2],
+[a5,(3+2*b)^2],
+[a6,(4+2*b)^2]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];
+task:expand(BIN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die erste binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1994312303</deployedseed> <deployedseed>1744518788</deployedseed> <deployedseed>1627526666</deployedseed> <deployedseed>1566276649</deployedseed> <deployedseed>1138479794</deployedseed> <deployedseed>806677520</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-h Binomische Formeln Ib - Zweite binomische Formel</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Die zweite binomische Formel besagt:\((a - b)^2 = a^2 - 2\,a\,b + b^2\;\).<!--Diesmal musst du den Term erst umformen, damit er in der richtigen Form erscheint.--><br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:4;
+b:5;
+c:3;
+d:2;
+
+e:1;
+f:2;
+
+BIN_A:[
+[a1,a,e],
+[a2,b,e],
+[a3,c,e],
+[a4,d,e],
+[a5,a,f],
+[a6,c,f]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]-BIN_a[3]*y)^2;
+taalt:(BIN_a[3]*y-BIN_a[2])^2;
+task:expand(ta);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>893674818</deployedseed> <deployedseed>675538571</deployedseed> <deployedseed>985713485</deployedseed> <deployedseed>1039647874</deployedseed> <deployedseed>1781202861</deployedseed> <deployedseed>824682247</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-i Binomische Formeln Ic - Dritte binomische Formel</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p></p>
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Die dritte binomische Formel besagt: \((a + b)\,(a - b) = a^2 - b^2\;\).<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>aa:4;
+bb:5;
+c:3;
+d:2;
+
+
+BIN_A:[
+[a1,aa,bb],
+[a2,c,d],
+[a3,d,aa],
+[a4,d,bb],
+[a5,d,c],
+[a6,aa,c]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]*x-BIN_a[3]*y)*(BIN_a[2]*x+BIN_a[3]*y);
+task:expand(ta);
+wa:(BIN_a[2]^2*x-BIN_a[3]^2*y)*(BIN_a[2]^2*x+BIN_a[3]^2*y);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die dritte binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast zwar die Unbekannten x und y korrekt faktorisiert, aber die sie begleitenden Faktoren unverändert in die Klammern geschrieben. Um diese korrekt zu faktorisieren, musst du ihre Wurzeln berechnen. Richtig wäre {@ta@}.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>455750255</deployedseed> <deployedseed>970764179</deployedseed> <deployedseed>1971560923</deployedseed> <deployedseed>987956614</deployedseed> <deployedseed>533447380</deployedseed> <deployedseed>299284489</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-k Bruchrechenregeln Ig2 - Bruch mit binomischem Term erweitern 2 (copy)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen und faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Dies ist der Endgegner zur Mathe-Welt <strong>Bruchrechenregeln und binomische Formeln</strong>. Wenn du diese Aufgabe schaffst, hast du diese Welt schon gemeistert. Wende zuerst die binomischen Formeln an, um die Nenner zu vereinfachen. Um die Brüche dann zu addieren, musst du mit einem Term erweitern.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;
+b:3;
+c:4;
+
+aa:x-a;
+bb:x-b;
+cc:x-c;
+
+/*FRA_A:[
+[a1,(x^2-3)/(x^2-4),"\\(\\frac{x + 3}{x^2 - 4} + \\frac{x - 3}{x - 2}\\)",(x^2-3)/((x+2)*(x-2))]
+];*/
+
+FRA_A:[
+[a1,aa, a],
+[a2,bb, b],
+[a3,cc, c]
+];
+FRA_a:rand(FRA_A);
+task:(3*FRA_a[3]*x+FRA_a[3]^2)/expand(FRA_a[2]^2)+x/FRA_a[2];
+ta:(x+FRA_a[3])^2/(FRA_a[2])^2;
+
+simp:false;
+taalt:((x+FRA_a[3])/(FRA_a[2]))^2;
+simp:true;
+
+wa1:expand((x+FRA_a[3])^2)/(FRA_a[2])^2;
+wa2:(x+FRA_a[3])^2/expand((FRA_a[2])^2);
+wa3:expand((x+FRA_a[3])^2)/expand(FRA_a[2]^2);
+wa4:(3*FRA_a[3]*x+FRA_a[3]^2)/expand(FRA_a[2]^2)+x^2/FRA_a[2]^2; /*naively expanded fraction by squaring numerator and denominator*/
+wa5:(3*FRA_a[3]*x+FRA_a[3]^2+x)/(expand(FRA_a[2]^2)+FRA_a[2]); /*naively summed fractions, keeping the denominators*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@FRA_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>2</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die erste binomische Formel an, um den Zähler zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa2</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die zweite binomische Formel an, um den Nenner zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>4</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa3</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die erste binomische Formel an, um den Zähler zu faktorisieren und
+ wende die zweite binomische Formel an, um den Nenner zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa4</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich den zweiten Summanden mit sich selbst multipliziert (quadriert), damit die Nenner gleich sind. Allerdings wird ein Bruch so nicht erweitert. Der quadrierte Bruch ist nicht mehr äquivalent mit dem vorherigen Bruch. Beispiel: \((\frac{2}{5})^2 = \frac{4}{25} \ne \frac{2}{5}\;\) wohingegen \(\frac{2}{5} = \frac{2 \cdot 5}{5 \cdot 5} = \frac{10}{25}\;\). Bitte überlege erneut, womit der zweite Summand erweitert werden muss, damit die Nenner gleich sind.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa5</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich die beiden Brüche addiert, indem du Zähler plus Zähler (oben) und Nenner plus Nenner (unten) gerechnet hast. So können Brüche nicht addiert werden. Beispiel: \( \frac{1}{2} + \frac{1}{4} \ne \frac{1+1}{2+4}\;\) . Brüche müssen so erweitert werden, dass sie den gleichen Nenner haben. Dann können die Zähler addiert werden: \(\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}\).</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>2099085786</deployedseed> <deployedseed>245667775</deployedseed> <deployedseed>1806806387</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-a p-q-Formal Ia - Termumformung</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p>Formen Sie den Term so um, dass er in der Form \(x^2+px+q = 0\) erscheint. Sie können dies Zeile für Zeile tun.<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Um die p-q-Formel anzuwenden, müssen wir zunächst den Term in die richtige Form bringen. Um den folgenden Term wie gewünscht umzuformen, subtrahiere und dividiere auf beiden Seiten der Gleichung.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[6*x+3*x^2-2=10,x^2+2*x-4=0],6*x+3*x^2-2=10],
+[a2,[15*x+5*x^2=20,x^2+3*x-4=0],15*x+5*x^2=20],
+[a3,[8*x+2*x^2-2=12,x^2+4*x-7=0],8*x+2*x^2-2=12],
+[a4,[20*x+4*x^2=-16,x^2+5*x+4=0],20*x+4*x^2=-16]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Gut gemacht! Wenn ein Term auf diese Weise umgeformt ist, kannst du mit der p-q-Formel die möglichen Werte für \(x\) bestimmen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Weiter so! Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>equiv</type>
+ <tans>BIN_a[2]</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint>firstline</syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options>firstline</options>
+ </input><deployedseed>1126686893</deployedseed> <deployedseed>1832581792</deployedseed> <deployedseed>1406889611</deployedseed> <deployedseed>511391873</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-c p-q-Formel I - Endboss</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p>Bestimmen Sie alle reellen Lösungen der quadratischen Gleichung in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\(= ?\;\). Sie können Ihren Rechenweg angeben.<br></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Forme den Term um und wende dann die p-q-Formel an, um diese Endgegner-Aufgabe zu lösen. Dann bist du mit dieser Mathe-Welt fertig.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[-2*y^2+6*y=4, -2*y^2+6*y-4=0,y^2-3*y-2=0,stackeq(y=3/2+sqrt(9/4-2) nounor y=3/2-sqrt(9/4-2)),y=1 nounor y=2],-2*y^2+6*y=4,y,1,2,y=3/2+sqrt(9/4+2),y=3/2-sqrt(9/4+2)],
+[a2,[2*y^2-16=-4*y,2*y^2+4*y-16=0,y^2+2*y-8=0,stackeq(y=-1+sqrt((1)^2+8) nounor y=-1-sqrt((1)^2+8)),y=-4 nounor y=2],2*y^2-16=-4*y,y,-4,2,y=-1+sqrt((1)^2-8),y=-1-sqrt((1)^2-8)],
+[a3,[-2*d^2+2*d=-24,-2*d^2+2*d+24=0,d^2-d-12=0,d=1/2+sqrt((1/2)^2+12) nounor d=1/2-sqrt((1/2)^2+12),d=-3 nounor d=4],-2*d^2+2*d=-24,d,-3,4,d=1/2+sqrt((1/2)^2-12),d=1/2-sqrt((1/2)^2-12)],
+[a4,[-2*u^2-14*u=24,-2*u^2-14*u-24=0,u^2+7*u+12=0,u=-7/2+sqrt((7/2)^2-12) nounor u=-7/2-sqrt((7/2)^2-12),u=-4 nounor u=-3],-2*u^2-14*u=24,u,-4,-3,u=-7/2+sqrt((7/2)^2+12), u=-7/2-sqrt((7/2)^2+12)]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.</p><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast!
+ Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel
+in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2}
+\boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir="ltr">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir="ltr">Versuche es erneut und gib beide Lösungen an.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast! Offenbar hast du dich beim
+\(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet
+ \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil
+ am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du
+das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr">Außerdem
+ hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel
+ bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+}
+\sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-}
+\sqrt{...}\) gibt.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast!
+ Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>equiv</type>
+ <tans>BIN_a[2]</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint>firstline</syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options>firstline</options>
+ </input><deployedseed>1183308849</deployedseed> <deployedseed>1817300183</deployedseed> <deployedseed>1556042756</deployedseed> <deployedseed>493079990</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-b p-q-Formel Ib - pq-Formel</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p>Bestimmen Sie den Wert der Variable in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\( = ?\;\).<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Erinnerst du dich noch an die pq-Formel? Für \(\;x^2 + p\,x + q = 0\;\) gilt \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\).<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[h^2+3*h-4=0,h=-3/2+sqrt((3/2)^2+4) nounor h=-3/2-sqrt((3/2)^2+4),h=-3/2+sqrt(25/4) nounor h=-3/2-sqrt(25/4),h=-3/2+5/2 nounor h=-3/2-5/2,h=-4 nounor h=1],"\\(h^2+3\\,h-4=0\\)",h,1,-4,h=-3/2+sqrt(9/4-4),h=-3/2-sqrt(9/4-4)],
+[a2,[y^2-2*y-8=0,y=1+sqrt((-1)^2+8) nounor y=1-sqrt((-1)^2+8),y=-2 nounor y=4],"\\(y^2-2\\,y-8=0\\)",y,-2,4,y=1-sqrt(1-8),y=1+sqrt(1-8)],
+[a3,[z^2-4*z-5=0,z=2+sqrt((-2)^2+5) nounor z=2-sqrt((-2)^2+5),z=5 nounor z=-1],"\\(z^2-4\\,z-5=0\\)",z,5,-1,z=2+sqrt(4-5),z=2-sqrt(4-5)],
+[a4,[a^2-10*a+9=0,a=5+sqrt((-5)^2-9) nounor a=5-sqrt((-5)^2-9),a=9 nounor a=1],"\\(a^2-10\\,a+9=0\\)",a,9,1,a=5+sqrt(25+9),a=5-sqrt(25+9)]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr" style="text-align: left;">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2} \boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir="ltr" style="text-align: left;">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir="ltr" style="text-align: left;">Versuche es erneut und gib beide Lösungen an.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr" style="text-align: left;">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\) gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>equiv</type>
+ <tans>BIN_a[2]</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint>firstline</syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options>firstline</options>
+ </input><deployedseed>1183616185</deployedseed> <deployedseed>1771539896</deployedseed> <deployedseed>1420701792</deployedseed> <deployedseed>1009534997</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-f Potenzrechenregeln I - Endboss</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie folgenden Ausdruck; hierbei sind \(x,y \in \mathbb{R_{> 0}}\).</div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Dies ist die Endgegner-Aufgabe dieser Mathe-Welt <strong>Potenzrechenrelgen</strong>. Wenn du diese Aufgabe schaffst, hast du diese Mathe-Welt gemeistert. Viel Erfolg!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,stackeq(y^(-1/6)),"\\(\\frac{1}{\\sqrt[3]{y \\, \\sqrt x}} \\, \\sqrt[6]{x \\, y}\\)"],
+[a2,a^20*x^8,"\\(\\left( \\frac{a^3 x^5}{a^{-2} x^3} \\right)^4\\)"]
+];
+RUL_a:rand(RUL_A);
+
+/*ans1 is evaluated by ev(ans1,simp) to accept e. g. 1/(y^(1/6)) and y^(-1/6) and y^(-(1/6))*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ev(ans1,simp)</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1167231517</deployedseed> <deployedseed>1313491755</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-a Potenzrechenregeln Ia – Exponenten addieren</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Fangen wir damit an, die Exponenten zu addieren, wenn die Basis gleich ist und multipliziert wird.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^a*c^b,"\\(c^{\\,a}\\cdot c^{\\,b}\\)"],
+[a2,x^a*x^b,"\\(x^{\\,a}\\cdot x^{\\,b}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1724483596</deployedseed> <deployedseed>337440314</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-b Potenzrechenregeln Ib – Exponenten subtrahieren</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Das funktioniert auch in die andere Richtung.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^a/c^b,"\\(\\frac{c^{\\,a}}{c^{\\,b}}\\)"],
+[a2,x^a/x^b,"\\(\\frac{x^{\\,a}}{x^{\\,b}}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>29351489</deployedseed> <deployedseed>1996084793</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-c Potenzrechenregeln Ic - Wurzel als Potenz darstellen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p></p>
+<div>
+ <div>Stellen Sie den Ausdruck in der Form \(c^{\frac{1}{n}}\) dar.<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Mithilfe von Potenzen der Form \(c^{\frac{1}{n}}\) lässt sich die n-te Wurzel von \(c\), also \(\;\sqrt[n]{c}\;\), darstellen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(1/6),"\\(\\sqrt[6]{c}\\)"],
+[a2,c^(1/5),"\\(\\sqrt[5]{c}\\)"],
+[a3,c^(1/4),"\\(\\sqrt[4]{c}\\)"],
+[a4,c^(1/3),"\\(\\sqrt[3]{c}\\)"],
+[a5,c^(1/7),"\\(\\sqrt[7]{c}\\)"],
+[a6,c^(1/8),"\\(\\sqrt[8]{c}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Sie können noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1074873352</deployedseed> <deployedseed>460473552</deployedseed> <deployedseed>771365681</deployedseed> <deployedseed>1250006169</deployedseed> <deployedseed>259744359</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-d Potenzrechenregeln Id – Exponenten multiplizieren</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Wird ein Ausdruck, der eine Potenz enthält, potenziert, lassen sich die Exponenten miteinander multiplizieren.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(a*b),"\\((c^a)^b\\)",c^a*b],
+[a2,x^(a*b),"\\((x^a)^b\\)",x^a*b]
+];
+RUL_a:rand(RUL_A);
+wa:RUL_a[4];
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast die Klammer falsch gesetzt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1495340815</deployedseed> <deployedseed>1196787611</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-e Potenzrechenregeln Ie - Potenzrechenregeln anwenden</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p></p>
+<div>Nutzen Sie die Potenzrechenregeln, um folgenden Ausdruck zu vereinfachen.<br></div>
+<p>
+</p>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p>
+<div class="bubble in-modal no-arrow">
+ <div>Hier zur Erinnerung die wichtigsten Potenzrechenregeln. Für \(x, y \neq 0\) und \(n, m \in \mathbb{Z}\) gilt:</div>
+<div>
+ <div>
+ <div>
+ <ul>
+ <li>\(x^{n+m} = x^n\,x^m\;\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \(2^5 = 2^{2+3} = 2^2 \cdot 2^3 = 4 \cdot 8 = 32\)</span></div></li></ul><ul>
+ <li>
+ <div>
+ <div>\(\left( x^n \right)^m = x^{n\,m}\;\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \(\left( 2^2 \right)^3 = 2^6 = 64\)</span></div></div>
+ </div>
+ </li>
+ <li>
+ <div>
+ <div>
+ <div>
+ <div>\((x\,y)^n = x^n\,y^n\;\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \(6^2 = (2 \cdot 3)^2 = 2^2 \cdot 3^2 = 4 \cdot 9 = 36\)</span></div></div>
+ </div>
+ </div>
+ </div>
+ </li>
+ <li>\(\frac{1}{x^n} = x^{-n}\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \( \frac{1}{x^2} \cdot x^2 = x^{-2} \cdot x^2 = x^{-2+2} = x^0 = 1\)</span><br></div></li>
+ <li>\(\sqrt[n]{x} = x^{\frac{1}{n}}\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \( \sqrt[3]{x} \cdot x^3 = x^{\frac{1}{3}} \cdot x^3 = x^{\frac{1}{3}+3} = x^1 = x\)</span></div></li>
+ </ul>
+ </div>
+ </div>
+</div>
+<p></p>
+<div>
+ <div>
+ <div>
+ <ul></ul>
+ </div>
+ </div>
+</div>
+</div></p>
+<p class="hint">Um diese Aufgabe zu lösen, kannst du mehrere der gerade erläuterten Regeln kombinieren. </p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(13/6),"\\(\\sqrt[6]{c} \\cdot c^2\\)"],
+[a2,x^10,"\\(\\frac{x^5}{x^{-5}}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Richtig, aber du kannst noch weiter vereinfachen.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1602709371</deployedseed> <deployedseed>547016054</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-a Ganzzahlige Summanden ableiten</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Leite jeden Summanden einzeln ab.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i,i,10),4); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; exercise:nums[1]*myvar^powers[1]+nums[2]*myvar^powers[2]+nums[3]*myvar+nums[4]; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>351097132</deployedseed> <deployedseed>1047509677</deployedseed> <deployedseed>442872926</deployedseed> <deployedseed>286970886</deployedseed> <deployedseed>999400432</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-b Gebrochenrationale Summanden ableiten</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})={@fractions[1]@} \cdot {@myvar@}^{@powers[1]@}+{@fractions[2]@} \cdot {@myvar@}^{@powers[2]@}+{@fractions[3]@} \cdot {@myvar@}+{@myint@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Leite jeden Summanden einzeln ab.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myint:rand_with_step(1,10,1); numerators:rand_selection(makelist(i+2,i,6),3); denominators:makelist(rand_with_step(numerators[i]+1,numerators[i]+5,1),i,3); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; fractions:makelist(numerators[i]/denominators[i],i,3); exercise:fractions[1]*myvar^powers[1]+fractions[2]*myvar^powers[2]+fractions[3]*myvar+myint; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>857840145</deployedseed> <deployedseed>1543126498</deployedseed> <deployedseed>1871228756</deployedseed> <deployedseed>318121367</deployedseed> <deployedseed>2127933990</deployedseed> <deployedseed>484803571</deployedseed> <deployedseed>1056868370</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-c Produkte ableiten I</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:rand_selection(makelist(i+1,i,4),2); myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,4),2); exercise:(myvar^powers[1]+nums[1])*(myvar^powers[2]-nums[2]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1213180404</deployedseed> <deployedseed>1876101711</deployedseed> <deployedseed>1520468669</deployedseed> <deployedseed>1233734487</deployedseed> <deployedseed>1329784126</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-d Produkte ableiten II</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>num:rand_with_step(1,5,2); denom:rand_with_step(num+2, num+5,2); fraction:num/denom; nums:rand_selection(append(makelist(i-7,i,6),makelist(i,i,6)),4); myvar:rand([a,b,c,x,y,z]); power:rand([3,4]); exercise:(fraction*myvar+nums[1])*(nums[2]*myvar^power+nums[3]*myvar+nums[4]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>290055394</deployedseed> <deployedseed>1877259825</deployedseed> <deployedseed>1027269811</deployedseed> <deployedseed>1906880472</deployedseed> <deployedseed>1551769121</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-e Division ableiten I</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:[rand_with_step(3,4,1), 2]; nums:rand_selection(makelist(i,i,12),5); myvar:rand([a,b,c,x,y,z]); exercise:(myvar^powers[1]+nums[1]*myvar^powers[2]+myvar)/(nums[2]*myvar^2+nums[3]*myvar+nums[4]); ta1:diff(exercise, myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1439694172</deployedseed> <deployedseed>1028579078</deployedseed> <deployedseed>1454088108</deployedseed> <deployedseed>1063999325</deployedseed> <deployedseed>1974598074</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-f Division ableiten II</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:[rand([3,5,7,11]), rand_with_step(2,5,1)]; myvar:rand([a,b,c,x,y,z]); terms:[sqrt(nums[1])*myvar-nums[2], nums[1]*myvar^2-nums[2]]; terms:random_permutation(terms); exercise:terms[1]/terms[2]; ta1:diff(exercise, myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>525681144</deployedseed> <deployedseed>1447367624</deployedseed> <deployedseed>435810786</deployedseed> <deployedseed>1421496847</deployedseed> <deployedseed>918279888</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-g Kettenregel I</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root@}]{{@myvar@}^2-{@num@}}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); root:rand([3,5]); num:rand_with_step(3,9,1); exercise:(myvar^2-num)^(1/root); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1079586531</deployedseed> <deployedseed>1754291070</deployedseed> <deployedseed>1751932072</deployedseed> <deployedseed>1089076165</deployedseed> <deployedseed>215450400</deployedseed> <deployedseed>766534514</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-h Kettenregel II</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,5),3); power:rand_with_step(3,7,2); signs:makelist(rand([-1,1]),2); exercise:(nums[1]*myvar^2+signs[1]*nums[2]*myvar+signs[2]*nums[3])^power; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1676415387</deployedseed> <deployedseed>146672542</deployedseed> <deployedseed>1726255949</deployedseed> <deployedseed>1628089061</deployedseed> <deployedseed>633210403</deployedseed> <deployedseed>1850144475</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-i Gemischtes I</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,5),2); nums:rand_selection(makelist(i+1,i,58),2); exercise:(myvar^powers[1]+nums[1])^powers[2]*nums[2]*myvar; ta1:diff(exercise, myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>603470063</deployedseed> <deployedseed>1387533043</deployedseed> <deployedseed>820026169</deployedseed> <deployedseed>1884036955</deployedseed> <deployedseed>562165609</deployedseed> <deployedseed>931146921</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-j Gemischtes II</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,3),3); nums:rand_selection(makelist(i,i,5),2); exercise:(myvar^powers[1]-nums[1])^powers[2]*(myvar+nums[2])^powers[3]; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>949540891</deployedseed> <deployedseed>2032277992</deployedseed> <deployedseed>504654950</deployedseed> <deployedseed>906697601</deployedseed> <deployedseed>1241320418</deployedseed> <deployedseed>891184866</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-k Gemischtes III</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); terms:[rand_with_step(1,4,1)+myvar, myvar]; terms:random_permutation(terms); power:rand_with_step(3,7,1); exercise:(terms[1]/terms[2])^power; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1060600269</deployedseed> <deployedseed>1317786455</deployedseed> <deployedseed>2016195942</deployedseed> <deployedseed>79640143</deployedseed> <deployedseed>1481526612</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-l Gemischtes IV</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),2); power:rand_with_step(2,6,1); exercise:nums[1]*sqrt(nums[2]*myvar+myvar^power); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>63010318</deployedseed> <deployedseed>2022252790</deployedseed> <deployedseed>2032269463</deployedseed> <deployedseed>1301956355</deployedseed> <deployedseed>1085730060</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-m Gemischtes V</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),4); power:rand_with_step(2,5,1); terms:[(nums[1]*myvar+nums[2]), (nums[3]*myvar^power-nums[4])]; terms:random_permutation(terms); exercise:(terms[1]*terms[2])/myvar; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1627444094</deployedseed> <deployedseed>570947981</deployedseed> <deployedseed>1123631251</deployedseed> <deployedseed>566895213</deployedseed> <deployedseed>265672538</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-n Gemischtes VI</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); root_power:rand_with_step(3,6,1); power:rand_with_prohib(2,5,[root_power]); nums:rand_selection(makelist(i+2,i,6),2);exercise:(nums[1]*myvar-nums[2])^(power/root_power); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>466316231</deployedseed> <deployedseed>73259082</deployedseed> <deployedseed>253364053</deployedseed> <deployedseed>1197047345</deployedseed> <deployedseed>873528357</deployedseed> <deployedseed>10923026</deployedseed> <deployedseed>1464509121</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/000 Start Elements</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>000 Start 0.2</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-instant-tutoring.js"></script>
+<script>
+ ALQuiz.setCurrentQuestionId("start");
+</script>
+<p class="hint">Hey! Ich helfe dir beim Lösen der Mathe-Aufgaben. In diesem Übungsraum leite ich dich durch 5 Mathe-Welten. Jede Mathe-Welt besteht aus mehreren Hilfsschritt-Leveln und einem Endgegner <img src="https://marvin.hs-bochum.de/~mneugebauer/skull.svg" style="width:1em">. Das Ziel ist, in jeder Welt die Endgegner-Aufgabe zu lösen. Du brauchst die Hilfsschritt-Level nicht unbedingt lösen. Doch wenn du sie löst, wird es dir leichter fallen, die Endgegner-Aufgabe zu lösen.<br><br>Nutze die <span class="show-on-mobile-only"><a href="javascript:;" onclick="let showsidebarbutton = document.getElementById('showsidebaricon'); if (showsidebarbutton != undefined) { showsidebarbutton.click(); return; } let questionCard = document.querySelector('[id*=quiznavbutton]'); let drawerParent = questionCard.closest('.drawer'); if (drawerParent != undefined) { let target = drawerParent.id; let drawerOpener = document.querySelector('button[data-target='+target+'][data-action=toggle]'); if (drawerOpener != undefined) { drawerOpener.click(); } }">Navigation</a></span><span class="show-on-desktop-only">Navigation (rechts)</span> um dich durch die Level und Welten zu bewegen.<br><br>Mit Klick auf <a href="javascript:;" onclick="tutorialFocusElement(document.querySelector('.submitbtns'));">"Nächste Frage"</a>
+ <!--liefere ich dir automatisch die nächste Frage, die zu deinem Lernstand passt.-->Geht es los.<br>Viel Erfolg!<br>
+ Hier kannst du schon einmal die Eingabe ausprobieren. Versuche doch einfach Mal, die Zahl {@tasklist[1]@} einzugeben und deine Eingabe mit "Enter" überprüfen zu lassen.<br>
+</p>
+
+<p></p>
+<p>Machen Sie sich mithilfe des untenstehenden Eingabefelds mit der mathematischen Eingabe per Tastatur vertraut. Probieren Sie zum Beispiel <code>42</code>, <code>2*x+1</code>, <code>3/5</code> oder <code>sqrt(2)</code>. Schreiben Sie einen Ausdruck pro Zeile.</p>
+Durch das Beginnen einer neuen Zeile (Enter) wird Ihre Eingabe vom Digitalen Mentor geprüft.<br>
+<p></p>
+<p>[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><br>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1</defaultgrade>
+ <penalty>0.1</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>tasklist:[42,2*x+1,3/5,sqrt(2)];
+i:1;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text/>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text>Richtige Antwort, gut gemacht!</text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text>Ihre Antwort ist teilweise korrekt.</text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text>Falsche Antwort.</text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>equiv</type>
+ <tans>tasklist</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options>hideequiv</options>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>tasklist[1]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Genau! So kannst du eine Eingabe machen und sie prüfen lassen. Gibt jetzt darunter {@tasklist[2]@} ein.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>+</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>tasklist[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Genau! So kannst du eine Eingabe machen und sie prüfen lassen. Gibt jetzt {@tasklist[3]@} ein.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>tasklist[3]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Genau! So kannst du eine Eingabe machen und sie prüfen lassen. Gibt jetzt {@tasklist[4]@} ein.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>+</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>tasklist[4]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Prima, das soll für den Einstieg reichen! Viel Erfolg! Mit Klick auf "Nächste Frage" geht es los.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.1</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Genau, so kannst du eine Eingabe machen und sie prüfen lassen. Versuche doch noch einmal, einen der folgenden Ausdrücke einzugeben.</p><p dir="ltr" style="text-align: left;">{@tasklist[1]@}</p><p dir="ltr" style="text-align: left;">{@tasklist[2]@}</p><p dir="ltr" style="text-align: left;">{@tasklist[3]@}</p><p dir="ltr" style="text-align: left;">{@tasklist[4]@}<br></p>]]></text>
+ </falsefeedback>
+ </node>
+ </prt>
+ </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-a Gleichung eingeben (Multiplikation)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t0_syn_1_a')</script><p class="bubble"><div class="hint">Okay! Hier eine leichte Aufgabe zur Eingabe. Benutze für jede Multiplikation das Symbol * (Stern).
+ <!--<span class="show-on-mobile-only"><br><br>Nutze die <a href="javascript:;" onclick="let userFocusTop = document.createElement('div');userFocusTop.classList.add('user-focus', 'hide-top');let pageHeight = document.documentElement.scrollHeight;userFocusTop.style.height=Math.ceil(pageHeight+window.pageYOffset)+'px';userFocusTop.onclick = removeTutorialFocus;document.body.appendChild(userFocusTop);">Buttons über deiner Tastatur</a>, um die wichtigsten Mathe-Operatoren schnell zu finden.</span>-->
+ <br><br>Falls du ohne Tastatur unterwegs bist, kannst du mithilfe des <a href="javascript:;" onclick="tutorialFocusElement(document.querySelector('.mathsbutton'));">Mathe-Operatoren-Buttons</a> zusätzliche Buttons aktivieren, um alle Mathe-Operatoren schnell zu finden.
+
+ <!--<br><br>Drücke jederzeit den "Prüfen"-Button, um zu sehen, wie deine Eingabe interpretiert wurde.<br>Erst wenn du nach dem "Prüfen"-Button deine Eingabe nicht änderst und
+ erneut "Prüfen" klickst, wird deine Eingabe als Antwort abgeschickt.-->
+<br><br>Neben dem Eingabefeld siehst du, wie deine Eingabe interpretiert wird.<br>Wenn du auf den "Prüfen"-Button klickst, wird deine Eingabe als Antwort abgeschickt.
+</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Geben Sie die Gleichung \({@ta1@}\) in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,y=3*x+5],[a2,y=4*x+3],[a3,y=2*x+1],[a4,y=2*x-5],[a5,y=5*x-3],[a6,y=4*x-6]];SYN_a:rand(SYN_A);ta1:SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>480757020</deployedseed><deployedseed>585237317</deployedseed><deployedseed>1798333349</deployedseed><deployedseed>2118152732</deployedseed><deployedseed>1988707695</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-b Gleichung eingeben (Division)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t0_syn_1_b')</script><p class="bubble"><div class="hint">Okay! Divisionen werden mit / (Slash) dargestellt. Hier erscheinen Sie als Brüche.<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Geben Sie die Gleichung \({@TA@}\) in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,y=5/3],[a2,y=4/7],[a3,y=1/3],[a4,y=2/5],[a5,y=3/10],[a6,y=1/4]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);TA:SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>TA</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Wir arbeiten hier nur wenn explizit danach gefragt wird mit Dezimalzahlen. Brüche stellen das Ergebnis in der Regel genauer dar.<br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>TA</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords>3x</forbidwords><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>2690042</deployedseed><deployedseed>300094393</deployedseed><deployedseed>765518486</deployedseed><deployedseed>17019212</deployedseed><deployedseed>1233892964</deployedseed><deployedseed>147932577</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-c Potenzen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t0_syn_1_c')</script><p class="bubble"><div class="hint"><p>Mit dem Zeichen ^ (Caret) kannst du Potenzen darstellen.</p><div> <ul> <li>\(x^2\) wird so eingegeben: <code>x^2</code></li> <li>\(x^{-2}\) wird so eingegeben: <code>x^(-2)</code></li> <li>\(x^{1/3}\) wird so eingegeben: <code>x^(1/3)</code></li> </ul></div></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Geben Sie die Gleichung \[{@ta@}\] in das Eingabefeld ein.</p>
+<p><p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,(4+b)^2],[a2,(5+b)^2],[a3,(3+b)^2],[a4,(2+b)^2],[a5,(3+2*b)^2],[a6,(4+2*b)^2]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:expand(SYN_a[2])=SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[Sehr gut. Hier wurde übrigens eine binomische Formel angewendet, um einen Term zu faktorisieren.<br><p dir="ltr" style="text-align: left;" <br=""></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Deine Antwort ist zwar äquivalent mit der dargestellten Gleichung, aber du hast nicht genau die gleiche Gleichung dargestellt.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>93323135</deployedseed><deployedseed>1032837775</deployedseed><deployedseed>680315517</deployedseed><deployedseed>838329017</deployedseed><deployedseed>162866526</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-d Rationale Ausdrücke</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t0_syn_1_d')</script><p class="bubble"><div class="hint">Okay! Machen wir es etwas komplizierter. Um Terme in Brüchen darzustellen, musst du besonders auf die Klammersetzung achten.<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Geben Sie die Gleichung \[{@ta@}\] in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:x^2;b:(x+1);c:(x-5);SYN_A:[[a1,a,b,c],[a2,b,a,c],[a3,c,a,b]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:SYN_a[2]/(SYN_a[3]*SYN_a[4]);wa:SYN_a[2]/SYN_a[3]*SYN_a[4];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;" <br=""></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Bitte beachte, dass du um den Nenner zusätzliche Klammern setzen musst, damit er als zusammenhängender Divisor interpretiert wird.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>82298515</deployedseed><deployedseed>1458249622</deployedseed><deployedseed>1731794639</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-e Wurzelzeichen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t0_syn_1_e')</script><p class="bubble"><div class="hint">Gut. Um eine Wurzel darzustellen nutze <code>sqrt(x)</code> für \(\sqrt{x}\;\).</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Geben Sie \[{@ta1@}\] in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,3],[a2,5],[a3,7],[a4,11],[a5,13],[a6,19]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta1:sqrt(SYN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1136692395</deployedseed><deployedseed>659595513</deployedseed><deployedseed>2040368424</deployedseed><deployedseed>262860513</deployedseed><deployedseed>592365331</deployedseed><deployedseed>1218846808</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-f Mehrere Lösungen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t0_syn_1_f')</script><p class="bubble"><div class="hint">Gelegentlich müssen Ausdrücke mit logischen Verbindungen verknüpft werden. Nutze dafür <code>and</code> oder <code>or</code>. <br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Lösen Sie nach \(x\) auf. Geben Sie die Lösung in der Form \(x=? \mbox{ or } x=?\) ein.</p>
+<p><p>\[{@task@}\]<br></p><p>[[input:ans]] [[validation:ans]][[feedback:prt1]]</p><p><em>Achtung: Bitte setzen Sie kein zusätzliches +-Symbol vor positive Zahlen.<br></em></p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,4],[a2,9],[a3,16],[a4,25],[a5,36]];/*SYN_a:SYN_A[1];*/SYN_a:rand(SYN_A);ta:x=sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);taalt:x=+sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);task:x^2=SYN_a[2];wa1:x=sqrt(SYN_a[2]);wa2:x=-sqrt(SYN_a[2]);wa3:x=sqrt(SYN_a[2]) nounand x=-sqrt(SYN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>4</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>4</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>5</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>4</name><answertest>AlgEquiv</answertest><sans>1</sans><tans>1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-5-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr">Du hast nur eine von zwei richtigen Lösungen eingegeben.<br>Beispiel: \(5 \cdot 5 = 25\) und \(-5 \cdot -5 = 25\) (Minus Mal Minus ergibt Plus).<br>Für \(x^2 = 25\) gilt deshalb \(x = 5\) oder \(x = -5\), was hier in der Form <code>x=5 or x=-5</code> aufgeschrieben wird.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-5-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>5</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa3</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-6-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast alle richtigen Lösungen angegeben, allerdings hast du sie mit <code>and</code> verknüpft. Korrekt ist, sie mit <code>or</code> zu verknüpfen. Man schreibt</p><ul><li>entweder \(x=?\; oder \;x=?\)</li><li>oder \(x_1=?\; und \;x_2 = ?\;\).</li></ul>Hier benutzen wir ausschließlich die erste Form, die mit <code>x=? or x=?</code> dargestellt wird.<br>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-6-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords>4x</forbidwords><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>1032259226</deployedseed><deployedseed>2071301041</deployedseed><deployedseed>668615301</deployedseed><deployedseed>1810103727</deployedseed><deployedseed>2047586646</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-g Gleichung mehrschrittig lösen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t0_syn_1_g')</script><p class="bubble"><div class="hint">Um einen Rechenweg darzustellen, tippe jeden Schritt deiner Rechnung in eine neue Zeile in das Eingabefeld ein.</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p><p>Lösen Sie \(\;\){@p@}\(\;\) nach x auf.</p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.</p><p>Sie brauchen kein Äquivalenz-Zeichen eingeben.<br></p></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;b:3;c:4;SYN_A:[[a1,a,b,c],[a2,b,a,c],[a3,c,a,b],[a4,a,c,b],[a5,b,c,a],[a6,c,b,a]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:[SYN_a[2]*(SYN_a[3]+x)=SYN_a[4],SYN_a[2]*SYN_a[3]+SYN_a[2]*x=SYN_a[4],SYN_a[2]*x=SYN_a[4]-SYN_a[2]*SYN_a[3],x=(SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]];/*ta:[2*(3+x)=-3,2*x+6=-3,2*x=-9,x=-9/2];*/p:first(ta);/*p:"\\(2 \\cdot (3 + x) = -3\\)";*/wa1:x=-((SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]);wa2:x=SYN_a[4]-SYN_a[2]*SYN_a[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last(ans1)</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Aber fast richtig. Du hast dich offenbar mit dem Vorzeichen vertan.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar ist dir ein Fehler beim Lösen der Klammer unterlaufen. Um die Klammer aufzulösen, musst du beide beide Summanden in der Klammer mit dem Faktor vor der Klammer multiplizieren.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Weiter so. Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>equiv</type><tans>ta</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint>firstline</syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options>hideequiv</options></input><deployedseed>668615301</deployedseed><deployedseed>1810103727</deployedseed><deployedseed>2047586646</deployedseed><deployedseed>1032259226</deployedseed><deployedseed>2071301041</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-h Griechische Buchstaben</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t0_syn_1_h')</script><p class="bubble"><div class="hint">Wenn griechische Buchstaben einzugeben sind, schreibe sie einfach aus. Beispiel: \(\alpha=\) <code>alpha</code> , \(\beta=\) <code>beta</code><code></code> ,\(\pi=\) <code>pi </code><code></code>.<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Geben Sie \[{@ta@}\] in das Eingebefeld ein.</p>
+<p><p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p><em>Achtung: Bitte kopieren Sie keine Unicode-Zeichen, sondern benutzen Sie einfach Ihre Tastatur. <br></em></p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:beta;b:pi;c:alpha;SYN_A:[[a1,a,b],[a2,b,a],[a3,a,c],[a4,c,a],[a5,b,c],[a6,c,b]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:SYN_a[2]*z^(SYN_a[3]*x)wa1:SYN_a[2]*z^SYN_a[3]*x</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offenbar vergessen, eine Klammer um die Potenz zu schreiben. Schreibe Potenzen in Klammern, wenn sie aus mehr als einer Zahl bestehen. Beispiel: \(x^{-2a}\) wird so eingegeben: <code>x^(-2*a)</code>.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>1516837293</deployedseed><deployedseed>911975771</deployedseed><deployedseed>742782033</deployedseed><deployedseed>1709130663</deployedseed><deployedseed>648468622</deployedseed><deployedseed>272609913</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-i Syntax-Endboss</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t0_syn_1_i')</script><p class="bubble"><div class="hint">Willkommen zum Endgegner dieser Mathe-Welt. Mit dem Lösen dieser Aufgabe hast du die erste Mathe-Welt bereits abgeschlossen. Viel Erfolg!<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p><p>Lösen Sie {@p@} nach \(x\) auf.<br></p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.<br></p></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]<p></p><p><em>Zur Erinnerung: Das Kommando für</em> \(\sqrt{x}\)<em> lautet </em><code>sqrt(x)</code><em>. Nutzen Sie </em><code>or</code><em> um mehrere Lösungen anzugeben.</em></p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;b:3;c:4;d:2;e:3;SYN_A:[[a1,a,d],[a2,b,d],[a3,c,d],[a4,a,e],[a5,b,e],[a6,c,e]];SYN_a:rand(SYN_A);pifactor:ev(SYN_a[2]*(SYN_a[3]^2),simp);ta:[/*(SYN_a[2]*x^2)/(pifactor*pi)=1,*/SYN_a[2]*x^2=pifactor*pi,x^2=(SYN_a[3]^2)*pi,x=SYN_a[3]*sqrt(pi) nounor x=-SYN_a[3]*sqrt(pi)];p:first(ta);wa1:x=SYN_a[3]*sqrt(pi);wa2:x=-SYN_a[3]*sqrt(pi);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last(ans1)</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text><![CDATA[]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>4</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>3</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>3</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>1</sans><tans>1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast nur eine von zwei richtigen Lösungen eingegeben.<br>Beispiel: \(5\,\sqrt{\pi} \cdot 5\,\sqrt{\pi} = 25\,\pi\) und \(-5\,\sqrt{\pi} \cdot -5\,\sqrt{\pi} = 25\,\pi\) (Minus Mal Minus ergibt Plus).<br>Für \(x^2 = 25\pi\) gilt deshalb \(x = 5\,\sqrt{\pi}\) oder \(x = -5\,\sqrt{\pi}\), was hier in der Form <code>x=5*sqrt(pi) or x=-5*sqrt(pi)</code> aufgeschrieben wird.</p><p dir="ltr" style="text-align: left;"></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>4</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-5-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-5-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>equiv</type><tans>ta</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint>firstline</syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options>hideequiv</options></input><deployedseed>1169120426</deployedseed><deployedseed>1624332195</deployedseed><deployedseed>1578649438</deployedseed><deployedseed>1629124203</deployedseed><deployedseed>2120835467</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-a Kürzen zweier einfacher Brüche</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_bi-a')</script><p class="bubble"><div class="hint">Tipp: Gekürzt wird, indem man Zähler & Nenner durch dieselbe Zahl teilt.</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\({@f@} \cdot {@g@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(2,8,1); b:rand_with_step(20,40,10); c:a*b; d:b/5; e:a*b/10; ta1:1/a; simp:false; f:5/e; g:d/10; wa1:(5+d)/(e+10);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@f@} \cdot {@g@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir="ltr" style="text-align: left;">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>423191525</deployedseed><deployedseed>1756629135</deployedseed><deployedseed>505485688</deployedseed><deployedseed>813830513</deployedseed><deployedseed>1619258121</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-b Kürzen zweier Brüche mit Variablen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_bi-b')</script><p class="bubble"><div class="hint">Tipp: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\,a\,a\,b\,b\,c}{a\,a\,a\,a\,a\,b\,c\,c\,c}\)</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); powers:makelist(rand(5)+1, 6); myvar1: mya^powers[1]; myvar2: myb^powers[2]; myvar3: myc^powers[3]; myvar4: mya^powers[4]; myvar5: myb^powers[5]; myvar6: myc^powers[6]; d:(myvar1*myvar2*myvar3)/(myvar4*myvar5*myvar6); ta1:d;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Beispiel: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,b\,b\mkern-5mu/\,c\mkern-5mu/}{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,a\,a\,b\mkern-5mu/\,c\mkern-5mu/\,c\,c} = \frac{b}{a^2\,c^2}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>194802941</deployedseed><deployedseed>1917875187</deployedseed><deployedseed>1931041228</deployedseed><deployedseed>928137609</deployedseed><deployedseed>264598581</deployedseed><deployedseed>1633750828</deployedseed><deployedseed>1318198792</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-c Kürzen zweier Brüche mit Variablen und Zahlen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_bi-c')</script><p class="bubble"><div class="hint">Tipp: Erst auf einen Bruchstrich sortieren. Beispiel: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} = \frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c}\)</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>num1:rand_with_step(5,8,1); varlist:[a,b,c,u,v,w,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1], varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); num2:rand_with_step(3,7,1); num3:rand_with_step(3,7,1); nom1:num1*num2*myvars[1]; denom1:num1*myvars[2]; nom2:num1*num3*myvars[1]*myvars[2]; denom2:num1*myvars[1]*myvars[3]; ta1:(nom1/denom1)*(nom2/denom2); /*Alle Variablen in den Zählern mit einer Variable im Nenner gekürzt.*/wa1:((nom1/myvars[1])*(nom2/myvars[1]))/((denom1*denom2)/myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich die Variable {@myvars[1]@} im Nenner gegen beide Variablen in den Zählern gekürzt. Bei der Multiplikation von Brüchen kannst du immer nur einen Faktor gegen den anderen kürzen. Beispiel: \(\frac{36}{6} = \frac{6\cdot6}{6} = \frac{6\mkern-5mu/\cdot6}{6\mkern-5mu/} = \frac{6}{1} = 6\) und nicht \(\frac{36}{6} = \frac{6\cdot6}{6} \ne \frac{6\mkern-5mu/\cdot6\mkern-5mu/}{6\mkern-5mu/} = 1\;\).<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>So lassen sich Produkte auf einem Bruchstrich sortieren und kürzen: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} =\frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c} =\frac{49^7\mkern-14mu\large/ \small \; \cdot 21^3\mkern-14mu\large/\small \; \cdot a\mkern-5mu/ \cdot a \cdot b\mkern-5mu/}{7\mkern-5.5mu/ \cdot7\mkern-5.5mu/ \cdot a\mkern-5mu/\cdot b\mkern-5mu/\cdot c} =\frac{21\,a}{c}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1842189518</deployedseed><deployedseed>1601667602</deployedseed><deployedseed>2136766316</deployedseed><deployedseed>1542661342</deployedseed><deployedseed>2072145258</deployedseed><deployedseed>328965971</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-d Kürzen zweier Brüche mit Termen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_bi-d')</script><p class="bubble"><div class="hint">Tipp: Kennst du noch den Ausspruch „Aus Summen kürzen nur die Dummen“?!</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([x,y,z]); term_summand1:rand_with_prohib(-3,3,[0]); term_summand2:rand_with_prohib(-3,3,[0,term_summand1]); term1:myvar+term_summand1; term2:myvar+term_summand2; ta1:term1/myvar*(myvar^2/(term1*term2*myvar)); /*wa1 means: naive shortened fraction*/ wa1:(term1-myvar)/1*(myvar^2/(term1*term2*myvar));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Offensichtlich hast du beim ersten Bruch die Variable {@myvar@} im Nenner gegen die Variable {@myvar@} im Zähler gekürzt. Das geht aber nicht, weil die Variable {@myvar@} im Zähler mit einem anderen Summanden eine Summe bildet. Beispiel: \(3 = \frac{6}{2} = \frac{4+2}{2} \ne \frac{4 + 2\mkern-5.5mu/}{2\mkern-5.5mu/} = \frac{4}{1} = 4\;\).]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p> Nur ganze Faktoren dürfen gekürzt werden. Zum Beispiel: \(\frac{\boldsymbol{(x-1)}\cdot 2}{x \cdot \boldsymbol{(x-1)}} = \frac{2}{x}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>837792651</deployedseed><deployedseed>528135820</deployedseed><deployedseed>879656886</deployedseed><deployedseed>1917537516</deployedseed><deployedseed>1617668401</deployedseed><deployedseed>159039633</deployedseed><deployedseed>1131743594</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-a Einfachen Bruch erweitern</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_bii-a')</script><p class="bubble">Viel Erfolg beim Lösen dieser Aufgabe!</p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\({@c@} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(4,9,1); b:a-1; c:a/b; d:a*5; e:b*5; simp:false; ta1:d/e;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@c@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>437845679</deployedseed><deployedseed>2092409135</deployedseed><deployedseed>1712748750</deployedseed><deployedseed>182980498</deployedseed><deployedseed>388683995</deployedseed><deployedseed>1561500176</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-b Bruch mit Variablen erweitern</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_bii-b')</script><p class="bubble">Viel Erfolg beim Lösen dieser Aufgabe!</p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@numerator@}}{{@denominator@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,4); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[1]^powers[3]; fac4:myvars[2]^powers[4]; numerator:fac1*fac2; denominator:fac3*fac4; d:numerator/denominator; tanumerator:5*num(d); tadenominator:5*denom(d); simp:false; ta1:tanumerator/tadenominator;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@numerator@}}{{@denominator@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>36209422</deployedseed><deployedseed>1000344719</deployedseed><deployedseed>1827440244</deployedseed><deployedseed>1291739138</deployedseed><deployedseed>825866743</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-c Bruch mit Variablen und Zahlen erweitern</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_bii-c')</script><p class="bubble">Viel Erfolg beim Lösen dieser Aufgabe!</p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,3); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[2]^powers[3]; rand1:rand(4); rand2:rand_with_prohib(0,3,[rand1]); number1:rand1*2+3; number2:rand2*2+3; number3:rand_with_step(2,8,2); numerator:fac1*fac2; denominator:fac3; d:numerator/denominator; tanumerator:5*number1*number2*num(d); tadenominator:5*number3*denom(d); simp:false; ta1:tanumerator/tadenominator;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1516326427</deployedseed><deployedseed>1341581403</deployedseed><deployedseed>79491835</deployedseed><deployedseed>1422333316</deployedseed><deployedseed>1757641065</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ca Einfache Addition von Brüchen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_ca')</script><p class="bubble"><div class="hint">Tipp: Beim Addieren und Subtrahieren müssen die Nenner der Brüche gleich sein. Kannst du dich noch an das kleinste gemeinsame Vielfache erinnern?</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(1,4,1)*2+1; fac1:rand_with_step(1,4,1); fac2:rand_with_prohib(1,4,[fac1]); denoms:[a, a*fac1,a*fac2]; nums:makelist(rand_with_step(1,denoms[i]-1,2),i,3); signs:makelist(rand_with_prohib(-1,1,[0]),3); fractions:makelist(signs[i]*nums[i]/denoms[i],i,3); fractions:random_permutation(fractions); ta1:fractions[1]+fractions[2]+fractions[3]; simp:false; exercise:fractions[1]+fractions[2]+fractions[3]; /*wa1 means: naive addition*/ wa1:(num(fractions[1])+num(fractions[2])+num(fractions[3]))/(denom(fractions[1])+denom(fractions[2])+denom(fractions[3]));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir="ltr" style="text-align: left;">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um die Nenner gleich zu machen, musst du sie so erweitern, dass sie den gleichen Nenner haben. Dann können die Zähler addiert werden. Das kleinste gemeinsame Vielfache von 5, 10 und 15 lässt sich zum Beispiel finden, indem man die jeweiligen Reihen notiert und die kleinste gemeinsame Zahl sucht.</p><table><tr><th>5er-Reihe</th><th>10er-Reihe</th><th>15er-Reihe</th></tr><tr><td>5</td><td>10</td><td>15</td></tr><tr><td>10</td><td>20</td><td><strong>30</strong></td></tr><tr><td>15</td><td><strong>30</strong></td><td>...</td></tr><tr><td>20</td><td>...</td><td>...</td></tr><tr><td>25</td><td>...</td><td>...</td></tr><tr><td><strong>30</strong></td><td>...</td><td>...</td></tr><tr><td>...</td><td>...</td><td>...</td></tr></table></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>311233457</deployedseed><deployedseed>584289189</deployedseed><deployedseed>1338253474</deployedseed><deployedseed>933392702</deployedseed><deployedseed>236951333</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cb Addition von Brüchen mit Variablen und gleichem Nenner</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_cb')</script><p class="bubble"><div class="hint">Tipp: Überlege genau, was ein Minus vor einem Bruch bedeutet.</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c]); fractions_correct_and_wa1:[[(myvar+1)/myvar, -myvar+1], [(myvar-1)/myvar, -myvar-1], [(1-myvar)/myvar, -1-myvar]]; fractions_correct_and_wa1:random_permutation(fractions_correct_and_wa1); fractions:makelist(fractions_correct_and_wa1[i][1],i,3); terms_wa1:makelist(fractions_correct_and_wa1[i][2],i,3); exercise:fractions[1]-fractions[2]-fractions[3]; ta1:combine(exercise); wa1:(num(fractions[1])+terms_wa1[2]+terms_wa1[3])/myvar;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@}-{@fractions[2]@}-{@fractions[3]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
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+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
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+ <truescoremode>=</truescoremode>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast offenbar die Minuszeichen nicht korrekt aufgelöst.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
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+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Ein Minus vor dem Bruch gehört zum ganzen Bruch: gilt also für den ganzen Zähler oder ganzen Nenner (häufig nimmt man den Zähler).</p><p>\(\Rightarrow -\frac{a-1}{a} = \frac{-\boldsymbol{(a-1)}}{a} = \frac{-a+1}{a}\)</p><p>Wichtig bei Summen im Zähler!!!</p></p>]]></text>
+</truefeedback>
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+<falseanswernote>prt1-1000-F</falseanswernote>
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+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cc Addition von Brüchen mit Variablen und unterschiedlichen Nennern</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_cc')</script><p class="bubble"><div class="hint">Tipp: Jeder Teilnenner (hier: {@myvars[1]@}, {@myvars[2]@}, {@myvars[3]@}) muss als Faktor im gemeinsamen Nenner vorkommen.</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); fractions:[(1+myvars[1])/myvars[1], rand_with_step(2,5,1)/myvars[2], myvars[1]/myvars[3]]; fractions:random_permutation(fractions); exercise:fractions[1]+fractions[2]+fractions[3]; common_denom:denom(fractions[1])*denom(fractions[2])*denom(fractions[3]); ta1:((num(fractions[1])*denom(fractions[2])*denom(fractions[3]))+(num(fractions[2])*denom(fractions[1])*denom(fractions[3]))+(num(fractions[3])*denom(fractions[1])*denom(fractions[2])))/common_denom; ta1alt:(expand((num(fractions[1])*denom(fractions[2])*denom(fractions[3])))+expand((num(fractions[2])*denom(fractions[1])*denom(fractions[3])))+expand((num(fractions[3])*denom(fractions[1])*denom(fractions[2]))))/common_denom;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
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+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{1+a}{a}+\frac{2}{b}+\frac{a}{c}\) ist der gemeinsame Nenner \(a \cdot b \cdot c\). So muss erweitert werden, damit die Zähler addiert werden können:</p><p>\(\frac{(1+a) \boldsymbol{\cdot b \cdot c} }{a \boldsymbol{\cdot b \cdot c}}+\frac{2 \boldsymbol{\cdot a \cdot c}}{\boldsymbol{a} \cdot b \boldsymbol{\cdot c}}+\frac{a \boldsymbol{\cdot a \cdot b}}{\boldsymbol{a \cdot b} \cdot c}\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(1+a\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p></p>]]></text>
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+<falsepenalty/>
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+</node></prt><deployedseed>638235066</deployedseed><deployedseed>1053964038</deployedseed><deployedseed>625975426</deployedseed><deployedseed>1098133316</deployedseed><deployedseed>1880026849</deployedseed><deployedseed>1344755034</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cd Addition von Brüchen mit einer Variablen und unterschiedlichen Nennern</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_cd')</script><p class="bubble">Viel Erfolg beim Lösen dieser Aufgabe!</p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([x,y,z]); nums:makelist(rand_with_step(2,5,1),2); fractions:[(nums[1]+myvar)/myvar^2,(nums[2]-myvar^2)/myvar]; common_denom:myvar^2; ta1:(num(fractions[1])-num(fractions[2])*myvar)/common_denom; ta1alt:(num(fractions[1])-expand(num(fractions[2])*myvar))/common_denom; exercise:fractions[1]-fractions[2]; /*wa1 means: didn't consider minus sign before bracket*/ wa1:(num(fractions[1])+(-nums[2]-myvar^2)*myvar)/common_denom;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
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+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
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+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
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+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast offenbar die Minuszeichen nicht korrekt aufgelöst (siehe Tipp unten).]]></text>
+</truefeedback>
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+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um immer einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{3+x}{x^2}-\frac{5-x}{x}\) ist ein gemeinsame Nenner \(x^2 \cdot x = x^3\). Betrachtet man die Teilnenner \(x^2\) und \(x\) genauer, fällt auf, dass \(x\) bereits als Faktor in \(x^2\) vorkommt. Denn \(x^2 = x \cdot x\). Deswegen kann hier auch \(x^2\) als Hauptnenner gewählt werden.</p><p>Dazu muss so erweitert werden:</p><p>\(\frac{(3+x)}{x^{2}}-\frac{(5-x^2) \boldsymbol{ \cdot x}}{x \boldsymbol{\cdot x}} = \frac{3+x}{x^{2}}-\frac{5x-x^3}{x^{\boldsymbol{2}}} = \frac{3+x-(5x-x^3)}{x^2} = \dots\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(5-x^2\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p></p>]]></text>
+</truefeedback>
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+<falsepenalty/>
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+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>669633138</deployedseed><deployedseed>2093071884</deployedseed><deployedseed>1766326583</deployedseed><deployedseed>488830876</deployedseed><deployedseed>1210423031</deployedseed><deployedseed>158072256</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ce Addition von Brüchen mit Variablen und unterschiedlichen Nennern I (Update1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_ce')</script><p class="bubble"><div class="hint">Tipp: Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); numbers:makelist(rand_with_step(2,5,1), 5); factors:random_permutation([1,2,4]); /*only +*/ signs:makelist(rand_with_prohib(1,1,[0]),2); fractions:[(numbers[1]*myvars[1]-numbers[2]*myvars[2])/(factors[1]*5*myvars[1]*myvars[2]), (numbers[3]*myvars[3]-numbers[4]*myvars[1])/(factors[2]*5*myvars[1]*myvars[3]), (myvars[3]^2-numbers[5])/(factors[3]*5*myvars[2]*myvars[3])]; tanum:(num(fractions[1])*(4/factors[1])*myvars[3]+num(fractions[2])*(4/factors[2])*myvars[2]+num(fractions[3])*(4/factors[3])*myvars[1]); tanumalt:expand(tanum); tadenom:(5*4*myvars[1]*myvars[2]*myvars[3]); ta1:tanum/tadenom; /*fractions_to_show:random_permutation(fractions);*/ fractions_to_show:fractions; ta1alt:tanumalt/tadenom; fractions_to_show[2]:fractions_to_show[2]*signs[1]; fractions_to_show[3]:fractions_to_show[3]*signs[2]; exercise:fractions_to_show[1]+fractions_to_show[2]+fractions_to_show[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{5\,z-4\,x}{10\,x\,z}+\frac{7\,y-3\,z}{20\,y\,z}+\frac{y^2-2}{5\,x\,y}\) ist \(20\) das kleinste gemeinsame Vielfache (kgV) von \(10\), \(20\) und \(5\) und \(x \cdot y \cdot z\) ist das kgV von \(x \cdot z\), \(y \cdot z\) und \(x \cdot y\). Der Hauptnenner ist demnach \(20 \cdot x \cdot y \cdot z\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(20 \cdot x \cdot y \cdot z\;\) steht. \(\frac{5\,z-4\,x}{10\,x\,z}\) wird mit \(2 \cdot y\) erweitert, \(\frac{7\,y-3\,z}{20\,y\,z}\) wird mit \(x\) erweitert und \(\frac{y^2-2}{5\,x\,y}\) wird mit \(4 \cdot z\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(5\,z-4\,x)\boldsymbol{ \cdot 2\,y}}{10\,x\,z \boldsymbol{ \cdot 2\,y}}+\frac{(7\,y-3\,z) \boldsymbol{ \cdot x}}{20\,y\,z \boldsymbol{ \cdot x}}+\frac{(y^2-2) \boldsymbol{ \cdot 4\,z}}{5\,x\,y \boldsymbol{ \cdot 4\,z}}\)</p><p>\(= \frac{10\,y\,z-8\,x\,y}{20\,x\,y\,z}+\frac{7\,x\,y-3\,x\,z}{20\,x\,y\,z}+\frac{4\,y^2\,z-8\,z}{20\,x\,y\,z} = \dots\)</p></p>]]></text>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1330316881</deployedseed><deployedseed>2007639052</deployedseed><deployedseed>846124380</deployedseed><deployedseed>520216901</deployedseed><deployedseed>1618486590</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cf Addition von Brüchen mit Variablen und unterschiedlichen Nennern II</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_cf')</script><p class="bubble"><div class="hint">Tipp: 1) Überlege genau, was ein Minus vor einem Bruch bedeutet. 2) Jeder Teilnenner (hier: {@denom(main_fraction)@}, {@denom(fractions[1])@}, {@denom(fractions[2])@}) muss als Faktor im gemeinsamen Nenner vorkommen. 3) Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); numbers:rand_selection(makelist(i,i,5),2); denom_nums_origin:rand_selection([18,12,6],1)[1]; denom_nums:[denom_nums_origin, denom_nums_origin/2, denom_nums_origin/3]; main_fraction:(numbers[1]-myvars[1])/(denom_nums[1]*myvars[1]^2); fractions:[(myvars[2])/(denom_nums[2]*myvars[1]), (myvars[2]+numbers[2])/(denom_nums[3]*myvars[1]*myvars[2])]; tanum:num(main_fraction)*myvars[2]-num(fractions[1])*2*myvars[1]*myvars[2]-num(fractions[2])*3*myvars[1]; tanumalt:expand(tanum); tadenom:denom_nums_origin*myvars[1]^2*myvars[2]; ta1:tanum/tadenom; ta1alt:tanumalt/tadenom; fractions:random_permutation(fractions); simp:false; exercise:main_fraction-fractions[1]-fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{1-x}{18\,x^2}-\frac{y}{9\,x}-\frac{x+3}{6\,x\,y}\) ist \(18\) das kleinste gemeinsame Vielfache (kgV) von \(18\), \(9\) und \(6\) und \(x^2 \cdot y\) ist das kgV von \(x^2\), \(x\) und \(x \cdot y\). Der Hauptnenner ist demnach \(18 \cdot x^2 \cdot y\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(18 \cdot x^2 \cdot y\;\) steht. \(\frac{1-x}{18\,x^2}\) wird mit \(y\) erweitert, \(\frac{y}{9\,x}\) wird mit \(2\,x\,y\) erweitert und \(\frac{x+3}{6\,x\,y}\) wird mit \(3 \cdot x\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(1-x) \boldsymbol{\cdot y}}{18\,x^2 \boldsymbol{\cdot y}}-\frac{y \boldsymbol{\cdot 2\,x\,y}}{9\,x \boldsymbol{\cdot 2\,x\,y}}-\frac{(x+3) \boldsymbol{\cdot 3\,x}}{6\,x\,y \boldsymbol{\cdot 3\,x}}\)</p><p>\(= \frac{y-x\,y}{18\,x^2\,y}-\frac{2\,x\,y^2}{18\,x^2\,y}-\frac{3\,x^2+9\,x}{18\,x^2\,y} = \dots\)</p></p>]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>527686404</deployedseed><deployedseed>1918490776</deployedseed><deployedseed>2103547991</deployedseed><deployedseed>1091135158</deployedseed><deployedseed>1696865873</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-da Multiplikation zweier einfacher Brüche</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_da')</script><p class="bubble"><div class="hint">Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@}\cdot{@fractions[2]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8),4); fractions:[nums[1]/nums[2], nums[3]/nums[4]]; ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions*/ wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied*/ wa2:fractions[1]+fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@}\cdot{@fractions[2]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{2}{3} \cdot \frac{6}{5} = \frac{2 \cdot 6}{3 \cdot 5} = \frac{12}{15} = \frac{4}{5}\)</p></p>]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
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+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-db Multiplikation zweier Brüche mit Variablen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_db')</script><p class="bubble"><div class="hint">Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); fractions:[mya/myb, mya^2/(mya*myb)]; fractions:random_permutation(fractions); ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions with previously shortened the larger fraction*/ wa1:(2*mya)/(2*myb); /*wa2 means: naively summed fractions without previously shortening the larger fraction*/ wa2:(mya+myb^2)/(mya+myb*mya); /*wa3 means: correctly summed fractions instead of multiplied*/ wa3:fractions[1]+fractions[2]; /*wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied wa2:fractions[1]+fractions[2];*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
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+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
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+ <node>
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+ <tans>ta1</tans>
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+ <trueanswernote>prt1-1-T</trueanswernote>
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+ <falsefeedback format="html">
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+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
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+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
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+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden. Du hast außerdem den Bruch \({@mya@}^2/({@mya@}*{@myb@})\) nicht ausreichend vereinfacht. Er kann zu \({@mya@}/{@myb@}\) gekürzt werden.]]></text>
+</truefeedback>
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+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{a}{b} \cdot \frac{a^2}{a\,b} = \frac{a}{b} \cdot \frac{a \cdot a}{a\,b} = \frac{a \cdot a \cdot a}{a \cdot b \cdot b} = \frac{a^3}{a\,b^2}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>545658671</deployedseed><deployedseed>1228864607</deployedseed><deployedseed>806993602</deployedseed><deployedseed>1501016569</deployedseed><deployedseed>710282177</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dc Multiplikation Bruch mit Zahlen, Bruch mit Variablen, Ganzzahl</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_dc')</script><p class="bubble"><div class="hint">Tipp: Wie kann man eine ganze Zahl als Bruch schreiben?</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8),3); nums:sort(nums); varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); factors:[nums[1], (mya*myb)/myc, nums[2]/nums[3]]; factors:random_permutation(factors); ta1:factors[1]*factors[2]*factors[3]; simp:false; exercise:factors[1]*factors[2]*factors[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
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+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
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+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>999</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Jede ganze Zahl kann als Bruch geschrieben werden, indem man sie durch 1 teilt. Beispiel: \(3 \cdot \frac{a\,b}{c} \cdot \frac{5}{6} = \frac{3}{1} \cdot \frac{a\,b}{c} \cdot \frac{5}{6}\)</p><p>\( = \frac{3 \cdot a \cdot b \cdot 5}{1 \cdot c \cdot 6} = \frac{15\,a\,b}{6\,c} = \frac{5\,a\,b}{2\,c}\)</p><p>Hinweis: Generellt gilt \(\cdot 1\) und \(:\,1\) geht immer.</p></p>]]></text>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1569886884</deployedseed><deployedseed>1980675582</deployedseed><deployedseed>1601683210</deployedseed><deployedseed>51348788</deployedseed><deployedseed>726919830</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dd Multiplikation zweier Brüche mit Termen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_dd')</script><p class="bubble"><div class="hint">Tipp: Achtung: Summanden & Faktoren => Klammer!</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:rand_selection(varlist, 2); nums:rand_selection(makelist(i+1,i,9), 6); fractions:[(nums[1]*myvars[1]+nums[2]*myvars[2])/(nums[3]*myvars[2]+nums[4]*myvars[1]), (-nums[5]*myvars[1])/(nums[6]+myvars[1])]; ta1:fractions[1]*fractions[2]; taalt:combine(expand(ta1)); /*wa1 means: the multiplication of the numerator was done with only one summand of the first fraction’s numerator (the second one)*/ wa1:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(denom(fractions[1])*denom(fractions[2])); /*old_wa2 means the same as wa1 but with the first fraction numerator’s second summand*/ /*old_wa2: (nums[1]*myvars[1]*num(fractions[2])+nums[2]*myvars[2])/(denom(fractions[1])*denom(fractions[2]));*/ /*wa2 means the same as wa1 but with the denominators, so no brackets: first summand of second fraction is multiplied with last summand of first fraction*/ wa2:(num(fractions[1])*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]); /*wa3 is the combination of wa1 and wa2*/ wa3:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}= {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
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+ <requirelowestterms>0</requirelowestterms>
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+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Nenner richtig multipliziert, doch du hast den Faktor im Zähler des zweiten Bruches nur mit dem zweiten Summanden des Zählers im ersten Bruch multipliziert. Das heißt bei der Multiplikation der Zähler musst du Klammern um die Summe setzen und jeden Summanden des ersten Zählers mit dem Faktor des anderen Zählers multiplizieren.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Zähler richtig multipliziert, hast jedoch im Nenner nicht beachtet, dass Summen als Ganzes multipliziert werden. Das heißt bei der Multiplikation der Nenner musst du Klammern um die Summen setzen und jeden Summanden des einen Nenners mit jedem Summanden des anderen Nenners multiplizieren.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>5</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>5</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-6-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Summen nicht als Ganzes multipliziert. Das betrifft eine Summe im Zähler und die Summen im Nenner. Du musst jeweils Klammern setzen, damit jeder Summand mit jedem anderen Summanden multipliziert wird. ]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-6-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{4\,x+10\,y}{5\,y+2\,x} \cdot \frac{-4\,x}{3+x} = \)\(\frac{\boldsymbol{(4\,x+10\,y)} \cdot -4\,x}{\boldsymbol{(5\,y+2\,x)} \cdot \boldsymbol{(3+x)}} = \dots\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>783029466</deployedseed><deployedseed>1177445020</deployedseed><deployedseed>1009895582</deployedseed><deployedseed>1167689465</deployedseed><deployedseed>1922827729</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-de Einfacher Doppelbruch</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_de')</script><p class="bubble"><div class="hint">Tipp: Achtung: Doppelbruch</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8), 4); nums:sort(nums); ta1:((nums[1])/(nums[4]))/((nums[2])/(nums[3])); /*wa1 means: multiplied fractions instead of division*/ wa1:((nums[1])/(nums[4]))*((nums[2])/(nums[3])); /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:((nums[4])/(nums[1]))*((nums[2])/(nums[3]));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>352990161</deployedseed><deployedseed>467670994</deployedseed><deployedseed>1747402747</deployedseed><deployedseed>2135608811</deployedseed><deployedseed>460810681</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-df Bruch und Geteilt-Rechnung</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_df')</script><p class="bubble"><div class="hint">Achtung: Auch ein Doppelbruch ;)</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@dividend@}:{@divisor@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>power:rand_with_step(2,4,1); myvars:rand_selection([a,b,c,x,y,z],2); dividend:myvars[1]/myvars[2]; num:rand_with_step(1,5,1); divisor:(num-myvars[1])/(myvars[2]^power); ta1: dividend/divisor; /*wa1 means: multiplied fractions instead of division*/ wa1:dividend*divisor; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:dividend^(-1)*divisor; /*wa3 means: didn’t consider to multiply the denominator of the first fraction with the sum of the second fraction’s numerator as a whole*/ wa3:(num(dividend)*denom(divisor))/(myvars[2]*num-myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@dividend@}:{@divisor@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast den richtigen Kehrwert gebildet um die Brüche dann zu multiplizieren, jedoch hast du dann die Klammersetzung bei der Mutliplikation nicht beachtet.</p><p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{x}{a} : \frac{1-x}{a^2} = \frac{x}{a} \cdot \frac{a^2}{1-x}\)\(= \frac{x \cdot a^2}{a \cdot \boldsymbol{(1-x)}} = \dots\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: \(\boldsymbol{:}\) ist dasselbe wir ein Doppelbruchstrich.</p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>68495326</deployedseed><deployedseed>83279259</deployedseed><deployedseed>1848999895</deployedseed><deployedseed>1656521999</deployedseed><deployedseed>333378154</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dg Doppelbruch mit Zahlen und Variablen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_dg')</script><p class="bubble"><div class="hint">Tipp: Achtung: Doppelbruch</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:rand_selection(makelist(i+1,i,3),2); nums:rand_selection(makelist(i+1,i,4),2); myvars:rand_selection([a,b,c,x,y,z],2); fractions:[nums[1]/myvars[1]^powers[1], (nums[2]*myvars[2]^powers[2])/myvars[1]]; fractions:random_permutation(fractions); ta1:fractions[1]/fractions[2]; /*wa1 means: multiplied fractions instead of division*/ wa1:fractions[1]*fractions[2]; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:fractions[1]^(-1)*fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{2}{a^2}}{\frac{3\,b^2}{a}} = \frac{2}{a^2} \cdot \frac{a}{3\,b^2} = \frac{2\,a}{3\,a^2\,b^2}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1783639635</deployedseed><deployedseed>863915904</deployedseed><deployedseed>446314797</deployedseed><deployedseed>1562297660</deployedseed><deployedseed>1172377010</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dh Doppelbruch mit Termen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_dh')</script><p class="bubble"><div class="hint">Tipp: Achtung: Doppelbruch</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8), 3); nums:sort(nums); myvars:rand_selection([a,b,c,x,y,z],2); terms:[nums[1]*((1-myvars[1])/myvars[2]), (nums[2]/nums[3])*(myvars[2]^2/myvars[1])]; /*terms:random_permutation(terms);*/ ta1:terms[1]/terms[2]; taalt:combine(expand(ta1)); /*wa1 means: didn't consider to multiple first factor in the numerator with both summands of the fraction's numerator*/ wa1:((nums[1]*1-myvars[1])/myvars[2])/terms[2]; wa2:terms[1]*terms[2]; wa3:terms[1]^(-1)*terms[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Beim Multiplizieren des Faktors {@nums[1]@} und des Bruchs \(\frac{1-{@myvars[1]@}}{{@myvars[2]@}}\) im Zähler des Doppelbruchs musst du beachten, dass Summen als Ganzes multipliziert werden.</p><p>Beispiel: \(5 \cdot \frac{1-a}{b} = \frac{5 \cdot \boldsymbol{(1-a)}}{b} = \dots\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>5</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>5</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-6-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-6-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Lösungsweg für eine Beispielaufgabe:</p><p>\(\large\frac{5 \cdot \frac{1-a}{b}}{\frac{1}{3} \cdot \frac{b^2}{a}}\)\(\large = \frac{\frac{5 \cdot \boldsymbol{(1-a)}}{b}}{\frac{b^2}{3\,a}} = \frac{5 - 5\,a}{b} \cdot \frac{3\,a}{b^2}\)</p><p>\(\large = \frac{3\,a \cdot \boldsymbol{(5-5\,a)}}{b \cdot b^2} = \frac{15\,a - 15\,a^2}{b^3}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>611281053</deployedseed><deployedseed>439766047</deployedseed><deployedseed>725695831</deployedseed><deployedseed>1029360039</deployedseed><deployedseed>1825759080</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ea Bruchrechnung Kombination I</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_ea')</script><p class="bubble"><div class="hint">Tipp: Achtung: Doppelbrüche und Summanden => Punkt-vor-Strich-Rechnung</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(2,4,1); nums_real_frac:sort(rand_selection(makelist(i,i,9),4)); nums_unreal_frac:sort(rand_selection(makelist(i+3,i,7),6)); main_summand:((nums_real_frac[1])/(nums_real_frac[4]))/((nums_real_frac[2])/(nums_real_frac[3])); summands:[int*(nums_unreal_frac[6]/nums_unreal_frac[1]), ((nums_unreal_frac[5])/(nums_unreal_frac[2]))/((nums_unreal_frac[4])/(nums_unreal_frac[3]))]; ta1:main_summand+summands[1]-summands[2]; wa1:(main_summand+int)*summands[1]/int-summands[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast offensichtlich die Punkt-vor-Strich-Regel nicht beachtet.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6} = \frac{\frac{5}{6}}{\frac{1}{3}}+(2 \cdot \frac{9}{6}) \ne (\frac{\frac{5}{6}}{\frac{1}{3}}+2) \cdot \frac{9}{6}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Jeden Summanden einzeln betrachten und ausrechnen: Doppelbrüche auflösen und zusammenfassen.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6}-\frac{\frac{13}{4}}{\frac{6}{5}} = \frac{5}{6} \cdot \frac{3}{1}+\frac{2}{1} \cdot \frac{9}{6}-\frac{13}{5} \cdot \frac{5}{6}\)</p><p>\(= (\frac{5}{6\mkern-5mu/^2} \cdot \frac{3\mkern-5mu/^1}{1})+(\frac{2\mkern-5mu/^1}{1} \cdot \frac{9}{6\mkern-5mu/^2})-(\frac{13}{5\mkern-5mu/^1} \cdot \frac{5\mkern-5mu/^1}{6})\)</p><p>\(= \frac{5}{2} + \frac{9}{2} - \frac{13}{6} = \frac{5 \cdot 3}{2 \cdot 3} + \frac{9 \cdot 3}{2 \cdot 3} - \frac{13}{6} = \frac{15}{6} + \frac{27}{6} - \frac{13}{6}\)</p><p>\(= \frac{15+27+13}{6} = \frac{55}{6}\)<\p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>2022519868</deployedseed><deployedseed>2007714528</deployedseed><deployedseed>1652468809</deployedseed><deployedseed>1890021691</deployedseed><deployedseed>1160555762</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-eb Bruchrechnung Kombination II</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_eb')</script><p class="bubble"><div class="hint">Tipp: Sorgfältig ausmultiplizieren</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(3,7,1); nums:sort(rand_selection(makelist(i,i,9),6)); factors:[int, (nums[1]/nums[6]+nums[2]/nums[5]), (1-nums[3]/nums[4])]; ta1:factors[1]*factors[2]*factors[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})= {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>999</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Hier hast du zwei Möglichkeiten: Alles sauber ausmultiplizieren oder vor dem Multiplizieren die Klammern ausrechnen (Empfehlung!)</p><p>Beispiel: \(6 \cdot (\frac{3}{4}+\frac{1}{8}) \cdot (1-\frac{1}{4}) = 6 \cdot (\frac{3 \cdot 2}{4 \cdot 2}+\frac{1}{8}) \cdot (\frac{1 \cdot 4}{1 \cdot 4}-\frac{1}{4})\) </p><p>\(= 6 \cdot (\frac{6}{8}+\frac{1}{8}) \cdot (\frac{4}{4}-\frac{1}{4}) = 6 \cdot (\frac{7}{8}) \cdot (\frac{3}{4})\)</p><p>\( = \frac{6}{1} \cdot \frac{7}{8} \cdot \frac{3}{4} = \frac{6\mkern-5mu/^3 \cdot 7 \cdot 3}{1 \cdot 8\mkern-5mu/^4 \cdot 4} = \frac{63}{16}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>382901616</deployedseed><deployedseed>1683089904</deployedseed><deployedseed>724792720</deployedseed><deployedseed>857106597</deployedseed><deployedseed>2126061360</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ec Bruchrechnung Kombination III</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_ec')</script><p class="bubble"><div class="hint">Tipp: Achtung: Doppelbruch und gemischter Bruch vs. unechter Bruch</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(2,4,1); myvar:rand_selection([a,b,c,x,y,z],1)[1]; nums:sort(rand_selection(makelist(i,i,9),6)); summands:[(int+(nums[1]/nums[4]))*(myvar/nums[5]),1-((nums[6]-myvar)/((nums[4])/(nums[3])))]; ta1:combine(expand(summands[1]+summands[2])); wa1:(int*(nums[1]/nums[4]))*(myvar/nums[5])+summands[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast offenbar den gemischten Bruch \({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\) als Multiplikation \({@int@} \cdot \frac{{@nums[1]@}}{{@nums[4]@}}\) interpretiert. Allerdings meint der gemischte Bruch hier \({@int@}\) Ganze und \(\frac{{@nums[1]@}}{{@nums[4]@}}\) Anteil. Empfehlung: Gemischte Brüche als unechte Brüche umschreiben. Beispiel:\(2\frac{1}{6} = 2+\frac{1}{6} = \frac{2 \cdot 6}{1 \cdot 6} + \frac{1}{6} = \frac{12}{6}+\frac{1}{6} = \frac{13}{6}\)]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: \(\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}}\) ist auch ein Doppelbruch.</p><p>Achte darauf, dann die Klammer richtig zu setzen.</p><p>Beispiel: \(\frac{2-a}{\frac{7}{8}} = \boldsymbol{(}2-a\boldsymbol{)} \cdot \frac{8}{7}\)</p><p>Beachte: 1) Ganze Zahlen zum Bruch umschreiben. 2) Doppelbrüche umschreiben (Beispiel oben). 3) Gemischte Brüche umschreiben (Beispiel \(2\frac{1}{6}\) sind \(\frac{13}{6}\;\)). 4) Punkt-vor-Strich-Regel.</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>2024587341</deployedseed><deployedseed>1597148134</deployedseed><deployedseed>899831950</deployedseed><deployedseed>29495097</deployedseed><deployedseed>97014366</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-j Binomische Formeln I - Anwendungsaufgabe</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t3_frabin_1_j')</script><p class="bubble"><div class="hint">Um diese Aufgabe zu lösen, musst du mehrere binomische Formeln anwenden.<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen und faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.</div>
+</div>
+<p></p>
+<p>\(\frac{{@expand(BIN_a[2])@}}{{@expand(BIN_a[3])@}} \cdot {@BIN_a[3]@}\)\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p><br></p>
+<p><br></p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>aa:4;
+bb:5;
+c:3;
+d:2;
+
+u:(c*a-d*b)^2;
+ualt:(d*b-c*a)^2;
+v:(aa*a+d*b)^2;
+w:(bb*a-c*b)*(bb*a+c*b);
+
+x:(aa*a-d*b)^2;
+xalt:(d*b-aa*a)^2;
+y:(bb*a+c*b)^2;
+z:(c*a+d*b)*(c*a-d*b);
+
+/*BIN_A:[
+[a1,(2*a+5*b)^2,"\\(\\frac{4\\,a^2+20\\,a\\,b+25\\,b^2}{16\\,a^2-9\\,b^2}\\cdot(4\\,a-3\\,b)\\cdot(4\\,a+3\\,b)\\)"]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];*/
+
+BIN_A:[
+[a1,u,v,ualt],
+[a2,v,w,v],
+[a3,w,u,w],
+[a4,x,y,xalt],
+[a5,y,z,y],
+[a6,z,y,z]
+];
+BIN_a:rand(BIN_A);
+
+ta:BIN_a[2];
+taalt:BIN_a[4];
+
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>534740616</deployedseed> <deployedseed>47766652</deployedseed> <deployedseed>1657775726</deployedseed> <deployedseed>931829986</deployedseed> <deployedseed>1703936373</deployedseed> <deployedseed>151644710</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-g Binomische Formeln Ia - Erste binomische Formel</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t3_frabin_1_g')</script><p class="bubble"><div class="hint">Um den Bruch aus der Endgegner-Aufgabe zu vereinfachen, musst du binomische Formeln anwenden. Deshalb kommen wir nun zu den binomischen Formeln. Die erste binomische Formel besagt: \((a + b)^2 = a^2 + 2\,a\,b + b^2\;\).</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,(4+b)^2],
+[a2,(5+b)^2],
+[a3,(3+b)^2],
+[a4,(2+b)^2],
+[a5,(3+2*b)^2],
+[a6,(4+2*b)^2]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];
+task:expand(BIN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die erste binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1994312303</deployedseed> <deployedseed>1744518788</deployedseed> <deployedseed>1627526666</deployedseed> <deployedseed>1566276649</deployedseed> <deployedseed>1138479794</deployedseed> <deployedseed>806677520</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-h Binomische Formeln Ib - Zweite binomische Formel</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t3_frabin_1_h')</script><p class="bubble"><div class="hint">Die zweite binomische Formel besagt:\((a - b)^2 = a^2 - 2\,a\,b + b^2\;\).<!--Diesmal musst du den Term erst umformen, damit er in der richtigen Form erscheint.--><br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:4;
+b:5;
+c:3;
+d:2;
+
+e:1;
+f:2;
+
+BIN_A:[
+[a1,a,e],
+[a2,b,e],
+[a3,c,e],
+[a4,d,e],
+[a5,a,f],
+[a6,c,f]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]-BIN_a[3]*y)^2;
+taalt:(BIN_a[3]*y-BIN_a[2])^2;
+task:expand(ta);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>893674818</deployedseed> <deployedseed>675538571</deployedseed> <deployedseed>985713485</deployedseed> <deployedseed>1039647874</deployedseed> <deployedseed>1781202861</deployedseed> <deployedseed>824682247</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-i Binomische Formeln Ic - Dritte binomische Formel</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t3_frabin_1_i')</script><p class="bubble"><div class="hint">Die dritte binomische Formel besagt: \((a + b)\,(a - b) = a^2 - b^2\;\).<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p></p>
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>aa:4;
+bb:5;
+c:3;
+d:2;
+
+
+BIN_A:[
+[a1,aa,bb],
+[a2,c,d],
+[a3,d,aa],
+[a4,d,bb],
+[a5,d,c],
+[a6,aa,c]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]*x-BIN_a[3]*y)*(BIN_a[2]*x+BIN_a[3]*y);
+task:expand(ta);
+wa:(BIN_a[2]^2*x-BIN_a[3]^2*y)*(BIN_a[2]^2*x+BIN_a[3]^2*y);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die dritte binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast zwar die Unbekannten x und y korrekt faktorisiert, aber die sie begleitenden Faktoren unverändert in die Klammern geschrieben. Um diese korrekt zu faktorisieren, musst du ihre Wurzeln berechnen. Richtig wäre {@ta@}.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>455750255</deployedseed> <deployedseed>970764179</deployedseed> <deployedseed>1971560923</deployedseed> <deployedseed>987956614</deployedseed> <deployedseed>533447380</deployedseed> <deployedseed>299284489</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-k Bruchrechenregeln Ig2 - Bruch mit binomischem Term erweitern 2 (copy)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t3_frabin_1_k')</script><p class="bubble"><div class="hint">Dies ist der Endgegner zur Mathe-Welt <strong>Bruchrechenregeln und binomische Formeln</strong>. Wenn du diese Aufgabe schaffst, hast du diese Welt schon gemeistert. Wende zuerst die binomischen Formeln an, um die Nenner zu vereinfachen. Um die Brüche dann zu addieren, musst du mit einem Term erweitern.<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen und faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;
+b:3;
+c:4;
+
+aa:x-a;
+bb:x-b;
+cc:x-c;
+
+/*FRA_A:[
+[a1,(x^2-3)/(x^2-4),"\\(\\frac{x + 3}{x^2 - 4} + \\frac{x - 3}{x - 2}\\)",(x^2-3)/((x+2)*(x-2))]
+];*/
+
+FRA_A:[
+[a1,aa, a],
+[a2,bb, b],
+[a3,cc, c]
+];
+FRA_a:rand(FRA_A);
+task:(3*FRA_a[3]*x+FRA_a[3]^2)/expand(FRA_a[2]^2)+x/FRA_a[2];
+ta:(x+FRA_a[3])^2/(FRA_a[2])^2;
+
+simp:false;
+taalt:((x+FRA_a[3])/(FRA_a[2]))^2;
+simp:true;
+
+wa1:expand((x+FRA_a[3])^2)/(FRA_a[2])^2;
+wa2:(x+FRA_a[3])^2/expand((FRA_a[2])^2);
+wa3:expand((x+FRA_a[3])^2)/expand(FRA_a[2]^2);
+wa4:(3*FRA_a[3]*x+FRA_a[3]^2)/expand(FRA_a[2]^2)+x^2/FRA_a[2]^2; /*naively expanded fraction by squaring numerator and denominator*/
+wa5:(3*FRA_a[3]*x+FRA_a[3]^2+x)/(expand(FRA_a[2]^2)+FRA_a[2]); /*naively summed fractions, keeping the denominators*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@FRA_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>2</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die erste binomische Formel an, um den Zähler zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa2</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die zweite binomische Formel an, um den Nenner zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>4</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa3</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die erste binomische Formel an, um den Zähler zu faktorisieren und
+ wende die zweite binomische Formel an, um den Nenner zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa4</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich den zweiten Summanden mit sich selbst multipliziert (quadriert), damit die Nenner gleich sind. Allerdings wird ein Bruch so nicht erweitert. Der quadrierte Bruch ist nicht mehr äquivalent mit dem vorherigen Bruch. Beispiel: \((\frac{2}{5})^2 = \frac{4}{25} \ne \frac{2}{5}\;\) wohingegen \(\frac{2}{5} = \frac{2 \cdot 5}{5 \cdot 5} = \frac{10}{25}\;\). Bitte überlege erneut, womit der zweite Summand erweitert werden muss, damit die Nenner gleich sind.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa5</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich die beiden Brüche addiert, indem du Zähler plus Zähler (oben) und Nenner plus Nenner (unten) gerechnet hast. So können Brüche nicht addiert werden. Beispiel: \( \frac{1}{2} + \frac{1}{4} \ne \frac{1+1}{2+4}\;\) . Brüche müssen so erweitert werden, dass sie den gleichen Nenner haben. Dann können die Zähler addiert werden: \(\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}\).</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>2099085786</deployedseed> <deployedseed>245667775</deployedseed> <deployedseed>1806806387</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-a p-q-Formal Ia - Termumformung</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t4_pq_1_a')</script><p class="bubble"><div class="hint">Um die p-q-Formel anzuwenden, müssen wir zunächst den Term in die richtige Form bringen. Um den folgenden Term wie gewünscht umzuformen, subtrahiere und dividiere auf beiden Seiten der Gleichung.<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p>Formen Sie den Term so um, dass er in der Form \(x^2+px+q = 0\) erscheint. Sie können dies Zeile für Zeile tun.<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[6*x+3*x^2-2=10,x^2+2*x-4=0],6*x+3*x^2-2=10],
+[a2,[15*x+5*x^2=20,x^2+3*x-4=0],15*x+5*x^2=20],
+[a3,[8*x+2*x^2-2=12,x^2+4*x-7=0],8*x+2*x^2-2=12],
+[a4,[20*x+4*x^2=-16,x^2+5*x+4=0],20*x+4*x^2=-16]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Gut gemacht! Wenn ein Term auf diese Weise umgeformt ist, kannst du mit der p-q-Formel die möglichen Werte für \(x\) bestimmen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Weiter so! Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>equiv</type>
+ <tans>BIN_a[2]</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint>firstline</syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options>firstline</options>
+ </input><deployedseed>1126686893</deployedseed> <deployedseed>1832581792</deployedseed> <deployedseed>1406889611</deployedseed> <deployedseed>511391873</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-c p-q-Formel I - Endboss</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t4_pq_1_c')</script><p class="bubble"><div class="hint">Forme den Term um und wende dann die p-q-Formel an, um diese Endgegner-Aufgabe zu lösen. Dann bist du mit dieser Mathe-Welt fertig.<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p>Bestimmen Sie alle reellen Lösungen der quadratischen Gleichung in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\(= ?\;\). Sie können Ihren Rechenweg angeben.<br></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[-2*y^2+6*y=4, -2*y^2+6*y-4=0,y^2-3*y-2=0,stackeq(y=3/2+sqrt(9/4-2) nounor y=3/2-sqrt(9/4-2)),y=1 nounor y=2],-2*y^2+6*y=4,y,1,2,y=3/2+sqrt(9/4+2),y=3/2-sqrt(9/4+2)],
+[a2,[2*y^2-16=-4*y,2*y^2+4*y-16=0,y^2+2*y-8=0,stackeq(y=-1+sqrt((1)^2+8) nounor y=-1-sqrt((1)^2+8)),y=-4 nounor y=2],2*y^2-16=-4*y,y,-4,2,y=-1+sqrt((1)^2-8),y=-1-sqrt((1)^2-8)],
+[a3,[-2*d^2+2*d=-24,-2*d^2+2*d+24=0,d^2-d-12=0,d=1/2+sqrt((1/2)^2+12) nounor d=1/2-sqrt((1/2)^2+12),d=-3 nounor d=4],-2*d^2+2*d=-24,d,-3,4,d=1/2+sqrt((1/2)^2-12),d=1/2-sqrt((1/2)^2-12)],
+[a4,[-2*u^2-14*u=24,-2*u^2-14*u-24=0,u^2+7*u+12=0,u=-7/2+sqrt((7/2)^2-12) nounor u=-7/2-sqrt((7/2)^2-12),u=-4 nounor u=-3],-2*u^2-14*u=24,u,-4,-3,u=-7/2+sqrt((7/2)^2+12), u=-7/2-sqrt((7/2)^2+12)]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.</p><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast!
+ Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel
+in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2}
+\boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir="ltr">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir="ltr">Versuche es erneut und gib beide Lösungen an.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast! Offenbar hast du dich beim
+\(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet
+ \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil
+ am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du
+das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr">Außerdem
+ hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel
+ bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+}
+\sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-}
+\sqrt{...}\) gibt.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast!
+ Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>equiv</type>
+ <tans>BIN_a[2]</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint>firstline</syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options>firstline</options>
+ </input><deployedseed>1183308849</deployedseed> <deployedseed>1817300183</deployedseed> <deployedseed>1556042756</deployedseed> <deployedseed>493079990</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-b p-q-Formel Ib - pq-Formel</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t4_pq_1_b')</script><p class="bubble"><div class="hint">Erinnerst du dich noch an die pq-Formel? Für \(\;x^2 + p\,x + q = 0\;\) gilt \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\).<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p>Bestimmen Sie den Wert der Variable in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\( = ?\;\).<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[h^2+3*h-4=0,h=-3/2+sqrt((3/2)^2+4) nounor h=-3/2-sqrt((3/2)^2+4),h=-3/2+sqrt(25/4) nounor h=-3/2-sqrt(25/4),h=-3/2+5/2 nounor h=-3/2-5/2,h=-4 nounor h=1],"\\(h^2+3\\,h-4=0\\)",h,1,-4,h=-3/2+sqrt(9/4-4),h=-3/2-sqrt(9/4-4)],
+[a2,[y^2-2*y-8=0,y=1+sqrt((-1)^2+8) nounor y=1-sqrt((-1)^2+8),y=-2 nounor y=4],"\\(y^2-2\\,y-8=0\\)",y,-2,4,y=1-sqrt(1-8),y=1+sqrt(1-8)],
+[a3,[z^2-4*z-5=0,z=2+sqrt((-2)^2+5) nounor z=2-sqrt((-2)^2+5),z=5 nounor z=-1],"\\(z^2-4\\,z-5=0\\)",z,5,-1,z=2+sqrt(4-5),z=2-sqrt(4-5)],
+[a4,[a^2-10*a+9=0,a=5+sqrt((-5)^2-9) nounor a=5-sqrt((-5)^2-9),a=9 nounor a=1],"\\(a^2-10\\,a+9=0\\)",a,9,1,a=5+sqrt(25+9),a=5-sqrt(25+9)]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr" style="text-align: left;">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2} \boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir="ltr" style="text-align: left;">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir="ltr" style="text-align: left;">Versuche es erneut und gib beide Lösungen an.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr" style="text-align: left;">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\) gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>equiv</type>
+ <tans>BIN_a[2]</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint>firstline</syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options>firstline</options>
+ </input><deployedseed>1183616185</deployedseed> <deployedseed>1771539896</deployedseed> <deployedseed>1420701792</deployedseed> <deployedseed>1009534997</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-f Potenzrechenregeln I - Endboss</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t5_rul_1_f')</script><p class="bubble"><div class="hint">Dies ist die Endgegner-Aufgabe dieser Mathe-Welt <strong>Potenzrechenrelgen</strong>. Wenn du diese Aufgabe schaffst, hast du diese Mathe-Welt gemeistert. Viel Erfolg!</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie folgenden Ausdruck; hierbei sind \(x,y \in \mathbb{R_{> 0}}\).</div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,stackeq(y^(-1/6)),"\\(\\frac{1}{\\sqrt[3]{y \\, \\sqrt x}} \\, \\sqrt[6]{x \\, y}\\)"],
+[a2,a^20*x^8,"\\(\\left( \\frac{a^3 x^5}{a^{-2} x^3} \\right)^4\\)"]
+];
+RUL_a:rand(RUL_A);
+
+/*ans1 is evaluated by ev(ans1,simp) to accept e. g. 1/(y^(1/6)) and y^(-1/6) and y^(-(1/6))*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ev(ans1,simp)</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1167231517</deployedseed> <deployedseed>1313491755</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-a Potenzrechenregeln Ia – Exponenten addieren</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t5_rul_1_a')</script><p class="bubble"><div class="hint">Fangen wir damit an, die Exponenten zu addieren, wenn die Basis gleich ist und multipliziert wird.<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^a*c^b,"\\(c^{\\,a}\\cdot c^{\\,b}\\)"],
+[a2,x^a*x^b,"\\(x^{\\,a}\\cdot x^{\\,b}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1724483596</deployedseed> <deployedseed>337440314</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-b Potenzrechenregeln Ib – Exponenten subtrahieren</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t5_rul_1_b')</script><p class="bubble"><div class="hint">Das funktioniert auch in die andere Richtung.<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^a/c^b,"\\(\\frac{c^{\\,a}}{c^{\\,b}}\\)"],
+[a2,x^a/x^b,"\\(\\frac{x^{\\,a}}{x^{\\,b}}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>29351489</deployedseed> <deployedseed>1996084793</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-c Potenzrechenregeln Ic - Wurzel als Potenz darstellen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t5_rul_1_c')</script><p class="bubble"><div class="hint">Mithilfe von Potenzen der Form \(c^{\frac{1}{n}}\) lässt sich die n-te Wurzel von \(c\), also \(\;\sqrt[n]{c}\;\), darstellen.</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p></p>
+<div>
+ <div>Stellen Sie den Ausdruck in der Form \(c^{\frac{1}{n}}\) dar.<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(1/6),"\\(\\sqrt[6]{c}\\)"],
+[a2,c^(1/5),"\\(\\sqrt[5]{c}\\)"],
+[a3,c^(1/4),"\\(\\sqrt[4]{c}\\)"],
+[a4,c^(1/3),"\\(\\sqrt[3]{c}\\)"],
+[a5,c^(1/7),"\\(\\sqrt[7]{c}\\)"],
+[a6,c^(1/8),"\\(\\sqrt[8]{c}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Sie können noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1074873352</deployedseed> <deployedseed>460473552</deployedseed> <deployedseed>771365681</deployedseed> <deployedseed>1250006169</deployedseed> <deployedseed>259744359</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-d Potenzrechenregeln Id – Exponenten multiplizieren</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t5_rul_1_d')</script><p class="bubble"><div class="hint">Wird ein Ausdruck, der eine Potenz enthält, potenziert, lassen sich die Exponenten miteinander multiplizieren.<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(a*b),"\\((c^a)^b\\)",c^a*b],
+[a2,x^(a*b),"\\((x^a)^b\\)",x^a*b]
+];
+RUL_a:rand(RUL_A);
+wa:RUL_a[4];
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast die Klammer falsch gesetzt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1495340815</deployedseed> <deployedseed>1196787611</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-e Potenzrechenregeln Ie - Potenzrechenregeln anwenden</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t5_rul_1_e')</script><p class="bubble"><div class="hint">Um diese Aufgabe zu lösen, kannst du mehrere der gerade erläuterten Regeln kombinieren. </div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p></p>
+<div>Nutzen Sie die Potenzrechenregeln, um folgenden Ausdruck zu vereinfachen.<br></div>
+<p>
+</p>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p>
+<div class="bubble in-modal no-arrow">
+ <div>Hier zur Erinnerung die wichtigsten Potenzrechenregeln. Für \(x, y \neq 0\) und \(n, m \in \mathbb{Z}\) gilt:</div>
+<div>
+ <div>
+ <div>
+ <ul>
+ <li>\(x^{n+m} = x^n\,x^m\;\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \(2^5 = 2^{2+3} = 2^2 \cdot 2^3 = 4 \cdot 8 = 32\)</span></div></li></ul><ul>
+ <li>
+ <div>
+ <div>\(\left( x^n \right)^m = x^{n\,m}\;\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \(\left( 2^2 \right)^3 = 2^6 = 64\)</span></div></div>
+ </div>
+ </li>
+ <li>
+ <div>
+ <div>
+ <div>
+ <div>\((x\,y)^n = x^n\,y^n\;\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \(6^2 = (2 \cdot 3)^2 = 2^2 \cdot 3^2 = 4 \cdot 9 = 36\)</span></div></div>
+ </div>
+ </div>
+ </div>
+ </li>
+ <li>\(\frac{1}{x^n} = x^{-n}\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \( \frac{1}{x^2} \cdot x^2 = x^{-2} \cdot x^2 = x^{-2+2} = x^0 = 1\)</span><br></div></li>
+ <li>\(\sqrt[n]{x} = x^{\frac{1}{n}}\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \( \sqrt[3]{x} \cdot x^3 = x^{\frac{1}{3}} \cdot x^3 = x^{\frac{1}{3}+3} = x^1 = x\)</span></div></li>
+ </ul>
+ </div>
+ </div>
+</div>
+<p></p>
+<div>
+ <div>
+ <div>
+ <ul></ul>
+ </div>
+ </div>
+</div>
+</div></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(13/6),"\\(\\sqrt[6]{c} \\cdot c^2\\)"],
+[a2,x^10,"\\(\\frac{x^5}{x^{-5}}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Richtig, aber du kannst noch weiter vereinfachen.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1602709371</deployedseed> <deployedseed>547016054</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-a Ganzzahlige Summanden ableiten</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_a')</script><p class="bubble"><div class="hint">Tipp: Leite jeden Summanden einzeln ab.</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i,i,10),4); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; exercise:nums[1]*myvar^powers[1]+nums[2]*myvar^powers[2]+nums[3]*myvar+nums[4]; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>351097132</deployedseed> <deployedseed>1047509677</deployedseed> <deployedseed>442872926</deployedseed> <deployedseed>286970886</deployedseed> <deployedseed>999400432</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-b Gebrochenrationale Summanden ableiten</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_b')</script><p class="bubble"><div class="hint">Tipp: Leite jeden Summanden einzeln ab.</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})={@fractions[1]@} \cdot {@myvar@}^{@powers[1]@}+{@fractions[2]@} \cdot {@myvar@}^{@powers[2]@}+{@fractions[3]@} \cdot {@myvar@}+{@myint@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myint:rand_with_step(1,10,1); numerators:rand_selection(makelist(i+2,i,6),3); denominators:makelist(rand_with_step(numerators[i]+1,numerators[i]+5,1),i,3); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; fractions:makelist(numerators[i]/denominators[i],i,3); exercise:fractions[1]*myvar^powers[1]+fractions[2]*myvar^powers[2]+fractions[3]*myvar+myint; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>857840145</deployedseed> <deployedseed>1543126498</deployedseed> <deployedseed>1871228756</deployedseed> <deployedseed>318121367</deployedseed> <deployedseed>2127933990</deployedseed> <deployedseed>484803571</deployedseed> <deployedseed>1056868370</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-c Produkte ableiten I</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_c')</script><p class="bubble"><div class="hint"><p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:rand_selection(makelist(i+1,i,4),2); myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,4),2); exercise:(myvar^powers[1]+nums[1])*(myvar^powers[2]-nums[2]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1213180404</deployedseed> <deployedseed>1876101711</deployedseed> <deployedseed>1520468669</deployedseed> <deployedseed>1233734487</deployedseed> <deployedseed>1329784126</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-d Produkte ableiten II</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_d')</script><p class="bubble"><div class="hint"><p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>num:rand_with_step(1,5,2); denom:rand_with_step(num+2, num+5,2); fraction:num/denom; nums:rand_selection(append(makelist(i-7,i,6),makelist(i,i,6)),4); myvar:rand([a,b,c,x,y,z]); power:rand([3,4]); exercise:(fraction*myvar+nums[1])*(nums[2]*myvar^power+nums[3]*myvar+nums[4]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>290055394</deployedseed> <deployedseed>1877259825</deployedseed> <deployedseed>1027269811</deployedseed> <deployedseed>1906880472</deployedseed> <deployedseed>1551769121</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-e Division ableiten I</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_e')</script><p class="bubble"><div class="hint"><p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:[rand_with_step(3,4,1), 2]; nums:rand_selection(makelist(i,i,12),5); myvar:rand([a,b,c,x,y,z]); exercise:(myvar^powers[1]+nums[1]*myvar^powers[2]+myvar)/(nums[2]*myvar^2+nums[3]*myvar+nums[4]); ta1:diff(exercise, myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1439694172</deployedseed> <deployedseed>1028579078</deployedseed> <deployedseed>1454088108</deployedseed> <deployedseed>1063999325</deployedseed> <deployedseed>1974598074</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-f Division ableiten II</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_f')</script><p class="bubble"><div class="hint"><p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:[rand([3,5,7,11]), rand_with_step(2,5,1)]; myvar:rand([a,b,c,x,y,z]); terms:[sqrt(nums[1])*myvar-nums[2], nums[1]*myvar^2-nums[2]]; terms:random_permutation(terms); exercise:terms[1]/terms[2]; ta1:diff(exercise, myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>525681144</deployedseed> <deployedseed>1447367624</deployedseed> <deployedseed>435810786</deployedseed> <deployedseed>1421496847</deployedseed> <deployedseed>918279888</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-g Kettenregel I</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_g')</script><p class="bubble"><div class="hint"><p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root@}]{{@myvar@}^2-{@num@}}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); root:rand([3,5]); num:rand_with_step(3,9,1); exercise:(myvar^2-num)^(1/root); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1079586531</deployedseed> <deployedseed>1754291070</deployedseed> <deployedseed>1751932072</deployedseed> <deployedseed>1089076165</deployedseed> <deployedseed>215450400</deployedseed> <deployedseed>766534514</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-h Kettenregel II</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_h')</script><p class="bubble"><div class="hint"><p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,5),3); power:rand_with_step(3,7,2); signs:makelist(rand([-1,1]),2); exercise:(nums[1]*myvar^2+signs[1]*nums[2]*myvar+signs[2]*nums[3])^power; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1676415387</deployedseed> <deployedseed>146672542</deployedseed> <deployedseed>1726255949</deployedseed> <deployedseed>1628089061</deployedseed> <deployedseed>633210403</deployedseed> <deployedseed>1850144475</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-i Gemischtes I</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_i')</script><p class="bubble">Viel Erfolg beim Lösen dieser Aufgabe!</p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,5),2); nums:rand_selection(makelist(i+1,i,58),2); exercise:(myvar^powers[1]+nums[1])^powers[2]*nums[2]*myvar; ta1:diff(exercise, myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>603470063</deployedseed> <deployedseed>1387533043</deployedseed> <deployedseed>820026169</deployedseed> <deployedseed>1884036955</deployedseed> <deployedseed>562165609</deployedseed> <deployedseed>931146921</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-j Gemischtes II</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_j')</script><p class="bubble">Viel Erfolg beim Lösen dieser Aufgabe!</p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,3),3); nums:rand_selection(makelist(i,i,5),2); exercise:(myvar^powers[1]-nums[1])^powers[2]*(myvar+nums[2])^powers[3]; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>949540891</deployedseed> <deployedseed>2032277992</deployedseed> <deployedseed>504654950</deployedseed> <deployedseed>906697601</deployedseed> <deployedseed>1241320418</deployedseed> <deployedseed>891184866</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-k Gemischtes III</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_k')</script><p class="bubble">Viel Erfolg beim Lösen dieser Aufgabe!</p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); terms:[rand_with_step(1,4,1)+myvar, myvar]; terms:random_permutation(terms); power:rand_with_step(3,7,1); exercise:(terms[1]/terms[2])^power; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1060600269</deployedseed> <deployedseed>1317786455</deployedseed> <deployedseed>2016195942</deployedseed> <deployedseed>79640143</deployedseed> <deployedseed>1481526612</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-l Gemischtes IV</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_l')</script><p class="bubble">Viel Erfolg beim Lösen dieser Aufgabe!</p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),2); power:rand_with_step(2,6,1); exercise:nums[1]*sqrt(nums[2]*myvar+myvar^power); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>63010318</deployedseed> <deployedseed>2022252790</deployedseed> <deployedseed>2032269463</deployedseed> <deployedseed>1301956355</deployedseed> <deployedseed>1085730060</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-m Gemischtes V</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_m')</script><p class="bubble">Viel Erfolg beim Lösen dieser Aufgabe!</p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),4); power:rand_with_step(2,5,1); terms:[(nums[1]*myvar+nums[2]), (nums[3]*myvar^power-nums[4])]; terms:random_permutation(terms); exercise:(terms[1]*terms[2])/myvar; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1627444094</deployedseed> <deployedseed>570947981</deployedseed> <deployedseed>1123631251</deployedseed> <deployedseed>566895213</deployedseed> <deployedseed>265672538</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-n Gemischtes VI</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_n')</script><p class="bubble">Viel Erfolg beim Lösen dieser Aufgabe!</p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); root_power:rand_with_step(3,6,1); power:rand_with_prohib(2,5,[root_power]); nums:rand_selection(makelist(i+2,i,6),2);exercise:(nums[1]*myvar-nums[2])^(power/root_power); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>466316231</deployedseed> <deployedseed>73259082</deployedseed> <deployedseed>253364053</deployedseed> <deployedseed>1197047345</deployedseed> <deployedseed>873528357</deployedseed> <deployedseed>10923026</deployedseed> <deployedseed>1464509121</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/zzz Config Elements</text><info><text/></info></category><idnumber/></question><question type="description">
+ <name>
+ <text>zzz INSTANT TUTORING default-config</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href;</script>
+<p>Sie sind in der Konfigurationsdatei vom Digitalen Mentor gelandet. Klicken sie bitte auf eine der anderen Fragen in der Test-Navigation, um zurück zum Übungsraum zu gelangen.</p>
+{"groups": {"start": "Start", "t0_syn_1": "Syntax", "t1_fra_1": "Bruchrechnung", "t3_frabin_1": "Binom. Formeln", "t4_pq_1": "pq-Formel", "t5_rul_1": "Potenzrechenregeln", "t7_der_1": "Ableitungen"}, "questions": {"start": {"name": "Start", "group": "start"}, "t0_syn_1_a": {"name": "Gleichung eingeben (Multiplikation)", "variants": 5}, "t0_syn_1_b": {"name": "Gleichung eingeben (Division)", "variants": 6}, "t0_syn_1_c": {"name": "Potenzen", "variants": 5}, "t0_syn_1_d": {"name": "Rationale Ausdr\u00fccke", "variants": 3}, "t0_syn_1_e": {"name": "Wurzelzeichen", "variants": 6}, "t0_syn_1_f": {"name": "Mehrere L\u00f6sungen", "variants": 5}, "t0_syn_1_g": {"name": "Gleichung mehrschrittig l\u00f6sen", "variants": 5}, "t0_syn_1_h": {"name": "Griechische Buchstaben", "variants": 6}, "t0_syn_1_i": {"name": "Syntax-Endboss", "variants": 5}, "t1_fra_1_bi-a": {"name": "K\u00fcrzen zweier einfacher Br\u00fcche", "variants": 5}, "t1_fra_1_bi-b": {"name": "K\u00fcrzen zweier Br\u00fcche mit Variablen", "variants": 7}, "t1_fra_1_bi-c": {"name": "K\u00fcrzen zweier Br\u00fcche mit Variablen und Zahlen", "variants": 6}, "t1_fra_1_bi-d": {"name": "K\u00fcrzen zweier Br\u00fcche mit Termen", "variants": 7}, "t1_fra_1_bii-a": {"name": "Einfachen Bruch erweitern", "variants": 6}, "t1_fra_1_bii-b": {"name": "Bruch mit Variablen erweitern", "variants": 5}, "t1_fra_1_bii-c": {"name": "Bruch mit Variablen und Zahlen erweitern", "variants": 5}, "t1_fra_1_ca": {"name": "Einfache Addition von Br\u00fcchen", "variants": 5}, "t1_fra_1_cb": {"name": "Addition von Br\u00fcchen mit Variablen und gleichem Nenner", "variants": 5}, "t1_fra_1_cc": {"name": "Addition von Br\u00fcchen mit Variablen und unterschiedlichen Nennern", "variants": 6}, "t1_fra_1_cd": {"name": "Addition von Br\u00fcchen mit einer Variablen und unterschiedlichen Nennern", "variants": 6}, "t1_fra_1_ce": {"name": "Addition von Br\u00fcchen mit Variablen und unterschiedlichen Nennern I (Update1)", "variants": 5}, "t1_fra_1_cf": {"name": "Addition von Br\u00fcchen mit Variablen und unterschiedlichen Nennern II", "variants": 5}, "t1_fra_1_da": {"name": "Multiplikation zweier einfacher Br\u00fcche", "variants": 5}, "t1_fra_1_db": {"name": "Multiplikation zweier Br\u00fcche mit Variablen", "variants": 5}, "t1_fra_1_dc": {"name": "Multiplikation Bruch mit Zahlen, Bruch mit Variablen, Ganzzahl", "variants": 5}, "t1_fra_1_dd": {"name": "Multiplikation zweier Br\u00fcche mit Termen", "variants": 5}, "t1_fra_1_de": {"name": "Einfacher Doppelbruch", "variants": 5}, "t1_fra_1_df": {"name": "Bruch und Geteilt-Rechnung", "variants": 5}, "t1_fra_1_dg": {"name": "Doppelbruch mit Zahlen und Variablen", "variants": 5}, "t1_fra_1_dh": {"name": "Doppelbruch mit Termen", "variants": 5}, "t1_fra_1_ea": {"name": "Bruchrechnung Kombination I", "variants": 5}, "t1_fra_1_eb": {"name": "Bruchrechnung Kombination II", "variants": 5}, "t1_fra_1_ec": {"name": "Bruchrechnung Kombination III", "variants": 5}, "t3_frabin_1_g": {"name": "Binomische Formeln Ia - Erste binomische Formel", "variants": 6}, "t3_frabin_1_h": {"name": "Binomische Formeln Ib - Zweite binomische Formel", "variants": 6}, "t3_frabin_1_i": {"name": "Binomische Formeln Ic - Dritte binomische Formel", "variants": 6}, "t3_frabin_1_j": {"name": "Binomische Formeln I - Anwendungsaufgabe", "variants": 6}, "t3_frabin_1_k": {"name": "Bruchrechenregeln Ig2 - Bruch mit binomischem Term erweitern 2 (copy)", "variants": 3}, "t4_pq_1_a": {"name": "p-q-Formal Ia - Termumformung", "variants": 4}, "t4_pq_1_b": {"name": "p-q-Formel Ib - pq-Formel", "variants": 4}, "t4_pq_1_c": {"name": "p-q-Formel I - Endboss", "variants": 4}, "t5_rul_1_a": {"name": "Potenzrechenregeln Ia \u2013 Exponenten addieren", "variants": 2}, "t5_rul_1_b": {"name": "Potenzrechenregeln Ib \u2013 Exponenten subtrahieren", "variants": 2}, "t5_rul_1_c": {"name": "Potenzrechenregeln Ic - Wurzel als Potenz darstellen", "variants": 5}, "t5_rul_1_d": {"name": "Potenzrechenregeln Id \u2013 Exponenten multiplizieren", "variants": 2}, "t5_rul_1_e": {"name": "Potenzrechenregeln Ie - Potenzrechenregeln anwenden", "variants": 2}, "t5_rul_1_f": {"name": "Potenzrechenregeln I - Endboss", "variants": 2}, "t7_der_1_a": {"name": "Ganzzahlige Summanden ableiten", "variants": 5}, "t7_der_1_b": {"name": "Gebrochenrationale Summanden ableiten", "variants": 7}, "t7_der_1_c": {"name": "Produkte ableiten I", "variants": 5}, "t7_der_1_d": {"name": "Produkte ableiten II", "variants": 5}, "t7_der_1_e": {"name": "Division ableiten I", "variants": 5}, "t7_der_1_f": {"name": "Division ableiten II", "variants": 5}, "t7_der_1_g": {"name": "Kettenregel I", "variants": 6}, "t7_der_1_h": {"name": "Kettenregel II", "variants": 6}, "t7_der_1_i": {"name": "Gemischtes I", "variants": 6}, "t7_der_1_j": {"name": "Gemischtes II", "variants": 6}, "t7_der_1_k": {"name": "Gemischtes III", "variants": 5}, "t7_der_1_l": {"name": "Gemischtes IV", "variants": 5}, "t7_der_1_m": {"name": "Gemischtes V", "variants": 5}, "t7_der_1_n": {"name": "Gemischtes VI", "variants": 7}}}]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>0</defaultgrade>
+ <penalty>0</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ </question>
+
+ <question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/000 Start Elements</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>Start GamiExamPrep 0.8 (Einstiegsakademie)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[
+<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-fantasy-bg-ver3.js"></script>
+<script>
+ let quizObjectAsString = '{"groups": {"start": "Start", "t0_syn_1": "Syntax", "t1_fra_1": "Bruchrechnung", "t3_frabin_1": "Binom. Formeln", "t4_pq_1": "pq-Formel", "t5_rul_1": "Potenzrechenregeln", "t7_der_1": "Ableitungen"}, "questions": {"start": {"name": "Start", "group": "start"}, "t0_syn_1_a": {"name": "Gleichung eingeben (Multiplikation)", "variants": 4, "color": "#573036", "filter": "invert(20%) sepia(11%) saturate(2292%) hue-rotate(301deg) brightness(88%) contrast(87%)"}, "t0_syn_1_b": {"name": "Gleichung eingeben (Division)", "variants": 4, "color": "#1BA1C7", "filter": "invert(46%) sepia(89%) saturate(419%) hue-rotate(147deg) brightness(97%) contrast(96%)"}, "t0_syn_1_c": {"name": "Potenzen", "variants": 4, "color": "#B38ABB", "filter": "invert(67%) sepia(28%) saturate(423%) hue-rotate(244deg) brightness(85%) contrast(89%)"}, "t0_syn_1_d": {"name": "Rationale Ausdr\u00fccke", "variants": 3, "color": "#D558A8", "filter": "invert(50%) sepia(90%) saturate(907%) hue-rotate(290deg) brightness(87%) contrast(90%)"}, "t0_syn_1_e": {"name": "Wurzelzeichen", "variants": 4, "color": "#1B5658", "filter": "invert(26%) sepia(12%) saturate(2407%) hue-rotate(133deg) brightness(95%) contrast(86%)"}, "t0_syn_1_f": {"name": "Mehrere L\u00f6sungen", "variants": 4, "color": "#810311", "filter": "invert(8%) sepia(64%) saturate(6140%) hue-rotate(346deg) brightness(93%) contrast(104%)"}, "t0_syn_1_g": {"name": "Gleichung mehrschrittig l\u00f6sen", "variants": 4, "color": "#74CD27", "filter": "invert(68%) sepia(76%) saturate(507%) hue-rotate(42deg) brightness(95%) contrast(83%)"}, "t0_syn_1_h": {"name": "Griechische Buchstaben", "variants": 4, "color": "#3CF48A", "filter": "invert(72%) sepia(40%) saturate(699%) hue-rotate(89deg) brightness(101%) contrast(98%)"}, "t0_syn_1_i": {"name": "Syntax-Endboss", "variants": 4, "color": "#77B211", "filter": "invert(64%) sepia(52%) saturate(5261%) hue-rotate(48deg) brightness(107%) contrast(87%)"}, "t1_fra_1_bi-a": {"name": "K\u00fcrzen zweier einfacher Br\u00fcche", "variants": 4, "color": "#FD9C80", "filter": "invert(84%) sepia(53%) saturate(4565%) hue-rotate(313deg) brightness(115%) contrast(108%)"}, "t1_fra_1_bi-b": {"name": "K\u00fcrzen zweier Br\u00fcche mit Variablen", "variants": 4, "color": "#E249B2", "filter": "invert(52%) sepia(64%) saturate(4425%) hue-rotate(292deg) brightness(93%) contrast(90%)"}, "t1_fra_1_bi-c": {"name": "K\u00fcrzen zweier Br\u00fcche mit Variablen und Zahlen", "variants": 4, "color": "#D57774", "filter": "invert(81%) sepia(50%) saturate(3032%) hue-rotate(305deg) brightness(86%) contrast(94%)"}, "t1_fra_1_bi-d": {"name": "K\u00fcrzen zweier Br\u00fcche mit Termen", "variants": 4, "color": "#944A6C", "filter": "invert(34%) sepia(25%) saturate(1028%) hue-rotate(280deg) brightness(96%) contrast(89%)"}, "t1_fra_1_bii-a": {"name": "Einfachen Bruch erweitern", "variants": 4, "color": "#9B49A2", "filter": "invert(35%) sepia(65%) saturate(573%) hue-rotate(248deg) brightness(92%) contrast(92%)"}, "t1_fra_1_bii-b": {"name": "Bruch mit Variablen erweitern", "variants": 4, "color": "#FA00D1", "filter": "invert(54%) sepia(100%) saturate(7435%) hue-rotate(298deg) brightness(97%) contrast(127%)"}, "t1_fra_1_bii-c": {"name": "Bruch mit Variablen und Zahlen erweitern", "variants": 4, "color": "#E2AFDA", "filter": "invert(96%) sepia(86%) saturate(2059%) hue-rotate(203deg) brightness(96%) contrast(83%)"}, "t1_fra_1_ca": {"name": "Einfache Addition von Br\u00fcchen", "variants": 4, "color": "#EB3E57", "filter": "invert(33%) sepia(19%) saturate(6570%) hue-rotate(328deg) brightness(97%) contrast(89%)"}, "t1_fra_1_cb": {"name": "Addition von Br\u00fcchen mit Variablen und gleichem Nenner", "variants": 4, "color": "#7E182C", "filter": "invert(14%) sepia(27%) saturate(5843%) hue-rotate(328deg) brightness(98%) contrast(98%)"}, "t1_fra_1_cc": {"name": "Addition von Br\u00fcchen mit Variablen und unterschiedlichen Nennern", "variants": 4, "color": "#3960A7", "filter": "invert(33%) sepia(56%) saturate(621%) hue-rotate(180deg) brightness(96%) contrast(95%)"}, "t1_fra_1_cd": {"name": "Addition von Br\u00fcchen mit einer Variablen und unterschiedlichen Nennern", "variants": 4, "color": "#E44FCD", "filter": "invert(76%) sepia(58%) saturate(7362%) hue-rotate(280deg) brightness(93%) contrast(93%)"}, "t1_fra_1_ce": {"name": "Addition von Br\u00fcchen mit Variablen und unterschiedlichen Nennern I (Update1)", "variants": 4, "color": "#278495", "filter": "invert(40%) sepia(10%) saturate(2946%) hue-rotate(142deg) brightness(107%) contrast(86%)"}, "t1_fra_1_cf": {"name": "Addition von Br\u00fcchen mit Variablen und unterschiedlichen Nennern II", "variants": 4, "color": "#6D9D29", "filter": "invert(53%) sepia(90%) saturate(357%) hue-rotate(43deg) brightness(87%) contrast(88%)"}, "t1_fra_1_da": {"name": "Multiplikation zweier einfacher Br\u00fcche", "variants": 4, "color": "#302FFF", "filter": "invert(12%) sepia(96%) saturate(6720%) hue-rotate(247deg) brightness(102%) contrast(101%)"}, "t1_fra_1_db": {"name": "Multiplikation zweier Br\u00fcche mit Variablen", "variants": 4, "color": "#BBCBC4", "filter": "invert(93%) sepia(3%) saturate(752%) hue-rotate(102deg) brightness(89%) contrast(85%)"}, "t1_fra_1_dc": {"name": "Multiplikation Bruch mit Zahlen, Bruch mit Variablen, Ganzzahl", "variants": 4, "color": "#C5F99B", "filter": "invert(100%) sepia(16%) saturate(5613%) hue-rotate(328deg) brightness(109%) contrast(92%)"}, "t1_fra_1_dd": {"name": "Multiplikation zweier Br\u00fcche mit Termen", "variants": 4, "color": "#A3717F", "filter": "invert(51%) sepia(4%) saturate(3367%) hue-rotate(293deg) brightness(95%) contrast(75%)"}, "t1_fra_1_de": {"name": "Einfacher Doppelbruch", "variants": 4, "color": "#395C44", "filter": "invert(28%) sepia(21%) saturate(737%) hue-rotate(86deg) brightness(102%) contrast(87%)"}, "t1_fra_1_df": {"name": "Bruch und Geteilt-Rechnung", "variants": 4, "color": "#10F046", "filter": "invert(52%) sepia(95%) saturate(903%) hue-rotate(88deg) brightness(115%) contrast(90%)"}, "t1_fra_1_dg": {"name": "Doppelbruch mit Zahlen und Variablen", "variants": 4, "color": "#E39FB2", "filter": "invert(78%) sepia(4%) saturate(2863%) hue-rotate(296deg) brightness(88%) contrast(102%)"}, "t1_fra_1_dh": {"name": "Doppelbruch mit Termen", "variants": 4, "color": "#23F5CC", "filter": "invert(100%) sepia(72%) saturate(2181%) hue-rotate(84deg) brightness(106%) contrast(91%)"}, "t1_fra_1_ea": {"name": "Bruchrechnung Kombination I", "variants": 4, "color": "#01D504", "filter": "invert(43%) sepia(74%) saturate(1175%) hue-rotate(89deg) brightness(106%) contrast(114%)"}, "t1_fra_1_eb": {"name": "Bruchrechnung Kombination II", "variants": 4, "color": "#C6F237", "filter": "invert(96%) sepia(38%) saturate(4597%) hue-rotate(13deg) brightness(104%) contrast(89%)"}, "t1_fra_1_ec": {"name": "Bruchrechnung Kombination III", "variants": 4, "color": "#B64537", "filter": "invert(36%) sepia(12%) saturate(4301%) hue-rotate(324deg) brightness(93%) contrast(92%)"}, "t3_frabin_1_g": {"name": "Binomische Formeln Ia - Erste binomische Formel", "variants": 4, "color": "#8C9BF5", "filter": "invert(64%) sepia(5%) saturate(3975%) hue-rotate(195deg) brightness(98%) contrast(96%)"}, "t3_frabin_1_h": {"name": "Binomische Formeln Ib - Zweite binomische Formel", "variants": 4, "color": "#9F6D55", "filter": "invert(49%) sepia(5%) saturate(4049%) hue-rotate(334deg) brightness(89%) contrast(72%)"}, "t3_frabin_1_i": {"name": "Binomische Formeln Ic - Dritte binomische Formel", "variants": 4, "color": "#65D794", "filter": "invert(80%) sepia(24%) saturate(818%) hue-rotate(88deg) brightness(91%) contrast(88%)"}, "t3_frabin_1_j": {"name": "Binomische Formeln I - Anwendungsaufgabe", "variants": 4, "color": "#162095", "filter": "invert(18%) sepia(23%) saturate(6913%) hue-rotate(217deg) brightness(94%) contrast(98%)"}, "t3_frabin_1_k": {"name": "Bruchrechenregeln Ig2 - Bruch mit binomischem Term erweitern 2 (copy)", "variants": 3, "color": "#DD5BE4", "filter": "invert(46%) sepia(92%) saturate(1381%) hue-rotate(268deg) brightness(96%) contrast(85%)"}, "t4_pq_1_a": {"name": "p-q-Formal Ia - Termumformung", "variants": 4, "color": "#A4FFDC", "filter": "invert(91%) sepia(24%) saturate(563%) hue-rotate(85deg) brightness(103%) contrast(103%)"}, "t4_pq_1_b": {"name": "p-q-Formel Ib - pq-Formel", "variants": 4, "color": "#BA9DCC", "filter": "invert(70%) sepia(13%) saturate(705%) hue-rotate(233deg) brightness(94%) contrast(91%)"}, "t4_pq_1_c": {"name": "p-q-Formel I - Endboss", "variants": 4, "color": "#D34FDB", "filter": "invert(45%) sepia(84%) saturate(1892%) hue-rotate(259deg) brightness(88%) contrast(94%)"}, "t5_rul_1_a": {"name": "Potenzrechenregeln Ia \u2013 Exponenten addieren", "variants": 2, "color": "#910602", "filter": "invert(11%) sepia(63%) saturate(4965%) hue-rotate(14deg) brightness(103%) contrast(124%)"}, "t5_rul_1_b": {"name": "Potenzrechenregeln Ib \u2013 Exponenten subtrahieren", "variants": 2, "color": "#C8B210", "filter": "invert(72%) sepia(81%) saturate(1388%) hue-rotate(8deg) brightness(93%) contrast(87%)"}, "t5_rul_1_c": {"name": "Potenzrechenregeln Ic - Wurzel als Potenz darstellen", "variants": 4, "color": "#3BDBAA", "filter": "invert(92%) sepia(80%) saturate(1117%) hue-rotate(82deg) brightness(101%) contrast(69%)"}, "t5_rul_1_d": {"name": "Potenzrechenregeln Id \u2013 Exponenten multiplizieren", "variants": 2, "color": "#916F06", "filter": "invert(43%) sepia(44%) saturate(6440%) hue-rotate(38deg) brightness(93%) contrast(95%)"}, "t5_rul_1_e": {"name": "Potenzrechenregeln Ie - Potenzrechenregeln anwenden", "variants": 2, "color": "#C5B6C7", "filter": "invert(80%) sepia(6%) saturate(490%) hue-rotate(246deg) brightness(91%) contrast(96%)"}, "t5_rul_1_f": {"name": "Potenzrechenregeln I - Endboss", "variants": 2, "color": "#88383B", "filter": "invert(27%) sepia(85%) saturate(439%) hue-rotate(308deg) brightness(84%) contrast(94%)"}, "t7_der_1_a": {"name": "Ganzzahlige Summanden ableiten", "variants": 4, "color": "#71BC2E", "filter": "invert(61%) sepia(95%) saturate(366%) hue-rotate(48deg) brightness(91%) contrast(84%)"}, "t7_der_1_b": {"name": "Gebrochenrationale Summanden ableiten", "variants": 4, "color": "#B20EE3", "filter": "invert(22%) sepia(84%) saturate(4934%) hue-rotate(280deg) brightness(90%) contrast(116%)"}, "t7_der_1_c": {"name": "Produkte ableiten I", "variants": 4, "color": "#C751FB", "filter": "invert(41%) sepia(23%) saturate(6695%) hue-rotate(255deg) brightness(101%) contrast(97%)"}, "t7_der_1_d": {"name": "Produkte ableiten II", "variants": 4, "color": "#496108", "filter": "invert(32%) sepia(17%) saturate(2438%) hue-rotate(36deg) brightness(96%) contrast(94%)"}, "t7_der_1_e": {"name": "Division ableiten I", "variants": 4, "color": "#4DA97E", "filter": "invert(54%) sepia(42%) saturate(476%) hue-rotate(100deg) brightness(100%) contrast(84%)"}, "t7_der_1_f": {"name": "Division ableiten II", "variants": 4, "color": "#F8C255", "filter": "invert(76%) sepia(85%) saturate(388%) hue-rotate(335deg) brightness(100%) contrast(95%)"}, "t7_der_1_g": {"name": "Kettenregel I", "variants": 4, "color": "#642E0E", "filter": "invert(18%) sepia(12%) saturate(6525%) hue-rotate(354deg) brightness(97%) contrast(92%)"}, "t7_der_1_h": {"name": "Kettenregel II", "variants": 4, "color": "#16C9D7", "filter": "invert(67%) sepia(27%) saturate(3791%) hue-rotate(137deg) brightness(101%) contrast(83%)"}, "t7_der_1_i": {"name": "Gemischtes I", "variants": 4, "color": "#C768E5", "filter": "invert(51%) sepia(33%) saturate(1489%) hue-rotate(239deg) brightness(96%) contrast(86%)"}, "t7_der_1_j": {"name": "Gemischtes II", "variants": 4, "color": "#DA8376", "filter": "invert(76%) sepia(76%) saturate(1360%) hue-rotate(305deg) brightness(86%) contrast(86%)"}, "t7_der_1_k": {"name": "Gemischtes III", "variants": 4, "color": "#93916B", "filter": "invert(62%) sepia(7%) saturate(1282%) hue-rotate(19deg) brightness(91%) contrast(88%)"}, "t7_der_1_l": {"name": "Gemischtes IV", "variants": 4, "color": "#A4AA17", "filter": "invert(57%) sepia(80%) saturate(463%) hue-rotate(23deg) brightness(95%) contrast(84%)"}, "t7_der_1_m": {"name": "Gemischtes V", "variants": 4, "color": "#62CB69", "filter": "invert(99%) sepia(33%) saturate(3140%) hue-rotate(51deg) brightness(87%) contrast(79%)"}, "t7_der_1_n": {"name": "Gemischtes VI", "variants": 4, "color": "#CD51BA", "filter": "invert(52%) sepia(46%) saturate(3109%) hue-rotate(280deg) brightness(85%) contrast(86%)"}}}';
+ let quizObject = JSON.parse(quizObjectAsString)
+ let ALQuiz = new FantasyQuiz(quizObject);
+ ALQuiz.setCurrentQuestionId("start");
+ document.addEventListener("DOMContentLoaded", function() {
+ ALQuiz.init();
+ });
+</script>
+<p dir="ltr" style="text-align: left;display:none;">Some formula to load Mathjax \(x=1\)<br></p>
+
+<p>[[input:ans1]] [[validation:ans1]]</p>
+<p>[[input:ans2]] [[validation:ans2]]<br></p>
+ ]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1</defaultgrade>
+ <penalty>0.1</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>ta1:x=42;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text><![CDATA[<p>[[feedback:prt1]]</p>]]></text>
+ </specificfeedback>
+ <questionnote>
+ <text/>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text>Richtige Antwort, gut gemacht!</text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text>Ihre Antwort ist teilweise korrekt.</text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text>Falsche Antwort.</text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <input>
+ <name>ans2</name>
+ <type>string</type>
+ <tans><![CDATA["Filled by Javascript"]]></tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>0</mustverify>
+ <showvalidation>0</showvalidation>
+ <options>hideanswer</options>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-a Gleichung eingeben (Multiplikation) (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \({@ta1@}\) in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Hier eine leichte Aufgabe zur Eingabe. Benutze für jede Multiplikation das Symbol * (Stern).
+ <!--<span class="show-on-mobile-only"><br><br>Nutze die <a href="javascript:;" onclick="let userFocusTop = document.createElement('div');userFocusTop.classList.add('user-focus', 'hide-top');let pageHeight = document.documentElement.scrollHeight;userFocusTop.style.height=Math.ceil(pageHeight+window.pageYOffset)+'px';userFocusTop.onclick = removeTutorialFocus;document.body.appendChild(userFocusTop);">Buttons über deiner Tastatur</a>, um die wichtigsten Mathe-Operatoren schnell zu finden.</span>-->
+ <br><br>Falls du ohne Tastatur unterwegs bist, kannst du mithilfe des <a href="javascript:;" onclick="tutorialFocusElement(document.querySelector('.mathsbutton'));">Mathe-Operatoren-Buttons</a> zusätzliche Buttons aktivieren, um alle Mathe-Operatoren schnell zu finden.
+
+ <!--<br><br>Drücke jederzeit den "Prüfen"-Button, um zu sehen, wie deine Eingabe interpretiert wurde.<br>Erst wenn du nach dem "Prüfen"-Button deine Eingabe nicht änderst und
+ erneut "Prüfen" klickst, wird deine Eingabe als Antwort abgeschickt.-->
+<br><br>Neben dem Eingabefeld siehst du, wie deine Eingabe interpretiert wird.<br>Wenn du auf den "Prüfen"-Button klickst, wird deine Eingabe als Antwort abgeschickt.
+</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,y=3*x+5],[a2,y=4*x+3],[a3,y=2*x+1],[a4,y=2*x-5],[a5,y=5*x-3],[a6,y=4*x-6]];SYN_a:rand(SYN_A);ta1:SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
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+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>480757020</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-a Gleichung eingeben (Multiplikation) (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \({@ta1@}\) in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Hier eine leichte Aufgabe zur Eingabe. Benutze für jede Multiplikation das Symbol * (Stern).
+ <!--<span class="show-on-mobile-only"><br><br>Nutze die <a href="javascript:;" onclick="let userFocusTop = document.createElement('div');userFocusTop.classList.add('user-focus', 'hide-top');let pageHeight = document.documentElement.scrollHeight;userFocusTop.style.height=Math.ceil(pageHeight+window.pageYOffset)+'px';userFocusTop.onclick = removeTutorialFocus;document.body.appendChild(userFocusTop);">Buttons über deiner Tastatur</a>, um die wichtigsten Mathe-Operatoren schnell zu finden.</span>-->
+ <br><br>Falls du ohne Tastatur unterwegs bist, kannst du mithilfe des <a href="javascript:;" onclick="tutorialFocusElement(document.querySelector('.mathsbutton'));">Mathe-Operatoren-Buttons</a> zusätzliche Buttons aktivieren, um alle Mathe-Operatoren schnell zu finden.
+
+ <!--<br><br>Drücke jederzeit den "Prüfen"-Button, um zu sehen, wie deine Eingabe interpretiert wurde.<br>Erst wenn du nach dem "Prüfen"-Button deine Eingabe nicht änderst und
+ erneut "Prüfen" klickst, wird deine Eingabe als Antwort abgeschickt.-->
+<br><br>Neben dem Eingabefeld siehst du, wie deine Eingabe interpretiert wird.<br>Wenn du auf den "Prüfen"-Button klickst, wird deine Eingabe als Antwort abgeschickt.
+</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,y=3*x+5],[a2,y=4*x+3],[a3,y=2*x+1],[a4,y=2*x-5],[a5,y=5*x-3],[a6,y=4*x-6]];SYN_a:rand(SYN_A);ta1:SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>585237317</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-a Gleichung eingeben (Multiplikation) (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \({@ta1@}\) in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Hier eine leichte Aufgabe zur Eingabe. Benutze für jede Multiplikation das Symbol * (Stern).
+ <!--<span class="show-on-mobile-only"><br><br>Nutze die <a href="javascript:;" onclick="let userFocusTop = document.createElement('div');userFocusTop.classList.add('user-focus', 'hide-top');let pageHeight = document.documentElement.scrollHeight;userFocusTop.style.height=Math.ceil(pageHeight+window.pageYOffset)+'px';userFocusTop.onclick = removeTutorialFocus;document.body.appendChild(userFocusTop);">Buttons über deiner Tastatur</a>, um die wichtigsten Mathe-Operatoren schnell zu finden.</span>-->
+ <br><br>Falls du ohne Tastatur unterwegs bist, kannst du mithilfe des <a href="javascript:;" onclick="tutorialFocusElement(document.querySelector('.mathsbutton'));">Mathe-Operatoren-Buttons</a> zusätzliche Buttons aktivieren, um alle Mathe-Operatoren schnell zu finden.
+
+ <!--<br><br>Drücke jederzeit den "Prüfen"-Button, um zu sehen, wie deine Eingabe interpretiert wurde.<br>Erst wenn du nach dem "Prüfen"-Button deine Eingabe nicht änderst und
+ erneut "Prüfen" klickst, wird deine Eingabe als Antwort abgeschickt.-->
+<br><br>Neben dem Eingabefeld siehst du, wie deine Eingabe interpretiert wird.<br>Wenn du auf den "Prüfen"-Button klickst, wird deine Eingabe als Antwort abgeschickt.
+</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,y=3*x+5],[a2,y=4*x+3],[a3,y=2*x+1],[a4,y=2*x-5],[a5,y=5*x-3],[a6,y=4*x-6]];SYN_a:rand(SYN_A);ta1:SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1798333349</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-a Gleichung eingeben (Multiplikation) (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \({@ta1@}\) in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Hier eine leichte Aufgabe zur Eingabe. Benutze für jede Multiplikation das Symbol * (Stern).
+ <!--<span class="show-on-mobile-only"><br><br>Nutze die <a href="javascript:;" onclick="let userFocusTop = document.createElement('div');userFocusTop.classList.add('user-focus', 'hide-top');let pageHeight = document.documentElement.scrollHeight;userFocusTop.style.height=Math.ceil(pageHeight+window.pageYOffset)+'px';userFocusTop.onclick = removeTutorialFocus;document.body.appendChild(userFocusTop);">Buttons über deiner Tastatur</a>, um die wichtigsten Mathe-Operatoren schnell zu finden.</span>-->
+ <br><br>Falls du ohne Tastatur unterwegs bist, kannst du mithilfe des <a href="javascript:;" onclick="tutorialFocusElement(document.querySelector('.mathsbutton'));">Mathe-Operatoren-Buttons</a> zusätzliche Buttons aktivieren, um alle Mathe-Operatoren schnell zu finden.
+
+ <!--<br><br>Drücke jederzeit den "Prüfen"-Button, um zu sehen, wie deine Eingabe interpretiert wurde.<br>Erst wenn du nach dem "Prüfen"-Button deine Eingabe nicht änderst und
+ erneut "Prüfen" klickst, wird deine Eingabe als Antwort abgeschickt.-->
+<br><br>Neben dem Eingabefeld siehst du, wie deine Eingabe interpretiert wird.<br>Wenn du auf den "Prüfen"-Button klickst, wird deine Eingabe als Antwort abgeschickt.
+</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,y=3*x+5],[a2,y=4*x+3],[a3,y=2*x+1],[a4,y=2*x-5],[a5,y=5*x-3],[a6,y=4*x-6]];SYN_a:rand(SYN_A);ta1:SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>2118152732</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-b Gleichung eingeben (Division) (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \({@TA@}\) in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Divisionen werden mit / (Slash) dargestellt. Hier erscheinen Sie als Brüche.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,y=5/3],[a2,y=4/7],[a3,y=1/3],[a4,y=2/5],[a5,y=3/10],[a6,y=1/4]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);TA:SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>TA</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Wir arbeiten hier nur wenn explizit danach gefragt wird mit Dezimalzahlen. Brüche stellen das Ergebnis in der Regel genauer dar.<br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>TA</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords>3x</forbidwords><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>2690042</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-b Gleichung eingeben (Division) (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \({@TA@}\) in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Divisionen werden mit / (Slash) dargestellt. Hier erscheinen Sie als Brüche.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,y=5/3],[a2,y=4/7],[a3,y=1/3],[a4,y=2/5],[a5,y=3/10],[a6,y=1/4]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);TA:SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>TA</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Wir arbeiten hier nur wenn explizit danach gefragt wird mit Dezimalzahlen. Brüche stellen das Ergebnis in der Regel genauer dar.<br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>TA</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords>3x</forbidwords><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>300094393</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-b Gleichung eingeben (Division) (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \({@TA@}\) in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Divisionen werden mit / (Slash) dargestellt. Hier erscheinen Sie als Brüche.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,y=5/3],[a2,y=4/7],[a3,y=1/3],[a4,y=2/5],[a5,y=3/10],[a6,y=1/4]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);TA:SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>TA</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Wir arbeiten hier nur wenn explizit danach gefragt wird mit Dezimalzahlen. Brüche stellen das Ergebnis in der Regel genauer dar.<br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>TA</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords>3x</forbidwords><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>765518486</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-b Gleichung eingeben (Division) (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \({@TA@}\) in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Divisionen werden mit / (Slash) dargestellt. Hier erscheinen Sie als Brüche.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,y=5/3],[a2,y=4/7],[a3,y=1/3],[a4,y=2/5],[a5,y=3/10],[a6,y=1/4]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);TA:SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>TA</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Wir arbeiten hier nur wenn explizit danach gefragt wird mit Dezimalzahlen. Brüche stellen das Ergebnis in der Regel genauer dar.<br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>TA</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords>3x</forbidwords><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>17019212</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-c Potenzen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \[{@ta@}\] in das Eingabefeld ein.</p>
+<p><p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p><p class="hint"><p>Mit dem Zeichen ^ (Caret) kannst du Potenzen darstellen.</p><div> <ul> <li>\(x^2\) wird so eingegeben: <code>x^2</code></li> <li>\(x^{-2}\) wird so eingegeben: <code>x^(-2)</code></li> <li>\(x^{1/3}\) wird so eingegeben: <code>x^(1/3)</code></li> </ul></div></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,(4+b)^2],[a2,(5+b)^2],[a3,(3+b)^2],[a4,(2+b)^2],[a5,(3+2*b)^2],[a6,(4+2*b)^2]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:expand(SYN_a[2])=SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[Sehr gut. Hier wurde übrigens eine binomische Formel angewendet, um einen Term zu faktorisieren.<br><p dir="ltr" style="text-align: left;" <br=""></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Deine Antwort ist zwar äquivalent mit der dargestellten Gleichung, aber du hast nicht genau die gleiche Gleichung dargestellt.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>93323135</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-c Potenzen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \[{@ta@}\] in das Eingabefeld ein.</p>
+<p><p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p><p class="hint"><p>Mit dem Zeichen ^ (Caret) kannst du Potenzen darstellen.</p><div> <ul> <li>\(x^2\) wird so eingegeben: <code>x^2</code></li> <li>\(x^{-2}\) wird so eingegeben: <code>x^(-2)</code></li> <li>\(x^{1/3}\) wird so eingegeben: <code>x^(1/3)</code></li> </ul></div></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,(4+b)^2],[a2,(5+b)^2],[a3,(3+b)^2],[a4,(2+b)^2],[a5,(3+2*b)^2],[a6,(4+2*b)^2]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:expand(SYN_a[2])=SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[Sehr gut. Hier wurde übrigens eine binomische Formel angewendet, um einen Term zu faktorisieren.<br><p dir="ltr" style="text-align: left;" <br=""></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Deine Antwort ist zwar äquivalent mit der dargestellten Gleichung, aber du hast nicht genau die gleiche Gleichung dargestellt.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>1032837775</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-c Potenzen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \[{@ta@}\] in das Eingabefeld ein.</p>
+<p><p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p><p class="hint"><p>Mit dem Zeichen ^ (Caret) kannst du Potenzen darstellen.</p><div> <ul> <li>\(x^2\) wird so eingegeben: <code>x^2</code></li> <li>\(x^{-2}\) wird so eingegeben: <code>x^(-2)</code></li> <li>\(x^{1/3}\) wird so eingegeben: <code>x^(1/3)</code></li> </ul></div></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,(4+b)^2],[a2,(5+b)^2],[a3,(3+b)^2],[a4,(2+b)^2],[a5,(3+2*b)^2],[a6,(4+2*b)^2]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:expand(SYN_a[2])=SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[Sehr gut. Hier wurde übrigens eine binomische Formel angewendet, um einen Term zu faktorisieren.<br><p dir="ltr" style="text-align: left;" <br=""></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Deine Antwort ist zwar äquivalent mit der dargestellten Gleichung, aber du hast nicht genau die gleiche Gleichung dargestellt.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>680315517</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-c Potenzen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \[{@ta@}\] in das Eingabefeld ein.</p>
+<p><p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p><p class="hint"><p>Mit dem Zeichen ^ (Caret) kannst du Potenzen darstellen.</p><div> <ul> <li>\(x^2\) wird so eingegeben: <code>x^2</code></li> <li>\(x^{-2}\) wird so eingegeben: <code>x^(-2)</code></li> <li>\(x^{1/3}\) wird so eingegeben: <code>x^(1/3)</code></li> </ul></div></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,(4+b)^2],[a2,(5+b)^2],[a3,(3+b)^2],[a4,(2+b)^2],[a5,(3+2*b)^2],[a6,(4+2*b)^2]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:expand(SYN_a[2])=SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[Sehr gut. Hier wurde übrigens eine binomische Formel angewendet, um einen Term zu faktorisieren.<br><p dir="ltr" style="text-align: left;" <br=""></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Deine Antwort ist zwar äquivalent mit der dargestellten Gleichung, aber du hast nicht genau die gleiche Gleichung dargestellt.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>838329017</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-d Rationale Ausdrücke (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \[{@ta@}\] in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Machen wir es etwas komplizierter. Um Terme in Brüchen darzustellen, musst du besonders auf die Klammersetzung achten.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:x^2;b:(x+1);c:(x-5);SYN_A:[[a1,a,b,c],[a2,b,a,c],[a3,c,a,b]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:SYN_a[2]/(SYN_a[3]*SYN_a[4]);wa:SYN_a[2]/SYN_a[3]*SYN_a[4];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;" <br=""></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Bitte beachte, dass du um den Nenner zusätzliche Klammern setzen musst, damit er als zusammenhängender Divisor interpretiert wird.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>82298515</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-d Rationale Ausdrücke (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \[{@ta@}\] in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Machen wir es etwas komplizierter. Um Terme in Brüchen darzustellen, musst du besonders auf die Klammersetzung achten.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:x^2;b:(x+1);c:(x-5);SYN_A:[[a1,a,b,c],[a2,b,a,c],[a3,c,a,b]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:SYN_a[2]/(SYN_a[3]*SYN_a[4]);wa:SYN_a[2]/SYN_a[3]*SYN_a[4];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;" <br=""></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Bitte beachte, dass du um den Nenner zusätzliche Klammern setzen musst, damit er als zusammenhängender Divisor interpretiert wird.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>1458249622</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-d Rationale Ausdrücke (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \[{@ta@}\] in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Machen wir es etwas komplizierter. Um Terme in Brüchen darzustellen, musst du besonders auf die Klammersetzung achten.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:x^2;b:(x+1);c:(x-5);SYN_A:[[a1,a,b,c],[a2,b,a,c],[a3,c,a,b]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:SYN_a[2]/(SYN_a[3]*SYN_a[4]);wa:SYN_a[2]/SYN_a[3]*SYN_a[4];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;" <br=""></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Bitte beachte, dass du um den Nenner zusätzliche Klammern setzen musst, damit er als zusammenhängender Divisor interpretiert wird.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>1731794639</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-e Wurzelzeichen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie \[{@ta1@}\] in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Gut. Um eine Wurzel darzustellen nutze <code>sqrt(x)</code> für \(\sqrt{x}\;\).</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,3],[a2,5],[a3,7],[a4,11],[a5,13],[a6,19]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta1:sqrt(SYN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1136692395</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-e Wurzelzeichen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie \[{@ta1@}\] in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Gut. Um eine Wurzel darzustellen nutze <code>sqrt(x)</code> für \(\sqrt{x}\;\).</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,3],[a2,5],[a3,7],[a4,11],[a5,13],[a6,19]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta1:sqrt(SYN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>659595513</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-e Wurzelzeichen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie \[{@ta1@}\] in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Gut. Um eine Wurzel darzustellen nutze <code>sqrt(x)</code> für \(\sqrt{x}\;\).</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,3],[a2,5],[a3,7],[a4,11],[a5,13],[a6,19]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta1:sqrt(SYN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>2040368424</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-e Wurzelzeichen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie \[{@ta1@}\] in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Gut. Um eine Wurzel darzustellen nutze <code>sqrt(x)</code> für \(\sqrt{x}\;\).</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,3],[a2,5],[a3,7],[a4,11],[a5,13],[a6,19]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta1:sqrt(SYN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
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+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
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+ <truescoremode>=</truescoremode>
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+ <truepenalty/>
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+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
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+ </prt>
+ <deployedseed>262860513</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-f Mehrere Lösungen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Lösen Sie nach \(x\) auf. Geben Sie die Lösung in der Form \(x=? \mbox{ or } x=?\) ein.</p>
+<p><p>\[{@task@}\]<br></p><p>[[input:ans]] [[validation:ans]][[feedback:prt1]]</p><p><em>Achtung: Bitte setzen Sie kein zusätzliches +-Symbol vor positive Zahlen.<br></em></p></p><p class="hint">Gelegentlich müssen Ausdrücke mit logischen Verbindungen verknüpft werden. Nutze dafür <code>and</code> oder <code>or</code>. <br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
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+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,4],[a2,9],[a3,16],[a4,25],[a5,36]];/*SYN_a:SYN_A[1];*/SYN_a:rand(SYN_A);ta:x=sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);taalt:x=+sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);task:x^2=SYN_a[2];wa1:x=sqrt(SYN_a[2]);wa2:x=-sqrt(SYN_a[2]);wa3:x=sqrt(SYN_a[2]) nounand x=-sqrt(SYN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>4</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>4</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>5</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>4</name><answertest>AlgEquiv</answertest><sans>1</sans><tans>1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-5-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr">Du hast nur eine von zwei richtigen Lösungen eingegeben.<br>Beispiel: \(5 \cdot 5 = 25\) und \(-5 \cdot -5 = 25\) (Minus Mal Minus ergibt Plus).<br>Für \(x^2 = 25\) gilt deshalb \(x = 5\) oder \(x = -5\), was hier in der Form <code>x=5 or x=-5</code> aufgeschrieben wird.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-5-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>5</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa3</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-6-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast alle richtigen Lösungen angegeben, allerdings hast du sie mit <code>and</code> verknüpft. Korrekt ist, sie mit <code>or</code> zu verknüpfen. Man schreibt</p><ul><li>entweder \(x=?\; oder \;x=?\)</li><li>oder \(x_1=?\; und \;x_2 = ?\;\).</li></ul>Hier benutzen wir ausschließlich die erste Form, die mit <code>x=? or x=?</code> dargestellt wird.<br>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-6-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords>4x</forbidwords><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>1032259226</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-f Mehrere Lösungen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Lösen Sie nach \(x\) auf. Geben Sie die Lösung in der Form \(x=? \mbox{ or } x=?\) ein.</p>
+<p><p>\[{@task@}\]<br></p><p>[[input:ans]] [[validation:ans]][[feedback:prt1]]</p><p><em>Achtung: Bitte setzen Sie kein zusätzliches +-Symbol vor positive Zahlen.<br></em></p></p><p class="hint">Gelegentlich müssen Ausdrücke mit logischen Verbindungen verknüpft werden. Nutze dafür <code>and</code> oder <code>or</code>. <br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
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+ <text>SYN_A:[[a1,4],[a2,9],[a3,16],[a4,25],[a5,36]];/*SYN_a:SYN_A[1];*/SYN_a:rand(SYN_A);ta:x=sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);taalt:x=+sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);task:x^2=SYN_a[2];wa1:x=sqrt(SYN_a[2]);wa2:x=-sqrt(SYN_a[2]);wa3:x=sqrt(SYN_a[2]) nounand x=-sqrt(SYN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
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+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
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+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-f Mehrere Lösungen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Lösen Sie nach \(x\) auf. Geben Sie die Lösung in der Form \(x=? \mbox{ or } x=?\) ein.</p>
+<p><p>\[{@task@}\]<br></p><p>[[input:ans]] [[validation:ans]][[feedback:prt1]]</p><p><em>Achtung: Bitte setzen Sie kein zusätzliches +-Symbol vor positive Zahlen.<br></em></p></p><p class="hint">Gelegentlich müssen Ausdrücke mit logischen Verbindungen verknüpft werden. Nutze dafür <code>and</code> oder <code>or</code>. <br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,4],[a2,9],[a3,16],[a4,25],[a5,36]];/*SYN_a:SYN_A[1];*/SYN_a:rand(SYN_A);ta:x=sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);taalt:x=+sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);task:x^2=SYN_a[2];wa1:x=sqrt(SYN_a[2]);wa2:x=-sqrt(SYN_a[2]);wa3:x=sqrt(SYN_a[2]) nounand x=-sqrt(SYN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
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+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>4</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>4</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>5</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>4</name><answertest>AlgEquiv</answertest><sans>1</sans><tans>1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-5-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr">Du hast nur eine von zwei richtigen Lösungen eingegeben.<br>Beispiel: \(5 \cdot 5 = 25\) und \(-5 \cdot -5 = 25\) (Minus Mal Minus ergibt Plus).<br>Für \(x^2 = 25\) gilt deshalb \(x = 5\) oder \(x = -5\), was hier in der Form <code>x=5 or x=-5</code> aufgeschrieben wird.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-5-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>5</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa3</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-6-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast alle richtigen Lösungen angegeben, allerdings hast du sie mit <code>and</code> verknüpft. Korrekt ist, sie mit <code>or</code> zu verknüpfen. Man schreibt</p><ul><li>entweder \(x=?\; oder \;x=?\)</li><li>oder \(x_1=?\; und \;x_2 = ?\;\).</li></ul>Hier benutzen wir ausschließlich die erste Form, die mit <code>x=? or x=?</code> dargestellt wird.<br>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-6-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords>4x</forbidwords><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>668615301</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-f Mehrere Lösungen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Lösen Sie nach \(x\) auf. Geben Sie die Lösung in der Form \(x=? \mbox{ or } x=?\) ein.</p>
+<p><p>\[{@task@}\]<br></p><p>[[input:ans]] [[validation:ans]][[feedback:prt1]]</p><p><em>Achtung: Bitte setzen Sie kein zusätzliches +-Symbol vor positive Zahlen.<br></em></p></p><p class="hint">Gelegentlich müssen Ausdrücke mit logischen Verbindungen verknüpft werden. Nutze dafür <code>and</code> oder <code>or</code>. <br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,4],[a2,9],[a3,16],[a4,25],[a5,36]];/*SYN_a:SYN_A[1];*/SYN_a:rand(SYN_A);ta:x=sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);taalt:x=+sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);task:x^2=SYN_a[2];wa1:x=sqrt(SYN_a[2]);wa2:x=-sqrt(SYN_a[2]);wa3:x=sqrt(SYN_a[2]) nounand x=-sqrt(SYN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>4</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>4</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>5</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>4</name><answertest>AlgEquiv</answertest><sans>1</sans><tans>1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-5-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr">Du hast nur eine von zwei richtigen Lösungen eingegeben.<br>Beispiel: \(5 \cdot 5 = 25\) und \(-5 \cdot -5 = 25\) (Minus Mal Minus ergibt Plus).<br>Für \(x^2 = 25\) gilt deshalb \(x = 5\) oder \(x = -5\), was hier in der Form <code>x=5 or x=-5</code> aufgeschrieben wird.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-5-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>5</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa3</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-6-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast alle richtigen Lösungen angegeben, allerdings hast du sie mit <code>and</code> verknüpft. Korrekt ist, sie mit <code>or</code> zu verknüpfen. Man schreibt</p><ul><li>entweder \(x=?\; oder \;x=?\)</li><li>oder \(x_1=?\; und \;x_2 = ?\;\).</li></ul>Hier benutzen wir ausschließlich die erste Form, die mit <code>x=? or x=?</code> dargestellt wird.<br>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-6-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords>4x</forbidwords><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>1810103727</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-g Gleichung mehrschrittig lösen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p><p>Lösen Sie \(\;\){@p@}\(\;\) nach x auf.</p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.</p><p>Sie brauchen kein Äquivalenz-Zeichen eingeben.<br></p></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Um einen Rechenweg darzustellen, tippe jeden Schritt deiner Rechnung in eine neue Zeile in das Eingabefeld ein.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;b:3;c:4;SYN_A:[[a1,a,b,c],[a2,b,a,c],[a3,c,a,b],[a4,a,c,b],[a5,b,c,a],[a6,c,b,a]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:[SYN_a[2]*(SYN_a[3]+x)=SYN_a[4],SYN_a[2]*SYN_a[3]+SYN_a[2]*x=SYN_a[4],SYN_a[2]*x=SYN_a[4]-SYN_a[2]*SYN_a[3],x=(SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]];/*ta:[2*(3+x)=-3,2*x+6=-3,2*x=-9,x=-9/2];*/p:first(ta);/*p:"\\(2 \\cdot (3 + x) = -3\\)";*/wa1:x=-((SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]);wa2:x=SYN_a[4]-SYN_a[2]*SYN_a[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Aber fast richtig. Du hast dich offenbar mit dem Vorzeichen vertan.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar ist dir ein Fehler beim Lösen der Klammer unterlaufen. Um die Klammer aufzulösen, musst du beide beide Summanden in der Klammer mit dem Faktor vor der Klammer multiplizieren.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Weiter so. Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>last(ta)</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint></syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options></options></input><deployedseed>668615301</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-g Gleichung mehrschrittig lösen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p><p>Lösen Sie \(\;\){@p@}\(\;\) nach x auf.</p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.</p><p>Sie brauchen kein Äquivalenz-Zeichen eingeben.<br></p></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Um einen Rechenweg darzustellen, tippe jeden Schritt deiner Rechnung in eine neue Zeile in das Eingabefeld ein.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;b:3;c:4;SYN_A:[[a1,a,b,c],[a2,b,a,c],[a3,c,a,b],[a4,a,c,b],[a5,b,c,a],[a6,c,b,a]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:[SYN_a[2]*(SYN_a[3]+x)=SYN_a[4],SYN_a[2]*SYN_a[3]+SYN_a[2]*x=SYN_a[4],SYN_a[2]*x=SYN_a[4]-SYN_a[2]*SYN_a[3],x=(SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]];/*ta:[2*(3+x)=-3,2*x+6=-3,2*x=-9,x=-9/2];*/p:first(ta);/*p:"\\(2 \\cdot (3 + x) = -3\\)";*/wa1:x=-((SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]);wa2:x=SYN_a[4]-SYN_a[2]*SYN_a[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Aber fast richtig. Du hast dich offenbar mit dem Vorzeichen vertan.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar ist dir ein Fehler beim Lösen der Klammer unterlaufen. Um die Klammer aufzulösen, musst du beide beide Summanden in der Klammer mit dem Faktor vor der Klammer multiplizieren.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Weiter so. Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>last(ta)</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint></syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options></options></input><deployedseed>1810103727</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-g Gleichung mehrschrittig lösen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p><p>Lösen Sie \(\;\){@p@}\(\;\) nach x auf.</p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.</p><p>Sie brauchen kein Äquivalenz-Zeichen eingeben.<br></p></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Um einen Rechenweg darzustellen, tippe jeden Schritt deiner Rechnung in eine neue Zeile in das Eingabefeld ein.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;b:3;c:4;SYN_A:[[a1,a,b,c],[a2,b,a,c],[a3,c,a,b],[a4,a,c,b],[a5,b,c,a],[a6,c,b,a]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:[SYN_a[2]*(SYN_a[3]+x)=SYN_a[4],SYN_a[2]*SYN_a[3]+SYN_a[2]*x=SYN_a[4],SYN_a[2]*x=SYN_a[4]-SYN_a[2]*SYN_a[3],x=(SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]];/*ta:[2*(3+x)=-3,2*x+6=-3,2*x=-9,x=-9/2];*/p:first(ta);/*p:"\\(2 \\cdot (3 + x) = -3\\)";*/wa1:x=-((SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]);wa2:x=SYN_a[4]-SYN_a[2]*SYN_a[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Aber fast richtig. Du hast dich offenbar mit dem Vorzeichen vertan.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar ist dir ein Fehler beim Lösen der Klammer unterlaufen. Um die Klammer aufzulösen, musst du beide beide Summanden in der Klammer mit dem Faktor vor der Klammer multiplizieren.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Weiter so. Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>last(ta)</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint></syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options></options></input><deployedseed>2047586646</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-g Gleichung mehrschrittig lösen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p><p>Lösen Sie \(\;\){@p@}\(\;\) nach x auf.</p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.</p><p>Sie brauchen kein Äquivalenz-Zeichen eingeben.<br></p></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Um einen Rechenweg darzustellen, tippe jeden Schritt deiner Rechnung in eine neue Zeile in das Eingabefeld ein.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;b:3;c:4;SYN_A:[[a1,a,b,c],[a2,b,a,c],[a3,c,a,b],[a4,a,c,b],[a5,b,c,a],[a6,c,b,a]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:[SYN_a[2]*(SYN_a[3]+x)=SYN_a[4],SYN_a[2]*SYN_a[3]+SYN_a[2]*x=SYN_a[4],SYN_a[2]*x=SYN_a[4]-SYN_a[2]*SYN_a[3],x=(SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]];/*ta:[2*(3+x)=-3,2*x+6=-3,2*x=-9,x=-9/2];*/p:first(ta);/*p:"\\(2 \\cdot (3 + x) = -3\\)";*/wa1:x=-((SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]);wa2:x=SYN_a[4]-SYN_a[2]*SYN_a[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Aber fast richtig. Du hast dich offenbar mit dem Vorzeichen vertan.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar ist dir ein Fehler beim Lösen der Klammer unterlaufen. Um die Klammer aufzulösen, musst du beide beide Summanden in der Klammer mit dem Faktor vor der Klammer multiplizieren.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Weiter so. Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>last(ta)</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint></syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options></options></input><deployedseed>1032259226</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-h Griechische Buchstaben (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie \[{@ta@}\] in das Eingebefeld ein.</p>
+<p><p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p><em>Achtung: Bitte kopieren Sie keine Unicode-Zeichen, sondern benutzen Sie einfach Ihre Tastatur. <br></em></p></p><p class="hint">Wenn griechische Buchstaben einzugeben sind, schreibe sie einfach aus. Beispiel: \(\alpha=\) <code>alpha</code> , \(\beta=\) <code>beta</code><code></code> ,\(\pi=\) <code>pi </code><code></code>.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:beta;b:pi;c:alpha;SYN_A:[[a1,a,b],[a2,b,a],[a3,a,c],[a4,c,a],[a5,b,c],[a6,c,b]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:SYN_a[2]*z^(SYN_a[3]*x)wa1:SYN_a[2]*z^SYN_a[3]*x</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offenbar vergessen, eine Klammer um die Potenz zu schreiben. Schreibe Potenzen in Klammern, wenn sie aus mehr als einer Zahl bestehen. Beispiel: \(x^{-2a}\) wird so eingegeben: <code>x^(-2*a)</code>.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>1516837293</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-h Griechische Buchstaben (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie \[{@ta@}\] in das Eingebefeld ein.</p>
+<p><p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p><em>Achtung: Bitte kopieren Sie keine Unicode-Zeichen, sondern benutzen Sie einfach Ihre Tastatur. <br></em></p></p><p class="hint">Wenn griechische Buchstaben einzugeben sind, schreibe sie einfach aus. Beispiel: \(\alpha=\) <code>alpha</code> , \(\beta=\) <code>beta</code><code></code> ,\(\pi=\) <code>pi </code><code></code>.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:beta;b:pi;c:alpha;SYN_A:[[a1,a,b],[a2,b,a],[a3,a,c],[a4,c,a],[a5,b,c],[a6,c,b]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:SYN_a[2]*z^(SYN_a[3]*x)wa1:SYN_a[2]*z^SYN_a[3]*x</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offenbar vergessen, eine Klammer um die Potenz zu schreiben. Schreibe Potenzen in Klammern, wenn sie aus mehr als einer Zahl bestehen. Beispiel: \(x^{-2a}\) wird so eingegeben: <code>x^(-2*a)</code>.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>911975771</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-h Griechische Buchstaben (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie \[{@ta@}\] in das Eingebefeld ein.</p>
+<p><p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p><em>Achtung: Bitte kopieren Sie keine Unicode-Zeichen, sondern benutzen Sie einfach Ihre Tastatur. <br></em></p></p><p class="hint">Wenn griechische Buchstaben einzugeben sind, schreibe sie einfach aus. Beispiel: \(\alpha=\) <code>alpha</code> , \(\beta=\) <code>beta</code><code></code> ,\(\pi=\) <code>pi </code><code></code>.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:beta;b:pi;c:alpha;SYN_A:[[a1,a,b],[a2,b,a],[a3,a,c],[a4,c,a],[a5,b,c],[a6,c,b]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:SYN_a[2]*z^(SYN_a[3]*x)wa1:SYN_a[2]*z^SYN_a[3]*x</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offenbar vergessen, eine Klammer um die Potenz zu schreiben. Schreibe Potenzen in Klammern, wenn sie aus mehr als einer Zahl bestehen. Beispiel: \(x^{-2a}\) wird so eingegeben: <code>x^(-2*a)</code>.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>742782033</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-h Griechische Buchstaben (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie \[{@ta@}\] in das Eingebefeld ein.</p>
+<p><p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p><em>Achtung: Bitte kopieren Sie keine Unicode-Zeichen, sondern benutzen Sie einfach Ihre Tastatur. <br></em></p></p><p class="hint">Wenn griechische Buchstaben einzugeben sind, schreibe sie einfach aus. Beispiel: \(\alpha=\) <code>alpha</code> , \(\beta=\) <code>beta</code><code></code> ,\(\pi=\) <code>pi </code><code></code>.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:beta;b:pi;c:alpha;SYN_A:[[a1,a,b],[a2,b,a],[a3,a,c],[a4,c,a],[a5,b,c],[a6,c,b]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:SYN_a[2]*z^(SYN_a[3]*x)wa1:SYN_a[2]*z^SYN_a[3]*x</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offenbar vergessen, eine Klammer um die Potenz zu schreiben. Schreibe Potenzen in Klammern, wenn sie aus mehr als einer Zahl bestehen. Beispiel: \(x^{-2a}\) wird so eingegeben: <code>x^(-2*a)</code>.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>1709130663</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-i Syntax-Endboss (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p><p>Lösen Sie {@p@} nach \(x\) auf.<br></p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.<br></p></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]<p></p><p><em>Zur Erinnerung: Das Kommando für</em> \(\sqrt{x}\)<em> lautet </em><code>sqrt(x)</code><em>. Nutzen Sie </em><code>or</code><em> um mehrere Lösungen anzugeben.</em></p></p><p class="hint">Willkommen zum Endgegner dieser Mathe-Welt. Mit dem Lösen dieser Aufgabe hast du die erste Mathe-Welt bereits abgeschlossen. Viel Erfolg!<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;b:3;c:4;d:2;e:3;SYN_A:[[a1,a,d],[a2,b,d],[a3,c,d],[a4,a,e],[a5,b,e],[a6,c,e]];SYN_a:rand(SYN_A);pifactor:ev(SYN_a[2]*(SYN_a[3]^2),simp);ta:[/*(SYN_a[2]*x^2)/(pifactor*pi)=1,*/SYN_a[2]*x^2=pifactor*pi,x^2=(SYN_a[3]^2)*pi,x=SYN_a[3]*sqrt(pi) nounor x=-SYN_a[3]*sqrt(pi)];p:first(ta);wa1:x=SYN_a[3]*sqrt(pi);wa2:x=-SYN_a[3]*sqrt(pi);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text><![CDATA[]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>4</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>3</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>3</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>1</sans><tans>1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast nur eine von zwei richtigen Lösungen eingegeben.<br>Beispiel: \(5\,\sqrt{\pi} \cdot 5\,\sqrt{\pi} = 25\,\pi\) und \(-5\,\sqrt{\pi} \cdot -5\,\sqrt{\pi} = 25\,\pi\) (Minus Mal Minus ergibt Plus).<br>Für \(x^2 = 25\pi\) gilt deshalb \(x = 5\,\sqrt{\pi}\) oder \(x = -5\,\sqrt{\pi}\), was hier in der Form <code>x=5*sqrt(pi) or x=-5*sqrt(pi)</code> aufgeschrieben wird.</p><p dir="ltr" style="text-align: left;"></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>4</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-5-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-5-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>last(ta)</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint></syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options></options></input><deployedseed>1169120426</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-i Syntax-Endboss (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p><p>Lösen Sie {@p@} nach \(x\) auf.<br></p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.<br></p></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]<p></p><p><em>Zur Erinnerung: Das Kommando für</em> \(\sqrt{x}\)<em> lautet </em><code>sqrt(x)</code><em>. Nutzen Sie </em><code>or</code><em> um mehrere Lösungen anzugeben.</em></p></p><p class="hint">Willkommen zum Endgegner dieser Mathe-Welt. Mit dem Lösen dieser Aufgabe hast du die erste Mathe-Welt bereits abgeschlossen. Viel Erfolg!<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;b:3;c:4;d:2;e:3;SYN_A:[[a1,a,d],[a2,b,d],[a3,c,d],[a4,a,e],[a5,b,e],[a6,c,e]];SYN_a:rand(SYN_A);pifactor:ev(SYN_a[2]*(SYN_a[3]^2),simp);ta:[/*(SYN_a[2]*x^2)/(pifactor*pi)=1,*/SYN_a[2]*x^2=pifactor*pi,x^2=(SYN_a[3]^2)*pi,x=SYN_a[3]*sqrt(pi) nounor x=-SYN_a[3]*sqrt(pi)];p:first(ta);wa1:x=SYN_a[3]*sqrt(pi);wa2:x=-SYN_a[3]*sqrt(pi);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text><![CDATA[]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>4</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>3</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>3</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>1</sans><tans>1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast nur eine von zwei richtigen Lösungen eingegeben.<br>Beispiel: \(5\,\sqrt{\pi} \cdot 5\,\sqrt{\pi} = 25\,\pi\) und \(-5\,\sqrt{\pi} \cdot -5\,\sqrt{\pi} = 25\,\pi\) (Minus Mal Minus ergibt Plus).<br>Für \(x^2 = 25\pi\) gilt deshalb \(x = 5\,\sqrt{\pi}\) oder \(x = -5\,\sqrt{\pi}\), was hier in der Form <code>x=5*sqrt(pi) or x=-5*sqrt(pi)</code> aufgeschrieben wird.</p><p dir="ltr" style="text-align: left;"></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>4</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-5-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-5-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>last(ta)</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint></syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options></options></input><deployedseed>1624332195</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-i Syntax-Endboss (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p><p>Lösen Sie {@p@} nach \(x\) auf.<br></p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.<br></p></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]<p></p><p><em>Zur Erinnerung: Das Kommando für</em> \(\sqrt{x}\)<em> lautet </em><code>sqrt(x)</code><em>. Nutzen Sie </em><code>or</code><em> um mehrere Lösungen anzugeben.</em></p></p><p class="hint">Willkommen zum Endgegner dieser Mathe-Welt. Mit dem Lösen dieser Aufgabe hast du die erste Mathe-Welt bereits abgeschlossen. Viel Erfolg!<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;b:3;c:4;d:2;e:3;SYN_A:[[a1,a,d],[a2,b,d],[a3,c,d],[a4,a,e],[a5,b,e],[a6,c,e]];SYN_a:rand(SYN_A);pifactor:ev(SYN_a[2]*(SYN_a[3]^2),simp);ta:[/*(SYN_a[2]*x^2)/(pifactor*pi)=1,*/SYN_a[2]*x^2=pifactor*pi,x^2=(SYN_a[3]^2)*pi,x=SYN_a[3]*sqrt(pi) nounor x=-SYN_a[3]*sqrt(pi)];p:first(ta);wa1:x=SYN_a[3]*sqrt(pi);wa2:x=-SYN_a[3]*sqrt(pi);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text><![CDATA[]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>4</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>3</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>3</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>1</sans><tans>1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast nur eine von zwei richtigen Lösungen eingegeben.<br>Beispiel: \(5\,\sqrt{\pi} \cdot 5\,\sqrt{\pi} = 25\,\pi\) und \(-5\,\sqrt{\pi} \cdot -5\,\sqrt{\pi} = 25\,\pi\) (Minus Mal Minus ergibt Plus).<br>Für \(x^2 = 25\pi\) gilt deshalb \(x = 5\,\sqrt{\pi}\) oder \(x = -5\,\sqrt{\pi}\), was hier in der Form <code>x=5*sqrt(pi) or x=-5*sqrt(pi)</code> aufgeschrieben wird.</p><p dir="ltr" style="text-align: left;"></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>4</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-5-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-5-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>last(ta)</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint></syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options></options></input><deployedseed>1578649438</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-i Syntax-Endboss (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p><p>Lösen Sie {@p@} nach \(x\) auf.<br></p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.<br></p></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]<p></p><p><em>Zur Erinnerung: Das Kommando für</em> \(\sqrt{x}\)<em> lautet </em><code>sqrt(x)</code><em>. Nutzen Sie </em><code>or</code><em> um mehrere Lösungen anzugeben.</em></p></p><p class="hint">Willkommen zum Endgegner dieser Mathe-Welt. Mit dem Lösen dieser Aufgabe hast du die erste Mathe-Welt bereits abgeschlossen. Viel Erfolg!<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;b:3;c:4;d:2;e:3;SYN_A:[[a1,a,d],[a2,b,d],[a3,c,d],[a4,a,e],[a5,b,e],[a6,c,e]];SYN_a:rand(SYN_A);pifactor:ev(SYN_a[2]*(SYN_a[3]^2),simp);ta:[/*(SYN_a[2]*x^2)/(pifactor*pi)=1,*/SYN_a[2]*x^2=pifactor*pi,x^2=(SYN_a[3]^2)*pi,x=SYN_a[3]*sqrt(pi) nounor x=-SYN_a[3]*sqrt(pi)];p:first(ta);wa1:x=SYN_a[3]*sqrt(pi);wa2:x=-SYN_a[3]*sqrt(pi);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text><![CDATA[]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>4</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>3</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>3</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>1</sans><tans>1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast nur eine von zwei richtigen Lösungen eingegeben.<br>Beispiel: \(5\,\sqrt{\pi} \cdot 5\,\sqrt{\pi} = 25\,\pi\) und \(-5\,\sqrt{\pi} \cdot -5\,\sqrt{\pi} = 25\,\pi\) (Minus Mal Minus ergibt Plus).<br>Für \(x^2 = 25\pi\) gilt deshalb \(x = 5\,\sqrt{\pi}\) oder \(x = -5\,\sqrt{\pi}\), was hier in der Form <code>x=5*sqrt(pi) or x=-5*sqrt(pi)</code> aufgeschrieben wird.</p><p dir="ltr" style="text-align: left;"></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>4</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-5-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-5-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>last(ta)</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint></syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options></options></input><deployedseed>1629124203</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-a Kürzen zweier einfacher Brüche (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\({@f@} \cdot {@g@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Gekürzt wird, indem man Zähler & Nenner durch dieselbe Zahl teilt.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(2,8,1); b:rand_with_step(20,40,10); c:a*b; d:b/5; e:a*b/10; ta1:1/a; simp:false; f:5/e; g:d/10; wa1:(5+d)/(e+10);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@f@} \cdot {@g@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir="ltr" style="text-align: left;">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>423191525</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-a Kürzen zweier einfacher Brüche (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\({@f@} \cdot {@g@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Gekürzt wird, indem man Zähler & Nenner durch dieselbe Zahl teilt.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(2,8,1); b:rand_with_step(20,40,10); c:a*b; d:b/5; e:a*b/10; ta1:1/a; simp:false; f:5/e; g:d/10; wa1:(5+d)/(e+10);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@f@} \cdot {@g@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
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+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir="ltr" style="text-align: left;">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1756629135</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-a Kürzen zweier einfacher Brüche (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\({@f@} \cdot {@g@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Gekürzt wird, indem man Zähler & Nenner durch dieselbe Zahl teilt.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(2,8,1); b:rand_with_step(20,40,10); c:a*b; d:b/5; e:a*b/10; ta1:1/a; simp:false; f:5/e; g:d/10; wa1:(5+d)/(e+10);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@f@} \cdot {@g@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
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+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
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+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir="ltr" style="text-align: left;">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>505485688</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-a Kürzen zweier einfacher Brüche (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\({@f@} \cdot {@g@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Gekürzt wird, indem man Zähler & Nenner durch dieselbe Zahl teilt.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(2,8,1); b:rand_with_step(20,40,10); c:a*b; d:b/5; e:a*b/10; ta1:1/a; simp:false; f:5/e; g:d/10; wa1:(5+d)/(e+10);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@f@} \cdot {@g@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir="ltr" style="text-align: left;">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>813830513</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-b Kürzen zweier Brüche mit Variablen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\,a\,a\,b\,b\,c}{a\,a\,a\,a\,a\,b\,c\,c\,c}\)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); powers:makelist(rand(5)+1, 6); myvar1: mya^powers[1]; myvar2: myb^powers[2]; myvar3: myc^powers[3]; myvar4: mya^powers[4]; myvar5: myb^powers[5]; myvar6: myc^powers[6]; d:(myvar1*myvar2*myvar3)/(myvar4*myvar5*myvar6); ta1:d;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Beispiel: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,b\,b\mkern-5mu/\,c\mkern-5mu/}{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,a\,a\,b\mkern-5mu/\,c\mkern-5mu/\,c\,c} = \frac{b}{a^2\,c^2}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>194802941</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-b Kürzen zweier Brüche mit Variablen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\,a\,a\,b\,b\,c}{a\,a\,a\,a\,a\,b\,c\,c\,c}\)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); powers:makelist(rand(5)+1, 6); myvar1: mya^powers[1]; myvar2: myb^powers[2]; myvar3: myc^powers[3]; myvar4: mya^powers[4]; myvar5: myb^powers[5]; myvar6: myc^powers[6]; d:(myvar1*myvar2*myvar3)/(myvar4*myvar5*myvar6); ta1:d;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Beispiel: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,b\,b\mkern-5mu/\,c\mkern-5mu/}{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,a\,a\,b\mkern-5mu/\,c\mkern-5mu/\,c\,c} = \frac{b}{a^2\,c^2}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1917875187</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-b Kürzen zweier Brüche mit Variablen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\,a\,a\,b\,b\,c}{a\,a\,a\,a\,a\,b\,c\,c\,c}\)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); powers:makelist(rand(5)+1, 6); myvar1: mya^powers[1]; myvar2: myb^powers[2]; myvar3: myc^powers[3]; myvar4: mya^powers[4]; myvar5: myb^powers[5]; myvar6: myc^powers[6]; d:(myvar1*myvar2*myvar3)/(myvar4*myvar5*myvar6); ta1:d;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Beispiel: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,b\,b\mkern-5mu/\,c\mkern-5mu/}{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,a\,a\,b\mkern-5mu/\,c\mkern-5mu/\,c\,c} = \frac{b}{a^2\,c^2}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1931041228</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-b Kürzen zweier Brüche mit Variablen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\,a\,a\,b\,b\,c}{a\,a\,a\,a\,a\,b\,c\,c\,c}\)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); powers:makelist(rand(5)+1, 6); myvar1: mya^powers[1]; myvar2: myb^powers[2]; myvar3: myc^powers[3]; myvar4: mya^powers[4]; myvar5: myb^powers[5]; myvar6: myc^powers[6]; d:(myvar1*myvar2*myvar3)/(myvar4*myvar5*myvar6); ta1:d;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Beispiel: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,b\,b\mkern-5mu/\,c\mkern-5mu/}{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,a\,a\,b\mkern-5mu/\,c\mkern-5mu/\,c\,c} = \frac{b}{a^2\,c^2}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>928137609</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-c Kürzen zweier Brüche mit Variablen und Zahlen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Erst auf einen Bruchstrich sortieren. Beispiel: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} = \frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c}\)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>num1:rand_with_step(5,8,1); varlist:[a,b,c,u,v,w,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1], varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); num2:rand_with_step(3,7,1); num3:rand_with_step(3,7,1); nom1:num1*num2*myvars[1]; denom1:num1*myvars[2]; nom2:num1*num3*myvars[1]*myvars[2]; denom2:num1*myvars[1]*myvars[3]; ta1:(nom1/denom1)*(nom2/denom2); /*Alle Variablen in den Zählern mit einer Variable im Nenner gekürzt.*/wa1:((nom1/myvars[1])*(nom2/myvars[1]))/((denom1*denom2)/myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich die Variable {@myvars[1]@} im Nenner gegen beide Variablen in den Zählern gekürzt. Bei der Multiplikation von Brüchen kannst du immer nur einen Faktor gegen den anderen kürzen. Beispiel: \(\frac{36}{6} = \frac{6\cdot6}{6} = \frac{6\mkern-5mu/\cdot6}{6\mkern-5mu/} = \frac{6}{1} = 6\) und nicht \(\frac{36}{6} = \frac{6\cdot6}{6} \ne \frac{6\mkern-5mu/\cdot6\mkern-5mu/}{6\mkern-5mu/} = 1\;\).<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>So lassen sich Produkte auf einem Bruchstrich sortieren und kürzen: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} =\frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c} =\frac{49^7\mkern-14mu\large/ \small \; \cdot 21^3\mkern-14mu\large/\small \; \cdot a\mkern-5mu/ \cdot a \cdot b\mkern-5mu/}{7\mkern-5.5mu/ \cdot7\mkern-5.5mu/ \cdot a\mkern-5mu/\cdot b\mkern-5mu/\cdot c} =\frac{21\,a}{c}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1842189518</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-c Kürzen zweier Brüche mit Variablen und Zahlen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Erst auf einen Bruchstrich sortieren. Beispiel: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} = \frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c}\)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>num1:rand_with_step(5,8,1); varlist:[a,b,c,u,v,w,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1], varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); num2:rand_with_step(3,7,1); num3:rand_with_step(3,7,1); nom1:num1*num2*myvars[1]; denom1:num1*myvars[2]; nom2:num1*num3*myvars[1]*myvars[2]; denom2:num1*myvars[1]*myvars[3]; ta1:(nom1/denom1)*(nom2/denom2); /*Alle Variablen in den Zählern mit einer Variable im Nenner gekürzt.*/wa1:((nom1/myvars[1])*(nom2/myvars[1]))/((denom1*denom2)/myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich die Variable {@myvars[1]@} im Nenner gegen beide Variablen in den Zählern gekürzt. Bei der Multiplikation von Brüchen kannst du immer nur einen Faktor gegen den anderen kürzen. Beispiel: \(\frac{36}{6} = \frac{6\cdot6}{6} = \frac{6\mkern-5mu/\cdot6}{6\mkern-5mu/} = \frac{6}{1} = 6\) und nicht \(\frac{36}{6} = \frac{6\cdot6}{6} \ne \frac{6\mkern-5mu/\cdot6\mkern-5mu/}{6\mkern-5mu/} = 1\;\).<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>So lassen sich Produkte auf einem Bruchstrich sortieren und kürzen: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} =\frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c} =\frac{49^7\mkern-14mu\large/ \small \; \cdot 21^3\mkern-14mu\large/\small \; \cdot a\mkern-5mu/ \cdot a \cdot b\mkern-5mu/}{7\mkern-5.5mu/ \cdot7\mkern-5.5mu/ \cdot a\mkern-5mu/\cdot b\mkern-5mu/\cdot c} =\frac{21\,a}{c}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1601667602</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-c Kürzen zweier Brüche mit Variablen und Zahlen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Erst auf einen Bruchstrich sortieren. Beispiel: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} = \frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c}\)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>num1:rand_with_step(5,8,1); varlist:[a,b,c,u,v,w,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1], varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); num2:rand_with_step(3,7,1); num3:rand_with_step(3,7,1); nom1:num1*num2*myvars[1]; denom1:num1*myvars[2]; nom2:num1*num3*myvars[1]*myvars[2]; denom2:num1*myvars[1]*myvars[3]; ta1:(nom1/denom1)*(nom2/denom2); /*Alle Variablen in den Zählern mit einer Variable im Nenner gekürzt.*/wa1:((nom1/myvars[1])*(nom2/myvars[1]))/((denom1*denom2)/myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich die Variable {@myvars[1]@} im Nenner gegen beide Variablen in den Zählern gekürzt. Bei der Multiplikation von Brüchen kannst du immer nur einen Faktor gegen den anderen kürzen. Beispiel: \(\frac{36}{6} = \frac{6\cdot6}{6} = \frac{6\mkern-5mu/\cdot6}{6\mkern-5mu/} = \frac{6}{1} = 6\) und nicht \(\frac{36}{6} = \frac{6\cdot6}{6} \ne \frac{6\mkern-5mu/\cdot6\mkern-5mu/}{6\mkern-5mu/} = 1\;\).<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>So lassen sich Produkte auf einem Bruchstrich sortieren und kürzen: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} =\frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c} =\frac{49^7\mkern-14mu\large/ \small \; \cdot 21^3\mkern-14mu\large/\small \; \cdot a\mkern-5mu/ \cdot a \cdot b\mkern-5mu/}{7\mkern-5.5mu/ \cdot7\mkern-5.5mu/ \cdot a\mkern-5mu/\cdot b\mkern-5mu/\cdot c} =\frac{21\,a}{c}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>2136766316</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-c Kürzen zweier Brüche mit Variablen und Zahlen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Erst auf einen Bruchstrich sortieren. Beispiel: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} = \frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c}\)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>num1:rand_with_step(5,8,1); varlist:[a,b,c,u,v,w,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1], varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); num2:rand_with_step(3,7,1); num3:rand_with_step(3,7,1); nom1:num1*num2*myvars[1]; denom1:num1*myvars[2]; nom2:num1*num3*myvars[1]*myvars[2]; denom2:num1*myvars[1]*myvars[3]; ta1:(nom1/denom1)*(nom2/denom2); /*Alle Variablen in den Zählern mit einer Variable im Nenner gekürzt.*/wa1:((nom1/myvars[1])*(nom2/myvars[1]))/((denom1*denom2)/myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich die Variable {@myvars[1]@} im Nenner gegen beide Variablen in den Zählern gekürzt. Bei der Multiplikation von Brüchen kannst du immer nur einen Faktor gegen den anderen kürzen. Beispiel: \(\frac{36}{6} = \frac{6\cdot6}{6} = \frac{6\mkern-5mu/\cdot6}{6\mkern-5mu/} = \frac{6}{1} = 6\) und nicht \(\frac{36}{6} = \frac{6\cdot6}{6} \ne \frac{6\mkern-5mu/\cdot6\mkern-5mu/}{6\mkern-5mu/} = 1\;\).<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>So lassen sich Produkte auf einem Bruchstrich sortieren und kürzen: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} =\frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c} =\frac{49^7\mkern-14mu\large/ \small \; \cdot 21^3\mkern-14mu\large/\small \; \cdot a\mkern-5mu/ \cdot a \cdot b\mkern-5mu/}{7\mkern-5.5mu/ \cdot7\mkern-5.5mu/ \cdot a\mkern-5mu/\cdot b\mkern-5mu/\cdot c} =\frac{21\,a}{c}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1542661342</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-d Kürzen zweier Brüche mit Termen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Kennst du noch den Ausspruch „Aus Summen kürzen nur die Dummen“?!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([x,y,z]); term_summand1:rand_with_prohib(-3,3,[0]); term_summand2:rand_with_prohib(-3,3,[0,term_summand1]); term1:myvar+term_summand1; term2:myvar+term_summand2; ta1:term1/myvar*(myvar^2/(term1*term2*myvar)); /*wa1 means: naive shortened fraction*/ wa1:(term1-myvar)/1*(myvar^2/(term1*term2*myvar));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Offensichtlich hast du beim ersten Bruch die Variable {@myvar@} im Nenner gegen die Variable {@myvar@} im Zähler gekürzt. Das geht aber nicht, weil die Variable {@myvar@} im Zähler mit einem anderen Summanden eine Summe bildet. Beispiel: \(3 = \frac{6}{2} = \frac{4+2}{2} \ne \frac{4 + 2\mkern-5.5mu/}{2\mkern-5.5mu/} = \frac{4}{1} = 4\;\).]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p> Nur ganze Faktoren dürfen gekürzt werden. Zum Beispiel: \(\frac{\boldsymbol{(x-1)}\cdot 2}{x \cdot \boldsymbol{(x-1)}} = \frac{2}{x}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>837792651</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-d Kürzen zweier Brüche mit Termen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Kennst du noch den Ausspruch „Aus Summen kürzen nur die Dummen“?!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([x,y,z]); term_summand1:rand_with_prohib(-3,3,[0]); term_summand2:rand_with_prohib(-3,3,[0,term_summand1]); term1:myvar+term_summand1; term2:myvar+term_summand2; ta1:term1/myvar*(myvar^2/(term1*term2*myvar)); /*wa1 means: naive shortened fraction*/ wa1:(term1-myvar)/1*(myvar^2/(term1*term2*myvar));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Offensichtlich hast du beim ersten Bruch die Variable {@myvar@} im Nenner gegen die Variable {@myvar@} im Zähler gekürzt. Das geht aber nicht, weil die Variable {@myvar@} im Zähler mit einem anderen Summanden eine Summe bildet. Beispiel: \(3 = \frac{6}{2} = \frac{4+2}{2} \ne \frac{4 + 2\mkern-5.5mu/}{2\mkern-5.5mu/} = \frac{4}{1} = 4\;\).]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p> Nur ganze Faktoren dürfen gekürzt werden. Zum Beispiel: \(\frac{\boldsymbol{(x-1)}\cdot 2}{x \cdot \boldsymbol{(x-1)}} = \frac{2}{x}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>528135820</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-d Kürzen zweier Brüche mit Termen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Kennst du noch den Ausspruch „Aus Summen kürzen nur die Dummen“?!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([x,y,z]); term_summand1:rand_with_prohib(-3,3,[0]); term_summand2:rand_with_prohib(-3,3,[0,term_summand1]); term1:myvar+term_summand1; term2:myvar+term_summand2; ta1:term1/myvar*(myvar^2/(term1*term2*myvar)); /*wa1 means: naive shortened fraction*/ wa1:(term1-myvar)/1*(myvar^2/(term1*term2*myvar));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Offensichtlich hast du beim ersten Bruch die Variable {@myvar@} im Nenner gegen die Variable {@myvar@} im Zähler gekürzt. Das geht aber nicht, weil die Variable {@myvar@} im Zähler mit einem anderen Summanden eine Summe bildet. Beispiel: \(3 = \frac{6}{2} = \frac{4+2}{2} \ne \frac{4 + 2\mkern-5.5mu/}{2\mkern-5.5mu/} = \frac{4}{1} = 4\;\).]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p> Nur ganze Faktoren dürfen gekürzt werden. Zum Beispiel: \(\frac{\boldsymbol{(x-1)}\cdot 2}{x \cdot \boldsymbol{(x-1)}} = \frac{2}{x}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>879656886</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-d Kürzen zweier Brüche mit Termen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Kennst du noch den Ausspruch „Aus Summen kürzen nur die Dummen“?!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([x,y,z]); term_summand1:rand_with_prohib(-3,3,[0]); term_summand2:rand_with_prohib(-3,3,[0,term_summand1]); term1:myvar+term_summand1; term2:myvar+term_summand2; ta1:term1/myvar*(myvar^2/(term1*term2*myvar)); /*wa1 means: naive shortened fraction*/ wa1:(term1-myvar)/1*(myvar^2/(term1*term2*myvar));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Offensichtlich hast du beim ersten Bruch die Variable {@myvar@} im Nenner gegen die Variable {@myvar@} im Zähler gekürzt. Das geht aber nicht, weil die Variable {@myvar@} im Zähler mit einem anderen Summanden eine Summe bildet. Beispiel: \(3 = \frac{6}{2} = \frac{4+2}{2} \ne \frac{4 + 2\mkern-5.5mu/}{2\mkern-5.5mu/} = \frac{4}{1} = 4\;\).]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p> Nur ganze Faktoren dürfen gekürzt werden. Zum Beispiel: \(\frac{\boldsymbol{(x-1)}\cdot 2}{x \cdot \boldsymbol{(x-1)}} = \frac{2}{x}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1917537516</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-a Einfachen Bruch erweitern (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\({@c@} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(4,9,1); b:a-1; c:a/b; d:a*5; e:b*5; simp:false; ta1:d/e;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@c@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>437845679</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-a Einfachen Bruch erweitern (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\({@c@} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(4,9,1); b:a-1; c:a/b; d:a*5; e:b*5; simp:false; ta1:d/e;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@c@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>2092409135</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-a Einfachen Bruch erweitern (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\({@c@} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(4,9,1); b:a-1; c:a/b; d:a*5; e:b*5; simp:false; ta1:d/e;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@c@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1712748750</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-a Einfachen Bruch erweitern (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\({@c@} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(4,9,1); b:a-1; c:a/b; d:a*5; e:b*5; simp:false; ta1:d/e;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@c@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
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+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>182980498</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-b Bruch mit Variablen erweitern (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@numerator@}}{{@denominator@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,4); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[1]^powers[3]; fac4:myvars[2]^powers[4]; numerator:fac1*fac2; denominator:fac3*fac4; d:numerator/denominator; tanumerator:5*num(d); tadenominator:5*denom(d); simp:false; ta1:tanumerator/tadenominator;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@numerator@}}{{@denominator@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>36209422</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-b Bruch mit Variablen erweitern (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@numerator@}}{{@denominator@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,4); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[1]^powers[3]; fac4:myvars[2]^powers[4]; numerator:fac1*fac2; denominator:fac3*fac4; d:numerator/denominator; tanumerator:5*num(d); tadenominator:5*denom(d); simp:false; ta1:tanumerator/tadenominator;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@numerator@}}{{@denominator@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1000344719</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-b Bruch mit Variablen erweitern (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@numerator@}}{{@denominator@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,4); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[1]^powers[3]; fac4:myvars[2]^powers[4]; numerator:fac1*fac2; denominator:fac3*fac4; d:numerator/denominator; tanumerator:5*num(d); tadenominator:5*denom(d); simp:false; ta1:tanumerator/tadenominator;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@numerator@}}{{@denominator@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1827440244</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-b Bruch mit Variablen erweitern (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@numerator@}}{{@denominator@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,4); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[1]^powers[3]; fac4:myvars[2]^powers[4]; numerator:fac1*fac2; denominator:fac3*fac4; d:numerator/denominator; tanumerator:5*num(d); tadenominator:5*denom(d); simp:false; ta1:tanumerator/tadenominator;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@numerator@}}{{@denominator@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1291739138</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-c Bruch mit Variablen und Zahlen erweitern (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,3); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[2]^powers[3]; rand1:rand(4); rand2:rand_with_prohib(0,3,[rand1]); number1:rand1*2+3; number2:rand2*2+3; number3:rand_with_step(2,8,2); numerator:fac1*fac2; denominator:fac3; d:numerator/denominator; tanumerator:5*number1*number2*num(d); tadenominator:5*number3*denom(d); simp:false; ta1:tanumerator/tadenominator;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1516326427</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-c Bruch mit Variablen und Zahlen erweitern (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,3); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[2]^powers[3]; rand1:rand(4); rand2:rand_with_prohib(0,3,[rand1]); number1:rand1*2+3; number2:rand2*2+3; number3:rand_with_step(2,8,2); numerator:fac1*fac2; denominator:fac3; d:numerator/denominator; tanumerator:5*number1*number2*num(d); tadenominator:5*number3*denom(d); simp:false; ta1:tanumerator/tadenominator;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1341581403</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-c Bruch mit Variablen und Zahlen erweitern (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,3); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[2]^powers[3]; rand1:rand(4); rand2:rand_with_prohib(0,3,[rand1]); number1:rand1*2+3; number2:rand2*2+3; number3:rand_with_step(2,8,2); numerator:fac1*fac2; denominator:fac3; d:numerator/denominator; tanumerator:5*number1*number2*num(d); tadenominator:5*number3*denom(d); simp:false; ta1:tanumerator/tadenominator;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>79491835</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-c Bruch mit Variablen und Zahlen erweitern (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,3); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[2]^powers[3]; rand1:rand(4); rand2:rand_with_prohib(0,3,[rand1]); number1:rand1*2+3; number2:rand2*2+3; number3:rand_with_step(2,8,2); numerator:fac1*fac2; denominator:fac3; d:numerator/denominator; tanumerator:5*number1*number2*num(d); tadenominator:5*number3*denom(d); simp:false; ta1:tanumerator/tadenominator;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
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+ <deployedseed>1422333316</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ca Einfache Addition von Brüchen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Addieren und Subtrahieren müssen die Nenner der Brüche gleich sein. Kannst du dich noch an das kleinste gemeinsame Vielfache erinnern?</p>]]></text>
+ </questiontext>
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+ <text>2023010400</text>
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+ <questionvariables>
+ <text>a:rand_with_step(1,4,1)*2+1; fac1:rand_with_step(1,4,1); fac2:rand_with_prohib(1,4,[fac1]); denoms:[a, a*fac1,a*fac2]; nums:makelist(rand_with_step(1,denoms[i]-1,2),i,3); signs:makelist(rand_with_prohib(-1,1,[0]),3); fractions:makelist(signs[i]*nums[i]/denoms[i],i,3); fractions:random_permutation(fractions); ta1:fractions[1]+fractions[2]+fractions[3]; simp:false; exercise:fractions[1]+fractions[2]+fractions[3]; /*wa1 means: naive addition*/ wa1:(num(fractions[1])+num(fractions[2])+num(fractions[3]))/(denom(fractions[1])+denom(fractions[2])+denom(fractions[3]));</text>
+ </questionvariables>
+ <specificfeedback format="html">
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+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
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+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
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+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
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+ <falseanswernote>prt1-2-F</falseanswernote>
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+ <node>
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+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir="ltr" style="text-align: left;">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>]]></text>
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+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um die Nenner gleich zu machen, musst du sie so erweitern, dass sie den gleichen Nenner haben. Dann können die Zähler addiert werden. Das kleinste gemeinsame Vielfache von 5, 10 und 15 lässt sich zum Beispiel finden, indem man die jeweiligen Reihen notiert und die kleinste gemeinsame Zahl sucht.</p><table><tr><th>5er-Reihe</th><th>10er-Reihe</th><th>15er-Reihe</th></tr><tr><td>5</td><td>10</td><td>15</td></tr><tr><td>10</td><td>20</td><td><strong>30</strong></td></tr><tr><td>15</td><td><strong>30</strong></td><td>...</td></tr><tr><td>20</td><td>...</td><td>...</td></tr><tr><td>25</td><td>...</td><td>...</td></tr><tr><td><strong>30</strong></td><td>...</td><td>...</td></tr><tr><td>...</td><td>...</td><td>...</td></tr></table></p>]]></text>
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+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ca Einfache Addition von Brüchen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Addieren und Subtrahieren müssen die Nenner der Brüche gleich sein. Kannst du dich noch an das kleinste gemeinsame Vielfache erinnern?</p>]]></text>
+ </questiontext>
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+ </questionvariables>
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+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
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+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir="ltr" style="text-align: left;">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>]]></text>
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+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um die Nenner gleich zu machen, musst du sie so erweitern, dass sie den gleichen Nenner haben. Dann können die Zähler addiert werden. Das kleinste gemeinsame Vielfache von 5, 10 und 15 lässt sich zum Beispiel finden, indem man die jeweiligen Reihen notiert und die kleinste gemeinsame Zahl sucht.</p><table><tr><th>5er-Reihe</th><th>10er-Reihe</th><th>15er-Reihe</th></tr><tr><td>5</td><td>10</td><td>15</td></tr><tr><td>10</td><td>20</td><td><strong>30</strong></td></tr><tr><td>15</td><td><strong>30</strong></td><td>...</td></tr><tr><td>20</td><td>...</td><td>...</td></tr><tr><td>25</td><td>...</td><td>...</td></tr><tr><td><strong>30</strong></td><td>...</td><td>...</td></tr><tr><td>...</td><td>...</td><td>...</td></tr></table></p>]]></text>
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+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ca Einfache Addition von Brüchen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Addieren und Subtrahieren müssen die Nenner der Brüche gleich sein. Kannst du dich noch an das kleinste gemeinsame Vielfache erinnern?</p>]]></text>
+ </questiontext>
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+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
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+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
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+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir="ltr" style="text-align: left;">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um die Nenner gleich zu machen, musst du sie so erweitern, dass sie den gleichen Nenner haben. Dann können die Zähler addiert werden. Das kleinste gemeinsame Vielfache von 5, 10 und 15 lässt sich zum Beispiel finden, indem man die jeweiligen Reihen notiert und die kleinste gemeinsame Zahl sucht.</p><table><tr><th>5er-Reihe</th><th>10er-Reihe</th><th>15er-Reihe</th></tr><tr><td>5</td><td>10</td><td>15</td></tr><tr><td>10</td><td>20</td><td><strong>30</strong></td></tr><tr><td>15</td><td><strong>30</strong></td><td>...</td></tr><tr><td>20</td><td>...</td><td>...</td></tr><tr><td>25</td><td>...</td><td>...</td></tr><tr><td><strong>30</strong></td><td>...</td><td>...</td></tr><tr><td>...</td><td>...</td><td>...</td></tr></table></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1338253474</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ca Einfache Addition von Brüchen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Addieren und Subtrahieren müssen die Nenner der Brüche gleich sein. Kannst du dich noch an das kleinste gemeinsame Vielfache erinnern?</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(1,4,1)*2+1; fac1:rand_with_step(1,4,1); fac2:rand_with_prohib(1,4,[fac1]); denoms:[a, a*fac1,a*fac2]; nums:makelist(rand_with_step(1,denoms[i]-1,2),i,3); signs:makelist(rand_with_prohib(-1,1,[0]),3); fractions:makelist(signs[i]*nums[i]/denoms[i],i,3); fractions:random_permutation(fractions); ta1:fractions[1]+fractions[2]+fractions[3]; simp:false; exercise:fractions[1]+fractions[2]+fractions[3]; /*wa1 means: naive addition*/ wa1:(num(fractions[1])+num(fractions[2])+num(fractions[3]))/(denom(fractions[1])+denom(fractions[2])+denom(fractions[3]));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
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+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
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+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
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+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir="ltr" style="text-align: left;">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um die Nenner gleich zu machen, musst du sie so erweitern, dass sie den gleichen Nenner haben. Dann können die Zähler addiert werden. Das kleinste gemeinsame Vielfache von 5, 10 und 15 lässt sich zum Beispiel finden, indem man die jeweiligen Reihen notiert und die kleinste gemeinsame Zahl sucht.</p><table><tr><th>5er-Reihe</th><th>10er-Reihe</th><th>15er-Reihe</th></tr><tr><td>5</td><td>10</td><td>15</td></tr><tr><td>10</td><td>20</td><td><strong>30</strong></td></tr><tr><td>15</td><td><strong>30</strong></td><td>...</td></tr><tr><td>20</td><td>...</td><td>...</td></tr><tr><td>25</td><td>...</td><td>...</td></tr><tr><td><strong>30</strong></td><td>...</td><td>...</td></tr><tr><td>...</td><td>...</td><td>...</td></tr></table></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>933392702</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cb Addition von Brüchen mit Variablen und gleichem Nenner (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Überlege genau, was ein Minus vor einem Bruch bedeutet.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c]); fractions_correct_and_wa1:[[(myvar+1)/myvar, -myvar+1], [(myvar-1)/myvar, -myvar-1], [(1-myvar)/myvar, -1-myvar]]; fractions_correct_and_wa1:random_permutation(fractions_correct_and_wa1); fractions:makelist(fractions_correct_and_wa1[i][1],i,3); terms_wa1:makelist(fractions_correct_and_wa1[i][2],i,3); exercise:fractions[1]-fractions[2]-fractions[3]; ta1:combine(exercise); wa1:(num(fractions[1])+terms_wa1[2]+terms_wa1[3])/myvar;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@}-{@fractions[2]@}-{@fractions[3]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
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+ <checkanswertype>0</checkanswertype>
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+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
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+ <feedbackvariables>
+ <text/>
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+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast offenbar die Minuszeichen nicht korrekt aufgelöst.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Ein Minus vor dem Bruch gehört zum ganzen Bruch: gilt also für den ganzen Zähler oder ganzen Nenner (häufig nimmt man den Zähler).</p><p>\(\Rightarrow -\frac{a-1}{a} = \frac{-\boldsymbol{(a-1)}}{a} = \frac{-a+1}{a}\)</p><p>Wichtig bei Summen im Zähler!!!</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>471812117</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cb Addition von Brüchen mit Variablen und gleichem Nenner (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Überlege genau, was ein Minus vor einem Bruch bedeutet.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c]); fractions_correct_and_wa1:[[(myvar+1)/myvar, -myvar+1], [(myvar-1)/myvar, -myvar-1], [(1-myvar)/myvar, -1-myvar]]; fractions_correct_and_wa1:random_permutation(fractions_correct_and_wa1); fractions:makelist(fractions_correct_and_wa1[i][1],i,3); terms_wa1:makelist(fractions_correct_and_wa1[i][2],i,3); exercise:fractions[1]-fractions[2]-fractions[3]; ta1:combine(exercise); wa1:(num(fractions[1])+terms_wa1[2]+terms_wa1[3])/myvar;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@}-{@fractions[2]@}-{@fractions[3]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast offenbar die Minuszeichen nicht korrekt aufgelöst.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Ein Minus vor dem Bruch gehört zum ganzen Bruch: gilt also für den ganzen Zähler oder ganzen Nenner (häufig nimmt man den Zähler).</p><p>\(\Rightarrow -\frac{a-1}{a} = \frac{-\boldsymbol{(a-1)}}{a} = \frac{-a+1}{a}\)</p><p>Wichtig bei Summen im Zähler!!!</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>416709956</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cb Addition von Brüchen mit Variablen und gleichem Nenner (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Überlege genau, was ein Minus vor einem Bruch bedeutet.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c]); fractions_correct_and_wa1:[[(myvar+1)/myvar, -myvar+1], [(myvar-1)/myvar, -myvar-1], [(1-myvar)/myvar, -1-myvar]]; fractions_correct_and_wa1:random_permutation(fractions_correct_and_wa1); fractions:makelist(fractions_correct_and_wa1[i][1],i,3); terms_wa1:makelist(fractions_correct_and_wa1[i][2],i,3); exercise:fractions[1]-fractions[2]-fractions[3]; ta1:combine(exercise); wa1:(num(fractions[1])+terms_wa1[2]+terms_wa1[3])/myvar;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@}-{@fractions[2]@}-{@fractions[3]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast offenbar die Minuszeichen nicht korrekt aufgelöst.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Ein Minus vor dem Bruch gehört zum ganzen Bruch: gilt also für den ganzen Zähler oder ganzen Nenner (häufig nimmt man den Zähler).</p><p>\(\Rightarrow -\frac{a-1}{a} = \frac{-\boldsymbol{(a-1)}}{a} = \frac{-a+1}{a}\)</p><p>Wichtig bei Summen im Zähler!!!</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>743127794</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cb Addition von Brüchen mit Variablen und gleichem Nenner (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Überlege genau, was ein Minus vor einem Bruch bedeutet.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c]); fractions_correct_and_wa1:[[(myvar+1)/myvar, -myvar+1], [(myvar-1)/myvar, -myvar-1], [(1-myvar)/myvar, -1-myvar]]; fractions_correct_and_wa1:random_permutation(fractions_correct_and_wa1); fractions:makelist(fractions_correct_and_wa1[i][1],i,3); terms_wa1:makelist(fractions_correct_and_wa1[i][2],i,3); exercise:fractions[1]-fractions[2]-fractions[3]; ta1:combine(exercise); wa1:(num(fractions[1])+terms_wa1[2]+terms_wa1[3])/myvar;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@}-{@fractions[2]@}-{@fractions[3]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast offenbar die Minuszeichen nicht korrekt aufgelöst.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Ein Minus vor dem Bruch gehört zum ganzen Bruch: gilt also für den ganzen Zähler oder ganzen Nenner (häufig nimmt man den Zähler).</p><p>\(\Rightarrow -\frac{a-1}{a} = \frac{-\boldsymbol{(a-1)}}{a} = \frac{-a+1}{a}\)</p><p>Wichtig bei Summen im Zähler!!!</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>2005900637</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cc Addition von Brüchen mit Variablen und unterschiedlichen Nennern (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Jeder Teilnenner (hier: {@myvars[1]@}, {@myvars[2]@}, {@myvars[3]@}) muss als Faktor im gemeinsamen Nenner vorkommen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); fractions:[(1+myvars[1])/myvars[1], rand_with_step(2,5,1)/myvars[2], myvars[1]/myvars[3]]; fractions:random_permutation(fractions); exercise:fractions[1]+fractions[2]+fractions[3]; common_denom:denom(fractions[1])*denom(fractions[2])*denom(fractions[3]); ta1:((num(fractions[1])*denom(fractions[2])*denom(fractions[3]))+(num(fractions[2])*denom(fractions[1])*denom(fractions[3]))+(num(fractions[3])*denom(fractions[1])*denom(fractions[2])))/common_denom; ta1alt:(expand((num(fractions[1])*denom(fractions[2])*denom(fractions[3])))+expand((num(fractions[2])*denom(fractions[1])*denom(fractions[3])))+expand((num(fractions[3])*denom(fractions[1])*denom(fractions[2]))))/common_denom;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
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+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
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+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{1+a}{a}+\frac{2}{b}+\frac{a}{c}\) ist der gemeinsame Nenner \(a \cdot b \cdot c\). So muss erweitert werden, damit die Zähler addiert werden können:</p><p>\(\frac{(1+a) \boldsymbol{\cdot b \cdot c} }{a \boldsymbol{\cdot b \cdot c}}+\frac{2 \boldsymbol{\cdot a \cdot c}}{\boldsymbol{a} \cdot b \boldsymbol{\cdot c}}+\frac{a \boldsymbol{\cdot a \cdot b}}{\boldsymbol{a \cdot b} \cdot c}\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(1+a\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>638235066</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cc Addition von Brüchen mit Variablen und unterschiedlichen Nennern (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Jeder Teilnenner (hier: {@myvars[1]@}, {@myvars[2]@}, {@myvars[3]@}) muss als Faktor im gemeinsamen Nenner vorkommen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); fractions:[(1+myvars[1])/myvars[1], rand_with_step(2,5,1)/myvars[2], myvars[1]/myvars[3]]; fractions:random_permutation(fractions); exercise:fractions[1]+fractions[2]+fractions[3]; common_denom:denom(fractions[1])*denom(fractions[2])*denom(fractions[3]); ta1:((num(fractions[1])*denom(fractions[2])*denom(fractions[3]))+(num(fractions[2])*denom(fractions[1])*denom(fractions[3]))+(num(fractions[3])*denom(fractions[1])*denom(fractions[2])))/common_denom; ta1alt:(expand((num(fractions[1])*denom(fractions[2])*denom(fractions[3])))+expand((num(fractions[2])*denom(fractions[1])*denom(fractions[3])))+expand((num(fractions[3])*denom(fractions[1])*denom(fractions[2]))))/common_denom;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
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+ <forbidwords/>
+ <allowwords/>
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+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{1+a}{a}+\frac{2}{b}+\frac{a}{c}\) ist der gemeinsame Nenner \(a \cdot b \cdot c\). So muss erweitert werden, damit die Zähler addiert werden können:</p><p>\(\frac{(1+a) \boldsymbol{\cdot b \cdot c} }{a \boldsymbol{\cdot b \cdot c}}+\frac{2 \boldsymbol{\cdot a \cdot c}}{\boldsymbol{a} \cdot b \boldsymbol{\cdot c}}+\frac{a \boldsymbol{\cdot a \cdot b}}{\boldsymbol{a \cdot b} \cdot c}\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(1+a\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1053964038</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cc Addition von Brüchen mit Variablen und unterschiedlichen Nennern (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Jeder Teilnenner (hier: {@myvars[1]@}, {@myvars[2]@}, {@myvars[3]@}) muss als Faktor im gemeinsamen Nenner vorkommen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); fractions:[(1+myvars[1])/myvars[1], rand_with_step(2,5,1)/myvars[2], myvars[1]/myvars[3]]; fractions:random_permutation(fractions); exercise:fractions[1]+fractions[2]+fractions[3]; common_denom:denom(fractions[1])*denom(fractions[2])*denom(fractions[3]); ta1:((num(fractions[1])*denom(fractions[2])*denom(fractions[3]))+(num(fractions[2])*denom(fractions[1])*denom(fractions[3]))+(num(fractions[3])*denom(fractions[1])*denom(fractions[2])))/common_denom; ta1alt:(expand((num(fractions[1])*denom(fractions[2])*denom(fractions[3])))+expand((num(fractions[2])*denom(fractions[1])*denom(fractions[3])))+expand((num(fractions[3])*denom(fractions[1])*denom(fractions[2]))))/common_denom;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
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+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
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+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{1+a}{a}+\frac{2}{b}+\frac{a}{c}\) ist der gemeinsame Nenner \(a \cdot b \cdot c\). So muss erweitert werden, damit die Zähler addiert werden können:</p><p>\(\frac{(1+a) \boldsymbol{\cdot b \cdot c} }{a \boldsymbol{\cdot b \cdot c}}+\frac{2 \boldsymbol{\cdot a \cdot c}}{\boldsymbol{a} \cdot b \boldsymbol{\cdot c}}+\frac{a \boldsymbol{\cdot a \cdot b}}{\boldsymbol{a \cdot b} \cdot c}\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(1+a\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>625975426</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cc Addition von Brüchen mit Variablen und unterschiedlichen Nennern (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Jeder Teilnenner (hier: {@myvars[1]@}, {@myvars[2]@}, {@myvars[3]@}) muss als Faktor im gemeinsamen Nenner vorkommen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); fractions:[(1+myvars[1])/myvars[1], rand_with_step(2,5,1)/myvars[2], myvars[1]/myvars[3]]; fractions:random_permutation(fractions); exercise:fractions[1]+fractions[2]+fractions[3]; common_denom:denom(fractions[1])*denom(fractions[2])*denom(fractions[3]); ta1:((num(fractions[1])*denom(fractions[2])*denom(fractions[3]))+(num(fractions[2])*denom(fractions[1])*denom(fractions[3]))+(num(fractions[3])*denom(fractions[1])*denom(fractions[2])))/common_denom; ta1alt:(expand((num(fractions[1])*denom(fractions[2])*denom(fractions[3])))+expand((num(fractions[2])*denom(fractions[1])*denom(fractions[3])))+expand((num(fractions[3])*denom(fractions[1])*denom(fractions[2]))))/common_denom;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
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+ <checkanswertype>0</checkanswertype>
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+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{1+a}{a}+\frac{2}{b}+\frac{a}{c}\) ist der gemeinsame Nenner \(a \cdot b \cdot c\). So muss erweitert werden, damit die Zähler addiert werden können:</p><p>\(\frac{(1+a) \boldsymbol{\cdot b \cdot c} }{a \boldsymbol{\cdot b \cdot c}}+\frac{2 \boldsymbol{\cdot a \cdot c}}{\boldsymbol{a} \cdot b \boldsymbol{\cdot c}}+\frac{a \boldsymbol{\cdot a \cdot b}}{\boldsymbol{a \cdot b} \cdot c}\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(1+a\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p></p>]]></text>
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+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
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+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
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+</node></prt><deployedseed>1098133316</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cd Addition von Brüchen mit einer Variablen und unterschiedlichen Nennern (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([x,y,z]); nums:makelist(rand_with_step(2,5,1),2); fractions:[(nums[1]+myvar)/myvar^2,(nums[2]-myvar^2)/myvar]; common_denom:myvar^2; ta1:(num(fractions[1])-num(fractions[2])*myvar)/common_denom; ta1alt:(num(fractions[1])-expand(num(fractions[2])*myvar))/common_denom; exercise:fractions[1]-fractions[2]; /*wa1 means: didn't consider minus sign before bracket*/ wa1:(num(fractions[1])+(-nums[2]-myvar^2)*myvar)/common_denom;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
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+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast offenbar die Minuszeichen nicht korrekt aufgelöst (siehe Tipp unten).]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um immer einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{3+x}{x^2}-\frac{5-x}{x}\) ist ein gemeinsame Nenner \(x^2 \cdot x = x^3\). Betrachtet man die Teilnenner \(x^2\) und \(x\) genauer, fällt auf, dass \(x\) bereits als Faktor in \(x^2\) vorkommt. Denn \(x^2 = x \cdot x\). Deswegen kann hier auch \(x^2\) als Hauptnenner gewählt werden.</p><p>Dazu muss so erweitert werden:</p><p>\(\frac{(3+x)}{x^{2}}-\frac{(5-x^2) \boldsymbol{ \cdot x}}{x \boldsymbol{\cdot x}} = \frac{3+x}{x^{2}}-\frac{5x-x^3}{x^{\boldsymbol{2}}} = \frac{3+x-(5x-x^3)}{x^2} = \dots\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(5-x^2\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p></p>]]></text>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>669633138</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cd Addition von Brüchen mit einer Variablen und unterschiedlichen Nennern (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([x,y,z]); nums:makelist(rand_with_step(2,5,1),2); fractions:[(nums[1]+myvar)/myvar^2,(nums[2]-myvar^2)/myvar]; common_denom:myvar^2; ta1:(num(fractions[1])-num(fractions[2])*myvar)/common_denom; ta1alt:(num(fractions[1])-expand(num(fractions[2])*myvar))/common_denom; exercise:fractions[1]-fractions[2]; /*wa1 means: didn't consider minus sign before bracket*/ wa1:(num(fractions[1])+(-nums[2]-myvar^2)*myvar)/common_denom;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
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+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast offenbar die Minuszeichen nicht korrekt aufgelöst (siehe Tipp unten).]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um immer einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{3+x}{x^2}-\frac{5-x}{x}\) ist ein gemeinsame Nenner \(x^2 \cdot x = x^3\). Betrachtet man die Teilnenner \(x^2\) und \(x\) genauer, fällt auf, dass \(x\) bereits als Faktor in \(x^2\) vorkommt. Denn \(x^2 = x \cdot x\). Deswegen kann hier auch \(x^2\) als Hauptnenner gewählt werden.</p><p>Dazu muss so erweitert werden:</p><p>\(\frac{(3+x)}{x^{2}}-\frac{(5-x^2) \boldsymbol{ \cdot x}}{x \boldsymbol{\cdot x}} = \frac{3+x}{x^{2}}-\frac{5x-x^3}{x^{\boldsymbol{2}}} = \frac{3+x-(5x-x^3)}{x^2} = \dots\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(5-x^2\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
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+</node></prt><deployedseed>2093071884</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cd Addition von Brüchen mit einer Variablen und unterschiedlichen Nennern (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([x,y,z]); nums:makelist(rand_with_step(2,5,1),2); fractions:[(nums[1]+myvar)/myvar^2,(nums[2]-myvar^2)/myvar]; common_denom:myvar^2; ta1:(num(fractions[1])-num(fractions[2])*myvar)/common_denom; ta1alt:(num(fractions[1])-expand(num(fractions[2])*myvar))/common_denom; exercise:fractions[1]-fractions[2]; /*wa1 means: didn't consider minus sign before bracket*/ wa1:(num(fractions[1])+(-nums[2]-myvar^2)*myvar)/common_denom;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast offenbar die Minuszeichen nicht korrekt aufgelöst (siehe Tipp unten).]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um immer einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{3+x}{x^2}-\frac{5-x}{x}\) ist ein gemeinsame Nenner \(x^2 \cdot x = x^3\). Betrachtet man die Teilnenner \(x^2\) und \(x\) genauer, fällt auf, dass \(x\) bereits als Faktor in \(x^2\) vorkommt. Denn \(x^2 = x \cdot x\). Deswegen kann hier auch \(x^2\) als Hauptnenner gewählt werden.</p><p>Dazu muss so erweitert werden:</p><p>\(\frac{(3+x)}{x^{2}}-\frac{(5-x^2) \boldsymbol{ \cdot x}}{x \boldsymbol{\cdot x}} = \frac{3+x}{x^{2}}-\frac{5x-x^3}{x^{\boldsymbol{2}}} = \frac{3+x-(5x-x^3)}{x^2} = \dots\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(5-x^2\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1766326583</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cd Addition von Brüchen mit einer Variablen und unterschiedlichen Nennern (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([x,y,z]); nums:makelist(rand_with_step(2,5,1),2); fractions:[(nums[1]+myvar)/myvar^2,(nums[2]-myvar^2)/myvar]; common_denom:myvar^2; ta1:(num(fractions[1])-num(fractions[2])*myvar)/common_denom; ta1alt:(num(fractions[1])-expand(num(fractions[2])*myvar))/common_denom; exercise:fractions[1]-fractions[2]; /*wa1 means: didn't consider minus sign before bracket*/ wa1:(num(fractions[1])+(-nums[2]-myvar^2)*myvar)/common_denom;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast offenbar die Minuszeichen nicht korrekt aufgelöst (siehe Tipp unten).]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um immer einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{3+x}{x^2}-\frac{5-x}{x}\) ist ein gemeinsame Nenner \(x^2 \cdot x = x^3\). Betrachtet man die Teilnenner \(x^2\) und \(x\) genauer, fällt auf, dass \(x\) bereits als Faktor in \(x^2\) vorkommt. Denn \(x^2 = x \cdot x\). Deswegen kann hier auch \(x^2\) als Hauptnenner gewählt werden.</p><p>Dazu muss so erweitert werden:</p><p>\(\frac{(3+x)}{x^{2}}-\frac{(5-x^2) \boldsymbol{ \cdot x}}{x \boldsymbol{\cdot x}} = \frac{3+x}{x^{2}}-\frac{5x-x^3}{x^{\boldsymbol{2}}} = \frac{3+x-(5x-x^3)}{x^2} = \dots\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(5-x^2\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>488830876</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ce Addition von Brüchen mit Variablen und unterschiedlichen Nennern I (Update1) (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); numbers:makelist(rand_with_step(2,5,1), 5); factors:random_permutation([1,2,4]); /*only +*/ signs:makelist(rand_with_prohib(1,1,[0]),2); fractions:[(numbers[1]*myvars[1]-numbers[2]*myvars[2])/(factors[1]*5*myvars[1]*myvars[2]), (numbers[3]*myvars[3]-numbers[4]*myvars[1])/(factors[2]*5*myvars[1]*myvars[3]), (myvars[3]^2-numbers[5])/(factors[3]*5*myvars[2]*myvars[3])]; tanum:(num(fractions[1])*(4/factors[1])*myvars[3]+num(fractions[2])*(4/factors[2])*myvars[2]+num(fractions[3])*(4/factors[3])*myvars[1]); tanumalt:expand(tanum); tadenom:(5*4*myvars[1]*myvars[2]*myvars[3]); ta1:tanum/tadenom; /*fractions_to_show:random_permutation(fractions);*/ fractions_to_show:fractions; ta1alt:tanumalt/tadenom; fractions_to_show[2]:fractions_to_show[2]*signs[1]; fractions_to_show[3]:fractions_to_show[3]*signs[2]; exercise:fractions_to_show[1]+fractions_to_show[2]+fractions_to_show[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{5\,z-4\,x}{10\,x\,z}+\frac{7\,y-3\,z}{20\,y\,z}+\frac{y^2-2}{5\,x\,y}\) ist \(20\) das kleinste gemeinsame Vielfache (kgV) von \(10\), \(20\) und \(5\) und \(x \cdot y \cdot z\) ist das kgV von \(x \cdot z\), \(y \cdot z\) und \(x \cdot y\). Der Hauptnenner ist demnach \(20 \cdot x \cdot y \cdot z\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(20 \cdot x \cdot y \cdot z\;\) steht. \(\frac{5\,z-4\,x}{10\,x\,z}\) wird mit \(2 \cdot y\) erweitert, \(\frac{7\,y-3\,z}{20\,y\,z}\) wird mit \(x\) erweitert und \(\frac{y^2-2}{5\,x\,y}\) wird mit \(4 \cdot z\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(5\,z-4\,x)\boldsymbol{ \cdot 2\,y}}{10\,x\,z \boldsymbol{ \cdot 2\,y}}+\frac{(7\,y-3\,z) \boldsymbol{ \cdot x}}{20\,y\,z \boldsymbol{ \cdot x}}+\frac{(y^2-2) \boldsymbol{ \cdot 4\,z}}{5\,x\,y \boldsymbol{ \cdot 4\,z}}\)</p><p>\(= \frac{10\,y\,z-8\,x\,y}{20\,x\,y\,z}+\frac{7\,x\,y-3\,x\,z}{20\,x\,y\,z}+\frac{4\,y^2\,z-8\,z}{20\,x\,y\,z} = \dots\)</p></p>]]></text>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1330316881</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ce Addition von Brüchen mit Variablen und unterschiedlichen Nennern I (Update1) (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); numbers:makelist(rand_with_step(2,5,1), 5); factors:random_permutation([1,2,4]); /*only +*/ signs:makelist(rand_with_prohib(1,1,[0]),2); fractions:[(numbers[1]*myvars[1]-numbers[2]*myvars[2])/(factors[1]*5*myvars[1]*myvars[2]), (numbers[3]*myvars[3]-numbers[4]*myvars[1])/(factors[2]*5*myvars[1]*myvars[3]), (myvars[3]^2-numbers[5])/(factors[3]*5*myvars[2]*myvars[3])]; tanum:(num(fractions[1])*(4/factors[1])*myvars[3]+num(fractions[2])*(4/factors[2])*myvars[2]+num(fractions[3])*(4/factors[3])*myvars[1]); tanumalt:expand(tanum); tadenom:(5*4*myvars[1]*myvars[2]*myvars[3]); ta1:tanum/tadenom; /*fractions_to_show:random_permutation(fractions);*/ fractions_to_show:fractions; ta1alt:tanumalt/tadenom; fractions_to_show[2]:fractions_to_show[2]*signs[1]; fractions_to_show[3]:fractions_to_show[3]*signs[2]; exercise:fractions_to_show[1]+fractions_to_show[2]+fractions_to_show[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
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+ <type>algebraic</type>
+ <tans>ta1</tans>
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+<name>999</name>
+<answertest>AlgEquiv</answertest>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{5\,z-4\,x}{10\,x\,z}+\frac{7\,y-3\,z}{20\,y\,z}+\frac{y^2-2}{5\,x\,y}\) ist \(20\) das kleinste gemeinsame Vielfache (kgV) von \(10\), \(20\) und \(5\) und \(x \cdot y \cdot z\) ist das kgV von \(x \cdot z\), \(y \cdot z\) und \(x \cdot y\). Der Hauptnenner ist demnach \(20 \cdot x \cdot y \cdot z\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(20 \cdot x \cdot y \cdot z\;\) steht. \(\frac{5\,z-4\,x}{10\,x\,z}\) wird mit \(2 \cdot y\) erweitert, \(\frac{7\,y-3\,z}{20\,y\,z}\) wird mit \(x\) erweitert und \(\frac{y^2-2}{5\,x\,y}\) wird mit \(4 \cdot z\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(5\,z-4\,x)\boldsymbol{ \cdot 2\,y}}{10\,x\,z \boldsymbol{ \cdot 2\,y}}+\frac{(7\,y-3\,z) \boldsymbol{ \cdot x}}{20\,y\,z \boldsymbol{ \cdot x}}+\frac{(y^2-2) \boldsymbol{ \cdot 4\,z}}{5\,x\,y \boldsymbol{ \cdot 4\,z}}\)</p><p>\(= \frac{10\,y\,z-8\,x\,y}{20\,x\,y\,z}+\frac{7\,x\,y-3\,x\,z}{20\,x\,y\,z}+\frac{4\,y^2\,z-8\,z}{20\,x\,y\,z} = \dots\)</p></p>]]></text>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>2007639052</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ce Addition von Brüchen mit Variablen und unterschiedlichen Nennern I (Update1) (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); numbers:makelist(rand_with_step(2,5,1), 5); factors:random_permutation([1,2,4]); /*only +*/ signs:makelist(rand_with_prohib(1,1,[0]),2); fractions:[(numbers[1]*myvars[1]-numbers[2]*myvars[2])/(factors[1]*5*myvars[1]*myvars[2]), (numbers[3]*myvars[3]-numbers[4]*myvars[1])/(factors[2]*5*myvars[1]*myvars[3]), (myvars[3]^2-numbers[5])/(factors[3]*5*myvars[2]*myvars[3])]; tanum:(num(fractions[1])*(4/factors[1])*myvars[3]+num(fractions[2])*(4/factors[2])*myvars[2]+num(fractions[3])*(4/factors[3])*myvars[1]); tanumalt:expand(tanum); tadenom:(5*4*myvars[1]*myvars[2]*myvars[3]); ta1:tanum/tadenom; /*fractions_to_show:random_permutation(fractions);*/ fractions_to_show:fractions; ta1alt:tanumalt/tadenom; fractions_to_show[2]:fractions_to_show[2]*signs[1]; fractions_to_show[3]:fractions_to_show[3]*signs[2]; exercise:fractions_to_show[1]+fractions_to_show[2]+fractions_to_show[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
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+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
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+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
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+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
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+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{5\,z-4\,x}{10\,x\,z}+\frac{7\,y-3\,z}{20\,y\,z}+\frac{y^2-2}{5\,x\,y}\) ist \(20\) das kleinste gemeinsame Vielfache (kgV) von \(10\), \(20\) und \(5\) und \(x \cdot y \cdot z\) ist das kgV von \(x \cdot z\), \(y \cdot z\) und \(x \cdot y\). Der Hauptnenner ist demnach \(20 \cdot x \cdot y \cdot z\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(20 \cdot x \cdot y \cdot z\;\) steht. \(\frac{5\,z-4\,x}{10\,x\,z}\) wird mit \(2 \cdot y\) erweitert, \(\frac{7\,y-3\,z}{20\,y\,z}\) wird mit \(x\) erweitert und \(\frac{y^2-2}{5\,x\,y}\) wird mit \(4 \cdot z\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(5\,z-4\,x)\boldsymbol{ \cdot 2\,y}}{10\,x\,z \boldsymbol{ \cdot 2\,y}}+\frac{(7\,y-3\,z) \boldsymbol{ \cdot x}}{20\,y\,z \boldsymbol{ \cdot x}}+\frac{(y^2-2) \boldsymbol{ \cdot 4\,z}}{5\,x\,y \boldsymbol{ \cdot 4\,z}}\)</p><p>\(= \frac{10\,y\,z-8\,x\,y}{20\,x\,y\,z}+\frac{7\,x\,y-3\,x\,z}{20\,x\,y\,z}+\frac{4\,y^2\,z-8\,z}{20\,x\,y\,z} = \dots\)</p></p>]]></text>
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+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>846124380</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ce Addition von Brüchen mit Variablen und unterschiedlichen Nennern I (Update1) (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); numbers:makelist(rand_with_step(2,5,1), 5); factors:random_permutation([1,2,4]); /*only +*/ signs:makelist(rand_with_prohib(1,1,[0]),2); fractions:[(numbers[1]*myvars[1]-numbers[2]*myvars[2])/(factors[1]*5*myvars[1]*myvars[2]), (numbers[3]*myvars[3]-numbers[4]*myvars[1])/(factors[2]*5*myvars[1]*myvars[3]), (myvars[3]^2-numbers[5])/(factors[3]*5*myvars[2]*myvars[3])]; tanum:(num(fractions[1])*(4/factors[1])*myvars[3]+num(fractions[2])*(4/factors[2])*myvars[2]+num(fractions[3])*(4/factors[3])*myvars[1]); tanumalt:expand(tanum); tadenom:(5*4*myvars[1]*myvars[2]*myvars[3]); ta1:tanum/tadenom; /*fractions_to_show:random_permutation(fractions);*/ fractions_to_show:fractions; ta1alt:tanumalt/tadenom; fractions_to_show[2]:fractions_to_show[2]*signs[1]; fractions_to_show[3]:fractions_to_show[3]*signs[2]; exercise:fractions_to_show[1]+fractions_to_show[2]+fractions_to_show[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
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+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
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+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{5\,z-4\,x}{10\,x\,z}+\frac{7\,y-3\,z}{20\,y\,z}+\frac{y^2-2}{5\,x\,y}\) ist \(20\) das kleinste gemeinsame Vielfache (kgV) von \(10\), \(20\) und \(5\) und \(x \cdot y \cdot z\) ist das kgV von \(x \cdot z\), \(y \cdot z\) und \(x \cdot y\). Der Hauptnenner ist demnach \(20 \cdot x \cdot y \cdot z\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(20 \cdot x \cdot y \cdot z\;\) steht. \(\frac{5\,z-4\,x}{10\,x\,z}\) wird mit \(2 \cdot y\) erweitert, \(\frac{7\,y-3\,z}{20\,y\,z}\) wird mit \(x\) erweitert und \(\frac{y^2-2}{5\,x\,y}\) wird mit \(4 \cdot z\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(5\,z-4\,x)\boldsymbol{ \cdot 2\,y}}{10\,x\,z \boldsymbol{ \cdot 2\,y}}+\frac{(7\,y-3\,z) \boldsymbol{ \cdot x}}{20\,y\,z \boldsymbol{ \cdot x}}+\frac{(y^2-2) \boldsymbol{ \cdot 4\,z}}{5\,x\,y \boldsymbol{ \cdot 4\,z}}\)</p><p>\(= \frac{10\,y\,z-8\,x\,y}{20\,x\,y\,z}+\frac{7\,x\,y-3\,x\,z}{20\,x\,y\,z}+\frac{4\,y^2\,z-8\,z}{20\,x\,y\,z} = \dots\)</p></p>]]></text>
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+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>520216901</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cf Addition von Brüchen mit Variablen und unterschiedlichen Nennern II (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: 1) Überlege genau, was ein Minus vor einem Bruch bedeutet. 2) Jeder Teilnenner (hier: {@denom(main_fraction)@}, {@denom(fractions[1])@}, {@denom(fractions[2])@}) muss als Faktor im gemeinsamen Nenner vorkommen. 3) Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); numbers:rand_selection(makelist(i,i,5),2); denom_nums_origin:rand_selection([18,12,6],1)[1]; denom_nums:[denom_nums_origin, denom_nums_origin/2, denom_nums_origin/3]; main_fraction:(numbers[1]-myvars[1])/(denom_nums[1]*myvars[1]^2); fractions:[(myvars[2])/(denom_nums[2]*myvars[1]), (myvars[2]+numbers[2])/(denom_nums[3]*myvars[1]*myvars[2])]; tanum:num(main_fraction)*myvars[2]-num(fractions[1])*2*myvars[1]*myvars[2]-num(fractions[2])*3*myvars[1]; tanumalt:expand(tanum); tadenom:denom_nums_origin*myvars[1]^2*myvars[2]; ta1:tanum/tadenom; ta1alt:tanumalt/tadenom; fractions:random_permutation(fractions); simp:false; exercise:main_fraction-fractions[1]-fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
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+ <forbidfloat>1</forbidfloat>
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+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{1-x}{18\,x^2}-\frac{y}{9\,x}-\frac{x+3}{6\,x\,y}\) ist \(18\) das kleinste gemeinsame Vielfache (kgV) von \(18\), \(9\) und \(6\) und \(x^2 \cdot y\) ist das kgV von \(x^2\), \(x\) und \(x \cdot y\). Der Hauptnenner ist demnach \(18 \cdot x^2 \cdot y\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(18 \cdot x^2 \cdot y\;\) steht. \(\frac{1-x}{18\,x^2}\) wird mit \(y\) erweitert, \(\frac{y}{9\,x}\) wird mit \(2\,x\,y\) erweitert und \(\frac{x+3}{6\,x\,y}\) wird mit \(3 \cdot x\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(1-x) \boldsymbol{\cdot y}}{18\,x^2 \boldsymbol{\cdot y}}-\frac{y \boldsymbol{\cdot 2\,x\,y}}{9\,x \boldsymbol{\cdot 2\,x\,y}}-\frac{(x+3) \boldsymbol{\cdot 3\,x}}{6\,x\,y \boldsymbol{\cdot 3\,x}}\)</p><p>\(= \frac{y-x\,y}{18\,x^2\,y}-\frac{2\,x\,y^2}{18\,x^2\,y}-\frac{3\,x^2+9\,x}{18\,x^2\,y} = \dots\)</p></p>]]></text>
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+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
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+</node></prt><deployedseed>527686404</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cf Addition von Brüchen mit Variablen und unterschiedlichen Nennern II (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: 1) Überlege genau, was ein Minus vor einem Bruch bedeutet. 2) Jeder Teilnenner (hier: {@denom(main_fraction)@}, {@denom(fractions[1])@}, {@denom(fractions[2])@}) muss als Faktor im gemeinsamen Nenner vorkommen. 3) Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); numbers:rand_selection(makelist(i,i,5),2); denom_nums_origin:rand_selection([18,12,6],1)[1]; denom_nums:[denom_nums_origin, denom_nums_origin/2, denom_nums_origin/3]; main_fraction:(numbers[1]-myvars[1])/(denom_nums[1]*myvars[1]^2); fractions:[(myvars[2])/(denom_nums[2]*myvars[1]), (myvars[2]+numbers[2])/(denom_nums[3]*myvars[1]*myvars[2])]; tanum:num(main_fraction)*myvars[2]-num(fractions[1])*2*myvars[1]*myvars[2]-num(fractions[2])*3*myvars[1]; tanumalt:expand(tanum); tadenom:denom_nums_origin*myvars[1]^2*myvars[2]; ta1:tanum/tadenom; ta1alt:tanumalt/tadenom; fractions:random_permutation(fractions); simp:false; exercise:main_fraction-fractions[1]-fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
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+ <insertstars>5</insertstars>
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+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{1-x}{18\,x^2}-\frac{y}{9\,x}-\frac{x+3}{6\,x\,y}\) ist \(18\) das kleinste gemeinsame Vielfache (kgV) von \(18\), \(9\) und \(6\) und \(x^2 \cdot y\) ist das kgV von \(x^2\), \(x\) und \(x \cdot y\). Der Hauptnenner ist demnach \(18 \cdot x^2 \cdot y\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(18 \cdot x^2 \cdot y\;\) steht. \(\frac{1-x}{18\,x^2}\) wird mit \(y\) erweitert, \(\frac{y}{9\,x}\) wird mit \(2\,x\,y\) erweitert und \(\frac{x+3}{6\,x\,y}\) wird mit \(3 \cdot x\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(1-x) \boldsymbol{\cdot y}}{18\,x^2 \boldsymbol{\cdot y}}-\frac{y \boldsymbol{\cdot 2\,x\,y}}{9\,x \boldsymbol{\cdot 2\,x\,y}}-\frac{(x+3) \boldsymbol{\cdot 3\,x}}{6\,x\,y \boldsymbol{\cdot 3\,x}}\)</p><p>\(= \frac{y-x\,y}{18\,x^2\,y}-\frac{2\,x\,y^2}{18\,x^2\,y}-\frac{3\,x^2+9\,x}{18\,x^2\,y} = \dots\)</p></p>]]></text>
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+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
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+</node></prt><deployedseed>1918490776</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cf Addition von Brüchen mit Variablen und unterschiedlichen Nennern II (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: 1) Überlege genau, was ein Minus vor einem Bruch bedeutet. 2) Jeder Teilnenner (hier: {@denom(main_fraction)@}, {@denom(fractions[1])@}, {@denom(fractions[2])@}) muss als Faktor im gemeinsamen Nenner vorkommen. 3) Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); numbers:rand_selection(makelist(i,i,5),2); denom_nums_origin:rand_selection([18,12,6],1)[1]; denom_nums:[denom_nums_origin, denom_nums_origin/2, denom_nums_origin/3]; main_fraction:(numbers[1]-myvars[1])/(denom_nums[1]*myvars[1]^2); fractions:[(myvars[2])/(denom_nums[2]*myvars[1]), (myvars[2]+numbers[2])/(denom_nums[3]*myvars[1]*myvars[2])]; tanum:num(main_fraction)*myvars[2]-num(fractions[1])*2*myvars[1]*myvars[2]-num(fractions[2])*3*myvars[1]; tanumalt:expand(tanum); tadenom:denom_nums_origin*myvars[1]^2*myvars[2]; ta1:tanum/tadenom; ta1alt:tanumalt/tadenom; fractions:random_permutation(fractions); simp:false; exercise:main_fraction-fractions[1]-fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{1-x}{18\,x^2}-\frac{y}{9\,x}-\frac{x+3}{6\,x\,y}\) ist \(18\) das kleinste gemeinsame Vielfache (kgV) von \(18\), \(9\) und \(6\) und \(x^2 \cdot y\) ist das kgV von \(x^2\), \(x\) und \(x \cdot y\). Der Hauptnenner ist demnach \(18 \cdot x^2 \cdot y\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(18 \cdot x^2 \cdot y\;\) steht. \(\frac{1-x}{18\,x^2}\) wird mit \(y\) erweitert, \(\frac{y}{9\,x}\) wird mit \(2\,x\,y\) erweitert und \(\frac{x+3}{6\,x\,y}\) wird mit \(3 \cdot x\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(1-x) \boldsymbol{\cdot y}}{18\,x^2 \boldsymbol{\cdot y}}-\frac{y \boldsymbol{\cdot 2\,x\,y}}{9\,x \boldsymbol{\cdot 2\,x\,y}}-\frac{(x+3) \boldsymbol{\cdot 3\,x}}{6\,x\,y \boldsymbol{\cdot 3\,x}}\)</p><p>\(= \frac{y-x\,y}{18\,x^2\,y}-\frac{2\,x\,y^2}{18\,x^2\,y}-\frac{3\,x^2+9\,x}{18\,x^2\,y} = \dots\)</p></p>]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>2103547991</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cf Addition von Brüchen mit Variablen und unterschiedlichen Nennern II (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: 1) Überlege genau, was ein Minus vor einem Bruch bedeutet. 2) Jeder Teilnenner (hier: {@denom(main_fraction)@}, {@denom(fractions[1])@}, {@denom(fractions[2])@}) muss als Faktor im gemeinsamen Nenner vorkommen. 3) Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); numbers:rand_selection(makelist(i,i,5),2); denom_nums_origin:rand_selection([18,12,6],1)[1]; denom_nums:[denom_nums_origin, denom_nums_origin/2, denom_nums_origin/3]; main_fraction:(numbers[1]-myvars[1])/(denom_nums[1]*myvars[1]^2); fractions:[(myvars[2])/(denom_nums[2]*myvars[1]), (myvars[2]+numbers[2])/(denom_nums[3]*myvars[1]*myvars[2])]; tanum:num(main_fraction)*myvars[2]-num(fractions[1])*2*myvars[1]*myvars[2]-num(fractions[2])*3*myvars[1]; tanumalt:expand(tanum); tadenom:denom_nums_origin*myvars[1]^2*myvars[2]; ta1:tanum/tadenom; ta1alt:tanumalt/tadenom; fractions:random_permutation(fractions); simp:false; exercise:main_fraction-fractions[1]-fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{1-x}{18\,x^2}-\frac{y}{9\,x}-\frac{x+3}{6\,x\,y}\) ist \(18\) das kleinste gemeinsame Vielfache (kgV) von \(18\), \(9\) und \(6\) und \(x^2 \cdot y\) ist das kgV von \(x^2\), \(x\) und \(x \cdot y\). Der Hauptnenner ist demnach \(18 \cdot x^2 \cdot y\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(18 \cdot x^2 \cdot y\;\) steht. \(\frac{1-x}{18\,x^2}\) wird mit \(y\) erweitert, \(\frac{y}{9\,x}\) wird mit \(2\,x\,y\) erweitert und \(\frac{x+3}{6\,x\,y}\) wird mit \(3 \cdot x\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(1-x) \boldsymbol{\cdot y}}{18\,x^2 \boldsymbol{\cdot y}}-\frac{y \boldsymbol{\cdot 2\,x\,y}}{9\,x \boldsymbol{\cdot 2\,x\,y}}-\frac{(x+3) \boldsymbol{\cdot 3\,x}}{6\,x\,y \boldsymbol{\cdot 3\,x}}\)</p><p>\(= \frac{y-x\,y}{18\,x^2\,y}-\frac{2\,x\,y^2}{18\,x^2\,y}-\frac{3\,x^2+9\,x}{18\,x^2\,y} = \dots\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1091135158</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-da Multiplikation zweier einfacher Brüche (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@}\cdot{@fractions[2]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8),4); fractions:[nums[1]/nums[2], nums[3]/nums[4]]; ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions*/ wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied*/ wa2:fractions[1]+fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@}\cdot{@fractions[2]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{2}{3} \cdot \frac{6}{5} = \frac{2 \cdot 6}{3 \cdot 5} = \frac{12}{15} = \frac{4}{5}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1088212423</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-da Multiplikation zweier einfacher Brüche (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@}\cdot{@fractions[2]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8),4); fractions:[nums[1]/nums[2], nums[3]/nums[4]]; ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions*/ wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied*/ wa2:fractions[1]+fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@}\cdot{@fractions[2]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
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+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
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+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
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+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{2}{3} \cdot \frac{6}{5} = \frac{2 \cdot 6}{3 \cdot 5} = \frac{12}{15} = \frac{4}{5}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1553109555</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-da Multiplikation zweier einfacher Brüche (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@}\cdot{@fractions[2]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8),4); fractions:[nums[1]/nums[2], nums[3]/nums[4]]; ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions*/ wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied*/ wa2:fractions[1]+fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@}\cdot{@fractions[2]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
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+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
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+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
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+ <autosimplify>1</autosimplify>
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+ <truepenalty/>
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+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
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+ <falsepenalty/>
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+ <falseanswernote>prt1-1-F</falseanswernote>
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+ </falsefeedback>
+ </node>
+ <node>
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+ <sans>ans1</sans>
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+ <truepenalty/>
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+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
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+ <node>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.]]></text>
+</truefeedback>
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+<falsepenalty/>
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+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{2}{3} \cdot \frac{6}{5} = \frac{2 \cdot 6}{3 \cdot 5} = \frac{12}{15} = \frac{4}{5}\)</p></p>]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>777390971</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-da Multiplikation zweier einfacher Brüche (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@}\cdot{@fractions[2]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8),4); fractions:[nums[1]/nums[2], nums[3]/nums[4]]; ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions*/ wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied*/ wa2:fractions[1]+fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@}\cdot{@fractions[2]@} = {@ta1@}\)</text>
+ </questionnote>
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+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
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+ <complexno>i</complexno>
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+ <type>algebraic</type>
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+ <trueanswernote>prt1-1-T</trueanswernote>
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+ <falsescore>0</falsescore>
+ <falsepenalty/>
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+ <falseanswernote>prt1-1-F</falseanswernote>
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+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.]]></text>
+</truefeedback>
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+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
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+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{2}{3} \cdot \frac{6}{5} = \frac{2 \cdot 6}{3 \cdot 5} = \frac{12}{15} = \frac{4}{5}\)</p></p>]]></text>
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+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1688656099</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-db Multiplikation zweier Brüche mit Variablen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
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+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); fractions:[mya/myb, mya^2/(mya*myb)]; fractions:random_permutation(fractions); ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions with previously shortened the larger fraction*/ wa1:(2*mya)/(2*myb); /*wa2 means: naively summed fractions without previously shortening the larger fraction*/ wa2:(mya+myb^2)/(mya+myb*mya); /*wa3 means: correctly summed fractions instead of multiplied*/ wa3:fractions[1]+fractions[2]; /*wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied wa2:fractions[1]+fractions[2];*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
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+ <prt>
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+ <value>1.0000000</value>
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+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
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+ <falsescore>0</falsescore>
+ <falsepenalty/>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
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+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.]]></text>
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+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden. Du hast außerdem den Bruch \({@mya@}^2/({@mya@}*{@myb@})\) nicht ausreichend vereinfacht. Er kann zu \({@mya@}/{@myb@}\) gekürzt werden.]]></text>
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+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{a}{b} \cdot \frac{a^2}{a\,b} = \frac{a}{b} \cdot \frac{a \cdot a}{a\,b} = \frac{a \cdot a \cdot a}{a \cdot b \cdot b} = \frac{a^3}{a\,b^2}\)</p></p>]]></text>
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+ <deployedseed>545658671</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-db Multiplikation zweier Brüche mit Variablen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); fractions:[mya/myb, mya^2/(mya*myb)]; fractions:random_permutation(fractions); ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions with previously shortened the larger fraction*/ wa1:(2*mya)/(2*myb); /*wa2 means: naively summed fractions without previously shortening the larger fraction*/ wa2:(mya+myb^2)/(mya+myb*mya); /*wa3 means: correctly summed fractions instead of multiplied*/ wa3:fractions[1]+fractions[2]; /*wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied wa2:fractions[1]+fractions[2];*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} = {@ta1@}\)</text>
+ </questionnote>
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+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
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+ <tans>ta1</tans>
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+ <node>
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+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
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+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.]]></text>
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+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
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+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden. Du hast außerdem den Bruch \({@mya@}^2/({@mya@}*{@myb@})\) nicht ausreichend vereinfacht. Er kann zu \({@mya@}/{@myb@}\) gekürzt werden.]]></text>
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+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
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+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{a}{b} \cdot \frac{a^2}{a\,b} = \frac{a}{b} \cdot \frac{a \cdot a}{a\,b} = \frac{a \cdot a \cdot a}{a \cdot b \cdot b} = \frac{a^3}{a\,b^2}\)</p></p>]]></text>
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+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1228864607</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-db Multiplikation zweier Brüche mit Variablen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
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+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); fractions:[mya/myb, mya^2/(mya*myb)]; fractions:random_permutation(fractions); ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions with previously shortened the larger fraction*/ wa1:(2*mya)/(2*myb); /*wa2 means: naively summed fractions without previously shortening the larger fraction*/ wa2:(mya+myb^2)/(mya+myb*mya); /*wa3 means: correctly summed fractions instead of multiplied*/ wa3:fractions[1]+fractions[2]; /*wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied wa2:fractions[1]+fractions[2];*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} = {@ta1@}\)</text>
+ </questionnote>
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+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
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+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
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+ <value>1.0000000</value>
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+ <trueanswernote>prt1-1-T</trueanswernote>
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+ <text/>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.]]></text>
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+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
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+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden. Du hast außerdem den Bruch \({@mya@}^2/({@mya@}*{@myb@})\) nicht ausreichend vereinfacht. Er kann zu \({@mya@}/{@myb@}\) gekürzt werden.]]></text>
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+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{a}{b} \cdot \frac{a^2}{a\,b} = \frac{a}{b} \cdot \frac{a \cdot a}{a\,b} = \frac{a \cdot a \cdot a}{a \cdot b \cdot b} = \frac{a^3}{a\,b^2}\)</p></p>]]></text>
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+ <deployedseed>806993602</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-db Multiplikation zweier Brüche mit Variablen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); fractions:[mya/myb, mya^2/(mya*myb)]; fractions:random_permutation(fractions); ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions with previously shortened the larger fraction*/ wa1:(2*mya)/(2*myb); /*wa2 means: naively summed fractions without previously shortening the larger fraction*/ wa2:(mya+myb^2)/(mya+myb*mya); /*wa3 means: correctly summed fractions instead of multiplied*/ wa3:fractions[1]+fractions[2]; /*wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied wa2:fractions[1]+fractions[2];*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} = {@ta1@}\)</text>
+ </questionnote>
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+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
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+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
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+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
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+ <falsescore>0</falsescore>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
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+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
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+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.]]></text>
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+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden. Du hast außerdem den Bruch \({@mya@}^2/({@mya@}*{@myb@})\) nicht ausreichend vereinfacht. Er kann zu \({@mya@}/{@myb@}\) gekürzt werden.]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{a}{b} \cdot \frac{a^2}{a\,b} = \frac{a}{b} \cdot \frac{a \cdot a}{a\,b} = \frac{a \cdot a \cdot a}{a \cdot b \cdot b} = \frac{a^3}{a\,b^2}\)</p></p>]]></text>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1501016569</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dc Multiplikation Bruch mit Zahlen, Bruch mit Variablen, Ganzzahl (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Wie kann man eine ganze Zahl als Bruch schreiben?</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
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+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8),3); nums:sort(nums); varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); factors:[nums[1], (mya*myb)/myc, nums[2]/nums[3]]; factors:random_permutation(factors); ta1:factors[1]*factors[2]*factors[3]; simp:false; exercise:factors[1]*factors[2]*factors[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} = {@ta1@}\)</text>
+ </questionnote>
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+ <assumepositive>0</assumepositive>
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+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
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+ <inversetrig>cos-1</inversetrig>
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+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
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+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
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+ <falsescore>0</falsescore>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>999</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Jede ganze Zahl kann als Bruch geschrieben werden, indem man sie durch 1 teilt. Beispiel: \(3 \cdot \frac{a\,b}{c} \cdot \frac{5}{6} = \frac{3}{1} \cdot \frac{a\,b}{c} \cdot \frac{5}{6}\)</p><p>\( = \frac{3 \cdot a \cdot b \cdot 5}{1 \cdot c \cdot 6} = \frac{15\,a\,b}{6\,c} = \frac{5\,a\,b}{2\,c}\)</p><p>Hinweis: Generellt gilt \(\cdot 1\) und \(:\,1\) geht immer.</p></p>]]></text>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1569886884</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dc Multiplikation Bruch mit Zahlen, Bruch mit Variablen, Ganzzahl (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Wie kann man eine ganze Zahl als Bruch schreiben?</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8),3); nums:sort(nums); varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); factors:[nums[1], (mya*myb)/myc, nums[2]/nums[3]]; factors:random_permutation(factors); ta1:factors[1]*factors[2]*factors[3]; simp:false; exercise:factors[1]*factors[2]*factors[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
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+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
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+ <text/>
+ </feedbackvariables>
+ <node>
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+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
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+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
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+ </falsefeedback>
+ </node>
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+ <answertest>AlgEquiv</answertest>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>999</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Jede ganze Zahl kann als Bruch geschrieben werden, indem man sie durch 1 teilt. Beispiel: \(3 \cdot \frac{a\,b}{c} \cdot \frac{5}{6} = \frac{3}{1} \cdot \frac{a\,b}{c} \cdot \frac{5}{6}\)</p><p>\( = \frac{3 \cdot a \cdot b \cdot 5}{1 \cdot c \cdot 6} = \frac{15\,a\,b}{6\,c} = \frac{5\,a\,b}{2\,c}\)</p><p>Hinweis: Generellt gilt \(\cdot 1\) und \(:\,1\) geht immer.</p></p>]]></text>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1980675582</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dc Multiplikation Bruch mit Zahlen, Bruch mit Variablen, Ganzzahl (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Wie kann man eine ganze Zahl als Bruch schreiben?</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8),3); nums:sort(nums); varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); factors:[nums[1], (mya*myb)/myc, nums[2]/nums[3]]; factors:random_permutation(factors); ta1:factors[1]*factors[2]*factors[3]; simp:false; exercise:factors[1]*factors[2]*factors[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
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+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
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+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>999</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Jede ganze Zahl kann als Bruch geschrieben werden, indem man sie durch 1 teilt. Beispiel: \(3 \cdot \frac{a\,b}{c} \cdot \frac{5}{6} = \frac{3}{1} \cdot \frac{a\,b}{c} \cdot \frac{5}{6}\)</p><p>\( = \frac{3 \cdot a \cdot b \cdot 5}{1 \cdot c \cdot 6} = \frac{15\,a\,b}{6\,c} = \frac{5\,a\,b}{2\,c}\)</p><p>Hinweis: Generellt gilt \(\cdot 1\) und \(:\,1\) geht immer.</p></p>]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1601683210</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dc Multiplikation Bruch mit Zahlen, Bruch mit Variablen, Ganzzahl (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Wie kann man eine ganze Zahl als Bruch schreiben?</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8),3); nums:sort(nums); varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); factors:[nums[1], (mya*myb)/myc, nums[2]/nums[3]]; factors:random_permutation(factors); ta1:factors[1]*factors[2]*factors[3]; simp:false; exercise:factors[1]*factors[2]*factors[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
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+ <insertstars>5</insertstars>
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+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
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+ <truepenalty/>
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+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
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+ <truescoremode>=</truescoremode>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Jede ganze Zahl kann als Bruch geschrieben werden, indem man sie durch 1 teilt. Beispiel: \(3 \cdot \frac{a\,b}{c} \cdot \frac{5}{6} = \frac{3}{1} \cdot \frac{a\,b}{c} \cdot \frac{5}{6}\)</p><p>\( = \frac{3 \cdot a \cdot b \cdot 5}{1 \cdot c \cdot 6} = \frac{15\,a\,b}{6\,c} = \frac{5\,a\,b}{2\,c}\)</p><p>Hinweis: Generellt gilt \(\cdot 1\) und \(:\,1\) geht immer.</p></p>]]></text>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>51348788</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dd Multiplikation zweier Brüche mit Termen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Summanden & Faktoren => Klammer!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:rand_selection(varlist, 2); nums:rand_selection(makelist(i+1,i,9), 6); fractions:[(nums[1]*myvars[1]+nums[2]*myvars[2])/(nums[3]*myvars[2]+nums[4]*myvars[1]), (-nums[5]*myvars[1])/(nums[6]+myvars[1])]; ta1:fractions[1]*fractions[2]; taalt:combine(expand(ta1)); /*wa1 means: the multiplication of the numerator was done with only one summand of the first fraction’s numerator (the second one)*/ wa1:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(denom(fractions[1])*denom(fractions[2])); /*old_wa2 means the same as wa1 but with the first fraction numerator’s second summand*/ /*old_wa2: (nums[1]*myvars[1]*num(fractions[2])+nums[2]*myvars[2])/(denom(fractions[1])*denom(fractions[2]));*/ /*wa2 means the same as wa1 but with the denominators, so no brackets: first summand of second fraction is multiplied with last summand of first fraction*/ wa2:(num(fractions[1])*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]); /*wa3 is the combination of wa1 and wa2*/ wa3:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}= {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
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+ <mustverify>1</mustverify>
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+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Nenner richtig multipliziert, doch du hast den Faktor im Zähler des zweiten Bruches nur mit dem zweiten Summanden des Zählers im ersten Bruch multipliziert. Das heißt bei der Multiplikation der Zähler musst du Klammern um die Summe setzen und jeden Summanden des ersten Zählers mit dem Faktor des anderen Zählers multiplizieren.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Zähler richtig multipliziert, hast jedoch im Nenner nicht beachtet, dass Summen als Ganzes multipliziert werden. Das heißt bei der Multiplikation der Nenner musst du Klammern um die Summen setzen und jeden Summanden des einen Nenners mit jedem Summanden des anderen Nenners multiplizieren.]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>5</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>5</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
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+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-6-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Summen nicht als Ganzes multipliziert. Das betrifft eine Summe im Zähler und die Summen im Nenner. Du musst jeweils Klammern setzen, damit jeder Summand mit jedem anderen Summanden multipliziert wird. ]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
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+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-6-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
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+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{4\,x+10\,y}{5\,y+2\,x} \cdot \frac{-4\,x}{3+x} = \)\(\frac{\boldsymbol{(4\,x+10\,y)} \cdot -4\,x}{\boldsymbol{(5\,y+2\,x)} \cdot \boldsymbol{(3+x)}} = \dots\)</p></p>]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>783029466</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dd Multiplikation zweier Brüche mit Termen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Summanden & Faktoren => Klammer!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:rand_selection(varlist, 2); nums:rand_selection(makelist(i+1,i,9), 6); fractions:[(nums[1]*myvars[1]+nums[2]*myvars[2])/(nums[3]*myvars[2]+nums[4]*myvars[1]), (-nums[5]*myvars[1])/(nums[6]+myvars[1])]; ta1:fractions[1]*fractions[2]; taalt:combine(expand(ta1)); /*wa1 means: the multiplication of the numerator was done with only one summand of the first fraction’s numerator (the second one)*/ wa1:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(denom(fractions[1])*denom(fractions[2])); /*old_wa2 means the same as wa1 but with the first fraction numerator’s second summand*/ /*old_wa2: (nums[1]*myvars[1]*num(fractions[2])+nums[2]*myvars[2])/(denom(fractions[1])*denom(fractions[2]));*/ /*wa2 means the same as wa1 but with the denominators, so no brackets: first summand of second fraction is multiplied with last summand of first fraction*/ wa2:(num(fractions[1])*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]); /*wa3 is the combination of wa1 and wa2*/ wa3:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}= {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
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+ <name>ans1</name>
+ <type>algebraic</type>
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+ <boxsize>15</boxsize>
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+ <insertstars>5</insertstars>
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+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
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+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Nenner richtig multipliziert, doch du hast den Faktor im Zähler des zweiten Bruches nur mit dem zweiten Summanden des Zählers im ersten Bruch multipliziert. Das heißt bei der Multiplikation der Zähler musst du Klammern um die Summe setzen und jeden Summanden des ersten Zählers mit dem Faktor des anderen Zählers multiplizieren.]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Zähler richtig multipliziert, hast jedoch im Nenner nicht beachtet, dass Summen als Ganzes multipliziert werden. Das heißt bei der Multiplikation der Nenner musst du Klammern um die Summen setzen und jeden Summanden des einen Nenners mit jedem Summanden des anderen Nenners multiplizieren.]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>5</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>5</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-6-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Summen nicht als Ganzes multipliziert. Das betrifft eine Summe im Zähler und die Summen im Nenner. Du musst jeweils Klammern setzen, damit jeder Summand mit jedem anderen Summanden multipliziert wird. ]]></text>
+</truefeedback>
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+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-6-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{4\,x+10\,y}{5\,y+2\,x} \cdot \frac{-4\,x}{3+x} = \)\(\frac{\boldsymbol{(4\,x+10\,y)} \cdot -4\,x}{\boldsymbol{(5\,y+2\,x)} \cdot \boldsymbol{(3+x)}} = \dots\)</p></p>]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1177445020</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dd Multiplikation zweier Brüche mit Termen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Summanden & Faktoren => Klammer!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:rand_selection(varlist, 2); nums:rand_selection(makelist(i+1,i,9), 6); fractions:[(nums[1]*myvars[1]+nums[2]*myvars[2])/(nums[3]*myvars[2]+nums[4]*myvars[1]), (-nums[5]*myvars[1])/(nums[6]+myvars[1])]; ta1:fractions[1]*fractions[2]; taalt:combine(expand(ta1)); /*wa1 means: the multiplication of the numerator was done with only one summand of the first fraction’s numerator (the second one)*/ wa1:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(denom(fractions[1])*denom(fractions[2])); /*old_wa2 means the same as wa1 but with the first fraction numerator’s second summand*/ /*old_wa2: (nums[1]*myvars[1]*num(fractions[2])+nums[2]*myvars[2])/(denom(fractions[1])*denom(fractions[2]));*/ /*wa2 means the same as wa1 but with the denominators, so no brackets: first summand of second fraction is multiplied with last summand of first fraction*/ wa2:(num(fractions[1])*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]); /*wa3 is the combination of wa1 and wa2*/ wa3:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}= {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
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+ <insertstars>5</insertstars>
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+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Nenner richtig multipliziert, doch du hast den Faktor im Zähler des zweiten Bruches nur mit dem zweiten Summanden des Zählers im ersten Bruch multipliziert. Das heißt bei der Multiplikation der Zähler musst du Klammern um die Summe setzen und jeden Summanden des ersten Zählers mit dem Faktor des anderen Zählers multiplizieren.]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Zähler richtig multipliziert, hast jedoch im Nenner nicht beachtet, dass Summen als Ganzes multipliziert werden. Das heißt bei der Multiplikation der Nenner musst du Klammern um die Summen setzen und jeden Summanden des einen Nenners mit jedem Summanden des anderen Nenners multiplizieren.]]></text>
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+<falsepenalty/>
+<falsenextnode>5</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>5</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-6-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Summen nicht als Ganzes multipliziert. Das betrifft eine Summe im Zähler und die Summen im Nenner. Du musst jeweils Klammern setzen, damit jeder Summand mit jedem anderen Summanden multipliziert wird. ]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-6-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
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+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{4\,x+10\,y}{5\,y+2\,x} \cdot \frac{-4\,x}{3+x} = \)\(\frac{\boldsymbol{(4\,x+10\,y)} \cdot -4\,x}{\boldsymbol{(5\,y+2\,x)} \cdot \boldsymbol{(3+x)}} = \dots\)</p></p>]]></text>
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+<falsepenalty/>
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+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1009895582</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dd Multiplikation zweier Brüche mit Termen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Summanden & Faktoren => Klammer!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:rand_selection(varlist, 2); nums:rand_selection(makelist(i+1,i,9), 6); fractions:[(nums[1]*myvars[1]+nums[2]*myvars[2])/(nums[3]*myvars[2]+nums[4]*myvars[1]), (-nums[5]*myvars[1])/(nums[6]+myvars[1])]; ta1:fractions[1]*fractions[2]; taalt:combine(expand(ta1)); /*wa1 means: the multiplication of the numerator was done with only one summand of the first fraction’s numerator (the second one)*/ wa1:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(denom(fractions[1])*denom(fractions[2])); /*old_wa2 means the same as wa1 but with the first fraction numerator’s second summand*/ /*old_wa2: (nums[1]*myvars[1]*num(fractions[2])+nums[2]*myvars[2])/(denom(fractions[1])*denom(fractions[2]));*/ /*wa2 means the same as wa1 but with the denominators, so no brackets: first summand of second fraction is multiplied with last summand of first fraction*/ wa2:(num(fractions[1])*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]); /*wa3 is the combination of wa1 and wa2*/ wa3:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}= {@ta1@}\)</text>
+ </questionnote>
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+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
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+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Nenner richtig multipliziert, doch du hast den Faktor im Zähler des zweiten Bruches nur mit dem zweiten Summanden des Zählers im ersten Bruch multipliziert. Das heißt bei der Multiplikation der Zähler musst du Klammern um die Summe setzen und jeden Summanden des ersten Zählers mit dem Faktor des anderen Zählers multiplizieren.]]></text>
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+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
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+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Zähler richtig multipliziert, hast jedoch im Nenner nicht beachtet, dass Summen als Ganzes multipliziert werden. Das heißt bei der Multiplikation der Nenner musst du Klammern um die Summen setzen und jeden Summanden des einen Nenners mit jedem Summanden des anderen Nenners multiplizieren.]]></text>
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+<name>5</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-6-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Summen nicht als Ganzes multipliziert. Das betrifft eine Summe im Zähler und die Summen im Nenner. Du musst jeweils Klammern setzen, damit jeder Summand mit jedem anderen Summanden multipliziert wird. ]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-6-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{4\,x+10\,y}{5\,y+2\,x} \cdot \frac{-4\,x}{3+x} = \)\(\frac{\boldsymbol{(4\,x+10\,y)} \cdot -4\,x}{\boldsymbol{(5\,y+2\,x)} \cdot \boldsymbol{(3+x)}} = \dots\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1167689465</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-de Einfacher Doppelbruch (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8), 4); nums:sort(nums); ta1:((nums[1])/(nums[4]))/((nums[2])/(nums[3])); /*wa1 means: multiplied fractions instead of division*/ wa1:((nums[1])/(nums[4]))*((nums[2])/(nums[3])); /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:((nums[4])/(nums[1]))*((nums[2])/(nums[3]));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>352990161</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-de Einfacher Doppelbruch (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8), 4); nums:sort(nums); ta1:((nums[1])/(nums[4]))/((nums[2])/(nums[3])); /*wa1 means: multiplied fractions instead of division*/ wa1:((nums[1])/(nums[4]))*((nums[2])/(nums[3])); /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:((nums[4])/(nums[1]))*((nums[2])/(nums[3]));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>467670994</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-de Einfacher Doppelbruch (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8), 4); nums:sort(nums); ta1:((nums[1])/(nums[4]))/((nums[2])/(nums[3])); /*wa1 means: multiplied fractions instead of division*/ wa1:((nums[1])/(nums[4]))*((nums[2])/(nums[3])); /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:((nums[4])/(nums[1]))*((nums[2])/(nums[3]));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
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+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1747402747</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-de Einfacher Doppelbruch (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8), 4); nums:sort(nums); ta1:((nums[1])/(nums[4]))/((nums[2])/(nums[3])); /*wa1 means: multiplied fractions instead of division*/ wa1:((nums[1])/(nums[4]))*((nums[2])/(nums[3])); /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:((nums[4])/(nums[1]))*((nums[2])/(nums[3]));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>2135608811</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-df Bruch und Geteilt-Rechnung (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@dividend@}:{@divisor@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Achtung: Auch ein Doppelbruch ;)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>power:rand_with_step(2,4,1); myvars:rand_selection([a,b,c,x,y,z],2); dividend:myvars[1]/myvars[2]; num:rand_with_step(1,5,1); divisor:(num-myvars[1])/(myvars[2]^power); ta1: dividend/divisor; /*wa1 means: multiplied fractions instead of division*/ wa1:dividend*divisor; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:dividend^(-1)*divisor; /*wa3 means: didn’t consider to multiply the denominator of the first fraction with the sum of the second fraction’s numerator as a whole*/ wa3:(num(dividend)*denom(divisor))/(myvars[2]*num-myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@dividend@}:{@divisor@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast den richtigen Kehrwert gebildet um die Brüche dann zu multiplizieren, jedoch hast du dann die Klammersetzung bei der Mutliplikation nicht beachtet.</p><p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{x}{a} : \frac{1-x}{a^2} = \frac{x}{a} \cdot \frac{a^2}{1-x}\)\(= \frac{x \cdot a^2}{a \cdot \boldsymbol{(1-x)}} = \dots\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: \(\boldsymbol{:}\) ist dasselbe wir ein Doppelbruchstrich.</p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p></p>]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>68495326</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-df Bruch und Geteilt-Rechnung (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@dividend@}:{@divisor@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Achtung: Auch ein Doppelbruch ;)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>power:rand_with_step(2,4,1); myvars:rand_selection([a,b,c,x,y,z],2); dividend:myvars[1]/myvars[2]; num:rand_with_step(1,5,1); divisor:(num-myvars[1])/(myvars[2]^power); ta1: dividend/divisor; /*wa1 means: multiplied fractions instead of division*/ wa1:dividend*divisor; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:dividend^(-1)*divisor; /*wa3 means: didn’t consider to multiply the denominator of the first fraction with the sum of the second fraction’s numerator as a whole*/ wa3:(num(dividend)*denom(divisor))/(myvars[2]*num-myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@dividend@}:{@divisor@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
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+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
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+ <node>
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+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
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+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
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+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
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+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast den richtigen Kehrwert gebildet um die Brüche dann zu multiplizieren, jedoch hast du dann die Klammersetzung bei der Mutliplikation nicht beachtet.</p><p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{x}{a} : \frac{1-x}{a^2} = \frac{x}{a} \cdot \frac{a^2}{1-x}\)\(= \frac{x \cdot a^2}{a \cdot \boldsymbol{(1-x)}} = \dots\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: \(\boldsymbol{:}\) ist dasselbe wir ein Doppelbruchstrich.</p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p></p>]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>83279259</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-df Bruch und Geteilt-Rechnung (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@dividend@}:{@divisor@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Achtung: Auch ein Doppelbruch ;)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>power:rand_with_step(2,4,1); myvars:rand_selection([a,b,c,x,y,z],2); dividend:myvars[1]/myvars[2]; num:rand_with_step(1,5,1); divisor:(num-myvars[1])/(myvars[2]^power); ta1: dividend/divisor; /*wa1 means: multiplied fractions instead of division*/ wa1:dividend*divisor; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:dividend^(-1)*divisor; /*wa3 means: didn’t consider to multiply the denominator of the first fraction with the sum of the second fraction’s numerator as a whole*/ wa3:(num(dividend)*denom(divisor))/(myvars[2]*num-myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@dividend@}:{@divisor@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
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+ <variantsselectionseed/>
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+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
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+ <insertstars>5</insertstars>
+ <syntaxhint/>
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+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
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+ <mustverify>1</mustverify>
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+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
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+ <node>
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+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
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+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
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+ <tans>ta1</tans>
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+ <truepenalty/>
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+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
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+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
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+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast den richtigen Kehrwert gebildet um die Brüche dann zu multiplizieren, jedoch hast du dann die Klammersetzung bei der Mutliplikation nicht beachtet.</p><p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{x}{a} : \frac{1-x}{a^2} = \frac{x}{a} \cdot \frac{a^2}{1-x}\)\(= \frac{x \cdot a^2}{a \cdot \boldsymbol{(1-x)}} = \dots\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: \(\boldsymbol{:}\) ist dasselbe wir ein Doppelbruchstrich.</p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p></p>]]></text>
+</truefeedback>
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+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1848999895</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-df Bruch und Geteilt-Rechnung (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@dividend@}:{@divisor@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Achtung: Auch ein Doppelbruch ;)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>power:rand_with_step(2,4,1); myvars:rand_selection([a,b,c,x,y,z],2); dividend:myvars[1]/myvars[2]; num:rand_with_step(1,5,1); divisor:(num-myvars[1])/(myvars[2]^power); ta1: dividend/divisor; /*wa1 means: multiplied fractions instead of division*/ wa1:dividend*divisor; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:dividend^(-1)*divisor; /*wa3 means: didn’t consider to multiply the denominator of the first fraction with the sum of the second fraction’s numerator as a whole*/ wa3:(num(dividend)*denom(divisor))/(myvars[2]*num-myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@dividend@}:{@divisor@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
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+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
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+ <node>
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+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
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+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
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+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
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+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
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+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
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+<falseanswernote>prt1-4-F</falseanswernote>
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+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast den richtigen Kehrwert gebildet um die Brüche dann zu multiplizieren, jedoch hast du dann die Klammersetzung bei der Mutliplikation nicht beachtet.</p><p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{x}{a} : \frac{1-x}{a^2} = \frac{x}{a} \cdot \frac{a^2}{1-x}\)\(= \frac{x \cdot a^2}{a \cdot \boldsymbol{(1-x)}} = \dots\)</p>]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: \(\boldsymbol{:}\) ist dasselbe wir ein Doppelbruchstrich.</p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p></p>]]></text>
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+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1656521999</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dg Doppelbruch mit Zahlen und Variablen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:rand_selection(makelist(i+1,i,3),2); nums:rand_selection(makelist(i+1,i,4),2); myvars:rand_selection([a,b,c,x,y,z],2); fractions:[nums[1]/myvars[1]^powers[1], (nums[2]*myvars[2]^powers[2])/myvars[1]]; fractions:random_permutation(fractions); ta1:fractions[1]/fractions[2]; /*wa1 means: multiplied fractions instead of division*/ wa1:fractions[1]*fractions[2]; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:fractions[1]^(-1)*fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
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+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
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+ <node>
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+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
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+ <falsescore>0</falsescore>
+ <falsepenalty/>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
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+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
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+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
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+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
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+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
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+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{2}{a^2}}{\frac{3\,b^2}{a}} = \frac{2}{a^2} \cdot \frac{a}{3\,b^2} = \frac{2\,a}{3\,a^2\,b^2}\)</p></p>]]></text>
+</truefeedback>
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+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1783639635</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dg Doppelbruch mit Zahlen und Variablen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:rand_selection(makelist(i+1,i,3),2); nums:rand_selection(makelist(i+1,i,4),2); myvars:rand_selection([a,b,c,x,y,z],2); fractions:[nums[1]/myvars[1]^powers[1], (nums[2]*myvars[2]^powers[2])/myvars[1]]; fractions:random_permutation(fractions); ta1:fractions[1]/fractions[2]; /*wa1 means: multiplied fractions instead of division*/ wa1:fractions[1]*fractions[2]; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:fractions[1]^(-1)*fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
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+ <boxsize>15</boxsize>
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+ <options/>
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+ <prt>
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+ <truepenalty/>
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+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
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+ <falsescore>0</falsescore>
+ <falsepenalty/>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
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+ <truepenalty/>
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+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
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+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
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+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{2}{a^2}}{\frac{3\,b^2}{a}} = \frac{2}{a^2} \cdot \frac{a}{3\,b^2} = \frac{2\,a}{3\,a^2\,b^2}\)</p></p>]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>863915904</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dg Doppelbruch mit Zahlen und Variablen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:rand_selection(makelist(i+1,i,3),2); nums:rand_selection(makelist(i+1,i,4),2); myvars:rand_selection([a,b,c,x,y,z],2); fractions:[nums[1]/myvars[1]^powers[1], (nums[2]*myvars[2]^powers[2])/myvars[1]]; fractions:random_permutation(fractions); ta1:fractions[1]/fractions[2]; /*wa1 means: multiplied fractions instead of division*/ wa1:fractions[1]*fractions[2]; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:fractions[1]^(-1)*fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{2}{a^2}}{\frac{3\,b^2}{a}} = \frac{2}{a^2} \cdot \frac{a}{3\,b^2} = \frac{2\,a}{3\,a^2\,b^2}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>446314797</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dg Doppelbruch mit Zahlen und Variablen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:rand_selection(makelist(i+1,i,3),2); nums:rand_selection(makelist(i+1,i,4),2); myvars:rand_selection([a,b,c,x,y,z],2); fractions:[nums[1]/myvars[1]^powers[1], (nums[2]*myvars[2]^powers[2])/myvars[1]]; fractions:random_permutation(fractions); ta1:fractions[1]/fractions[2]; /*wa1 means: multiplied fractions instead of division*/ wa1:fractions[1]*fractions[2]; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:fractions[1]^(-1)*fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{2}{a^2}}{\frac{3\,b^2}{a}} = \frac{2}{a^2} \cdot \frac{a}{3\,b^2} = \frac{2\,a}{3\,a^2\,b^2}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1562297660</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dh Doppelbruch mit Termen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8), 3); nums:sort(nums); myvars:rand_selection([a,b,c,x,y,z],2); terms:[nums[1]*((1-myvars[1])/myvars[2]), (nums[2]/nums[3])*(myvars[2]^2/myvars[1])]; /*terms:random_permutation(terms);*/ ta1:terms[1]/terms[2]; taalt:combine(expand(ta1)); /*wa1 means: didn't consider to multiple first factor in the numerator with both summands of the fraction's numerator*/ wa1:((nums[1]*1-myvars[1])/myvars[2])/terms[2]; wa2:terms[1]*terms[2]; wa3:terms[1]^(-1)*terms[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Beim Multiplizieren des Faktors {@nums[1]@} und des Bruchs \(\frac{1-{@myvars[1]@}}{{@myvars[2]@}}\) im Zähler des Doppelbruchs musst du beachten, dass Summen als Ganzes multipliziert werden.</p><p>Beispiel: \(5 \cdot \frac{1-a}{b} = \frac{5 \cdot \boldsymbol{(1-a)}}{b} = \dots\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>5</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>5</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-6-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-6-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Lösungsweg für eine Beispielaufgabe:</p><p>\(\large\frac{5 \cdot \frac{1-a}{b}}{\frac{1}{3} \cdot \frac{b^2}{a}}\)\(\large = \frac{\frac{5 \cdot \boldsymbol{(1-a)}}{b}}{\frac{b^2}{3\,a}} = \frac{5 - 5\,a}{b} \cdot \frac{3\,a}{b^2}\)</p><p>\(\large = \frac{3\,a \cdot \boldsymbol{(5-5\,a)}}{b \cdot b^2} = \frac{15\,a - 15\,a^2}{b^3}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>611281053</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dh Doppelbruch mit Termen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8), 3); nums:sort(nums); myvars:rand_selection([a,b,c,x,y,z],2); terms:[nums[1]*((1-myvars[1])/myvars[2]), (nums[2]/nums[3])*(myvars[2]^2/myvars[1])]; /*terms:random_permutation(terms);*/ ta1:terms[1]/terms[2]; taalt:combine(expand(ta1)); /*wa1 means: didn't consider to multiple first factor in the numerator with both summands of the fraction's numerator*/ wa1:((nums[1]*1-myvars[1])/myvars[2])/terms[2]; wa2:terms[1]*terms[2]; wa3:terms[1]^(-1)*terms[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Beim Multiplizieren des Faktors {@nums[1]@} und des Bruchs \(\frac{1-{@myvars[1]@}}{{@myvars[2]@}}\) im Zähler des Doppelbruchs musst du beachten, dass Summen als Ganzes multipliziert werden.</p><p>Beispiel: \(5 \cdot \frac{1-a}{b} = \frac{5 \cdot \boldsymbol{(1-a)}}{b} = \dots\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>5</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>5</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-6-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-6-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Lösungsweg für eine Beispielaufgabe:</p><p>\(\large\frac{5 \cdot \frac{1-a}{b}}{\frac{1}{3} \cdot \frac{b^2}{a}}\)\(\large = \frac{\frac{5 \cdot \boldsymbol{(1-a)}}{b}}{\frac{b^2}{3\,a}} = \frac{5 - 5\,a}{b} \cdot \frac{3\,a}{b^2}\)</p><p>\(\large = \frac{3\,a \cdot \boldsymbol{(5-5\,a)}}{b \cdot b^2} = \frac{15\,a - 15\,a^2}{b^3}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>439766047</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dh Doppelbruch mit Termen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8), 3); nums:sort(nums); myvars:rand_selection([a,b,c,x,y,z],2); terms:[nums[1]*((1-myvars[1])/myvars[2]), (nums[2]/nums[3])*(myvars[2]^2/myvars[1])]; /*terms:random_permutation(terms);*/ ta1:terms[1]/terms[2]; taalt:combine(expand(ta1)); /*wa1 means: didn't consider to multiple first factor in the numerator with both summands of the fraction's numerator*/ wa1:((nums[1]*1-myvars[1])/myvars[2])/terms[2]; wa2:terms[1]*terms[2]; wa3:terms[1]^(-1)*terms[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Beim Multiplizieren des Faktors {@nums[1]@} und des Bruchs \(\frac{1-{@myvars[1]@}}{{@myvars[2]@}}\) im Zähler des Doppelbruchs musst du beachten, dass Summen als Ganzes multipliziert werden.</p><p>Beispiel: \(5 \cdot \frac{1-a}{b} = \frac{5 \cdot \boldsymbol{(1-a)}}{b} = \dots\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>5</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>5</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-6-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-6-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Lösungsweg für eine Beispielaufgabe:</p><p>\(\large\frac{5 \cdot \frac{1-a}{b}}{\frac{1}{3} \cdot \frac{b^2}{a}}\)\(\large = \frac{\frac{5 \cdot \boldsymbol{(1-a)}}{b}}{\frac{b^2}{3\,a}} = \frac{5 - 5\,a}{b} \cdot \frac{3\,a}{b^2}\)</p><p>\(\large = \frac{3\,a \cdot \boldsymbol{(5-5\,a)}}{b \cdot b^2} = \frac{15\,a - 15\,a^2}{b^3}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>725695831</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dh Doppelbruch mit Termen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8), 3); nums:sort(nums); myvars:rand_selection([a,b,c,x,y,z],2); terms:[nums[1]*((1-myvars[1])/myvars[2]), (nums[2]/nums[3])*(myvars[2]^2/myvars[1])]; /*terms:random_permutation(terms);*/ ta1:terms[1]/terms[2]; taalt:combine(expand(ta1)); /*wa1 means: didn't consider to multiple first factor in the numerator with both summands of the fraction's numerator*/ wa1:((nums[1]*1-myvars[1])/myvars[2])/terms[2]; wa2:terms[1]*terms[2]; wa3:terms[1]^(-1)*terms[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Beim Multiplizieren des Faktors {@nums[1]@} und des Bruchs \(\frac{1-{@myvars[1]@}}{{@myvars[2]@}}\) im Zähler des Doppelbruchs musst du beachten, dass Summen als Ganzes multipliziert werden.</p><p>Beispiel: \(5 \cdot \frac{1-a}{b} = \frac{5 \cdot \boldsymbol{(1-a)}}{b} = \dots\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>5</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>5</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-6-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-6-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Lösungsweg für eine Beispielaufgabe:</p><p>\(\large\frac{5 \cdot \frac{1-a}{b}}{\frac{1}{3} \cdot \frac{b^2}{a}}\)\(\large = \frac{\frac{5 \cdot \boldsymbol{(1-a)}}{b}}{\frac{b^2}{3\,a}} = \frac{5 - 5\,a}{b} \cdot \frac{3\,a}{b^2}\)</p><p>\(\large = \frac{3\,a \cdot \boldsymbol{(5-5\,a)}}{b \cdot b^2} = \frac{15\,a - 15\,a^2}{b^3}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1029360039</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ea Bruchrechnung Kombination I (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbrüche und Summanden => Punkt-vor-Strich-Rechnung</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(2,4,1); nums_real_frac:sort(rand_selection(makelist(i,i,9),4)); nums_unreal_frac:sort(rand_selection(makelist(i+3,i,7),6)); main_summand:((nums_real_frac[1])/(nums_real_frac[4]))/((nums_real_frac[2])/(nums_real_frac[3])); summands:[int*(nums_unreal_frac[6]/nums_unreal_frac[1]), ((nums_unreal_frac[5])/(nums_unreal_frac[2]))/((nums_unreal_frac[4])/(nums_unreal_frac[3]))]; ta1:main_summand+summands[1]-summands[2]; wa1:(main_summand+int)*summands[1]/int-summands[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast offensichtlich die Punkt-vor-Strich-Regel nicht beachtet.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6} = \frac{\frac{5}{6}}{\frac{1}{3}}+(2 \cdot \frac{9}{6}) \ne (\frac{\frac{5}{6}}{\frac{1}{3}}+2) \cdot \frac{9}{6}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Jeden Summanden einzeln betrachten und ausrechnen: Doppelbrüche auflösen und zusammenfassen.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6}-\frac{\frac{13}{4}}{\frac{6}{5}} = \frac{5}{6} \cdot \frac{3}{1}+\frac{2}{1} \cdot \frac{9}{6}-\frac{13}{5} \cdot \frac{5}{6}\)</p><p>\(= (\frac{5}{6\mkern-5mu/^2} \cdot \frac{3\mkern-5mu/^1}{1})+(\frac{2\mkern-5mu/^1}{1} \cdot \frac{9}{6\mkern-5mu/^2})-(\frac{13}{5\mkern-5mu/^1} \cdot \frac{5\mkern-5mu/^1}{6})\)</p><p>\(= \frac{5}{2} + \frac{9}{2} - \frac{13}{6} = \frac{5 \cdot 3}{2 \cdot 3} + \frac{9 \cdot 3}{2 \cdot 3} - \frac{13}{6} = \frac{15}{6} + \frac{27}{6} - \frac{13}{6}\)</p><p>\(= \frac{15+27+13}{6} = \frac{55}{6}\)<\p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>2022519868</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ea Bruchrechnung Kombination I (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbrüche und Summanden => Punkt-vor-Strich-Rechnung</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(2,4,1); nums_real_frac:sort(rand_selection(makelist(i,i,9),4)); nums_unreal_frac:sort(rand_selection(makelist(i+3,i,7),6)); main_summand:((nums_real_frac[1])/(nums_real_frac[4]))/((nums_real_frac[2])/(nums_real_frac[3])); summands:[int*(nums_unreal_frac[6]/nums_unreal_frac[1]), ((nums_unreal_frac[5])/(nums_unreal_frac[2]))/((nums_unreal_frac[4])/(nums_unreal_frac[3]))]; ta1:main_summand+summands[1]-summands[2]; wa1:(main_summand+int)*summands[1]/int-summands[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast offensichtlich die Punkt-vor-Strich-Regel nicht beachtet.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6} = \frac{\frac{5}{6}}{\frac{1}{3}}+(2 \cdot \frac{9}{6}) \ne (\frac{\frac{5}{6}}{\frac{1}{3}}+2) \cdot \frac{9}{6}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Jeden Summanden einzeln betrachten und ausrechnen: Doppelbrüche auflösen und zusammenfassen.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6}-\frac{\frac{13}{4}}{\frac{6}{5}} = \frac{5}{6} \cdot \frac{3}{1}+\frac{2}{1} \cdot \frac{9}{6}-\frac{13}{5} \cdot \frac{5}{6}\)</p><p>\(= (\frac{5}{6\mkern-5mu/^2} \cdot \frac{3\mkern-5mu/^1}{1})+(\frac{2\mkern-5mu/^1}{1} \cdot \frac{9}{6\mkern-5mu/^2})-(\frac{13}{5\mkern-5mu/^1} \cdot \frac{5\mkern-5mu/^1}{6})\)</p><p>\(= \frac{5}{2} + \frac{9}{2} - \frac{13}{6} = \frac{5 \cdot 3}{2 \cdot 3} + \frac{9 \cdot 3}{2 \cdot 3} - \frac{13}{6} = \frac{15}{6} + \frac{27}{6} - \frac{13}{6}\)</p><p>\(= \frac{15+27+13}{6} = \frac{55}{6}\)<\p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>2007714528</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ea Bruchrechnung Kombination I (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbrüche und Summanden => Punkt-vor-Strich-Rechnung</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(2,4,1); nums_real_frac:sort(rand_selection(makelist(i,i,9),4)); nums_unreal_frac:sort(rand_selection(makelist(i+3,i,7),6)); main_summand:((nums_real_frac[1])/(nums_real_frac[4]))/((nums_real_frac[2])/(nums_real_frac[3])); summands:[int*(nums_unreal_frac[6]/nums_unreal_frac[1]), ((nums_unreal_frac[5])/(nums_unreal_frac[2]))/((nums_unreal_frac[4])/(nums_unreal_frac[3]))]; ta1:main_summand+summands[1]-summands[2]; wa1:(main_summand+int)*summands[1]/int-summands[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast offensichtlich die Punkt-vor-Strich-Regel nicht beachtet.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6} = \frac{\frac{5}{6}}{\frac{1}{3}}+(2 \cdot \frac{9}{6}) \ne (\frac{\frac{5}{6}}{\frac{1}{3}}+2) \cdot \frac{9}{6}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Jeden Summanden einzeln betrachten und ausrechnen: Doppelbrüche auflösen und zusammenfassen.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6}-\frac{\frac{13}{4}}{\frac{6}{5}} = \frac{5}{6} \cdot \frac{3}{1}+\frac{2}{1} \cdot \frac{9}{6}-\frac{13}{5} \cdot \frac{5}{6}\)</p><p>\(= (\frac{5}{6\mkern-5mu/^2} \cdot \frac{3\mkern-5mu/^1}{1})+(\frac{2\mkern-5mu/^1}{1} \cdot \frac{9}{6\mkern-5mu/^2})-(\frac{13}{5\mkern-5mu/^1} \cdot \frac{5\mkern-5mu/^1}{6})\)</p><p>\(= \frac{5}{2} + \frac{9}{2} - \frac{13}{6} = \frac{5 \cdot 3}{2 \cdot 3} + \frac{9 \cdot 3}{2 \cdot 3} - \frac{13}{6} = \frac{15}{6} + \frac{27}{6} - \frac{13}{6}\)</p><p>\(= \frac{15+27+13}{6} = \frac{55}{6}\)<\p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1652468809</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ea Bruchrechnung Kombination I (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbrüche und Summanden => Punkt-vor-Strich-Rechnung</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(2,4,1); nums_real_frac:sort(rand_selection(makelist(i,i,9),4)); nums_unreal_frac:sort(rand_selection(makelist(i+3,i,7),6)); main_summand:((nums_real_frac[1])/(nums_real_frac[4]))/((nums_real_frac[2])/(nums_real_frac[3])); summands:[int*(nums_unreal_frac[6]/nums_unreal_frac[1]), ((nums_unreal_frac[5])/(nums_unreal_frac[2]))/((nums_unreal_frac[4])/(nums_unreal_frac[3]))]; ta1:main_summand+summands[1]-summands[2]; wa1:(main_summand+int)*summands[1]/int-summands[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast offensichtlich die Punkt-vor-Strich-Regel nicht beachtet.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6} = \frac{\frac{5}{6}}{\frac{1}{3}}+(2 \cdot \frac{9}{6}) \ne (\frac{\frac{5}{6}}{\frac{1}{3}}+2) \cdot \frac{9}{6}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Jeden Summanden einzeln betrachten und ausrechnen: Doppelbrüche auflösen und zusammenfassen.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6}-\frac{\frac{13}{4}}{\frac{6}{5}} = \frac{5}{6} \cdot \frac{3}{1}+\frac{2}{1} \cdot \frac{9}{6}-\frac{13}{5} \cdot \frac{5}{6}\)</p><p>\(= (\frac{5}{6\mkern-5mu/^2} \cdot \frac{3\mkern-5mu/^1}{1})+(\frac{2\mkern-5mu/^1}{1} \cdot \frac{9}{6\mkern-5mu/^2})-(\frac{13}{5\mkern-5mu/^1} \cdot \frac{5\mkern-5mu/^1}{6})\)</p><p>\(= \frac{5}{2} + \frac{9}{2} - \frac{13}{6} = \frac{5 \cdot 3}{2 \cdot 3} + \frac{9 \cdot 3}{2 \cdot 3} - \frac{13}{6} = \frac{15}{6} + \frac{27}{6} - \frac{13}{6}\)</p><p>\(= \frac{15+27+13}{6} = \frac{55}{6}\)<\p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1890021691</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-eb Bruchrechnung Kombination II (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Sorgfältig ausmultiplizieren</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(3,7,1); nums:sort(rand_selection(makelist(i,i,9),6)); factors:[int, (nums[1]/nums[6]+nums[2]/nums[5]), (1-nums[3]/nums[4])]; ta1:factors[1]*factors[2]*factors[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})= {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>999</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Hier hast du zwei Möglichkeiten: Alles sauber ausmultiplizieren oder vor dem Multiplizieren die Klammern ausrechnen (Empfehlung!)</p><p>Beispiel: \(6 \cdot (\frac{3}{4}+\frac{1}{8}) \cdot (1-\frac{1}{4}) = 6 \cdot (\frac{3 \cdot 2}{4 \cdot 2}+\frac{1}{8}) \cdot (\frac{1 \cdot 4}{1 \cdot 4}-\frac{1}{4})\) </p><p>\(= 6 \cdot (\frac{6}{8}+\frac{1}{8}) \cdot (\frac{4}{4}-\frac{1}{4}) = 6 \cdot (\frac{7}{8}) \cdot (\frac{3}{4})\)</p><p>\( = \frac{6}{1} \cdot \frac{7}{8} \cdot \frac{3}{4} = \frac{6\mkern-5mu/^3 \cdot 7 \cdot 3}{1 \cdot 8\mkern-5mu/^4 \cdot 4} = \frac{63}{16}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>382901616</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-eb Bruchrechnung Kombination II (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Sorgfältig ausmultiplizieren</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(3,7,1); nums:sort(rand_selection(makelist(i,i,9),6)); factors:[int, (nums[1]/nums[6]+nums[2]/nums[5]), (1-nums[3]/nums[4])]; ta1:factors[1]*factors[2]*factors[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})= {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>999</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Hier hast du zwei Möglichkeiten: Alles sauber ausmultiplizieren oder vor dem Multiplizieren die Klammern ausrechnen (Empfehlung!)</p><p>Beispiel: \(6 \cdot (\frac{3}{4}+\frac{1}{8}) \cdot (1-\frac{1}{4}) = 6 \cdot (\frac{3 \cdot 2}{4 \cdot 2}+\frac{1}{8}) \cdot (\frac{1 \cdot 4}{1 \cdot 4}-\frac{1}{4})\) </p><p>\(= 6 \cdot (\frac{6}{8}+\frac{1}{8}) \cdot (\frac{4}{4}-\frac{1}{4}) = 6 \cdot (\frac{7}{8}) \cdot (\frac{3}{4})\)</p><p>\( = \frac{6}{1} \cdot \frac{7}{8} \cdot \frac{3}{4} = \frac{6\mkern-5mu/^3 \cdot 7 \cdot 3}{1 \cdot 8\mkern-5mu/^4 \cdot 4} = \frac{63}{16}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1683089904</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-eb Bruchrechnung Kombination II (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Sorgfältig ausmultiplizieren</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(3,7,1); nums:sort(rand_selection(makelist(i,i,9),6)); factors:[int, (nums[1]/nums[6]+nums[2]/nums[5]), (1-nums[3]/nums[4])]; ta1:factors[1]*factors[2]*factors[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})= {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>999</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Hier hast du zwei Möglichkeiten: Alles sauber ausmultiplizieren oder vor dem Multiplizieren die Klammern ausrechnen (Empfehlung!)</p><p>Beispiel: \(6 \cdot (\frac{3}{4}+\frac{1}{8}) \cdot (1-\frac{1}{4}) = 6 \cdot (\frac{3 \cdot 2}{4 \cdot 2}+\frac{1}{8}) \cdot (\frac{1 \cdot 4}{1 \cdot 4}-\frac{1}{4})\) </p><p>\(= 6 \cdot (\frac{6}{8}+\frac{1}{8}) \cdot (\frac{4}{4}-\frac{1}{4}) = 6 \cdot (\frac{7}{8}) \cdot (\frac{3}{4})\)</p><p>\( = \frac{6}{1} \cdot \frac{7}{8} \cdot \frac{3}{4} = \frac{6\mkern-5mu/^3 \cdot 7 \cdot 3}{1 \cdot 8\mkern-5mu/^4 \cdot 4} = \frac{63}{16}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>724792720</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-eb Bruchrechnung Kombination II (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Sorgfältig ausmultiplizieren</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(3,7,1); nums:sort(rand_selection(makelist(i,i,9),6)); factors:[int, (nums[1]/nums[6]+nums[2]/nums[5]), (1-nums[3]/nums[4])]; ta1:factors[1]*factors[2]*factors[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})= {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>999</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Hier hast du zwei Möglichkeiten: Alles sauber ausmultiplizieren oder vor dem Multiplizieren die Klammern ausrechnen (Empfehlung!)</p><p>Beispiel: \(6 \cdot (\frac{3}{4}+\frac{1}{8}) \cdot (1-\frac{1}{4}) = 6 \cdot (\frac{3 \cdot 2}{4 \cdot 2}+\frac{1}{8}) \cdot (\frac{1 \cdot 4}{1 \cdot 4}-\frac{1}{4})\) </p><p>\(= 6 \cdot (\frac{6}{8}+\frac{1}{8}) \cdot (\frac{4}{4}-\frac{1}{4}) = 6 \cdot (\frac{7}{8}) \cdot (\frac{3}{4})\)</p><p>\( = \frac{6}{1} \cdot \frac{7}{8} \cdot \frac{3}{4} = \frac{6\mkern-5mu/^3 \cdot 7 \cdot 3}{1 \cdot 8\mkern-5mu/^4 \cdot 4} = \frac{63}{16}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>857106597</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ec Bruchrechnung Kombination III (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch und gemischter Bruch vs. unechter Bruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(2,4,1); myvar:rand_selection([a,b,c,x,y,z],1)[1]; nums:sort(rand_selection(makelist(i,i,9),6)); summands:[(int+(nums[1]/nums[4]))*(myvar/nums[5]),1-((nums[6]-myvar)/((nums[4])/(nums[3])))]; ta1:combine(expand(summands[1]+summands[2])); wa1:(int*(nums[1]/nums[4]))*(myvar/nums[5])+summands[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast offenbar den gemischten Bruch \({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\) als Multiplikation \({@int@} \cdot \frac{{@nums[1]@}}{{@nums[4]@}}\) interpretiert. Allerdings meint der gemischte Bruch hier \({@int@}\) Ganze und \(\frac{{@nums[1]@}}{{@nums[4]@}}\) Anteil. Empfehlung: Gemischte Brüche als unechte Brüche umschreiben. Beispiel:\(2\frac{1}{6} = 2+\frac{1}{6} = \frac{2 \cdot 6}{1 \cdot 6} + \frac{1}{6} = \frac{12}{6}+\frac{1}{6} = \frac{13}{6}\)]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: \(\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}}\) ist auch ein Doppelbruch.</p><p>Achte darauf, dann die Klammer richtig zu setzen.</p><p>Beispiel: \(\frac{2-a}{\frac{7}{8}} = \boldsymbol{(}2-a\boldsymbol{)} \cdot \frac{8}{7}\)</p><p>Beachte: 1) Ganze Zahlen zum Bruch umschreiben. 2) Doppelbrüche umschreiben (Beispiel oben). 3) Gemischte Brüche umschreiben (Beispiel \(2\frac{1}{6}\) sind \(\frac{13}{6}\;\)). 4) Punkt-vor-Strich-Regel.</p>]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>2024587341</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ec Bruchrechnung Kombination III (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch und gemischter Bruch vs. unechter Bruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(2,4,1); myvar:rand_selection([a,b,c,x,y,z],1)[1]; nums:sort(rand_selection(makelist(i,i,9),6)); summands:[(int+(nums[1]/nums[4]))*(myvar/nums[5]),1-((nums[6]-myvar)/((nums[4])/(nums[3])))]; ta1:combine(expand(summands[1]+summands[2])); wa1:(int*(nums[1]/nums[4]))*(myvar/nums[5])+summands[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
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+ <checkanswertype>0</checkanswertype>
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+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
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+ <falsescore>0</falsescore>
+ <falsepenalty/>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast offenbar den gemischten Bruch \({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\) als Multiplikation \({@int@} \cdot \frac{{@nums[1]@}}{{@nums[4]@}}\) interpretiert. Allerdings meint der gemischte Bruch hier \({@int@}\) Ganze und \(\frac{{@nums[1]@}}{{@nums[4]@}}\) Anteil. Empfehlung: Gemischte Brüche als unechte Brüche umschreiben. Beispiel:\(2\frac{1}{6} = 2+\frac{1}{6} = \frac{2 \cdot 6}{1 \cdot 6} + \frac{1}{6} = \frac{12}{6}+\frac{1}{6} = \frac{13}{6}\)]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
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+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: \(\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}}\) ist auch ein Doppelbruch.</p><p>Achte darauf, dann die Klammer richtig zu setzen.</p><p>Beispiel: \(\frac{2-a}{\frac{7}{8}} = \boldsymbol{(}2-a\boldsymbol{)} \cdot \frac{8}{7}\)</p><p>Beachte: 1) Ganze Zahlen zum Bruch umschreiben. 2) Doppelbrüche umschreiben (Beispiel oben). 3) Gemischte Brüche umschreiben (Beispiel \(2\frac{1}{6}\) sind \(\frac{13}{6}\;\)). 4) Punkt-vor-Strich-Regel.</p>]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1597148134</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ec Bruchrechnung Kombination III (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch und gemischter Bruch vs. unechter Bruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(2,4,1); myvar:rand_selection([a,b,c,x,y,z],1)[1]; nums:sort(rand_selection(makelist(i,i,9),6)); summands:[(int+(nums[1]/nums[4]))*(myvar/nums[5]),1-((nums[6]-myvar)/((nums[4])/(nums[3])))]; ta1:combine(expand(summands[1]+summands[2])); wa1:(int*(nums[1]/nums[4]))*(myvar/nums[5])+summands[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
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+ <options/>
+ </input>
+ <prt>
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+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
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+ <text/>
+ </feedbackvariables>
+ <node>
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+ <tans>ta1</tans>
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+ <truescoremode>=</truescoremode>
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+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
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+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast offenbar den gemischten Bruch \({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\) als Multiplikation \({@int@} \cdot \frac{{@nums[1]@}}{{@nums[4]@}}\) interpretiert. Allerdings meint der gemischte Bruch hier \({@int@}\) Ganze und \(\frac{{@nums[1]@}}{{@nums[4]@}}\) Anteil. Empfehlung: Gemischte Brüche als unechte Brüche umschreiben. Beispiel:\(2\frac{1}{6} = 2+\frac{1}{6} = \frac{2 \cdot 6}{1 \cdot 6} + \frac{1}{6} = \frac{12}{6}+\frac{1}{6} = \frac{13}{6}\)]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: \(\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}}\) ist auch ein Doppelbruch.</p><p>Achte darauf, dann die Klammer richtig zu setzen.</p><p>Beispiel: \(\frac{2-a}{\frac{7}{8}} = \boldsymbol{(}2-a\boldsymbol{)} \cdot \frac{8}{7}\)</p><p>Beachte: 1) Ganze Zahlen zum Bruch umschreiben. 2) Doppelbrüche umschreiben (Beispiel oben). 3) Gemischte Brüche umschreiben (Beispiel \(2\frac{1}{6}\) sind \(\frac{13}{6}\;\)). 4) Punkt-vor-Strich-Regel.</p>]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>899831950</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ec Bruchrechnung Kombination III (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch und gemischter Bruch vs. unechter Bruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(2,4,1); myvar:rand_selection([a,b,c,x,y,z],1)[1]; nums:sort(rand_selection(makelist(i,i,9),6)); summands:[(int+(nums[1]/nums[4]))*(myvar/nums[5]),1-((nums[6]-myvar)/((nums[4])/(nums[3])))]; ta1:combine(expand(summands[1]+summands[2])); wa1:(int*(nums[1]/nums[4]))*(myvar/nums[5])+summands[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
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+ </input>
+ <prt>
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+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast offenbar den gemischten Bruch \({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\) als Multiplikation \({@int@} \cdot \frac{{@nums[1]@}}{{@nums[4]@}}\) interpretiert. Allerdings meint der gemischte Bruch hier \({@int@}\) Ganze und \(\frac{{@nums[1]@}}{{@nums[4]@}}\) Anteil. Empfehlung: Gemischte Brüche als unechte Brüche umschreiben. Beispiel:\(2\frac{1}{6} = 2+\frac{1}{6} = \frac{2 \cdot 6}{1 \cdot 6} + \frac{1}{6} = \frac{12}{6}+\frac{1}{6} = \frac{13}{6}\)]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: \(\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}}\) ist auch ein Doppelbruch.</p><p>Achte darauf, dann die Klammer richtig zu setzen.</p><p>Beispiel: \(\frac{2-a}{\frac{7}{8}} = \boldsymbol{(}2-a\boldsymbol{)} \cdot \frac{8}{7}\)</p><p>Beachte: 1) Ganze Zahlen zum Bruch umschreiben. 2) Doppelbrüche umschreiben (Beispiel oben). 3) Gemischte Brüche umschreiben (Beispiel \(2\frac{1}{6}\) sind \(\frac{13}{6}\;\)). 4) Punkt-vor-Strich-Regel.</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>29495097</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-j Binomische Formeln I - Anwendungsaufgabe (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen und faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.</div>
+</div>
+<p></p>
+<p>\(\frac{{@expand(BIN_a[2])@}}{{@expand(BIN_a[3])@}} \cdot {@BIN_a[3]@}\)\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p><br></p>
+<p><br></p></p>
+<p class="hint">Um diese Aufgabe zu lösen, musst du mehrere binomische Formeln anwenden.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>aa:4;
+bb:5;
+c:3;
+d:2;
+
+u:(c*a-d*b)^2;
+ualt:(d*b-c*a)^2;
+v:(aa*a+d*b)^2;
+w:(bb*a-c*b)*(bb*a+c*b);
+
+x:(aa*a-d*b)^2;
+xalt:(d*b-aa*a)^2;
+y:(bb*a+c*b)^2;
+z:(c*a+d*b)*(c*a-d*b);
+
+/*BIN_A:[
+[a1,(2*a+5*b)^2,"\\(\\frac{4\\,a^2+20\\,a\\,b+25\\,b^2}{16\\,a^2-9\\,b^2}\\cdot(4\\,a-3\\,b)\\cdot(4\\,a+3\\,b)\\)"]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];*/
+
+BIN_A:[
+[a1,u,v,ualt],
+[a2,v,w,v],
+[a3,w,u,w],
+[a4,x,y,xalt],
+[a5,y,z,y],
+[a6,z,y,z]
+];
+BIN_a:rand(BIN_A);
+
+ta:BIN_a[2];
+taalt:BIN_a[4];
+
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>534740616</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-j Binomische Formeln I - Anwendungsaufgabe (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen und faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.</div>
+</div>
+<p></p>
+<p>\(\frac{{@expand(BIN_a[2])@}}{{@expand(BIN_a[3])@}} \cdot {@BIN_a[3]@}\)\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p><br></p>
+<p><br></p></p>
+<p class="hint">Um diese Aufgabe zu lösen, musst du mehrere binomische Formeln anwenden.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>aa:4;
+bb:5;
+c:3;
+d:2;
+
+u:(c*a-d*b)^2;
+ualt:(d*b-c*a)^2;
+v:(aa*a+d*b)^2;
+w:(bb*a-c*b)*(bb*a+c*b);
+
+x:(aa*a-d*b)^2;
+xalt:(d*b-aa*a)^2;
+y:(bb*a+c*b)^2;
+z:(c*a+d*b)*(c*a-d*b);
+
+/*BIN_A:[
+[a1,(2*a+5*b)^2,"\\(\\frac{4\\,a^2+20\\,a\\,b+25\\,b^2}{16\\,a^2-9\\,b^2}\\cdot(4\\,a-3\\,b)\\cdot(4\\,a+3\\,b)\\)"]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];*/
+
+BIN_A:[
+[a1,u,v,ualt],
+[a2,v,w,v],
+[a3,w,u,w],
+[a4,x,y,xalt],
+[a5,y,z,y],
+[a6,z,y,z]
+];
+BIN_a:rand(BIN_A);
+
+ta:BIN_a[2];
+taalt:BIN_a[4];
+
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>47766652</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-j Binomische Formeln I - Anwendungsaufgabe (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen und faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.</div>
+</div>
+<p></p>
+<p>\(\frac{{@expand(BIN_a[2])@}}{{@expand(BIN_a[3])@}} \cdot {@BIN_a[3]@}\)\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p><br></p>
+<p><br></p></p>
+<p class="hint">Um diese Aufgabe zu lösen, musst du mehrere binomische Formeln anwenden.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>aa:4;
+bb:5;
+c:3;
+d:2;
+
+u:(c*a-d*b)^2;
+ualt:(d*b-c*a)^2;
+v:(aa*a+d*b)^2;
+w:(bb*a-c*b)*(bb*a+c*b);
+
+x:(aa*a-d*b)^2;
+xalt:(d*b-aa*a)^2;
+y:(bb*a+c*b)^2;
+z:(c*a+d*b)*(c*a-d*b);
+
+/*BIN_A:[
+[a1,(2*a+5*b)^2,"\\(\\frac{4\\,a^2+20\\,a\\,b+25\\,b^2}{16\\,a^2-9\\,b^2}\\cdot(4\\,a-3\\,b)\\cdot(4\\,a+3\\,b)\\)"]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];*/
+
+BIN_A:[
+[a1,u,v,ualt],
+[a2,v,w,v],
+[a3,w,u,w],
+[a4,x,y,xalt],
+[a5,y,z,y],
+[a6,z,y,z]
+];
+BIN_a:rand(BIN_A);
+
+ta:BIN_a[2];
+taalt:BIN_a[4];
+
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1657775726</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-j Binomische Formeln I - Anwendungsaufgabe (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen und faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.</div>
+</div>
+<p></p>
+<p>\(\frac{{@expand(BIN_a[2])@}}{{@expand(BIN_a[3])@}} \cdot {@BIN_a[3]@}\)\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p><br></p>
+<p><br></p></p>
+<p class="hint">Um diese Aufgabe zu lösen, musst du mehrere binomische Formeln anwenden.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>aa:4;
+bb:5;
+c:3;
+d:2;
+
+u:(c*a-d*b)^2;
+ualt:(d*b-c*a)^2;
+v:(aa*a+d*b)^2;
+w:(bb*a-c*b)*(bb*a+c*b);
+
+x:(aa*a-d*b)^2;
+xalt:(d*b-aa*a)^2;
+y:(bb*a+c*b)^2;
+z:(c*a+d*b)*(c*a-d*b);
+
+/*BIN_A:[
+[a1,(2*a+5*b)^2,"\\(\\frac{4\\,a^2+20\\,a\\,b+25\\,b^2}{16\\,a^2-9\\,b^2}\\cdot(4\\,a-3\\,b)\\cdot(4\\,a+3\\,b)\\)"]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];*/
+
+BIN_A:[
+[a1,u,v,ualt],
+[a2,v,w,v],
+[a3,w,u,w],
+[a4,x,y,xalt],
+[a5,y,z,y],
+[a6,z,y,z]
+];
+BIN_a:rand(BIN_A);
+
+ta:BIN_a[2];
+taalt:BIN_a[4];
+
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>931829986</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-g Binomische Formeln Ia - Erste binomische Formel (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Um den Bruch aus der Endgegner-Aufgabe zu vereinfachen, musst du binomische Formeln anwenden. Deshalb kommen wir nun zu den binomischen Formeln. Die erste binomische Formel besagt: \((a + b)^2 = a^2 + 2\,a\,b + b^2\;\).</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,(4+b)^2],
+[a2,(5+b)^2],
+[a3,(3+b)^2],
+[a4,(2+b)^2],
+[a5,(3+2*b)^2],
+[a6,(4+2*b)^2]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];
+task:expand(BIN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die erste binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1994312303</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-g Binomische Formeln Ia - Erste binomische Formel (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Um den Bruch aus der Endgegner-Aufgabe zu vereinfachen, musst du binomische Formeln anwenden. Deshalb kommen wir nun zu den binomischen Formeln. Die erste binomische Formel besagt: \((a + b)^2 = a^2 + 2\,a\,b + b^2\;\).</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,(4+b)^2],
+[a2,(5+b)^2],
+[a3,(3+b)^2],
+[a4,(2+b)^2],
+[a5,(3+2*b)^2],
+[a6,(4+2*b)^2]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];
+task:expand(BIN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die erste binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1744518788</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-g Binomische Formeln Ia - Erste binomische Formel (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Um den Bruch aus der Endgegner-Aufgabe zu vereinfachen, musst du binomische Formeln anwenden. Deshalb kommen wir nun zu den binomischen Formeln. Die erste binomische Formel besagt: \((a + b)^2 = a^2 + 2\,a\,b + b^2\;\).</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,(4+b)^2],
+[a2,(5+b)^2],
+[a3,(3+b)^2],
+[a4,(2+b)^2],
+[a5,(3+2*b)^2],
+[a6,(4+2*b)^2]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];
+task:expand(BIN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die erste binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1627526666</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-g Binomische Formeln Ia - Erste binomische Formel (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Um den Bruch aus der Endgegner-Aufgabe zu vereinfachen, musst du binomische Formeln anwenden. Deshalb kommen wir nun zu den binomischen Formeln. Die erste binomische Formel besagt: \((a + b)^2 = a^2 + 2\,a\,b + b^2\;\).</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,(4+b)^2],
+[a2,(5+b)^2],
+[a3,(3+b)^2],
+[a4,(2+b)^2],
+[a5,(3+2*b)^2],
+[a6,(4+2*b)^2]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];
+task:expand(BIN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die erste binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1566276649</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-h Binomische Formeln Ib - Zweite binomische Formel (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Die zweite binomische Formel besagt:\((a - b)^2 = a^2 - 2\,a\,b + b^2\;\).<!--Diesmal musst du den Term erst umformen, damit er in der richtigen Form erscheint.--><br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:4;
+b:5;
+c:3;
+d:2;
+
+e:1;
+f:2;
+
+BIN_A:[
+[a1,a,e],
+[a2,b,e],
+[a3,c,e],
+[a4,d,e],
+[a5,a,f],
+[a6,c,f]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]-BIN_a[3]*y)^2;
+taalt:(BIN_a[3]*y-BIN_a[2])^2;
+task:expand(ta);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>893674818</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-h Binomische Formeln Ib - Zweite binomische Formel (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Die zweite binomische Formel besagt:\((a - b)^2 = a^2 - 2\,a\,b + b^2\;\).<!--Diesmal musst du den Term erst umformen, damit er in der richtigen Form erscheint.--><br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:4;
+b:5;
+c:3;
+d:2;
+
+e:1;
+f:2;
+
+BIN_A:[
+[a1,a,e],
+[a2,b,e],
+[a3,c,e],
+[a4,d,e],
+[a5,a,f],
+[a6,c,f]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]-BIN_a[3]*y)^2;
+taalt:(BIN_a[3]*y-BIN_a[2])^2;
+task:expand(ta);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>675538571</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-h Binomische Formeln Ib - Zweite binomische Formel (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Die zweite binomische Formel besagt:\((a - b)^2 = a^2 - 2\,a\,b + b^2\;\).<!--Diesmal musst du den Term erst umformen, damit er in der richtigen Form erscheint.--><br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:4;
+b:5;
+c:3;
+d:2;
+
+e:1;
+f:2;
+
+BIN_A:[
+[a1,a,e],
+[a2,b,e],
+[a3,c,e],
+[a4,d,e],
+[a5,a,f],
+[a6,c,f]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]-BIN_a[3]*y)^2;
+taalt:(BIN_a[3]*y-BIN_a[2])^2;
+task:expand(ta);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>985713485</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-h Binomische Formeln Ib - Zweite binomische Formel (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Die zweite binomische Formel besagt:\((a - b)^2 = a^2 - 2\,a\,b + b^2\;\).<!--Diesmal musst du den Term erst umformen, damit er in der richtigen Form erscheint.--><br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:4;
+b:5;
+c:3;
+d:2;
+
+e:1;
+f:2;
+
+BIN_A:[
+[a1,a,e],
+[a2,b,e],
+[a3,c,e],
+[a4,d,e],
+[a5,a,f],
+[a6,c,f]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]-BIN_a[3]*y)^2;
+taalt:(BIN_a[3]*y-BIN_a[2])^2;
+task:expand(ta);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1039647874</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-i Binomische Formeln Ic - Dritte binomische Formel (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Die dritte binomische Formel besagt: \((a + b)\,(a - b) = a^2 - b^2\;\).<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>aa:4;
+bb:5;
+c:3;
+d:2;
+
+
+BIN_A:[
+[a1,aa,bb],
+[a2,c,d],
+[a3,d,aa],
+[a4,d,bb],
+[a5,d,c],
+[a6,aa,c]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]*x-BIN_a[3]*y)*(BIN_a[2]*x+BIN_a[3]*y);
+task:expand(ta);
+wa:(BIN_a[2]^2*x-BIN_a[3]^2*y)*(BIN_a[2]^2*x+BIN_a[3]^2*y);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die dritte binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast zwar die Unbekannten x und y korrekt faktorisiert, aber die sie begleitenden Faktoren unverändert in die Klammern geschrieben. Um diese korrekt zu faktorisieren, musst du ihre Wurzeln berechnen. Richtig wäre {@ta@}.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>455750255</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-i Binomische Formeln Ic - Dritte binomische Formel (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Die dritte binomische Formel besagt: \((a + b)\,(a - b) = a^2 - b^2\;\).<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>aa:4;
+bb:5;
+c:3;
+d:2;
+
+
+BIN_A:[
+[a1,aa,bb],
+[a2,c,d],
+[a3,d,aa],
+[a4,d,bb],
+[a5,d,c],
+[a6,aa,c]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]*x-BIN_a[3]*y)*(BIN_a[2]*x+BIN_a[3]*y);
+task:expand(ta);
+wa:(BIN_a[2]^2*x-BIN_a[3]^2*y)*(BIN_a[2]^2*x+BIN_a[3]^2*y);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die dritte binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast zwar die Unbekannten x und y korrekt faktorisiert, aber die sie begleitenden Faktoren unverändert in die Klammern geschrieben. Um diese korrekt zu faktorisieren, musst du ihre Wurzeln berechnen. Richtig wäre {@ta@}.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>970764179</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-i Binomische Formeln Ic - Dritte binomische Formel (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Die dritte binomische Formel besagt: \((a + b)\,(a - b) = a^2 - b^2\;\).<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>aa:4;
+bb:5;
+c:3;
+d:2;
+
+
+BIN_A:[
+[a1,aa,bb],
+[a2,c,d],
+[a3,d,aa],
+[a4,d,bb],
+[a5,d,c],
+[a6,aa,c]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]*x-BIN_a[3]*y)*(BIN_a[2]*x+BIN_a[3]*y);
+task:expand(ta);
+wa:(BIN_a[2]^2*x-BIN_a[3]^2*y)*(BIN_a[2]^2*x+BIN_a[3]^2*y);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die dritte binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast zwar die Unbekannten x und y korrekt faktorisiert, aber die sie begleitenden Faktoren unverändert in die Klammern geschrieben. Um diese korrekt zu faktorisieren, musst du ihre Wurzeln berechnen. Richtig wäre {@ta@}.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1971560923</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-i Binomische Formeln Ic - Dritte binomische Formel (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Die dritte binomische Formel besagt: \((a + b)\,(a - b) = a^2 - b^2\;\).<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>aa:4;
+bb:5;
+c:3;
+d:2;
+
+
+BIN_A:[
+[a1,aa,bb],
+[a2,c,d],
+[a3,d,aa],
+[a4,d,bb],
+[a5,d,c],
+[a6,aa,c]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]*x-BIN_a[3]*y)*(BIN_a[2]*x+BIN_a[3]*y);
+task:expand(ta);
+wa:(BIN_a[2]^2*x-BIN_a[3]^2*y)*(BIN_a[2]^2*x+BIN_a[3]^2*y);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die dritte binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast zwar die Unbekannten x und y korrekt faktorisiert, aber die sie begleitenden Faktoren unverändert in die Klammern geschrieben. Um diese korrekt zu faktorisieren, musst du ihre Wurzeln berechnen. Richtig wäre {@ta@}.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>987956614</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-k Bruchrechenregeln Ig2 - Bruch mit binomischem Term erweitern 2 (copy) (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen und faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Dies ist der Endgegner zur Mathe-Welt <strong>Bruchrechenregeln und binomische Formeln</strong>. Wenn du diese Aufgabe schaffst, hast du diese Welt schon gemeistert. Wende zuerst die binomischen Formeln an, um die Nenner zu vereinfachen. Um die Brüche dann zu addieren, musst du mit einem Term erweitern.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;
+b:3;
+c:4;
+
+aa:x-a;
+bb:x-b;
+cc:x-c;
+
+/*FRA_A:[
+[a1,(x^2-3)/(x^2-4),"\\(\\frac{x + 3}{x^2 - 4} + \\frac{x - 3}{x - 2}\\)",(x^2-3)/((x+2)*(x-2))]
+];*/
+
+FRA_A:[
+[a1,aa, a],
+[a2,bb, b],
+[a3,cc, c]
+];
+FRA_a:rand(FRA_A);
+task:(3*FRA_a[3]*x+FRA_a[3]^2)/expand(FRA_a[2]^2)+x/FRA_a[2];
+ta:(x+FRA_a[3])^2/(FRA_a[2])^2;
+
+simp:false;
+taalt:((x+FRA_a[3])/(FRA_a[2]))^2;
+simp:true;
+
+wa1:expand((x+FRA_a[3])^2)/(FRA_a[2])^2;
+wa2:(x+FRA_a[3])^2/expand((FRA_a[2])^2);
+wa3:expand((x+FRA_a[3])^2)/expand(FRA_a[2]^2);
+wa4:(3*FRA_a[3]*x+FRA_a[3]^2)/expand(FRA_a[2]^2)+x^2/FRA_a[2]^2; /*naively expanded fraction by squaring numerator and denominator*/
+wa5:(3*FRA_a[3]*x+FRA_a[3]^2+x)/(expand(FRA_a[2]^2)+FRA_a[2]); /*naively summed fractions, keeping the denominators*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@FRA_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>2</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die erste binomische Formel an, um den Zähler zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa2</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die zweite binomische Formel an, um den Nenner zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>4</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa3</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die erste binomische Formel an, um den Zähler zu faktorisieren und
+ wende die zweite binomische Formel an, um den Nenner zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa4</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich den zweiten Summanden mit sich selbst multipliziert (quadriert), damit die Nenner gleich sind. Allerdings wird ein Bruch so nicht erweitert. Der quadrierte Bruch ist nicht mehr äquivalent mit dem vorherigen Bruch. Beispiel: \((\frac{2}{5})^2 = \frac{4}{25} \ne \frac{2}{5}\;\) wohingegen \(\frac{2}{5} = \frac{2 \cdot 5}{5 \cdot 5} = \frac{10}{25}\;\). Bitte überlege erneut, womit der zweite Summand erweitert werden muss, damit die Nenner gleich sind.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa5</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich die beiden Brüche addiert, indem du Zähler plus Zähler (oben) und Nenner plus Nenner (unten) gerechnet hast. So können Brüche nicht addiert werden. Beispiel: \( \frac{1}{2} + \frac{1}{4} \ne \frac{1+1}{2+4}\;\) . Brüche müssen so erweitert werden, dass sie den gleichen Nenner haben. Dann können die Zähler addiert werden: \(\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}\).</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>2099085786</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-k Bruchrechenregeln Ig2 - Bruch mit binomischem Term erweitern 2 (copy) (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen und faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Dies ist der Endgegner zur Mathe-Welt <strong>Bruchrechenregeln und binomische Formeln</strong>. Wenn du diese Aufgabe schaffst, hast du diese Welt schon gemeistert. Wende zuerst die binomischen Formeln an, um die Nenner zu vereinfachen. Um die Brüche dann zu addieren, musst du mit einem Term erweitern.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;
+b:3;
+c:4;
+
+aa:x-a;
+bb:x-b;
+cc:x-c;
+
+/*FRA_A:[
+[a1,(x^2-3)/(x^2-4),"\\(\\frac{x + 3}{x^2 - 4} + \\frac{x - 3}{x - 2}\\)",(x^2-3)/((x+2)*(x-2))]
+];*/
+
+FRA_A:[
+[a1,aa, a],
+[a2,bb, b],
+[a3,cc, c]
+];
+FRA_a:rand(FRA_A);
+task:(3*FRA_a[3]*x+FRA_a[3]^2)/expand(FRA_a[2]^2)+x/FRA_a[2];
+ta:(x+FRA_a[3])^2/(FRA_a[2])^2;
+
+simp:false;
+taalt:((x+FRA_a[3])/(FRA_a[2]))^2;
+simp:true;
+
+wa1:expand((x+FRA_a[3])^2)/(FRA_a[2])^2;
+wa2:(x+FRA_a[3])^2/expand((FRA_a[2])^2);
+wa3:expand((x+FRA_a[3])^2)/expand(FRA_a[2]^2);
+wa4:(3*FRA_a[3]*x+FRA_a[3]^2)/expand(FRA_a[2]^2)+x^2/FRA_a[2]^2; /*naively expanded fraction by squaring numerator and denominator*/
+wa5:(3*FRA_a[3]*x+FRA_a[3]^2+x)/(expand(FRA_a[2]^2)+FRA_a[2]); /*naively summed fractions, keeping the denominators*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@FRA_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>2</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die erste binomische Formel an, um den Zähler zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa2</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die zweite binomische Formel an, um den Nenner zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>4</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa3</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die erste binomische Formel an, um den Zähler zu faktorisieren und
+ wende die zweite binomische Formel an, um den Nenner zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa4</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich den zweiten Summanden mit sich selbst multipliziert (quadriert), damit die Nenner gleich sind. Allerdings wird ein Bruch so nicht erweitert. Der quadrierte Bruch ist nicht mehr äquivalent mit dem vorherigen Bruch. Beispiel: \((\frac{2}{5})^2 = \frac{4}{25} \ne \frac{2}{5}\;\) wohingegen \(\frac{2}{5} = \frac{2 \cdot 5}{5 \cdot 5} = \frac{10}{25}\;\). Bitte überlege erneut, womit der zweite Summand erweitert werden muss, damit die Nenner gleich sind.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa5</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich die beiden Brüche addiert, indem du Zähler plus Zähler (oben) und Nenner plus Nenner (unten) gerechnet hast. So können Brüche nicht addiert werden. Beispiel: \( \frac{1}{2} + \frac{1}{4} \ne \frac{1+1}{2+4}\;\) . Brüche müssen so erweitert werden, dass sie den gleichen Nenner haben. Dann können die Zähler addiert werden: \(\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}\).</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>245667775</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-k Bruchrechenregeln Ig2 - Bruch mit binomischem Term erweitern 2 (copy) (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen und faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Dies ist der Endgegner zur Mathe-Welt <strong>Bruchrechenregeln und binomische Formeln</strong>. Wenn du diese Aufgabe schaffst, hast du diese Welt schon gemeistert. Wende zuerst die binomischen Formeln an, um die Nenner zu vereinfachen. Um die Brüche dann zu addieren, musst du mit einem Term erweitern.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;
+b:3;
+c:4;
+
+aa:x-a;
+bb:x-b;
+cc:x-c;
+
+/*FRA_A:[
+[a1,(x^2-3)/(x^2-4),"\\(\\frac{x + 3}{x^2 - 4} + \\frac{x - 3}{x - 2}\\)",(x^2-3)/((x+2)*(x-2))]
+];*/
+
+FRA_A:[
+[a1,aa, a],
+[a2,bb, b],
+[a3,cc, c]
+];
+FRA_a:rand(FRA_A);
+task:(3*FRA_a[3]*x+FRA_a[3]^2)/expand(FRA_a[2]^2)+x/FRA_a[2];
+ta:(x+FRA_a[3])^2/(FRA_a[2])^2;
+
+simp:false;
+taalt:((x+FRA_a[3])/(FRA_a[2]))^2;
+simp:true;
+
+wa1:expand((x+FRA_a[3])^2)/(FRA_a[2])^2;
+wa2:(x+FRA_a[3])^2/expand((FRA_a[2])^2);
+wa3:expand((x+FRA_a[3])^2)/expand(FRA_a[2]^2);
+wa4:(3*FRA_a[3]*x+FRA_a[3]^2)/expand(FRA_a[2]^2)+x^2/FRA_a[2]^2; /*naively expanded fraction by squaring numerator and denominator*/
+wa5:(3*FRA_a[3]*x+FRA_a[3]^2+x)/(expand(FRA_a[2]^2)+FRA_a[2]); /*naively summed fractions, keeping the denominators*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@FRA_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>2</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die erste binomische Formel an, um den Zähler zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa2</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die zweite binomische Formel an, um den Nenner zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>4</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa3</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die erste binomische Formel an, um den Zähler zu faktorisieren und
+ wende die zweite binomische Formel an, um den Nenner zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa4</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich den zweiten Summanden mit sich selbst multipliziert (quadriert), damit die Nenner gleich sind. Allerdings wird ein Bruch so nicht erweitert. Der quadrierte Bruch ist nicht mehr äquivalent mit dem vorherigen Bruch. Beispiel: \((\frac{2}{5})^2 = \frac{4}{25} \ne \frac{2}{5}\;\) wohingegen \(\frac{2}{5} = \frac{2 \cdot 5}{5 \cdot 5} = \frac{10}{25}\;\). Bitte überlege erneut, womit der zweite Summand erweitert werden muss, damit die Nenner gleich sind.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa5</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich die beiden Brüche addiert, indem du Zähler plus Zähler (oben) und Nenner plus Nenner (unten) gerechnet hast. So können Brüche nicht addiert werden. Beispiel: \( \frac{1}{2} + \frac{1}{4} \ne \frac{1+1}{2+4}\;\) . Brüche müssen so erweitert werden, dass sie den gleichen Nenner haben. Dann können die Zähler addiert werden: \(\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}\).</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1806806387</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-a p-q-Formal Ia - Termumformung (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p>Formen Sie den Term so um, dass er in der Form \(x^2+px+q = 0\) erscheint. Sie können dies Zeile für Zeile tun.<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Um die p-q-Formel anzuwenden, müssen wir zunächst den Term in die richtige Form bringen. Um den folgenden Term wie gewünscht umzuformen, subtrahiere und dividiere auf beiden Seiten der Gleichung.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[6*x+3*x^2-2=10,x^2+2*x-4=0],6*x+3*x^2-2=10],
+[a2,[15*x+5*x^2=20,x^2+3*x-4=0],15*x+5*x^2=20],
+[a3,[8*x+2*x^2-2=12,x^2+4*x-7=0],8*x+2*x^2-2=12],
+[a4,[20*x+4*x^2=-16,x^2+5*x+4=0],20*x+4*x^2=-16]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Gut gemacht! Wenn ein Term auf diese Weise umgeformt ist, kannst du mit der p-q-Formel die möglichen Werte für \(x\) bestimmen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Weiter so! Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>last(BIN_a[2])</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint></syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options></options>
+ </input><deployedseed>1126686893</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-a p-q-Formal Ia - Termumformung (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p>Formen Sie den Term so um, dass er in der Form \(x^2+px+q = 0\) erscheint. Sie können dies Zeile für Zeile tun.<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Um die p-q-Formel anzuwenden, müssen wir zunächst den Term in die richtige Form bringen. Um den folgenden Term wie gewünscht umzuformen, subtrahiere und dividiere auf beiden Seiten der Gleichung.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[6*x+3*x^2-2=10,x^2+2*x-4=0],6*x+3*x^2-2=10],
+[a2,[15*x+5*x^2=20,x^2+3*x-4=0],15*x+5*x^2=20],
+[a3,[8*x+2*x^2-2=12,x^2+4*x-7=0],8*x+2*x^2-2=12],
+[a4,[20*x+4*x^2=-16,x^2+5*x+4=0],20*x+4*x^2=-16]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Gut gemacht! Wenn ein Term auf diese Weise umgeformt ist, kannst du mit der p-q-Formel die möglichen Werte für \(x\) bestimmen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Weiter so! Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>last(BIN_a[2])</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint></syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options></options>
+ </input><deployedseed>1832581792</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-a p-q-Formal Ia - Termumformung (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p>Formen Sie den Term so um, dass er in der Form \(x^2+px+q = 0\) erscheint. Sie können dies Zeile für Zeile tun.<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Um die p-q-Formel anzuwenden, müssen wir zunächst den Term in die richtige Form bringen. Um den folgenden Term wie gewünscht umzuformen, subtrahiere und dividiere auf beiden Seiten der Gleichung.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[6*x+3*x^2-2=10,x^2+2*x-4=0],6*x+3*x^2-2=10],
+[a2,[15*x+5*x^2=20,x^2+3*x-4=0],15*x+5*x^2=20],
+[a3,[8*x+2*x^2-2=12,x^2+4*x-7=0],8*x+2*x^2-2=12],
+[a4,[20*x+4*x^2=-16,x^2+5*x+4=0],20*x+4*x^2=-16]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Gut gemacht! Wenn ein Term auf diese Weise umgeformt ist, kannst du mit der p-q-Formel die möglichen Werte für \(x\) bestimmen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Weiter so! Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>last(BIN_a[2])</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint></syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options></options>
+ </input><deployedseed>1406889611</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-a p-q-Formal Ia - Termumformung (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p>Formen Sie den Term so um, dass er in der Form \(x^2+px+q = 0\) erscheint. Sie können dies Zeile für Zeile tun.<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Um die p-q-Formel anzuwenden, müssen wir zunächst den Term in die richtige Form bringen. Um den folgenden Term wie gewünscht umzuformen, subtrahiere und dividiere auf beiden Seiten der Gleichung.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[6*x+3*x^2-2=10,x^2+2*x-4=0],6*x+3*x^2-2=10],
+[a2,[15*x+5*x^2=20,x^2+3*x-4=0],15*x+5*x^2=20],
+[a3,[8*x+2*x^2-2=12,x^2+4*x-7=0],8*x+2*x^2-2=12],
+[a4,[20*x+4*x^2=-16,x^2+5*x+4=0],20*x+4*x^2=-16]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Gut gemacht! Wenn ein Term auf diese Weise umgeformt ist, kannst du mit der p-q-Formel die möglichen Werte für \(x\) bestimmen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Weiter so! Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>last(BIN_a[2])</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint></syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options></options>
+ </input><deployedseed>511391873</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-c p-q-Formel I - Endboss (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p>Bestimmen Sie alle reellen Lösungen der quadratischen Gleichung in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\(= ?\;\). Sie können Ihren Rechenweg angeben.<br></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Forme den Term um und wende dann die p-q-Formel an, um diese Endgegner-Aufgabe zu lösen. Dann bist du mit dieser Mathe-Welt fertig.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[-2*y^2+6*y=4, -2*y^2+6*y-4=0,y^2-3*y-2=0,stackeq(y=3/2+sqrt(9/4-2) nounor y=3/2-sqrt(9/4-2)),y=1 nounor y=2],-2*y^2+6*y=4,y,1,2,y=3/2+sqrt(9/4+2),y=3/2-sqrt(9/4+2)],
+[a2,[2*y^2-16=-4*y,2*y^2+4*y-16=0,y^2+2*y-8=0,stackeq(y=-1+sqrt((1)^2+8) nounor y=-1-sqrt((1)^2+8)),y=-4 nounor y=2],2*y^2-16=-4*y,y,-4,2,y=-1+sqrt((1)^2-8),y=-1-sqrt((1)^2-8)],
+[a3,[-2*d^2+2*d=-24,-2*d^2+2*d+24=0,d^2-d-12=0,d=1/2+sqrt((1/2)^2+12) nounor d=1/2-sqrt((1/2)^2+12),d=-3 nounor d=4],-2*d^2+2*d=-24,d,-3,4,d=1/2+sqrt((1/2)^2-12),d=1/2-sqrt((1/2)^2-12)],
+[a4,[-2*u^2-14*u=24,-2*u^2-14*u-24=0,u^2+7*u+12=0,u=-7/2+sqrt((7/2)^2-12) nounor u=-7/2-sqrt((7/2)^2-12),u=-4 nounor u=-3],-2*u^2-14*u=24,u,-4,-3,u=-7/2+sqrt((7/2)^2+12), u=-7/2-sqrt((7/2)^2+12)]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.</p><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast!
+ Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel
+in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2}
+\boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir="ltr">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir="ltr">Versuche es erneut und gib beide Lösungen an.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast! Offenbar hast du dich beim
+\(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet
+ \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil
+ am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du
+das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr">Außerdem
+ hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel
+ bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+}
+\sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-}
+\sqrt{...}\) gibt.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast!
+ Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>last(BIN_a[2])</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint></syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options></options>
+ </input><deployedseed>1183308849</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-c p-q-Formel I - Endboss (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p>Bestimmen Sie alle reellen Lösungen der quadratischen Gleichung in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\(= ?\;\). Sie können Ihren Rechenweg angeben.<br></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Forme den Term um und wende dann die p-q-Formel an, um diese Endgegner-Aufgabe zu lösen. Dann bist du mit dieser Mathe-Welt fertig.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[-2*y^2+6*y=4, -2*y^2+6*y-4=0,y^2-3*y-2=0,stackeq(y=3/2+sqrt(9/4-2) nounor y=3/2-sqrt(9/4-2)),y=1 nounor y=2],-2*y^2+6*y=4,y,1,2,y=3/2+sqrt(9/4+2),y=3/2-sqrt(9/4+2)],
+[a2,[2*y^2-16=-4*y,2*y^2+4*y-16=0,y^2+2*y-8=0,stackeq(y=-1+sqrt((1)^2+8) nounor y=-1-sqrt((1)^2+8)),y=-4 nounor y=2],2*y^2-16=-4*y,y,-4,2,y=-1+sqrt((1)^2-8),y=-1-sqrt((1)^2-8)],
+[a3,[-2*d^2+2*d=-24,-2*d^2+2*d+24=0,d^2-d-12=0,d=1/2+sqrt((1/2)^2+12) nounor d=1/2-sqrt((1/2)^2+12),d=-3 nounor d=4],-2*d^2+2*d=-24,d,-3,4,d=1/2+sqrt((1/2)^2-12),d=1/2-sqrt((1/2)^2-12)],
+[a4,[-2*u^2-14*u=24,-2*u^2-14*u-24=0,u^2+7*u+12=0,u=-7/2+sqrt((7/2)^2-12) nounor u=-7/2-sqrt((7/2)^2-12),u=-4 nounor u=-3],-2*u^2-14*u=24,u,-4,-3,u=-7/2+sqrt((7/2)^2+12), u=-7/2-sqrt((7/2)^2+12)]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
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+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
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+ <name>prt1</name>
+ <value>1.0000000</value>
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+ </feedbackvariables>
+ <node>
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+ <answertest>EqualComAss</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
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+ <truepenalty/>
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+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
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+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
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+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.</p><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
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+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast!
+ Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel
+in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2}
+\boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir="ltr">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir="ltr">Versuche es erneut und gib beide Lösungen an.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast! Offenbar hast du dich beim
+\(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet
+ \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil
+ am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du
+das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr">Außerdem
+ hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel
+ bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+}
+\sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-}
+\sqrt{...}\) gibt.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast!
+ Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>last(BIN_a[2])</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint></syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options></options>
+ </input><deployedseed>1817300183</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-c p-q-Formel I - Endboss (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p>Bestimmen Sie alle reellen Lösungen der quadratischen Gleichung in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\(= ?\;\). Sie können Ihren Rechenweg angeben.<br></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Forme den Term um und wende dann die p-q-Formel an, um diese Endgegner-Aufgabe zu lösen. Dann bist du mit dieser Mathe-Welt fertig.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[-2*y^2+6*y=4, -2*y^2+6*y-4=0,y^2-3*y-2=0,stackeq(y=3/2+sqrt(9/4-2) nounor y=3/2-sqrt(9/4-2)),y=1 nounor y=2],-2*y^2+6*y=4,y,1,2,y=3/2+sqrt(9/4+2),y=3/2-sqrt(9/4+2)],
+[a2,[2*y^2-16=-4*y,2*y^2+4*y-16=0,y^2+2*y-8=0,stackeq(y=-1+sqrt((1)^2+8) nounor y=-1-sqrt((1)^2+8)),y=-4 nounor y=2],2*y^2-16=-4*y,y,-4,2,y=-1+sqrt((1)^2-8),y=-1-sqrt((1)^2-8)],
+[a3,[-2*d^2+2*d=-24,-2*d^2+2*d+24=0,d^2-d-12=0,d=1/2+sqrt((1/2)^2+12) nounor d=1/2-sqrt((1/2)^2+12),d=-3 nounor d=4],-2*d^2+2*d=-24,d,-3,4,d=1/2+sqrt((1/2)^2-12),d=1/2-sqrt((1/2)^2-12)],
+[a4,[-2*u^2-14*u=24,-2*u^2-14*u-24=0,u^2+7*u+12=0,u=-7/2+sqrt((7/2)^2-12) nounor u=-7/2-sqrt((7/2)^2-12),u=-4 nounor u=-3],-2*u^2-14*u=24,u,-4,-3,u=-7/2+sqrt((7/2)^2+12), u=-7/2-sqrt((7/2)^2+12)]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.</p><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast!
+ Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel
+in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2}
+\boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir="ltr">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir="ltr">Versuche es erneut und gib beide Lösungen an.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast! Offenbar hast du dich beim
+\(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet
+ \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil
+ am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du
+das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr">Außerdem
+ hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel
+ bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+}
+\sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-}
+\sqrt{...}\) gibt.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast!
+ Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>last(BIN_a[2])</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint></syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options></options>
+ </input><deployedseed>1556042756</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-c p-q-Formel I - Endboss (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p>Bestimmen Sie alle reellen Lösungen der quadratischen Gleichung in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\(= ?\;\). Sie können Ihren Rechenweg angeben.<br></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Forme den Term um und wende dann die p-q-Formel an, um diese Endgegner-Aufgabe zu lösen. Dann bist du mit dieser Mathe-Welt fertig.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[-2*y^2+6*y=4, -2*y^2+6*y-4=0,y^2-3*y-2=0,stackeq(y=3/2+sqrt(9/4-2) nounor y=3/2-sqrt(9/4-2)),y=1 nounor y=2],-2*y^2+6*y=4,y,1,2,y=3/2+sqrt(9/4+2),y=3/2-sqrt(9/4+2)],
+[a2,[2*y^2-16=-4*y,2*y^2+4*y-16=0,y^2+2*y-8=0,stackeq(y=-1+sqrt((1)^2+8) nounor y=-1-sqrt((1)^2+8)),y=-4 nounor y=2],2*y^2-16=-4*y,y,-4,2,y=-1+sqrt((1)^2-8),y=-1-sqrt((1)^2-8)],
+[a3,[-2*d^2+2*d=-24,-2*d^2+2*d+24=0,d^2-d-12=0,d=1/2+sqrt((1/2)^2+12) nounor d=1/2-sqrt((1/2)^2+12),d=-3 nounor d=4],-2*d^2+2*d=-24,d,-3,4,d=1/2+sqrt((1/2)^2-12),d=1/2-sqrt((1/2)^2-12)],
+[a4,[-2*u^2-14*u=24,-2*u^2-14*u-24=0,u^2+7*u+12=0,u=-7/2+sqrt((7/2)^2-12) nounor u=-7/2-sqrt((7/2)^2-12),u=-4 nounor u=-3],-2*u^2-14*u=24,u,-4,-3,u=-7/2+sqrt((7/2)^2+12), u=-7/2-sqrt((7/2)^2+12)]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.</p><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast!
+ Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel
+in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2}
+\boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir="ltr">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir="ltr">Versuche es erneut und gib beide Lösungen an.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast! Offenbar hast du dich beim
+\(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet
+ \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil
+ am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du
+das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr">Außerdem
+ hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel
+ bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+}
+\sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-}
+\sqrt{...}\) gibt.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast!
+ Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>last(BIN_a[2])</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint></syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options></options>
+ </input><deployedseed>493079990</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-b p-q-Formel Ib - pq-Formel (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p>Bestimmen Sie den Wert der Variable in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\( = ?\;\).<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Erinnerst du dich noch an die pq-Formel? Für \(\;x^2 + p\,x + q = 0\;\) gilt \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\).<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[h^2+3*h-4=0,h=-3/2+sqrt((3/2)^2+4) nounor h=-3/2-sqrt((3/2)^2+4),h=-3/2+sqrt(25/4) nounor h=-3/2-sqrt(25/4),h=-3/2+5/2 nounor h=-3/2-5/2,h=-4 nounor h=1],"\\(h^2+3\\,h-4=0\\)",h,1,-4,h=-3/2+sqrt(9/4-4),h=-3/2-sqrt(9/4-4)],
+[a2,[y^2-2*y-8=0,y=1+sqrt((-1)^2+8) nounor y=1-sqrt((-1)^2+8),y=-2 nounor y=4],"\\(y^2-2\\,y-8=0\\)",y,-2,4,y=1-sqrt(1-8),y=1+sqrt(1-8)],
+[a3,[z^2-4*z-5=0,z=2+sqrt((-2)^2+5) nounor z=2-sqrt((-2)^2+5),z=5 nounor z=-1],"\\(z^2-4\\,z-5=0\\)",z,5,-1,z=2+sqrt(4-5),z=2-sqrt(4-5)],
+[a4,[a^2-10*a+9=0,a=5+sqrt((-5)^2-9) nounor a=5-sqrt((-5)^2-9),a=9 nounor a=1],"\\(a^2-10\\,a+9=0\\)",a,9,1,a=5+sqrt(25+9),a=5-sqrt(25+9)]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr" style="text-align: left;">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2} \boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir="ltr" style="text-align: left;">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir="ltr" style="text-align: left;">Versuche es erneut und gib beide Lösungen an.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr" style="text-align: left;">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\) gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>last(BIN_a[2])</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint></syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options></options>
+ </input><deployedseed>1183616185</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-b p-q-Formel Ib - pq-Formel (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p>Bestimmen Sie den Wert der Variable in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\( = ?\;\).<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Erinnerst du dich noch an die pq-Formel? Für \(\;x^2 + p\,x + q = 0\;\) gilt \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\).<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[h^2+3*h-4=0,h=-3/2+sqrt((3/2)^2+4) nounor h=-3/2-sqrt((3/2)^2+4),h=-3/2+sqrt(25/4) nounor h=-3/2-sqrt(25/4),h=-3/2+5/2 nounor h=-3/2-5/2,h=-4 nounor h=1],"\\(h^2+3\\,h-4=0\\)",h,1,-4,h=-3/2+sqrt(9/4-4),h=-3/2-sqrt(9/4-4)],
+[a2,[y^2-2*y-8=0,y=1+sqrt((-1)^2+8) nounor y=1-sqrt((-1)^2+8),y=-2 nounor y=4],"\\(y^2-2\\,y-8=0\\)",y,-2,4,y=1-sqrt(1-8),y=1+sqrt(1-8)],
+[a3,[z^2-4*z-5=0,z=2+sqrt((-2)^2+5) nounor z=2-sqrt((-2)^2+5),z=5 nounor z=-1],"\\(z^2-4\\,z-5=0\\)",z,5,-1,z=2+sqrt(4-5),z=2-sqrt(4-5)],
+[a4,[a^2-10*a+9=0,a=5+sqrt((-5)^2-9) nounor a=5-sqrt((-5)^2-9),a=9 nounor a=1],"\\(a^2-10\\,a+9=0\\)",a,9,1,a=5+sqrt(25+9),a=5-sqrt(25+9)]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr" style="text-align: left;">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2} \boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir="ltr" style="text-align: left;">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir="ltr" style="text-align: left;">Versuche es erneut und gib beide Lösungen an.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr" style="text-align: left;">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\) gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>last(BIN_a[2])</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint></syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options></options>
+ </input><deployedseed>1771539896</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-b p-q-Formel Ib - pq-Formel (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p>Bestimmen Sie den Wert der Variable in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\( = ?\;\).<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Erinnerst du dich noch an die pq-Formel? Für \(\;x^2 + p\,x + q = 0\;\) gilt \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\).<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[h^2+3*h-4=0,h=-3/2+sqrt((3/2)^2+4) nounor h=-3/2-sqrt((3/2)^2+4),h=-3/2+sqrt(25/4) nounor h=-3/2-sqrt(25/4),h=-3/2+5/2 nounor h=-3/2-5/2,h=-4 nounor h=1],"\\(h^2+3\\,h-4=0\\)",h,1,-4,h=-3/2+sqrt(9/4-4),h=-3/2-sqrt(9/4-4)],
+[a2,[y^2-2*y-8=0,y=1+sqrt((-1)^2+8) nounor y=1-sqrt((-1)^2+8),y=-2 nounor y=4],"\\(y^2-2\\,y-8=0\\)",y,-2,4,y=1-sqrt(1-8),y=1+sqrt(1-8)],
+[a3,[z^2-4*z-5=0,z=2+sqrt((-2)^2+5) nounor z=2-sqrt((-2)^2+5),z=5 nounor z=-1],"\\(z^2-4\\,z-5=0\\)",z,5,-1,z=2+sqrt(4-5),z=2-sqrt(4-5)],
+[a4,[a^2-10*a+9=0,a=5+sqrt((-5)^2-9) nounor a=5-sqrt((-5)^2-9),a=9 nounor a=1],"\\(a^2-10\\,a+9=0\\)",a,9,1,a=5+sqrt(25+9),a=5-sqrt(25+9)]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
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+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr" style="text-align: left;">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2} \boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir="ltr" style="text-align: left;">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir="ltr" style="text-align: left;">Versuche es erneut und gib beide Lösungen an.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr" style="text-align: left;">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\) gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>last(BIN_a[2])</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint></syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options></options>
+ </input><deployedseed>1420701792</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-b p-q-Formel Ib - pq-Formel (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p>Bestimmen Sie den Wert der Variable in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\( = ?\;\).<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Erinnerst du dich noch an die pq-Formel? Für \(\;x^2 + p\,x + q = 0\;\) gilt \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\).<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[h^2+3*h-4=0,h=-3/2+sqrt((3/2)^2+4) nounor h=-3/2-sqrt((3/2)^2+4),h=-3/2+sqrt(25/4) nounor h=-3/2-sqrt(25/4),h=-3/2+5/2 nounor h=-3/2-5/2,h=-4 nounor h=1],"\\(h^2+3\\,h-4=0\\)",h,1,-4,h=-3/2+sqrt(9/4-4),h=-3/2-sqrt(9/4-4)],
+[a2,[y^2-2*y-8=0,y=1+sqrt((-1)^2+8) nounor y=1-sqrt((-1)^2+8),y=-2 nounor y=4],"\\(y^2-2\\,y-8=0\\)",y,-2,4,y=1-sqrt(1-8),y=1+sqrt(1-8)],
+[a3,[z^2-4*z-5=0,z=2+sqrt((-2)^2+5) nounor z=2-sqrt((-2)^2+5),z=5 nounor z=-1],"\\(z^2-4\\,z-5=0\\)",z,5,-1,z=2+sqrt(4-5),z=2-sqrt(4-5)],
+[a4,[a^2-10*a+9=0,a=5+sqrt((-5)^2-9) nounor a=5-sqrt((-5)^2-9),a=9 nounor a=1],"\\(a^2-10\\,a+9=0\\)",a,9,1,a=5+sqrt(25+9),a=5-sqrt(25+9)]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr" style="text-align: left;">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2} \boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir="ltr" style="text-align: left;">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir="ltr" style="text-align: left;">Versuche es erneut und gib beide Lösungen an.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr" style="text-align: left;">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\) gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>last(BIN_a[2])</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint></syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options></options>
+ </input><deployedseed>1009534997</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-f Potenzrechenregeln I - Endboss (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie folgenden Ausdruck; hierbei sind \(x,y \in \mathbb{R_{> 0}}\).</div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Dies ist die Endgegner-Aufgabe dieser Mathe-Welt <strong>Potenzrechenrelgen</strong>. Wenn du diese Aufgabe schaffst, hast du diese Mathe-Welt gemeistert. Viel Erfolg!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,stackeq(y^(-1/6)),"\\(\\frac{1}{\\sqrt[3]{y \\, \\sqrt x}} \\, \\sqrt[6]{x \\, y}\\)"],
+[a2,a^20*x^8,"\\(\\left( \\frac{a^3 x^5}{a^{-2} x^3} \\right)^4\\)"]
+];
+RUL_a:rand(RUL_A);
+
+/*ans1 is evaluated by ev(ans1,simp) to accept e. g. 1/(y^(1/6)) and y^(-1/6) and y^(-(1/6))*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ev(ans1,simp)</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1167231517</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-f Potenzrechenregeln I - Endboss (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie folgenden Ausdruck; hierbei sind \(x,y \in \mathbb{R_{> 0}}\).</div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Dies ist die Endgegner-Aufgabe dieser Mathe-Welt <strong>Potenzrechenrelgen</strong>. Wenn du diese Aufgabe schaffst, hast du diese Mathe-Welt gemeistert. Viel Erfolg!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,stackeq(y^(-1/6)),"\\(\\frac{1}{\\sqrt[3]{y \\, \\sqrt x}} \\, \\sqrt[6]{x \\, y}\\)"],
+[a2,a^20*x^8,"\\(\\left( \\frac{a^3 x^5}{a^{-2} x^3} \\right)^4\\)"]
+];
+RUL_a:rand(RUL_A);
+
+/*ans1 is evaluated by ev(ans1,simp) to accept e. g. 1/(y^(1/6)) and y^(-1/6) and y^(-(1/6))*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ev(ans1,simp)</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1313491755</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-a Potenzrechenregeln Ia – Exponenten addieren (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Fangen wir damit an, die Exponenten zu addieren, wenn die Basis gleich ist und multipliziert wird.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^a*c^b,"\\(c^{\\,a}\\cdot c^{\\,b}\\)"],
+[a2,x^a*x^b,"\\(x^{\\,a}\\cdot x^{\\,b}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1724483596</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-a Potenzrechenregeln Ia – Exponenten addieren (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Fangen wir damit an, die Exponenten zu addieren, wenn die Basis gleich ist und multipliziert wird.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^a*c^b,"\\(c^{\\,a}\\cdot c^{\\,b}\\)"],
+[a2,x^a*x^b,"\\(x^{\\,a}\\cdot x^{\\,b}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>337440314</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-b Potenzrechenregeln Ib – Exponenten subtrahieren (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Das funktioniert auch in die andere Richtung.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^a/c^b,"\\(\\frac{c^{\\,a}}{c^{\\,b}}\\)"],
+[a2,x^a/x^b,"\\(\\frac{x^{\\,a}}{x^{\\,b}}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>29351489</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-b Potenzrechenregeln Ib – Exponenten subtrahieren (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Das funktioniert auch in die andere Richtung.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^a/c^b,"\\(\\frac{c^{\\,a}}{c^{\\,b}}\\)"],
+[a2,x^a/x^b,"\\(\\frac{x^{\\,a}}{x^{\\,b}}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1996084793</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-c Potenzrechenregeln Ic - Wurzel als Potenz darstellen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Stellen Sie den Ausdruck in der Form \(c^{\frac{1}{n}}\) dar.<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Mithilfe von Potenzen der Form \(c^{\frac{1}{n}}\) lässt sich die n-te Wurzel von \(c\), also \(\;\sqrt[n]{c}\;\), darstellen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(1/6),"\\(\\sqrt[6]{c}\\)"],
+[a2,c^(1/5),"\\(\\sqrt[5]{c}\\)"],
+[a3,c^(1/4),"\\(\\sqrt[4]{c}\\)"],
+[a4,c^(1/3),"\\(\\sqrt[3]{c}\\)"],
+[a5,c^(1/7),"\\(\\sqrt[7]{c}\\)"],
+[a6,c^(1/8),"\\(\\sqrt[8]{c}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Sie können noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1074873352</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-c Potenzrechenregeln Ic - Wurzel als Potenz darstellen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Stellen Sie den Ausdruck in der Form \(c^{\frac{1}{n}}\) dar.<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Mithilfe von Potenzen der Form \(c^{\frac{1}{n}}\) lässt sich die n-te Wurzel von \(c\), also \(\;\sqrt[n]{c}\;\), darstellen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(1/6),"\\(\\sqrt[6]{c}\\)"],
+[a2,c^(1/5),"\\(\\sqrt[5]{c}\\)"],
+[a3,c^(1/4),"\\(\\sqrt[4]{c}\\)"],
+[a4,c^(1/3),"\\(\\sqrt[3]{c}\\)"],
+[a5,c^(1/7),"\\(\\sqrt[7]{c}\\)"],
+[a6,c^(1/8),"\\(\\sqrt[8]{c}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Sie können noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>460473552</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-c Potenzrechenregeln Ic - Wurzel als Potenz darstellen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Stellen Sie den Ausdruck in der Form \(c^{\frac{1}{n}}\) dar.<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Mithilfe von Potenzen der Form \(c^{\frac{1}{n}}\) lässt sich die n-te Wurzel von \(c\), also \(\;\sqrt[n]{c}\;\), darstellen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(1/6),"\\(\\sqrt[6]{c}\\)"],
+[a2,c^(1/5),"\\(\\sqrt[5]{c}\\)"],
+[a3,c^(1/4),"\\(\\sqrt[4]{c}\\)"],
+[a4,c^(1/3),"\\(\\sqrt[3]{c}\\)"],
+[a5,c^(1/7),"\\(\\sqrt[7]{c}\\)"],
+[a6,c^(1/8),"\\(\\sqrt[8]{c}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Sie können noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>771365681</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-c Potenzrechenregeln Ic - Wurzel als Potenz darstellen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Stellen Sie den Ausdruck in der Form \(c^{\frac{1}{n}}\) dar.<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Mithilfe von Potenzen der Form \(c^{\frac{1}{n}}\) lässt sich die n-te Wurzel von \(c\), also \(\;\sqrt[n]{c}\;\), darstellen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(1/6),"\\(\\sqrt[6]{c}\\)"],
+[a2,c^(1/5),"\\(\\sqrt[5]{c}\\)"],
+[a3,c^(1/4),"\\(\\sqrt[4]{c}\\)"],
+[a4,c^(1/3),"\\(\\sqrt[3]{c}\\)"],
+[a5,c^(1/7),"\\(\\sqrt[7]{c}\\)"],
+[a6,c^(1/8),"\\(\\sqrt[8]{c}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Sie können noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1250006169</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-d Potenzrechenregeln Id – Exponenten multiplizieren (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Wird ein Ausdruck, der eine Potenz enthält, potenziert, lassen sich die Exponenten miteinander multiplizieren.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(a*b),"\\((c^a)^b\\)",c^a*b],
+[a2,x^(a*b),"\\((x^a)^b\\)",x^a*b]
+];
+RUL_a:rand(RUL_A);
+wa:RUL_a[4];
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast die Klammer falsch gesetzt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1495340815</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-d Potenzrechenregeln Id – Exponenten multiplizieren (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Wird ein Ausdruck, der eine Potenz enthält, potenziert, lassen sich die Exponenten miteinander multiplizieren.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(a*b),"\\((c^a)^b\\)",c^a*b],
+[a2,x^(a*b),"\\((x^a)^b\\)",x^a*b]
+];
+RUL_a:rand(RUL_A);
+wa:RUL_a[4];
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast die Klammer falsch gesetzt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1196787611</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-e Potenzrechenregeln Ie - Potenzrechenregeln anwenden (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>Nutzen Sie die Potenzrechenregeln, um folgenden Ausdruck zu vereinfachen.<br></div>
+<p>
+</p>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p>
+<div class="bubble in-modal no-arrow">
+ <div>Hier zur Erinnerung die wichtigsten Potenzrechenregeln. Für \(x, y \neq 0\) und \(n, m \in \mathbb{Z}\) gilt:</div>
+<div>
+ <div>
+ <div>
+ <ul>
+ <li>\(x^{n+m} = x^n\,x^m\;\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \(2^5 = 2^{2+3} = 2^2 \cdot 2^3 = 4 \cdot 8 = 32\)</span></div></li></ul><ul>
+ <li>
+ <div>
+ <div>\(\left( x^n \right)^m = x^{n\,m}\;\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \(\left( 2^2 \right)^3 = 2^6 = 64\)</span></div></div>
+ </div>
+ </li>
+ <li>
+ <div>
+ <div>
+ <div>
+ <div>\((x\,y)^n = x^n\,y^n\;\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \(6^2 = (2 \cdot 3)^2 = 2^2 \cdot 3^2 = 4 \cdot 9 = 36\)</span></div></div>
+ </div>
+ </div>
+ </div>
+ </li>
+ <li>\(\frac{1}{x^n} = x^{-n}\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \( \frac{1}{x^2} \cdot x^2 = x^{-2} \cdot x^2 = x^{-2+2} = x^0 = 1\)</span><br></div></li>
+ <li>\(\sqrt[n]{x} = x^{\frac{1}{n}}\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \( \sqrt[3]{x} \cdot x^3 = x^{\frac{1}{3}} \cdot x^3 = x^{\frac{1}{3}+3} = x^1 = x\)</span></div></li>
+ </ul>
+ </div>
+ </div>
+</div>
+<p></p>
+<div>
+ <div>
+ <div>
+ <ul></ul>
+ </div>
+ </div>
+</div>
+</div></p>
+<p class="hint">Um diese Aufgabe zu lösen, kannst du mehrere der gerade erläuterten Regeln kombinieren. </p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(13/6),"\\(\\sqrt[6]{c} \\cdot c^2\\)"],
+[a2,x^10,"\\(\\frac{x^5}{x^{-5}}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Richtig, aber du kannst noch weiter vereinfachen.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1602709371</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-e Potenzrechenregeln Ie - Potenzrechenregeln anwenden (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>Nutzen Sie die Potenzrechenregeln, um folgenden Ausdruck zu vereinfachen.<br></div>
+<p>
+</p>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p>
+<div class="bubble in-modal no-arrow">
+ <div>Hier zur Erinnerung die wichtigsten Potenzrechenregeln. Für \(x, y \neq 0\) und \(n, m \in \mathbb{Z}\) gilt:</div>
+<div>
+ <div>
+ <div>
+ <ul>
+ <li>\(x^{n+m} = x^n\,x^m\;\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \(2^5 = 2^{2+3} = 2^2 \cdot 2^3 = 4 \cdot 8 = 32\)</span></div></li></ul><ul>
+ <li>
+ <div>
+ <div>\(\left( x^n \right)^m = x^{n\,m}\;\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \(\left( 2^2 \right)^3 = 2^6 = 64\)</span></div></div>
+ </div>
+ </li>
+ <li>
+ <div>
+ <div>
+ <div>
+ <div>\((x\,y)^n = x^n\,y^n\;\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \(6^2 = (2 \cdot 3)^2 = 2^2 \cdot 3^2 = 4 \cdot 9 = 36\)</span></div></div>
+ </div>
+ </div>
+ </div>
+ </li>
+ <li>\(\frac{1}{x^n} = x^{-n}\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \( \frac{1}{x^2} \cdot x^2 = x^{-2} \cdot x^2 = x^{-2+2} = x^0 = 1\)</span><br></div></li>
+ <li>\(\sqrt[n]{x} = x^{\frac{1}{n}}\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \( \sqrt[3]{x} \cdot x^3 = x^{\frac{1}{3}} \cdot x^3 = x^{\frac{1}{3}+3} = x^1 = x\)</span></div></li>
+ </ul>
+ </div>
+ </div>
+</div>
+<p></p>
+<div>
+ <div>
+ <div>
+ <ul></ul>
+ </div>
+ </div>
+</div>
+</div></p>
+<p class="hint">Um diese Aufgabe zu lösen, kannst du mehrere der gerade erläuterten Regeln kombinieren. </p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(13/6),"\\(\\sqrt[6]{c} \\cdot c^2\\)"],
+[a2,x^10,"\\(\\frac{x^5}{x^{-5}}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Richtig, aber du kannst noch weiter vereinfachen.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>547016054</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-a Ganzzahlige Summanden ableiten (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Leite jeden Summanden einzeln ab.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i,i,10),4); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; exercise:nums[1]*myvar^powers[1]+nums[2]*myvar^powers[2]+nums[3]*myvar+nums[4]; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>351097132</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-a Ganzzahlige Summanden ableiten (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Leite jeden Summanden einzeln ab.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i,i,10),4); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; exercise:nums[1]*myvar^powers[1]+nums[2]*myvar^powers[2]+nums[3]*myvar+nums[4]; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1047509677</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-a Ganzzahlige Summanden ableiten (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Leite jeden Summanden einzeln ab.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i,i,10),4); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; exercise:nums[1]*myvar^powers[1]+nums[2]*myvar^powers[2]+nums[3]*myvar+nums[4]; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>442872926</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-a Ganzzahlige Summanden ableiten (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Leite jeden Summanden einzeln ab.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i,i,10),4); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; exercise:nums[1]*myvar^powers[1]+nums[2]*myvar^powers[2]+nums[3]*myvar+nums[4]; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>286970886</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-b Gebrochenrationale Summanden ableiten (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@fractions[1]@} \cdot {@myvar@}^{@powers[1]@}+{@fractions[2]@} \cdot {@myvar@}^{@powers[2]@}+{@fractions[3]@} \cdot {@myvar@}+{@myint@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Leite jeden Summanden einzeln ab.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myint:rand_with_step(1,10,1); numerators:rand_selection(makelist(i+2,i,6),3); denominators:makelist(rand_with_step(numerators[i]+1,numerators[i]+5,1),i,3); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; fractions:makelist(numerators[i]/denominators[i],i,3); exercise:fractions[1]*myvar^powers[1]+fractions[2]*myvar^powers[2]+fractions[3]*myvar+myint; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>857840145</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-b Gebrochenrationale Summanden ableiten (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@fractions[1]@} \cdot {@myvar@}^{@powers[1]@}+{@fractions[2]@} \cdot {@myvar@}^{@powers[2]@}+{@fractions[3]@} \cdot {@myvar@}+{@myint@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Leite jeden Summanden einzeln ab.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myint:rand_with_step(1,10,1); numerators:rand_selection(makelist(i+2,i,6),3); denominators:makelist(rand_with_step(numerators[i]+1,numerators[i]+5,1),i,3); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; fractions:makelist(numerators[i]/denominators[i],i,3); exercise:fractions[1]*myvar^powers[1]+fractions[2]*myvar^powers[2]+fractions[3]*myvar+myint; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1543126498</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-b Gebrochenrationale Summanden ableiten (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@fractions[1]@} \cdot {@myvar@}^{@powers[1]@}+{@fractions[2]@} \cdot {@myvar@}^{@powers[2]@}+{@fractions[3]@} \cdot {@myvar@}+{@myint@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Leite jeden Summanden einzeln ab.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myint:rand_with_step(1,10,1); numerators:rand_selection(makelist(i+2,i,6),3); denominators:makelist(rand_with_step(numerators[i]+1,numerators[i]+5,1),i,3); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; fractions:makelist(numerators[i]/denominators[i],i,3); exercise:fractions[1]*myvar^powers[1]+fractions[2]*myvar^powers[2]+fractions[3]*myvar+myint; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1871228756</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-b Gebrochenrationale Summanden ableiten (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@fractions[1]@} \cdot {@myvar@}^{@powers[1]@}+{@fractions[2]@} \cdot {@myvar@}^{@powers[2]@}+{@fractions[3]@} \cdot {@myvar@}+{@myint@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Leite jeden Summanden einzeln ab.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myint:rand_with_step(1,10,1); numerators:rand_selection(makelist(i+2,i,6),3); denominators:makelist(rand_with_step(numerators[i]+1,numerators[i]+5,1),i,3); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; fractions:makelist(numerators[i]/denominators[i],i,3); exercise:fractions[1]*myvar^powers[1]+fractions[2]*myvar^powers[2]+fractions[3]*myvar+myint; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>318121367</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-c Produkte ableiten I (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:rand_selection(makelist(i+1,i,4),2); myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,4),2); exercise:(myvar^powers[1]+nums[1])*(myvar^powers[2]-nums[2]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1213180404</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-c Produkte ableiten I (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:rand_selection(makelist(i+1,i,4),2); myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,4),2); exercise:(myvar^powers[1]+nums[1])*(myvar^powers[2]-nums[2]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1876101711</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-c Produkte ableiten I (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:rand_selection(makelist(i+1,i,4),2); myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,4),2); exercise:(myvar^powers[1]+nums[1])*(myvar^powers[2]-nums[2]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1520468669</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-c Produkte ableiten I (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:rand_selection(makelist(i+1,i,4),2); myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,4),2); exercise:(myvar^powers[1]+nums[1])*(myvar^powers[2]-nums[2]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1233734487</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-d Produkte ableiten II (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>num:rand_with_step(1,5,2); denom:rand_with_step(num+2, num+5,2); fraction:num/denom; nums:rand_selection(append(makelist(i-7,i,6),makelist(i,i,6)),4); myvar:rand([a,b,c,x,y,z]); power:rand([3,4]); exercise:(fraction*myvar+nums[1])*(nums[2]*myvar^power+nums[3]*myvar+nums[4]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>290055394</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-d Produkte ableiten II (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>num:rand_with_step(1,5,2); denom:rand_with_step(num+2, num+5,2); fraction:num/denom; nums:rand_selection(append(makelist(i-7,i,6),makelist(i,i,6)),4); myvar:rand([a,b,c,x,y,z]); power:rand([3,4]); exercise:(fraction*myvar+nums[1])*(nums[2]*myvar^power+nums[3]*myvar+nums[4]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1877259825</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-d Produkte ableiten II (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>num:rand_with_step(1,5,2); denom:rand_with_step(num+2, num+5,2); fraction:num/denom; nums:rand_selection(append(makelist(i-7,i,6),makelist(i,i,6)),4); myvar:rand([a,b,c,x,y,z]); power:rand([3,4]); exercise:(fraction*myvar+nums[1])*(nums[2]*myvar^power+nums[3]*myvar+nums[4]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1027269811</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-d Produkte ableiten II (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>num:rand_with_step(1,5,2); denom:rand_with_step(num+2, num+5,2); fraction:num/denom; nums:rand_selection(append(makelist(i-7,i,6),makelist(i,i,6)),4); myvar:rand([a,b,c,x,y,z]); power:rand([3,4]); exercise:(fraction*myvar+nums[1])*(nums[2]*myvar^power+nums[3]*myvar+nums[4]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1906880472</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-e Division ableiten I (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:[rand_with_step(3,4,1), 2]; nums:rand_selection(makelist(i,i,12),5); myvar:rand([a,b,c,x,y,z]); exercise:(myvar^powers[1]+nums[1]*myvar^powers[2]+myvar)/(nums[2]*myvar^2+nums[3]*myvar+nums[4]); ta1:diff(exercise, myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1439694172</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-e Division ableiten I (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:[rand_with_step(3,4,1), 2]; nums:rand_selection(makelist(i,i,12),5); myvar:rand([a,b,c,x,y,z]); exercise:(myvar^powers[1]+nums[1]*myvar^powers[2]+myvar)/(nums[2]*myvar^2+nums[3]*myvar+nums[4]); ta1:diff(exercise, myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1028579078</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-e Division ableiten I (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:[rand_with_step(3,4,1), 2]; nums:rand_selection(makelist(i,i,12),5); myvar:rand([a,b,c,x,y,z]); exercise:(myvar^powers[1]+nums[1]*myvar^powers[2]+myvar)/(nums[2]*myvar^2+nums[3]*myvar+nums[4]); ta1:diff(exercise, myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1454088108</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-e Division ableiten I (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:[rand_with_step(3,4,1), 2]; nums:rand_selection(makelist(i,i,12),5); myvar:rand([a,b,c,x,y,z]); exercise:(myvar^powers[1]+nums[1]*myvar^powers[2]+myvar)/(nums[2]*myvar^2+nums[3]*myvar+nums[4]); ta1:diff(exercise, myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1063999325</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-f Division ableiten II (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:[rand([3,5,7,11]), rand_with_step(2,5,1)]; myvar:rand([a,b,c,x,y,z]); terms:[sqrt(nums[1])*myvar-nums[2], nums[1]*myvar^2-nums[2]]; terms:random_permutation(terms); exercise:terms[1]/terms[2]; ta1:diff(exercise, myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>525681144</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-f Division ableiten II (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:[rand([3,5,7,11]), rand_with_step(2,5,1)]; myvar:rand([a,b,c,x,y,z]); terms:[sqrt(nums[1])*myvar-nums[2], nums[1]*myvar^2-nums[2]]; terms:random_permutation(terms); exercise:terms[1]/terms[2]; ta1:diff(exercise, myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1447367624</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-f Division ableiten II (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:[rand([3,5,7,11]), rand_with_step(2,5,1)]; myvar:rand([a,b,c,x,y,z]); terms:[sqrt(nums[1])*myvar-nums[2], nums[1]*myvar^2-nums[2]]; terms:random_permutation(terms); exercise:terms[1]/terms[2]; ta1:diff(exercise, myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>435810786</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-f Division ableiten II (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:[rand([3,5,7,11]), rand_with_step(2,5,1)]; myvar:rand([a,b,c,x,y,z]); terms:[sqrt(nums[1])*myvar-nums[2], nums[1]*myvar^2-nums[2]]; terms:random_permutation(terms); exercise:terms[1]/terms[2]; ta1:diff(exercise, myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1421496847</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-g Kettenregel I (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root@}]{{@myvar@}^2-{@num@}}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); root:rand([3,5]); num:rand_with_step(3,9,1); exercise:(myvar^2-num)^(1/root); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1079586531</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-g Kettenregel I (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root@}]{{@myvar@}^2-{@num@}}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); root:rand([3,5]); num:rand_with_step(3,9,1); exercise:(myvar^2-num)^(1/root); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1754291070</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-g Kettenregel I (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root@}]{{@myvar@}^2-{@num@}}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); root:rand([3,5]); num:rand_with_step(3,9,1); exercise:(myvar^2-num)^(1/root); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1751932072</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-g Kettenregel I (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root@}]{{@myvar@}^2-{@num@}}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); root:rand([3,5]); num:rand_with_step(3,9,1); exercise:(myvar^2-num)^(1/root); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1089076165</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-h Kettenregel II (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,5),3); power:rand_with_step(3,7,2); signs:makelist(rand([-1,1]),2); exercise:(nums[1]*myvar^2+signs[1]*nums[2]*myvar+signs[2]*nums[3])^power; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1676415387</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-h Kettenregel II (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,5),3); power:rand_with_step(3,7,2); signs:makelist(rand([-1,1]),2); exercise:(nums[1]*myvar^2+signs[1]*nums[2]*myvar+signs[2]*nums[3])^power; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>146672542</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-h Kettenregel II (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,5),3); power:rand_with_step(3,7,2); signs:makelist(rand([-1,1]),2); exercise:(nums[1]*myvar^2+signs[1]*nums[2]*myvar+signs[2]*nums[3])^power; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1726255949</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-h Kettenregel II (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,5),3); power:rand_with_step(3,7,2); signs:makelist(rand([-1,1]),2); exercise:(nums[1]*myvar^2+signs[1]*nums[2]*myvar+signs[2]*nums[3])^power; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1628089061</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-i Gemischtes I (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,5),2); nums:rand_selection(makelist(i+1,i,58),2); exercise:(myvar^powers[1]+nums[1])^powers[2]*nums[2]*myvar; ta1:diff(exercise, myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>603470063</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-i Gemischtes I (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,5),2); nums:rand_selection(makelist(i+1,i,58),2); exercise:(myvar^powers[1]+nums[1])^powers[2]*nums[2]*myvar; ta1:diff(exercise, myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1387533043</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-i Gemischtes I (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,5),2); nums:rand_selection(makelist(i+1,i,58),2); exercise:(myvar^powers[1]+nums[1])^powers[2]*nums[2]*myvar; ta1:diff(exercise, myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>820026169</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-i Gemischtes I (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,5),2); nums:rand_selection(makelist(i+1,i,58),2); exercise:(myvar^powers[1]+nums[1])^powers[2]*nums[2]*myvar; ta1:diff(exercise, myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1884036955</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-j Gemischtes II (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,3),3); nums:rand_selection(makelist(i,i,5),2); exercise:(myvar^powers[1]-nums[1])^powers[2]*(myvar+nums[2])^powers[3]; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>949540891</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-j Gemischtes II (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,3),3); nums:rand_selection(makelist(i,i,5),2); exercise:(myvar^powers[1]-nums[1])^powers[2]*(myvar+nums[2])^powers[3]; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>2032277992</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-j Gemischtes II (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,3),3); nums:rand_selection(makelist(i,i,5),2); exercise:(myvar^powers[1]-nums[1])^powers[2]*(myvar+nums[2])^powers[3]; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>504654950</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-j Gemischtes II (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,3),3); nums:rand_selection(makelist(i,i,5),2); exercise:(myvar^powers[1]-nums[1])^powers[2]*(myvar+nums[2])^powers[3]; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>906697601</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-k Gemischtes III (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); terms:[rand_with_step(1,4,1)+myvar, myvar]; terms:random_permutation(terms); power:rand_with_step(3,7,1); exercise:(terms[1]/terms[2])^power; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1060600269</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-k Gemischtes III (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); terms:[rand_with_step(1,4,1)+myvar, myvar]; terms:random_permutation(terms); power:rand_with_step(3,7,1); exercise:(terms[1]/terms[2])^power; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1317786455</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-k Gemischtes III (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); terms:[rand_with_step(1,4,1)+myvar, myvar]; terms:random_permutation(terms); power:rand_with_step(3,7,1); exercise:(terms[1]/terms[2])^power; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>2016195942</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-k Gemischtes III (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); terms:[rand_with_step(1,4,1)+myvar, myvar]; terms:random_permutation(terms); power:rand_with_step(3,7,1); exercise:(terms[1]/terms[2])^power; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>79640143</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-l Gemischtes IV (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),2); power:rand_with_step(2,6,1); exercise:nums[1]*sqrt(nums[2]*myvar+myvar^power); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>63010318</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-l Gemischtes IV (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),2); power:rand_with_step(2,6,1); exercise:nums[1]*sqrt(nums[2]*myvar+myvar^power); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>2022252790</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-l Gemischtes IV (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),2); power:rand_with_step(2,6,1); exercise:nums[1]*sqrt(nums[2]*myvar+myvar^power); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>2032269463</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-l Gemischtes IV (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),2); power:rand_with_step(2,6,1); exercise:nums[1]*sqrt(nums[2]*myvar+myvar^power); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1301956355</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-m Gemischtes V (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),4); power:rand_with_step(2,5,1); terms:[(nums[1]*myvar+nums[2]), (nums[3]*myvar^power-nums[4])]; terms:random_permutation(terms); exercise:(terms[1]*terms[2])/myvar; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1627444094</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-m Gemischtes V (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),4); power:rand_with_step(2,5,1); terms:[(nums[1]*myvar+nums[2]), (nums[3]*myvar^power-nums[4])]; terms:random_permutation(terms); exercise:(terms[1]*terms[2])/myvar; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>570947981</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-m Gemischtes V (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),4); power:rand_with_step(2,5,1); terms:[(nums[1]*myvar+nums[2]), (nums[3]*myvar^power-nums[4])]; terms:random_permutation(terms); exercise:(terms[1]*terms[2])/myvar; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1123631251</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-m Gemischtes V (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),4); power:rand_with_step(2,5,1); terms:[(nums[1]*myvar+nums[2]), (nums[3]*myvar^power-nums[4])]; terms:random_permutation(terms); exercise:(terms[1]*terms[2])/myvar; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>566895213</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-n Gemischtes VI (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); root_power:rand_with_step(3,6,1); power:rand_with_prohib(2,5,[root_power]); nums:rand_selection(makelist(i+2,i,6),2);exercise:(nums[1]*myvar-nums[2])^(power/root_power); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>466316231</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-n Gemischtes VI (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); root_power:rand_with_step(3,6,1); power:rand_with_prohib(2,5,[root_power]); nums:rand_selection(makelist(i+2,i,6),2);exercise:(nums[1]*myvar-nums[2])^(power/root_power); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>73259082</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-n Gemischtes VI (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); root_power:rand_with_step(3,6,1); power:rand_with_prohib(2,5,[root_power]); nums:rand_selection(makelist(i+2,i,6),2);exercise:(nums[1]*myvar-nums[2])^(power/root_power); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>253364053</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-n Gemischtes VI (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); root_power:rand_with_step(3,6,1); power:rand_with_prohib(2,5,[root_power]); nums:rand_selection(makelist(i+2,i,6),2);exercise:(nums[1]*myvar-nums[2])^(power/root_power); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1197047345</deployedseed> </question>
+
+</quiz>
diff --git a/question-files/questions-normal_ger.xml b/question-files/questions-normal_ger.xml
new file mode 100644
index 0000000000000000000000000000000000000000..7a972d0a7ea077cd23d54cca57a9fa53e460c329
--- /dev/null
+++ b/question-files/questions-normal_ger.xml
@@ -0,0 +1,7990 @@
+<quiz><question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-a Gleichung eingeben (Multiplikation)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Geben Sie die Gleichung \({@ta1@}\) in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Hier eine leichte Aufgabe zur Eingabe. Benutze für jede Multiplikation das Symbol * (Stern).
+ <!--<span class="show-on-mobile-only"><br><br>Nutze die <a href="javascript:;" onclick="let userFocusTop = document.createElement('div');userFocusTop.classList.add('user-focus', 'hide-top');let pageHeight = document.documentElement.scrollHeight;userFocusTop.style.height=Math.ceil(pageHeight+window.pageYOffset)+'px';userFocusTop.onclick = removeTutorialFocus;document.body.appendChild(userFocusTop);">Buttons über deiner Tastatur</a>, um die wichtigsten Mathe-Operatoren schnell zu finden.</span>-->
+ <br><br>Falls du ohne Tastatur unterwegs bist, kannst du mithilfe des <a href="javascript:;" onclick="tutorialFocusElement(document.querySelector('.mathsbutton'));">Mathe-Operatoren-Buttons</a> zusätzliche Buttons aktivieren, um alle Mathe-Operatoren schnell zu finden.
+
+ <!--<br><br>Drücke jederzeit den "Prüfen"-Button, um zu sehen, wie deine Eingabe interpretiert wurde.<br>Erst wenn du nach dem "Prüfen"-Button deine Eingabe nicht änderst und
+ erneut "Prüfen" klickst, wird deine Eingabe als Antwort abgeschickt.-->
+<br><br>Neben dem Eingabefeld siehst du, wie deine Eingabe interpretiert wird.<br>Wenn du auf den "Prüfen"-Button klickst, wird deine Eingabe als Antwort abgeschickt.
+</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,y=3*x+5],[a2,y=4*x+3],[a3,y=2*x+1],[a4,y=2*x-5],[a5,y=5*x-3],[a6,y=4*x-6]];SYN_a:rand(SYN_A);ta1:SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>480757020</deployedseed><deployedseed>585237317</deployedseed><deployedseed>1798333349</deployedseed><deployedseed>2118152732</deployedseed><deployedseed>1988707695</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-b Gleichung eingeben (Division)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Geben Sie die Gleichung \({@TA@}\) in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Divisionen werden mit / (Slash) dargestellt. Hier erscheinen Sie als Brüche.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,y=5/3],[a2,y=4/7],[a3,y=1/3],[a4,y=2/5],[a5,y=3/10],[a6,y=1/4]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);TA:SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>TA</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Wir arbeiten hier nur wenn explizit danach gefragt wird mit Dezimalzahlen. Brüche stellen das Ergebnis in der Regel genauer dar.<br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>TA</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords>3x</forbidwords><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>2690042</deployedseed><deployedseed>300094393</deployedseed><deployedseed>765518486</deployedseed><deployedseed>17019212</deployedseed><deployedseed>1233892964</deployedseed><deployedseed>147932577</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-c Potenzen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Geben Sie die Gleichung \[{@ta@}\] in das Eingabefeld ein.</p>
+<p><p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p><p class="hint"><p>Mit dem Zeichen ^ (Caret) kannst du Potenzen darstellen.</p><div> <ul> <li>\(x^2\) wird so eingegeben: <code>x^2</code></li> <li>\(x^{-2}\) wird so eingegeben: <code>x^(-2)</code></li> <li>\(x^{1/3}\) wird so eingegeben: <code>x^(1/3)</code></li> </ul></div></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,(4+b)^2],[a2,(5+b)^2],[a3,(3+b)^2],[a4,(2+b)^2],[a5,(3+2*b)^2],[a6,(4+2*b)^2]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:expand(SYN_a[2])=SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[Sehr gut. Hier wurde übrigens eine binomische Formel angewendet, um einen Term zu faktorisieren.<br><p dir="ltr" style="text-align: left;" <br=""></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Deine Antwort ist zwar äquivalent mit der dargestellten Gleichung, aber du hast nicht genau die gleiche Gleichung dargestellt.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>93323135</deployedseed><deployedseed>1032837775</deployedseed><deployedseed>680315517</deployedseed><deployedseed>838329017</deployedseed><deployedseed>162866526</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-d Rationale Ausdrücke</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Geben Sie die Gleichung \[{@ta@}\] in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Machen wir es etwas komplizierter. Um Terme in Brüchen darzustellen, musst du besonders auf die Klammersetzung achten.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:x^2;b:(x+1);c:(x-5);SYN_A:[[a1,a,b,c],[a2,b,a,c],[a3,c,a,b]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:SYN_a[2]/(SYN_a[3]*SYN_a[4]);wa:SYN_a[2]/SYN_a[3]*SYN_a[4];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;" <br=""></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Bitte beachte, dass du um den Nenner zusätzliche Klammern setzen musst, damit er als zusammenhängender Divisor interpretiert wird.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>82298515</deployedseed><deployedseed>1458249622</deployedseed><deployedseed>1731794639</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-e Wurzelzeichen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Geben Sie \[{@ta1@}\] in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Gut. Um eine Wurzel darzustellen nutze <code>sqrt(x)</code> für \(\sqrt{x}\;\).</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,3],[a2,5],[a3,7],[a4,11],[a5,13],[a6,19]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta1:sqrt(SYN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1136692395</deployedseed><deployedseed>659595513</deployedseed><deployedseed>2040368424</deployedseed><deployedseed>262860513</deployedseed><deployedseed>592365331</deployedseed><deployedseed>1218846808</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-f Mehrere Lösungen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Lösen Sie nach \(x\) auf. Geben Sie die Lösung in der Form \(x=? \mbox{ or } x=?\) ein.</p>
+<p><p>\[{@task@}\]<br></p><p>[[input:ans]] [[validation:ans]][[feedback:prt1]]</p><p><em>Achtung: Bitte setzen Sie kein zusätzliches +-Symbol vor positive Zahlen.<br></em></p></p><p class="hint">Gelegentlich müssen Ausdrücke mit logischen Verbindungen verknüpft werden. Nutze dafür <code>and</code> oder <code>or</code>. <br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,4],[a2,9],[a3,16],[a4,25],[a5,36]];/*SYN_a:SYN_A[1];*/SYN_a:rand(SYN_A);ta:x=sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);taalt:x=+sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);task:x^2=SYN_a[2];wa1:x=sqrt(SYN_a[2]);wa2:x=-sqrt(SYN_a[2]);wa3:x=sqrt(SYN_a[2]) nounand x=-sqrt(SYN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>4</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>4</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>5</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>4</name><answertest>AlgEquiv</answertest><sans>1</sans><tans>1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-5-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr">Du hast nur eine von zwei richtigen Lösungen eingegeben.<br>Beispiel: \(5 \cdot 5 = 25\) und \(-5 \cdot -5 = 25\) (Minus Mal Minus ergibt Plus).<br>Für \(x^2 = 25\) gilt deshalb \(x = 5\) oder \(x = -5\), was hier in der Form <code>x=5 or x=-5</code> aufgeschrieben wird.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-5-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>5</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa3</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-6-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast alle richtigen Lösungen angegeben, allerdings hast du sie mit <code>and</code> verknüpft. Korrekt ist, sie mit <code>or</code> zu verknüpfen. Man schreibt</p><ul><li>entweder \(x=?\; oder \;x=?\)</li><li>oder \(x_1=?\; und \;x_2 = ?\;\).</li></ul>Hier benutzen wir ausschließlich die erste Form, die mit <code>x=? or x=?</code> dargestellt wird.<br>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-6-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords>4x</forbidwords><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>1032259226</deployedseed><deployedseed>2071301041</deployedseed><deployedseed>668615301</deployedseed><deployedseed>1810103727</deployedseed><deployedseed>2047586646</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-g Gleichung mehrschrittig lösen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p><p>Lösen Sie \(\;\){@p@}\(\;\) nach x auf.</p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.</p><p>Sie brauchen kein Äquivalenz-Zeichen eingeben.<br></p></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Um einen Rechenweg darzustellen, tippe jeden Schritt deiner Rechnung in eine neue Zeile in das Eingabefeld ein.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;b:3;c:4;SYN_A:[[a1,a,b,c],[a2,b,a,c],[a3,c,a,b],[a4,a,c,b],[a5,b,c,a],[a6,c,b,a]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:[SYN_a[2]*(SYN_a[3]+x)=SYN_a[4],SYN_a[2]*SYN_a[3]+SYN_a[2]*x=SYN_a[4],SYN_a[2]*x=SYN_a[4]-SYN_a[2]*SYN_a[3],x=(SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]];/*ta:[2*(3+x)=-3,2*x+6=-3,2*x=-9,x=-9/2];*/p:first(ta);/*p:"\\(2 \\cdot (3 + x) = -3\\)";*/wa1:x=-((SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]);wa2:x=SYN_a[4]-SYN_a[2]*SYN_a[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last(ans1)</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Aber fast richtig. Du hast dich offenbar mit dem Vorzeichen vertan.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar ist dir ein Fehler beim Lösen der Klammer unterlaufen. Um die Klammer aufzulösen, musst du beide beide Summanden in der Klammer mit dem Faktor vor der Klammer multiplizieren.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Weiter so. Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>equiv</type><tans>ta</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint>firstline</syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options>hideequiv</options></input><deployedseed>668615301</deployedseed><deployedseed>1810103727</deployedseed><deployedseed>2047586646</deployedseed><deployedseed>1032259226</deployedseed><deployedseed>2071301041</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-h Griechische Buchstaben</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Geben Sie \[{@ta@}\] in das Eingebefeld ein.</p>
+<p><p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p><em>Achtung: Bitte kopieren Sie keine Unicode-Zeichen, sondern benutzen Sie einfach Ihre Tastatur. <br></em></p></p><p class="hint">Wenn griechische Buchstaben einzugeben sind, schreibe sie einfach aus. Beispiel: \(\alpha=\) <code>alpha</code> , \(\beta=\) <code>beta</code><code></code> ,\(\pi=\) <code>pi </code><code></code>.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:beta;b:pi;c:alpha;SYN_A:[[a1,a,b],[a2,b,a],[a3,a,c],[a4,c,a],[a5,b,c],[a6,c,b]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:SYN_a[2]*z^(SYN_a[3]*x)wa1:SYN_a[2]*z^SYN_a[3]*x</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offenbar vergessen, eine Klammer um die Potenz zu schreiben. Schreibe Potenzen in Klammern, wenn sie aus mehr als einer Zahl bestehen. Beispiel: \(x^{-2a}\) wird so eingegeben: <code>x^(-2*a)</code>.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>1516837293</deployedseed><deployedseed>911975771</deployedseed><deployedseed>742782033</deployedseed><deployedseed>1709130663</deployedseed><deployedseed>648468622</deployedseed><deployedseed>272609913</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-i Syntax-Endboss</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p><p>Lösen Sie {@p@} nach \(x\) auf.<br></p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.<br></p></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]<p></p><p><em>Zur Erinnerung: Das Kommando für</em> \(\sqrt{x}\)<em> lautet </em><code>sqrt(x)</code><em>. Nutzen Sie </em><code>or</code><em> um mehrere Lösungen anzugeben.</em></p></p><p class="hint">Willkommen zum Endgegner dieser Mathe-Welt. Mit dem Lösen dieser Aufgabe hast du die erste Mathe-Welt bereits abgeschlossen. Viel Erfolg!<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;b:3;c:4;d:2;e:3;SYN_A:[[a1,a,d],[a2,b,d],[a3,c,d],[a4,a,e],[a5,b,e],[a6,c,e]];SYN_a:rand(SYN_A);pifactor:ev(SYN_a[2]*(SYN_a[3]^2),simp);ta:[/*(SYN_a[2]*x^2)/(pifactor*pi)=1,*/SYN_a[2]*x^2=pifactor*pi,x^2=(SYN_a[3]^2)*pi,x=SYN_a[3]*sqrt(pi) nounor x=-SYN_a[3]*sqrt(pi)];p:first(ta);wa1:x=SYN_a[3]*sqrt(pi);wa2:x=-SYN_a[3]*sqrt(pi);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last(ans1)</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text><![CDATA[]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>4</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>3</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>3</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>1</sans><tans>1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast nur eine von zwei richtigen Lösungen eingegeben.<br>Beispiel: \(5\,\sqrt{\pi} \cdot 5\,\sqrt{\pi} = 25\,\pi\) und \(-5\,\sqrt{\pi} \cdot -5\,\sqrt{\pi} = 25\,\pi\) (Minus Mal Minus ergibt Plus).<br>Für \(x^2 = 25\pi\) gilt deshalb \(x = 5\,\sqrt{\pi}\) oder \(x = -5\,\sqrt{\pi}\), was hier in der Form <code>x=5*sqrt(pi) or x=-5*sqrt(pi)</code> aufgeschrieben wird.</p><p dir="ltr" style="text-align: left;"></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>4</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-5-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-5-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>equiv</type><tans>ta</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint>firstline</syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options>hideequiv</options></input><deployedseed>1169120426</deployedseed><deployedseed>1624332195</deployedseed><deployedseed>1578649438</deployedseed><deployedseed>1629124203</deployedseed><deployedseed>2120835467</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-a Kürzen zweier einfacher Brüche</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\({@f@} \cdot {@g@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Gekürzt wird, indem man Zähler & Nenner durch dieselbe Zahl teilt.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(2,8,1); b:rand_with_step(20,40,10); c:a*b; d:b/5; e:a*b/10; ta1:1/a; simp:false; f:5/e; g:d/10; wa1:(5+d)/(e+10);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@f@} \cdot {@g@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir="ltr" style="text-align: left;">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>423191525</deployedseed><deployedseed>1756629135</deployedseed><deployedseed>505485688</deployedseed><deployedseed>813830513</deployedseed><deployedseed>1619258121</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-b Kürzen zweier Brüche mit Variablen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\,a\,a\,b\,b\,c}{a\,a\,a\,a\,a\,b\,c\,c\,c}\)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); powers:makelist(rand(5)+1, 6); myvar1: mya^powers[1]; myvar2: myb^powers[2]; myvar3: myc^powers[3]; myvar4: mya^powers[4]; myvar5: myb^powers[5]; myvar6: myc^powers[6]; d:(myvar1*myvar2*myvar3)/(myvar4*myvar5*myvar6); ta1:d;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Beispiel: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,b\,b\mkern-5mu/\,c\mkern-5mu/}{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,a\,a\,b\mkern-5mu/\,c\mkern-5mu/\,c\,c} = \frac{b}{a^2\,c^2}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>194802941</deployedseed><deployedseed>1917875187</deployedseed><deployedseed>1931041228</deployedseed><deployedseed>928137609</deployedseed><deployedseed>264598581</deployedseed><deployedseed>1633750828</deployedseed><deployedseed>1318198792</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-c Kürzen zweier Brüche mit Variablen und Zahlen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Erst auf einen Bruchstrich sortieren. Beispiel: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} = \frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c}\)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>num1:rand_with_step(5,8,1); varlist:[a,b,c,u,v,w,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1], varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); num2:rand_with_step(3,7,1); num3:rand_with_step(3,7,1); nom1:num1*num2*myvars[1]; denom1:num1*myvars[2]; nom2:num1*num3*myvars[1]*myvars[2]; denom2:num1*myvars[1]*myvars[3]; ta1:(nom1/denom1)*(nom2/denom2); /*Alle Variablen in den Zählern mit einer Variable im Nenner gekürzt.*/wa1:((nom1/myvars[1])*(nom2/myvars[1]))/((denom1*denom2)/myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich die Variable {@myvars[1]@} im Nenner gegen beide Variablen in den Zählern gekürzt. Bei der Multiplikation von Brüchen kannst du immer nur einen Faktor gegen den anderen kürzen. Beispiel: \(\frac{36}{6} = \frac{6\cdot6}{6} = \frac{6\mkern-5mu/\cdot6}{6\mkern-5mu/} = \frac{6}{1} = 6\) und nicht \(\frac{36}{6} = \frac{6\cdot6}{6} \ne \frac{6\mkern-5mu/\cdot6\mkern-5mu/}{6\mkern-5mu/} = 1\;\).<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>So lassen sich Produkte auf einem Bruchstrich sortieren und kürzen: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} =\frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c} =\frac{49^7\mkern-14mu\large/ \small \; \cdot 21^3\mkern-14mu\large/\small \; \cdot a\mkern-5mu/ \cdot a \cdot b\mkern-5mu/}{7\mkern-5.5mu/ \cdot7\mkern-5.5mu/ \cdot a\mkern-5mu/\cdot b\mkern-5mu/\cdot c} =\frac{21\,a}{c}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1842189518</deployedseed><deployedseed>1601667602</deployedseed><deployedseed>2136766316</deployedseed><deployedseed>1542661342</deployedseed><deployedseed>2072145258</deployedseed><deployedseed>328965971</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-d Kürzen zweier Brüche mit Termen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Kennst du noch den Ausspruch „Aus Summen kürzen nur die Dummen“?!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([x,y,z]); term_summand1:rand_with_prohib(-3,3,[0]); term_summand2:rand_with_prohib(-3,3,[0,term_summand1]); term1:myvar+term_summand1; term2:myvar+term_summand2; ta1:term1/myvar*(myvar^2/(term1*term2*myvar)); /*wa1 means: naive shortened fraction*/ wa1:(term1-myvar)/1*(myvar^2/(term1*term2*myvar));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Offensichtlich hast du beim ersten Bruch die Variable {@myvar@} im Nenner gegen die Variable {@myvar@} im Zähler gekürzt. Das geht aber nicht, weil die Variable {@myvar@} im Zähler mit einem anderen Summanden eine Summe bildet. Beispiel: \(3 = \frac{6}{2} = \frac{4+2}{2} \ne \frac{4 + 2\mkern-5.5mu/}{2\mkern-5.5mu/} = \frac{4}{1} = 4\;\).]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p> Nur ganze Faktoren dürfen gekürzt werden. Zum Beispiel: \(\frac{\boldsymbol{(x-1)}\cdot 2}{x \cdot \boldsymbol{(x-1)}} = \frac{2}{x}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>837792651</deployedseed><deployedseed>528135820</deployedseed><deployedseed>879656886</deployedseed><deployedseed>1917537516</deployedseed><deployedseed>1617668401</deployedseed><deployedseed>159039633</deployedseed><deployedseed>1131743594</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-a Einfachen Bruch erweitern</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\({@c@} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(4,9,1); b:a-1; c:a/b; d:a*5; e:b*5; simp:false; ta1:d/e;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@c@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>437845679</deployedseed><deployedseed>2092409135</deployedseed><deployedseed>1712748750</deployedseed><deployedseed>182980498</deployedseed><deployedseed>388683995</deployedseed><deployedseed>1561500176</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-b Bruch mit Variablen erweitern</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@numerator@}}{{@denominator@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,4); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[1]^powers[3]; fac4:myvars[2]^powers[4]; numerator:fac1*fac2; denominator:fac3*fac4; d:numerator/denominator; tanumerator:5*num(d); tadenominator:5*denom(d); simp:false; ta1:tanumerator/tadenominator;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@numerator@}}{{@denominator@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>36209422</deployedseed><deployedseed>1000344719</deployedseed><deployedseed>1827440244</deployedseed><deployedseed>1291739138</deployedseed><deployedseed>825866743</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-c Bruch mit Variablen und Zahlen erweitern</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,3); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[2]^powers[3]; rand1:rand(4); rand2:rand_with_prohib(0,3,[rand1]); number1:rand1*2+3; number2:rand2*2+3; number3:rand_with_step(2,8,2); numerator:fac1*fac2; denominator:fac3; d:numerator/denominator; tanumerator:5*number1*number2*num(d); tadenominator:5*number3*denom(d); simp:false; ta1:tanumerator/tadenominator;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1516326427</deployedseed><deployedseed>1341581403</deployedseed><deployedseed>79491835</deployedseed><deployedseed>1422333316</deployedseed><deployedseed>1757641065</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ca Einfache Addition von Brüchen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Addieren und Subtrahieren müssen die Nenner der Brüche gleich sein. Kannst du dich noch an das kleinste gemeinsame Vielfache erinnern?</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(1,4,1)*2+1; fac1:rand_with_step(1,4,1); fac2:rand_with_prohib(1,4,[fac1]); denoms:[a, a*fac1,a*fac2]; nums:makelist(rand_with_step(1,denoms[i]-1,2),i,3); signs:makelist(rand_with_prohib(-1,1,[0]),3); fractions:makelist(signs[i]*nums[i]/denoms[i],i,3); fractions:random_permutation(fractions); ta1:fractions[1]+fractions[2]+fractions[3]; simp:false; exercise:fractions[1]+fractions[2]+fractions[3]; /*wa1 means: naive addition*/ wa1:(num(fractions[1])+num(fractions[2])+num(fractions[3]))/(denom(fractions[1])+denom(fractions[2])+denom(fractions[3]));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir="ltr" style="text-align: left;">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>]]></text>
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+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um die Nenner gleich zu machen, musst du sie so erweitern, dass sie den gleichen Nenner haben. Dann können die Zähler addiert werden. Das kleinste gemeinsame Vielfache von 5, 10 und 15 lässt sich zum Beispiel finden, indem man die jeweiligen Reihen notiert und die kleinste gemeinsame Zahl sucht.</p><table><tr><th>5er-Reihe</th><th>10er-Reihe</th><th>15er-Reihe</th></tr><tr><td>5</td><td>10</td><td>15</td></tr><tr><td>10</td><td>20</td><td><strong>30</strong></td></tr><tr><td>15</td><td><strong>30</strong></td><td>...</td></tr><tr><td>20</td><td>...</td><td>...</td></tr><tr><td>25</td><td>...</td><td>...</td></tr><tr><td><strong>30</strong></td><td>...</td><td>...</td></tr><tr><td>...</td><td>...</td><td>...</td></tr></table></p>]]></text>
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+<falsepenalty/>
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+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>311233457</deployedseed><deployedseed>584289189</deployedseed><deployedseed>1338253474</deployedseed><deployedseed>933392702</deployedseed><deployedseed>236951333</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cb Addition von Brüchen mit Variablen und gleichem Nenner</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Überlege genau, was ein Minus vor einem Bruch bedeutet.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c]); fractions_correct_and_wa1:[[(myvar+1)/myvar, -myvar+1], [(myvar-1)/myvar, -myvar-1], [(1-myvar)/myvar, -1-myvar]]; fractions_correct_and_wa1:random_permutation(fractions_correct_and_wa1); fractions:makelist(fractions_correct_and_wa1[i][1],i,3); terms_wa1:makelist(fractions_correct_and_wa1[i][2],i,3); exercise:fractions[1]-fractions[2]-fractions[3]; ta1:combine(exercise); wa1:(num(fractions[1])+terms_wa1[2]+terms_wa1[3])/myvar;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@}-{@fractions[2]@}-{@fractions[3]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
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+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
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+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
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+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
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+ <falsescore>0</falsescore>
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+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
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+ <truescoremode>=</truescoremode>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
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+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast offenbar die Minuszeichen nicht korrekt aufgelöst.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Ein Minus vor dem Bruch gehört zum ganzen Bruch: gilt also für den ganzen Zähler oder ganzen Nenner (häufig nimmt man den Zähler).</p><p>\(\Rightarrow -\frac{a-1}{a} = \frac{-\boldsymbol{(a-1)}}{a} = \frac{-a+1}{a}\)</p><p>Wichtig bei Summen im Zähler!!!</p></p>]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>471812117</deployedseed><deployedseed>416709956</deployedseed><deployedseed>743127794</deployedseed><deployedseed>2005900637</deployedseed><deployedseed>634867927</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cc Addition von Brüchen mit Variablen und unterschiedlichen Nennern</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Jeder Teilnenner (hier: {@myvars[1]@}, {@myvars[2]@}, {@myvars[3]@}) muss als Faktor im gemeinsamen Nenner vorkommen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); fractions:[(1+myvars[1])/myvars[1], rand_with_step(2,5,1)/myvars[2], myvars[1]/myvars[3]]; fractions:random_permutation(fractions); exercise:fractions[1]+fractions[2]+fractions[3]; common_denom:denom(fractions[1])*denom(fractions[2])*denom(fractions[3]); ta1:((num(fractions[1])*denom(fractions[2])*denom(fractions[3]))+(num(fractions[2])*denom(fractions[1])*denom(fractions[3]))+(num(fractions[3])*denom(fractions[1])*denom(fractions[2])))/common_denom; ta1alt:(expand((num(fractions[1])*denom(fractions[2])*denom(fractions[3])))+expand((num(fractions[2])*denom(fractions[1])*denom(fractions[3])))+expand((num(fractions[3])*denom(fractions[1])*denom(fractions[2]))))/common_denom;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
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+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
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+ <showvalidation>3</showvalidation>
+ <options/>
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+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{1+a}{a}+\frac{2}{b}+\frac{a}{c}\) ist der gemeinsame Nenner \(a \cdot b \cdot c\). So muss erweitert werden, damit die Zähler addiert werden können:</p><p>\(\frac{(1+a) \boldsymbol{\cdot b \cdot c} }{a \boldsymbol{\cdot b \cdot c}}+\frac{2 \boldsymbol{\cdot a \cdot c}}{\boldsymbol{a} \cdot b \boldsymbol{\cdot c}}+\frac{a \boldsymbol{\cdot a \cdot b}}{\boldsymbol{a \cdot b} \cdot c}\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(1+a\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p></p>]]></text>
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+</node></prt><deployedseed>638235066</deployedseed><deployedseed>1053964038</deployedseed><deployedseed>625975426</deployedseed><deployedseed>1098133316</deployedseed><deployedseed>1880026849</deployedseed><deployedseed>1344755034</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cd Addition von Brüchen mit einer Variablen und unterschiedlichen Nennern</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([x,y,z]); nums:makelist(rand_with_step(2,5,1),2); fractions:[(nums[1]+myvar)/myvar^2,(nums[2]-myvar^2)/myvar]; common_denom:myvar^2; ta1:(num(fractions[1])-num(fractions[2])*myvar)/common_denom; ta1alt:(num(fractions[1])-expand(num(fractions[2])*myvar))/common_denom; exercise:fractions[1]-fractions[2]; /*wa1 means: didn't consider minus sign before bracket*/ wa1:(num(fractions[1])+(-nums[2]-myvar^2)*myvar)/common_denom;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
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+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
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+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
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+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast offenbar die Minuszeichen nicht korrekt aufgelöst (siehe Tipp unten).]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um immer einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{3+x}{x^2}-\frac{5-x}{x}\) ist ein gemeinsame Nenner \(x^2 \cdot x = x^3\). Betrachtet man die Teilnenner \(x^2\) und \(x\) genauer, fällt auf, dass \(x\) bereits als Faktor in \(x^2\) vorkommt. Denn \(x^2 = x \cdot x\). Deswegen kann hier auch \(x^2\) als Hauptnenner gewählt werden.</p><p>Dazu muss so erweitert werden:</p><p>\(\frac{(3+x)}{x^{2}}-\frac{(5-x^2) \boldsymbol{ \cdot x}}{x \boldsymbol{\cdot x}} = \frac{3+x}{x^{2}}-\frac{5x-x^3}{x^{\boldsymbol{2}}} = \frac{3+x-(5x-x^3)}{x^2} = \dots\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(5-x^2\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p></p>]]></text>
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+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ce Addition von Brüchen mit Variablen und unterschiedlichen Nennern I (Update1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); numbers:makelist(rand_with_step(2,5,1), 5); factors:random_permutation([1,2,4]); /*only +*/ signs:makelist(rand_with_prohib(1,1,[0]),2); fractions:[(numbers[1]*myvars[1]-numbers[2]*myvars[2])/(factors[1]*5*myvars[1]*myvars[2]), (numbers[3]*myvars[3]-numbers[4]*myvars[1])/(factors[2]*5*myvars[1]*myvars[3]), (myvars[3]^2-numbers[5])/(factors[3]*5*myvars[2]*myvars[3])]; tanum:(num(fractions[1])*(4/factors[1])*myvars[3]+num(fractions[2])*(4/factors[2])*myvars[2]+num(fractions[3])*(4/factors[3])*myvars[1]); tanumalt:expand(tanum); tadenom:(5*4*myvars[1]*myvars[2]*myvars[3]); ta1:tanum/tadenom; /*fractions_to_show:random_permutation(fractions);*/ fractions_to_show:fractions; ta1alt:tanumalt/tadenom; fractions_to_show[2]:fractions_to_show[2]*signs[1]; fractions_to_show[3]:fractions_to_show[3]*signs[2]; exercise:fractions_to_show[1]+fractions_to_show[2]+fractions_to_show[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
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+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{5\,z-4\,x}{10\,x\,z}+\frac{7\,y-3\,z}{20\,y\,z}+\frac{y^2-2}{5\,x\,y}\) ist \(20\) das kleinste gemeinsame Vielfache (kgV) von \(10\), \(20\) und \(5\) und \(x \cdot y \cdot z\) ist das kgV von \(x \cdot z\), \(y \cdot z\) und \(x \cdot y\). Der Hauptnenner ist demnach \(20 \cdot x \cdot y \cdot z\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(20 \cdot x \cdot y \cdot z\;\) steht. \(\frac{5\,z-4\,x}{10\,x\,z}\) wird mit \(2 \cdot y\) erweitert, \(\frac{7\,y-3\,z}{20\,y\,z}\) wird mit \(x\) erweitert und \(\frac{y^2-2}{5\,x\,y}\) wird mit \(4 \cdot z\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(5\,z-4\,x)\boldsymbol{ \cdot 2\,y}}{10\,x\,z \boldsymbol{ \cdot 2\,y}}+\frac{(7\,y-3\,z) \boldsymbol{ \cdot x}}{20\,y\,z \boldsymbol{ \cdot x}}+\frac{(y^2-2) \boldsymbol{ \cdot 4\,z}}{5\,x\,y \boldsymbol{ \cdot 4\,z}}\)</p><p>\(= \frac{10\,y\,z-8\,x\,y}{20\,x\,y\,z}+\frac{7\,x\,y-3\,x\,z}{20\,x\,y\,z}+\frac{4\,y^2\,z-8\,z}{20\,x\,y\,z} = \dots\)</p></p>]]></text>
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+<falsepenalty/>
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+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1330316881</deployedseed><deployedseed>2007639052</deployedseed><deployedseed>846124380</deployedseed><deployedseed>520216901</deployedseed><deployedseed>1618486590</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cf Addition von Brüchen mit Variablen und unterschiedlichen Nennern II</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: 1) Überlege genau, was ein Minus vor einem Bruch bedeutet. 2) Jeder Teilnenner (hier: {@denom(main_fraction)@}, {@denom(fractions[1])@}, {@denom(fractions[2])@}) muss als Faktor im gemeinsamen Nenner vorkommen. 3) Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); numbers:rand_selection(makelist(i,i,5),2); denom_nums_origin:rand_selection([18,12,6],1)[1]; denom_nums:[denom_nums_origin, denom_nums_origin/2, denom_nums_origin/3]; main_fraction:(numbers[1]-myvars[1])/(denom_nums[1]*myvars[1]^2); fractions:[(myvars[2])/(denom_nums[2]*myvars[1]), (myvars[2]+numbers[2])/(denom_nums[3]*myvars[1]*myvars[2])]; tanum:num(main_fraction)*myvars[2]-num(fractions[1])*2*myvars[1]*myvars[2]-num(fractions[2])*3*myvars[1]; tanumalt:expand(tanum); tadenom:denom_nums_origin*myvars[1]^2*myvars[2]; ta1:tanum/tadenom; ta1alt:tanumalt/tadenom; fractions:random_permutation(fractions); simp:false; exercise:main_fraction-fractions[1]-fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
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+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
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+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{1-x}{18\,x^2}-\frac{y}{9\,x}-\frac{x+3}{6\,x\,y}\) ist \(18\) das kleinste gemeinsame Vielfache (kgV) von \(18\), \(9\) und \(6\) und \(x^2 \cdot y\) ist das kgV von \(x^2\), \(x\) und \(x \cdot y\). Der Hauptnenner ist demnach \(18 \cdot x^2 \cdot y\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(18 \cdot x^2 \cdot y\;\) steht. \(\frac{1-x}{18\,x^2}\) wird mit \(y\) erweitert, \(\frac{y}{9\,x}\) wird mit \(2\,x\,y\) erweitert und \(\frac{x+3}{6\,x\,y}\) wird mit \(3 \cdot x\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(1-x) \boldsymbol{\cdot y}}{18\,x^2 \boldsymbol{\cdot y}}-\frac{y \boldsymbol{\cdot 2\,x\,y}}{9\,x \boldsymbol{\cdot 2\,x\,y}}-\frac{(x+3) \boldsymbol{\cdot 3\,x}}{6\,x\,y \boldsymbol{\cdot 3\,x}}\)</p><p>\(= \frac{y-x\,y}{18\,x^2\,y}-\frac{2\,x\,y^2}{18\,x^2\,y}-\frac{3\,x^2+9\,x}{18\,x^2\,y} = \dots\)</p></p>]]></text>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>527686404</deployedseed><deployedseed>1918490776</deployedseed><deployedseed>2103547991</deployedseed><deployedseed>1091135158</deployedseed><deployedseed>1696865873</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-da Multiplikation zweier einfacher Brüche</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@}\cdot{@fractions[2]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8),4); fractions:[nums[1]/nums[2], nums[3]/nums[4]]; ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions*/ wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied*/ wa2:fractions[1]+fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@}\cdot{@fractions[2]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
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+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
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+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
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+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
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+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
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+ <falsescore>0</falsescore>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
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+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{2}{3} \cdot \frac{6}{5} = \frac{2 \cdot 6}{3 \cdot 5} = \frac{12}{15} = \frac{4}{5}\)</p></p>]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1088212423</deployedseed><deployedseed>1553109555</deployedseed><deployedseed>777390971</deployedseed><deployedseed>1688656099</deployedseed><deployedseed>1485690277</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-db Multiplikation zweier Brüche mit Variablen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); fractions:[mya/myb, mya^2/(mya*myb)]; fractions:random_permutation(fractions); ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions with previously shortened the larger fraction*/ wa1:(2*mya)/(2*myb); /*wa2 means: naively summed fractions without previously shortening the larger fraction*/ wa2:(mya+myb^2)/(mya+myb*mya); /*wa3 means: correctly summed fractions instead of multiplied*/ wa3:fractions[1]+fractions[2]; /*wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied wa2:fractions[1]+fractions[2];*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} = {@ta1@}\)</text>
+ </questionnote>
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+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
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+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden. Du hast außerdem den Bruch \({@mya@}^2/({@mya@}*{@myb@})\) nicht ausreichend vereinfacht. Er kann zu \({@mya@}/{@myb@}\) gekürzt werden.]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{a}{b} \cdot \frac{a^2}{a\,b} = \frac{a}{b} \cdot \frac{a \cdot a}{a\,b} = \frac{a \cdot a \cdot a}{a \cdot b \cdot b} = \frac{a^3}{a\,b^2}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>545658671</deployedseed><deployedseed>1228864607</deployedseed><deployedseed>806993602</deployedseed><deployedseed>1501016569</deployedseed><deployedseed>710282177</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dc Multiplikation Bruch mit Zahlen, Bruch mit Variablen, Ganzzahl</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Wie kann man eine ganze Zahl als Bruch schreiben?</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8),3); nums:sort(nums); varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); factors:[nums[1], (mya*myb)/myc, nums[2]/nums[3]]; factors:random_permutation(factors); ta1:factors[1]*factors[2]*factors[3]; simp:false; exercise:factors[1]*factors[2]*factors[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
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+ <requirelowestterms>0</requirelowestterms>
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+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
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+ <text/>
+ </feedbackvariables>
+ <node>
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+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
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+ <truescoremode>=</truescoremode>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>999</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truescoremode>+</truescoremode>
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+<truepenalty/>
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+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Jede ganze Zahl kann als Bruch geschrieben werden, indem man sie durch 1 teilt. Beispiel: \(3 \cdot \frac{a\,b}{c} \cdot \frac{5}{6} = \frac{3}{1} \cdot \frac{a\,b}{c} \cdot \frac{5}{6}\)</p><p>\( = \frac{3 \cdot a \cdot b \cdot 5}{1 \cdot c \cdot 6} = \frac{15\,a\,b}{6\,c} = \frac{5\,a\,b}{2\,c}\)</p><p>Hinweis: Generellt gilt \(\cdot 1\) und \(:\,1\) geht immer.</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1569886884</deployedseed><deployedseed>1980675582</deployedseed><deployedseed>1601683210</deployedseed><deployedseed>51348788</deployedseed><deployedseed>726919830</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dd Multiplikation zweier Brüche mit Termen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Summanden & Faktoren => Klammer!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:rand_selection(varlist, 2); nums:rand_selection(makelist(i+1,i,9), 6); fractions:[(nums[1]*myvars[1]+nums[2]*myvars[2])/(nums[3]*myvars[2]+nums[4]*myvars[1]), (-nums[5]*myvars[1])/(nums[6]+myvars[1])]; ta1:fractions[1]*fractions[2]; taalt:combine(expand(ta1)); /*wa1 means: the multiplication of the numerator was done with only one summand of the first fraction’s numerator (the second one)*/ wa1:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(denom(fractions[1])*denom(fractions[2])); /*old_wa2 means the same as wa1 but with the first fraction numerator’s second summand*/ /*old_wa2: (nums[1]*myvars[1]*num(fractions[2])+nums[2]*myvars[2])/(denom(fractions[1])*denom(fractions[2]));*/ /*wa2 means the same as wa1 but with the denominators, so no brackets: first summand of second fraction is multiplied with last summand of first fraction*/ wa2:(num(fractions[1])*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]); /*wa3 is the combination of wa1 and wa2*/ wa3:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}= {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Nenner richtig multipliziert, doch du hast den Faktor im Zähler des zweiten Bruches nur mit dem zweiten Summanden des Zählers im ersten Bruch multipliziert. Das heißt bei der Multiplikation der Zähler musst du Klammern um die Summe setzen und jeden Summanden des ersten Zählers mit dem Faktor des anderen Zählers multiplizieren.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Zähler richtig multipliziert, hast jedoch im Nenner nicht beachtet, dass Summen als Ganzes multipliziert werden. Das heißt bei der Multiplikation der Nenner musst du Klammern um die Summen setzen und jeden Summanden des einen Nenners mit jedem Summanden des anderen Nenners multiplizieren.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>5</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>5</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-6-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Summen nicht als Ganzes multipliziert. Das betrifft eine Summe im Zähler und die Summen im Nenner. Du musst jeweils Klammern setzen, damit jeder Summand mit jedem anderen Summanden multipliziert wird. ]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-6-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{4\,x+10\,y}{5\,y+2\,x} \cdot \frac{-4\,x}{3+x} = \)\(\frac{\boldsymbol{(4\,x+10\,y)} \cdot -4\,x}{\boldsymbol{(5\,y+2\,x)} \cdot \boldsymbol{(3+x)}} = \dots\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>783029466</deployedseed><deployedseed>1177445020</deployedseed><deployedseed>1009895582</deployedseed><deployedseed>1167689465</deployedseed><deployedseed>1922827729</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-de Einfacher Doppelbruch</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8), 4); nums:sort(nums); ta1:((nums[1])/(nums[4]))/((nums[2])/(nums[3])); /*wa1 means: multiplied fractions instead of division*/ wa1:((nums[1])/(nums[4]))*((nums[2])/(nums[3])); /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:((nums[4])/(nums[1]))*((nums[2])/(nums[3]));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>352990161</deployedseed><deployedseed>467670994</deployedseed><deployedseed>1747402747</deployedseed><deployedseed>2135608811</deployedseed><deployedseed>460810681</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-df Bruch und Geteilt-Rechnung</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@dividend@}:{@divisor@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Achtung: Auch ein Doppelbruch ;)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>power:rand_with_step(2,4,1); myvars:rand_selection([a,b,c,x,y,z],2); dividend:myvars[1]/myvars[2]; num:rand_with_step(1,5,1); divisor:(num-myvars[1])/(myvars[2]^power); ta1: dividend/divisor; /*wa1 means: multiplied fractions instead of division*/ wa1:dividend*divisor; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:dividend^(-1)*divisor; /*wa3 means: didn’t consider to multiply the denominator of the first fraction with the sum of the second fraction’s numerator as a whole*/ wa3:(num(dividend)*denom(divisor))/(myvars[2]*num-myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@dividend@}:{@divisor@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
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+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
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+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast den richtigen Kehrwert gebildet um die Brüche dann zu multiplizieren, jedoch hast du dann die Klammersetzung bei der Mutliplikation nicht beachtet.</p><p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{x}{a} : \frac{1-x}{a^2} = \frac{x}{a} \cdot \frac{a^2}{1-x}\)\(= \frac{x \cdot a^2}{a \cdot \boldsymbol{(1-x)}} = \dots\)</p>]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
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+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: \(\boldsymbol{:}\) ist dasselbe wir ein Doppelbruchstrich.</p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p></p>]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>68495326</deployedseed><deployedseed>83279259</deployedseed><deployedseed>1848999895</deployedseed><deployedseed>1656521999</deployedseed><deployedseed>333378154</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dg Doppelbruch mit Zahlen und Variablen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:rand_selection(makelist(i+1,i,3),2); nums:rand_selection(makelist(i+1,i,4),2); myvars:rand_selection([a,b,c,x,y,z],2); fractions:[nums[1]/myvars[1]^powers[1], (nums[2]*myvars[2]^powers[2])/myvars[1]]; fractions:random_permutation(fractions); ta1:fractions[1]/fractions[2]; /*wa1 means: multiplied fractions instead of division*/ wa1:fractions[1]*fractions[2]; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:fractions[1]^(-1)*fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{2}{a^2}}{\frac{3\,b^2}{a}} = \frac{2}{a^2} \cdot \frac{a}{3\,b^2} = \frac{2\,a}{3\,a^2\,b^2}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1783639635</deployedseed><deployedseed>863915904</deployedseed><deployedseed>446314797</deployedseed><deployedseed>1562297660</deployedseed><deployedseed>1172377010</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dh Doppelbruch mit Termen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8), 3); nums:sort(nums); myvars:rand_selection([a,b,c,x,y,z],2); terms:[nums[1]*((1-myvars[1])/myvars[2]), (nums[2]/nums[3])*(myvars[2]^2/myvars[1])]; /*terms:random_permutation(terms);*/ ta1:terms[1]/terms[2]; taalt:combine(expand(ta1)); /*wa1 means: didn't consider to multiple first factor in the numerator with both summands of the fraction's numerator*/ wa1:((nums[1]*1-myvars[1])/myvars[2])/terms[2]; wa2:terms[1]*terms[2]; wa3:terms[1]^(-1)*terms[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
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+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Beim Multiplizieren des Faktors {@nums[1]@} und des Bruchs \(\frac{1-{@myvars[1]@}}{{@myvars[2]@}}\) im Zähler des Doppelbruchs musst du beachten, dass Summen als Ganzes multipliziert werden.</p><p>Beispiel: \(5 \cdot \frac{1-a}{b} = \frac{5 \cdot \boldsymbol{(1-a)}}{b} = \dots\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>5</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>5</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-6-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-6-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Lösungsweg für eine Beispielaufgabe:</p><p>\(\large\frac{5 \cdot \frac{1-a}{b}}{\frac{1}{3} \cdot \frac{b^2}{a}}\)\(\large = \frac{\frac{5 \cdot \boldsymbol{(1-a)}}{b}}{\frac{b^2}{3\,a}} = \frac{5 - 5\,a}{b} \cdot \frac{3\,a}{b^2}\)</p><p>\(\large = \frac{3\,a \cdot \boldsymbol{(5-5\,a)}}{b \cdot b^2} = \frac{15\,a - 15\,a^2}{b^3}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>611281053</deployedseed><deployedseed>439766047</deployedseed><deployedseed>725695831</deployedseed><deployedseed>1029360039</deployedseed><deployedseed>1825759080</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ea Bruchrechnung Kombination I</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbrüche und Summanden => Punkt-vor-Strich-Rechnung</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(2,4,1); nums_real_frac:sort(rand_selection(makelist(i,i,9),4)); nums_unreal_frac:sort(rand_selection(makelist(i+3,i,7),6)); main_summand:((nums_real_frac[1])/(nums_real_frac[4]))/((nums_real_frac[2])/(nums_real_frac[3])); summands:[int*(nums_unreal_frac[6]/nums_unreal_frac[1]), ((nums_unreal_frac[5])/(nums_unreal_frac[2]))/((nums_unreal_frac[4])/(nums_unreal_frac[3]))]; ta1:main_summand+summands[1]-summands[2]; wa1:(main_summand+int)*summands[1]/int-summands[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast offensichtlich die Punkt-vor-Strich-Regel nicht beachtet.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6} = \frac{\frac{5}{6}}{\frac{1}{3}}+(2 \cdot \frac{9}{6}) \ne (\frac{\frac{5}{6}}{\frac{1}{3}}+2) \cdot \frac{9}{6}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Jeden Summanden einzeln betrachten und ausrechnen: Doppelbrüche auflösen und zusammenfassen.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6}-\frac{\frac{13}{4}}{\frac{6}{5}} = \frac{5}{6} \cdot \frac{3}{1}+\frac{2}{1} \cdot \frac{9}{6}-\frac{13}{5} \cdot \frac{5}{6}\)</p><p>\(= (\frac{5}{6\mkern-5mu/^2} \cdot \frac{3\mkern-5mu/^1}{1})+(\frac{2\mkern-5mu/^1}{1} \cdot \frac{9}{6\mkern-5mu/^2})-(\frac{13}{5\mkern-5mu/^1} \cdot \frac{5\mkern-5mu/^1}{6})\)</p><p>\(= \frac{5}{2} + \frac{9}{2} - \frac{13}{6} = \frac{5 \cdot 3}{2 \cdot 3} + \frac{9 \cdot 3}{2 \cdot 3} - \frac{13}{6} = \frac{15}{6} + \frac{27}{6} - \frac{13}{6}\)</p><p>\(= \frac{15+27+13}{6} = \frac{55}{6}\)<\p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>2022519868</deployedseed><deployedseed>2007714528</deployedseed><deployedseed>1652468809</deployedseed><deployedseed>1890021691</deployedseed><deployedseed>1160555762</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-eb Bruchrechnung Kombination II</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Sorgfältig ausmultiplizieren</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(3,7,1); nums:sort(rand_selection(makelist(i,i,9),6)); factors:[int, (nums[1]/nums[6]+nums[2]/nums[5]), (1-nums[3]/nums[4])]; ta1:factors[1]*factors[2]*factors[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})= {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>999</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Hier hast du zwei Möglichkeiten: Alles sauber ausmultiplizieren oder vor dem Multiplizieren die Klammern ausrechnen (Empfehlung!)</p><p>Beispiel: \(6 \cdot (\frac{3}{4}+\frac{1}{8}) \cdot (1-\frac{1}{4}) = 6 \cdot (\frac{3 \cdot 2}{4 \cdot 2}+\frac{1}{8}) \cdot (\frac{1 \cdot 4}{1 \cdot 4}-\frac{1}{4})\) </p><p>\(= 6 \cdot (\frac{6}{8}+\frac{1}{8}) \cdot (\frac{4}{4}-\frac{1}{4}) = 6 \cdot (\frac{7}{8}) \cdot (\frac{3}{4})\)</p><p>\( = \frac{6}{1} \cdot \frac{7}{8} \cdot \frac{3}{4} = \frac{6\mkern-5mu/^3 \cdot 7 \cdot 3}{1 \cdot 8\mkern-5mu/^4 \cdot 4} = \frac{63}{16}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>382901616</deployedseed><deployedseed>1683089904</deployedseed><deployedseed>724792720</deployedseed><deployedseed>857106597</deployedseed><deployedseed>2126061360</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ec Bruchrechnung Kombination III</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch und gemischter Bruch vs. unechter Bruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(2,4,1); myvar:rand_selection([a,b,c,x,y,z],1)[1]; nums:sort(rand_selection(makelist(i,i,9),6)); summands:[(int+(nums[1]/nums[4]))*(myvar/nums[5]),1-((nums[6]-myvar)/((nums[4])/(nums[3])))]; ta1:combine(expand(summands[1]+summands[2])); wa1:(int*(nums[1]/nums[4]))*(myvar/nums[5])+summands[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast offenbar den gemischten Bruch \({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\) als Multiplikation \({@int@} \cdot \frac{{@nums[1]@}}{{@nums[4]@}}\) interpretiert. Allerdings meint der gemischte Bruch hier \({@int@}\) Ganze und \(\frac{{@nums[1]@}}{{@nums[4]@}}\) Anteil. Empfehlung: Gemischte Brüche als unechte Brüche umschreiben. Beispiel:\(2\frac{1}{6} = 2+\frac{1}{6} = \frac{2 \cdot 6}{1 \cdot 6} + \frac{1}{6} = \frac{12}{6}+\frac{1}{6} = \frac{13}{6}\)]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: \(\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}}\) ist auch ein Doppelbruch.</p><p>Achte darauf, dann die Klammer richtig zu setzen.</p><p>Beispiel: \(\frac{2-a}{\frac{7}{8}} = \boldsymbol{(}2-a\boldsymbol{)} \cdot \frac{8}{7}\)</p><p>Beachte: 1) Ganze Zahlen zum Bruch umschreiben. 2) Doppelbrüche umschreiben (Beispiel oben). 3) Gemischte Brüche umschreiben (Beispiel \(2\frac{1}{6}\) sind \(\frac{13}{6}\;\)). 4) Punkt-vor-Strich-Regel.</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>2024587341</deployedseed><deployedseed>1597148134</deployedseed><deployedseed>899831950</deployedseed><deployedseed>29495097</deployedseed><deployedseed>97014366</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-j Binomische Formeln I - Anwendungsaufgabe</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen und faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.</div>
+</div>
+<p></p>
+<p>\(\frac{{@expand(BIN_a[2])@}}{{@expand(BIN_a[3])@}} \cdot {@BIN_a[3]@}\)\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p><br></p>
+<p><br></p></p>
+<p class="hint">Um diese Aufgabe zu lösen, musst du mehrere binomische Formeln anwenden.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>aa:4;
+bb:5;
+c:3;
+d:2;
+
+u:(c*a-d*b)^2;
+ualt:(d*b-c*a)^2;
+v:(aa*a+d*b)^2;
+w:(bb*a-c*b)*(bb*a+c*b);
+
+x:(aa*a-d*b)^2;
+xalt:(d*b-aa*a)^2;
+y:(bb*a+c*b)^2;
+z:(c*a+d*b)*(c*a-d*b);
+
+/*BIN_A:[
+[a1,(2*a+5*b)^2,"\\(\\frac{4\\,a^2+20\\,a\\,b+25\\,b^2}{16\\,a^2-9\\,b^2}\\cdot(4\\,a-3\\,b)\\cdot(4\\,a+3\\,b)\\)"]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];*/
+
+BIN_A:[
+[a1,u,v,ualt],
+[a2,v,w,v],
+[a3,w,u,w],
+[a4,x,y,xalt],
+[a5,y,z,y],
+[a6,z,y,z]
+];
+BIN_a:rand(BIN_A);
+
+ta:BIN_a[2];
+taalt:BIN_a[4];
+
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>534740616</deployedseed> <deployedseed>47766652</deployedseed> <deployedseed>1657775726</deployedseed> <deployedseed>931829986</deployedseed> <deployedseed>1703936373</deployedseed> <deployedseed>151644710</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-g Binomische Formeln Ia - Erste binomische Formel</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Um den Bruch aus der Endgegner-Aufgabe zu vereinfachen, musst du binomische Formeln anwenden. Deshalb kommen wir nun zu den binomischen Formeln. Die erste binomische Formel besagt: \((a + b)^2 = a^2 + 2\,a\,b + b^2\;\).</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,(4+b)^2],
+[a2,(5+b)^2],
+[a3,(3+b)^2],
+[a4,(2+b)^2],
+[a5,(3+2*b)^2],
+[a6,(4+2*b)^2]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];
+task:expand(BIN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die erste binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1994312303</deployedseed> <deployedseed>1744518788</deployedseed> <deployedseed>1627526666</deployedseed> <deployedseed>1566276649</deployedseed> <deployedseed>1138479794</deployedseed> <deployedseed>806677520</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-h Binomische Formeln Ib - Zweite binomische Formel</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Die zweite binomische Formel besagt:\((a - b)^2 = a^2 - 2\,a\,b + b^2\;\).<!--Diesmal musst du den Term erst umformen, damit er in der richtigen Form erscheint.--><br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:4;
+b:5;
+c:3;
+d:2;
+
+e:1;
+f:2;
+
+BIN_A:[
+[a1,a,e],
+[a2,b,e],
+[a3,c,e],
+[a4,d,e],
+[a5,a,f],
+[a6,c,f]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]-BIN_a[3]*y)^2;
+taalt:(BIN_a[3]*y-BIN_a[2])^2;
+task:expand(ta);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>893674818</deployedseed> <deployedseed>675538571</deployedseed> <deployedseed>985713485</deployedseed> <deployedseed>1039647874</deployedseed> <deployedseed>1781202861</deployedseed> <deployedseed>824682247</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-i Binomische Formeln Ic - Dritte binomische Formel</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p></p>
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Die dritte binomische Formel besagt: \((a + b)\,(a - b) = a^2 - b^2\;\).<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>aa:4;
+bb:5;
+c:3;
+d:2;
+
+
+BIN_A:[
+[a1,aa,bb],
+[a2,c,d],
+[a3,d,aa],
+[a4,d,bb],
+[a5,d,c],
+[a6,aa,c]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]*x-BIN_a[3]*y)*(BIN_a[2]*x+BIN_a[3]*y);
+task:expand(ta);
+wa:(BIN_a[2]^2*x-BIN_a[3]^2*y)*(BIN_a[2]^2*x+BIN_a[3]^2*y);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die dritte binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast zwar die Unbekannten x und y korrekt faktorisiert, aber die sie begleitenden Faktoren unverändert in die Klammern geschrieben. Um diese korrekt zu faktorisieren, musst du ihre Wurzeln berechnen. Richtig wäre {@ta@}.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>455750255</deployedseed> <deployedseed>970764179</deployedseed> <deployedseed>1971560923</deployedseed> <deployedseed>987956614</deployedseed> <deployedseed>533447380</deployedseed> <deployedseed>299284489</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-k Bruchrechenregeln Ig2 - Bruch mit binomischem Term erweitern 2 (copy)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen und faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Dies ist der Endgegner zur Mathe-Welt <strong>Bruchrechenregeln und binomische Formeln</strong>. Wenn du diese Aufgabe schaffst, hast du diese Welt schon gemeistert. Wende zuerst die binomischen Formeln an, um die Nenner zu vereinfachen. Um die Brüche dann zu addieren, musst du mit einem Term erweitern.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;
+b:3;
+c:4;
+
+aa:x-a;
+bb:x-b;
+cc:x-c;
+
+/*FRA_A:[
+[a1,(x^2-3)/(x^2-4),"\\(\\frac{x + 3}{x^2 - 4} + \\frac{x - 3}{x - 2}\\)",(x^2-3)/((x+2)*(x-2))]
+];*/
+
+FRA_A:[
+[a1,aa, a],
+[a2,bb, b],
+[a3,cc, c]
+];
+FRA_a:rand(FRA_A);
+task:(3*FRA_a[3]*x+FRA_a[3]^2)/expand(FRA_a[2]^2)+x/FRA_a[2];
+ta:(x+FRA_a[3])^2/(FRA_a[2])^2;
+
+simp:false;
+taalt:((x+FRA_a[3])/(FRA_a[2]))^2;
+simp:true;
+
+wa1:expand((x+FRA_a[3])^2)/(FRA_a[2])^2;
+wa2:(x+FRA_a[3])^2/expand((FRA_a[2])^2);
+wa3:expand((x+FRA_a[3])^2)/expand(FRA_a[2]^2);
+wa4:(3*FRA_a[3]*x+FRA_a[3]^2)/expand(FRA_a[2]^2)+x^2/FRA_a[2]^2; /*naively expanded fraction by squaring numerator and denominator*/
+wa5:(3*FRA_a[3]*x+FRA_a[3]^2+x)/(expand(FRA_a[2]^2)+FRA_a[2]); /*naively summed fractions, keeping the denominators*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@FRA_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>2</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die erste binomische Formel an, um den Zähler zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa2</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die zweite binomische Formel an, um den Nenner zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>4</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa3</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die erste binomische Formel an, um den Zähler zu faktorisieren und
+ wende die zweite binomische Formel an, um den Nenner zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa4</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich den zweiten Summanden mit sich selbst multipliziert (quadriert), damit die Nenner gleich sind. Allerdings wird ein Bruch so nicht erweitert. Der quadrierte Bruch ist nicht mehr äquivalent mit dem vorherigen Bruch. Beispiel: \((\frac{2}{5})^2 = \frac{4}{25} \ne \frac{2}{5}\;\) wohingegen \(\frac{2}{5} = \frac{2 \cdot 5}{5 \cdot 5} = \frac{10}{25}\;\). Bitte überlege erneut, womit der zweite Summand erweitert werden muss, damit die Nenner gleich sind.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa5</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich die beiden Brüche addiert, indem du Zähler plus Zähler (oben) und Nenner plus Nenner (unten) gerechnet hast. So können Brüche nicht addiert werden. Beispiel: \( \frac{1}{2} + \frac{1}{4} \ne \frac{1+1}{2+4}\;\) . Brüche müssen so erweitert werden, dass sie den gleichen Nenner haben. Dann können die Zähler addiert werden: \(\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}\).</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>2099085786</deployedseed> <deployedseed>245667775</deployedseed> <deployedseed>1806806387</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-a p-q-Formal Ia - Termumformung</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p>Formen Sie den Term so um, dass er in der Form \(x^2+px+q = 0\) erscheint. Sie können dies Zeile für Zeile tun.<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Um die p-q-Formel anzuwenden, müssen wir zunächst den Term in die richtige Form bringen. Um den folgenden Term wie gewünscht umzuformen, subtrahiere und dividiere auf beiden Seiten der Gleichung.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[6*x+3*x^2-2=10,x^2+2*x-4=0],6*x+3*x^2-2=10],
+[a2,[15*x+5*x^2=20,x^2+3*x-4=0],15*x+5*x^2=20],
+[a3,[8*x+2*x^2-2=12,x^2+4*x-7=0],8*x+2*x^2-2=12],
+[a4,[20*x+4*x^2=-16,x^2+5*x+4=0],20*x+4*x^2=-16]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Gut gemacht! Wenn ein Term auf diese Weise umgeformt ist, kannst du mit der p-q-Formel die möglichen Werte für \(x\) bestimmen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Weiter so! Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>equiv</type>
+ <tans>BIN_a[2]</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint>firstline</syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options>firstline</options>
+ </input><deployedseed>1126686893</deployedseed> <deployedseed>1832581792</deployedseed> <deployedseed>1406889611</deployedseed> <deployedseed>511391873</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-c p-q-Formel I - Endboss</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p>Bestimmen Sie alle reellen Lösungen der quadratischen Gleichung in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\(= ?\;\). Sie können Ihren Rechenweg angeben.<br></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Forme den Term um und wende dann die p-q-Formel an, um diese Endgegner-Aufgabe zu lösen. Dann bist du mit dieser Mathe-Welt fertig.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[-2*y^2+6*y=4, -2*y^2+6*y-4=0,y^2-3*y-2=0,stackeq(y=3/2+sqrt(9/4-2) nounor y=3/2-sqrt(9/4-2)),y=1 nounor y=2],-2*y^2+6*y=4,y,1,2,y=3/2+sqrt(9/4+2),y=3/2-sqrt(9/4+2)],
+[a2,[2*y^2-16=-4*y,2*y^2+4*y-16=0,y^2+2*y-8=0,stackeq(y=-1+sqrt((1)^2+8) nounor y=-1-sqrt((1)^2+8)),y=-4 nounor y=2],2*y^2-16=-4*y,y,-4,2,y=-1+sqrt((1)^2-8),y=-1-sqrt((1)^2-8)],
+[a3,[-2*d^2+2*d=-24,-2*d^2+2*d+24=0,d^2-d-12=0,d=1/2+sqrt((1/2)^2+12) nounor d=1/2-sqrt((1/2)^2+12),d=-3 nounor d=4],-2*d^2+2*d=-24,d,-3,4,d=1/2+sqrt((1/2)^2-12),d=1/2-sqrt((1/2)^2-12)],
+[a4,[-2*u^2-14*u=24,-2*u^2-14*u-24=0,u^2+7*u+12=0,u=-7/2+sqrt((7/2)^2-12) nounor u=-7/2-sqrt((7/2)^2-12),u=-4 nounor u=-3],-2*u^2-14*u=24,u,-4,-3,u=-7/2+sqrt((7/2)^2+12), u=-7/2-sqrt((7/2)^2+12)]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.</p><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast!
+ Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel
+in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2}
+\boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir="ltr">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir="ltr">Versuche es erneut und gib beide Lösungen an.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast! Offenbar hast du dich beim
+\(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet
+ \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil
+ am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du
+das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr">Außerdem
+ hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel
+ bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+}
+\sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-}
+\sqrt{...}\) gibt.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast!
+ Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>equiv</type>
+ <tans>BIN_a[2]</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint>firstline</syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options>firstline</options>
+ </input><deployedseed>1183308849</deployedseed> <deployedseed>1817300183</deployedseed> <deployedseed>1556042756</deployedseed> <deployedseed>493079990</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-b p-q-Formel Ib - pq-Formel</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p>Bestimmen Sie den Wert der Variable in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\( = ?\;\).<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Erinnerst du dich noch an die pq-Formel? Für \(\;x^2 + p\,x + q = 0\;\) gilt \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\).<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[h^2+3*h-4=0,h=-3/2+sqrt((3/2)^2+4) nounor h=-3/2-sqrt((3/2)^2+4),h=-3/2+sqrt(25/4) nounor h=-3/2-sqrt(25/4),h=-3/2+5/2 nounor h=-3/2-5/2,h=-4 nounor h=1],"\\(h^2+3\\,h-4=0\\)",h,1,-4,h=-3/2+sqrt(9/4-4),h=-3/2-sqrt(9/4-4)],
+[a2,[y^2-2*y-8=0,y=1+sqrt((-1)^2+8) nounor y=1-sqrt((-1)^2+8),y=-2 nounor y=4],"\\(y^2-2\\,y-8=0\\)",y,-2,4,y=1-sqrt(1-8),y=1+sqrt(1-8)],
+[a3,[z^2-4*z-5=0,z=2+sqrt((-2)^2+5) nounor z=2-sqrt((-2)^2+5),z=5 nounor z=-1],"\\(z^2-4\\,z-5=0\\)",z,5,-1,z=2+sqrt(4-5),z=2-sqrt(4-5)],
+[a4,[a^2-10*a+9=0,a=5+sqrt((-5)^2-9) nounor a=5-sqrt((-5)^2-9),a=9 nounor a=1],"\\(a^2-10\\,a+9=0\\)",a,9,1,a=5+sqrt(25+9),a=5-sqrt(25+9)]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr" style="text-align: left;">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2} \boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir="ltr" style="text-align: left;">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir="ltr" style="text-align: left;">Versuche es erneut und gib beide Lösungen an.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr" style="text-align: left;">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\) gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>equiv</type>
+ <tans>BIN_a[2]</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint>firstline</syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options>firstline</options>
+ </input><deployedseed>1183616185</deployedseed> <deployedseed>1771539896</deployedseed> <deployedseed>1420701792</deployedseed> <deployedseed>1009534997</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-f Potenzrechenregeln I - Endboss</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie folgenden Ausdruck; hierbei sind \(x,y \in \mathbb{R_{> 0}}\).</div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Dies ist die Endgegner-Aufgabe dieser Mathe-Welt <strong>Potenzrechenrelgen</strong>. Wenn du diese Aufgabe schaffst, hast du diese Mathe-Welt gemeistert. Viel Erfolg!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,stackeq(y^(-1/6)),"\\(\\frac{1}{\\sqrt[3]{y \\, \\sqrt x}} \\, \\sqrt[6]{x \\, y}\\)"],
+[a2,a^20*x^8,"\\(\\left( \\frac{a^3 x^5}{a^{-2} x^3} \\right)^4\\)"]
+];
+RUL_a:rand(RUL_A);
+
+/*ans1 is evaluated by ev(ans1,simp) to accept e. g. 1/(y^(1/6)) and y^(-1/6) and y^(-(1/6))*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ev(ans1,simp)</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1167231517</deployedseed> <deployedseed>1313491755</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-a Potenzrechenregeln Ia – Exponenten addieren</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Fangen wir damit an, die Exponenten zu addieren, wenn die Basis gleich ist und multipliziert wird.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^a*c^b,"\\(c^{\\,a}\\cdot c^{\\,b}\\)"],
+[a2,x^a*x^b,"\\(x^{\\,a}\\cdot x^{\\,b}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1724483596</deployedseed> <deployedseed>337440314</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-b Potenzrechenregeln Ib – Exponenten subtrahieren</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Das funktioniert auch in die andere Richtung.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^a/c^b,"\\(\\frac{c^{\\,a}}{c^{\\,b}}\\)"],
+[a2,x^a/x^b,"\\(\\frac{x^{\\,a}}{x^{\\,b}}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>29351489</deployedseed> <deployedseed>1996084793</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-c Potenzrechenregeln Ic - Wurzel als Potenz darstellen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p></p>
+<div>
+ <div>Stellen Sie den Ausdruck in der Form \(c^{\frac{1}{n}}\) dar.<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Mithilfe von Potenzen der Form \(c^{\frac{1}{n}}\) lässt sich die n-te Wurzel von \(c\), also \(\;\sqrt[n]{c}\;\), darstellen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(1/6),"\\(\\sqrt[6]{c}\\)"],
+[a2,c^(1/5),"\\(\\sqrt[5]{c}\\)"],
+[a3,c^(1/4),"\\(\\sqrt[4]{c}\\)"],
+[a4,c^(1/3),"\\(\\sqrt[3]{c}\\)"],
+[a5,c^(1/7),"\\(\\sqrt[7]{c}\\)"],
+[a6,c^(1/8),"\\(\\sqrt[8]{c}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Sie können noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1074873352</deployedseed> <deployedseed>460473552</deployedseed> <deployedseed>771365681</deployedseed> <deployedseed>1250006169</deployedseed> <deployedseed>259744359</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-d Potenzrechenregeln Id – Exponenten multiplizieren</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Wird ein Ausdruck, der eine Potenz enthält, potenziert, lassen sich die Exponenten miteinander multiplizieren.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(a*b),"\\((c^a)^b\\)",c^a*b],
+[a2,x^(a*b),"\\((x^a)^b\\)",x^a*b]
+];
+RUL_a:rand(RUL_A);
+wa:RUL_a[4];
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast die Klammer falsch gesetzt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1495340815</deployedseed> <deployedseed>1196787611</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-e Potenzrechenregeln Ie - Potenzrechenregeln anwenden</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>
+
+
+<p></p>
+<div>Nutzen Sie die Potenzrechenregeln, um folgenden Ausdruck zu vereinfachen.<br></div>
+<p>
+</p>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p>
+<div class="bubble in-modal no-arrow">
+ <div>Hier zur Erinnerung die wichtigsten Potenzrechenregeln. Für \(x, y \neq 0\) und \(n, m \in \mathbb{Z}\) gilt:</div>
+<div>
+ <div>
+ <div>
+ <ul>
+ <li>\(x^{n+m} = x^n\,x^m\;\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \(2^5 = 2^{2+3} = 2^2 \cdot 2^3 = 4 \cdot 8 = 32\)</span></div></li></ul><ul>
+ <li>
+ <div>
+ <div>\(\left( x^n \right)^m = x^{n\,m}\;\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \(\left( 2^2 \right)^3 = 2^6 = 64\)</span></div></div>
+ </div>
+ </li>
+ <li>
+ <div>
+ <div>
+ <div>
+ <div>\((x\,y)^n = x^n\,y^n\;\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \(6^2 = (2 \cdot 3)^2 = 2^2 \cdot 3^2 = 4 \cdot 9 = 36\)</span></div></div>
+ </div>
+ </div>
+ </div>
+ </li>
+ <li>\(\frac{1}{x^n} = x^{-n}\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \( \frac{1}{x^2} \cdot x^2 = x^{-2} \cdot x^2 = x^{-2+2} = x^0 = 1\)</span><br></div></li>
+ <li>\(\sqrt[n]{x} = x^{\frac{1}{n}}\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \( \sqrt[3]{x} \cdot x^3 = x^{\frac{1}{3}} \cdot x^3 = x^{\frac{1}{3}+3} = x^1 = x\)</span></div></li>
+ </ul>
+ </div>
+ </div>
+</div>
+<p></p>
+<div>
+ <div>
+ <div>
+ <ul></ul>
+ </div>
+ </div>
+</div>
+</div></p>
+<p class="hint">Um diese Aufgabe zu lösen, kannst du mehrere der gerade erläuterten Regeln kombinieren. </p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(13/6),"\\(\\sqrt[6]{c} \\cdot c^2\\)"],
+[a2,x^10,"\\(\\frac{x^5}{x^{-5}}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Richtig, aber du kannst noch weiter vereinfachen.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1602709371</deployedseed> <deployedseed>547016054</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-a Ganzzahlige Summanden ableiten</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Leite jeden Summanden einzeln ab.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i,i,10),4); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; exercise:nums[1]*myvar^powers[1]+nums[2]*myvar^powers[2]+nums[3]*myvar+nums[4]; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>351097132</deployedseed> <deployedseed>1047509677</deployedseed> <deployedseed>442872926</deployedseed> <deployedseed>286970886</deployedseed> <deployedseed>999400432</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-b Gebrochenrationale Summanden ableiten</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})={@fractions[1]@} \cdot {@myvar@}^{@powers[1]@}+{@fractions[2]@} \cdot {@myvar@}^{@powers[2]@}+{@fractions[3]@} \cdot {@myvar@}+{@myint@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Leite jeden Summanden einzeln ab.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myint:rand_with_step(1,10,1); numerators:rand_selection(makelist(i+2,i,6),3); denominators:makelist(rand_with_step(numerators[i]+1,numerators[i]+5,1),i,3); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; fractions:makelist(numerators[i]/denominators[i],i,3); exercise:fractions[1]*myvar^powers[1]+fractions[2]*myvar^powers[2]+fractions[3]*myvar+myint; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>857840145</deployedseed> <deployedseed>1543126498</deployedseed> <deployedseed>1871228756</deployedseed> <deployedseed>318121367</deployedseed> <deployedseed>2127933990</deployedseed> <deployedseed>484803571</deployedseed> <deployedseed>1056868370</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-c Produkte ableiten I</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:rand_selection(makelist(i+1,i,4),2); myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,4),2); exercise:(myvar^powers[1]+nums[1])*(myvar^powers[2]-nums[2]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1213180404</deployedseed> <deployedseed>1876101711</deployedseed> <deployedseed>1520468669</deployedseed> <deployedseed>1233734487</deployedseed> <deployedseed>1329784126</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-d Produkte ableiten II</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>num:rand_with_step(1,5,2); denom:rand_with_step(num+2, num+5,2); fraction:num/denom; nums:rand_selection(append(makelist(i-7,i,6),makelist(i,i,6)),4); myvar:rand([a,b,c,x,y,z]); power:rand([3,4]); exercise:(fraction*myvar+nums[1])*(nums[2]*myvar^power+nums[3]*myvar+nums[4]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>290055394</deployedseed> <deployedseed>1877259825</deployedseed> <deployedseed>1027269811</deployedseed> <deployedseed>1906880472</deployedseed> <deployedseed>1551769121</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-e Division ableiten I</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:[rand_with_step(3,4,1), 2]; nums:rand_selection(makelist(i,i,12),5); myvar:rand([a,b,c,x,y,z]); exercise:(myvar^powers[1]+nums[1]*myvar^powers[2]+myvar)/(nums[2]*myvar^2+nums[3]*myvar+nums[4]); ta1:diff(exercise, myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1439694172</deployedseed> <deployedseed>1028579078</deployedseed> <deployedseed>1454088108</deployedseed> <deployedseed>1063999325</deployedseed> <deployedseed>1974598074</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-f Division ableiten II</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:[rand([3,5,7,11]), rand_with_step(2,5,1)]; myvar:rand([a,b,c,x,y,z]); terms:[sqrt(nums[1])*myvar-nums[2], nums[1]*myvar^2-nums[2]]; terms:random_permutation(terms); exercise:terms[1]/terms[2]; ta1:diff(exercise, myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>525681144</deployedseed> <deployedseed>1447367624</deployedseed> <deployedseed>435810786</deployedseed> <deployedseed>1421496847</deployedseed> <deployedseed>918279888</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-g Kettenregel I</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root@}]{{@myvar@}^2-{@num@}}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); root:rand([3,5]); num:rand_with_step(3,9,1); exercise:(myvar^2-num)^(1/root); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1079586531</deployedseed> <deployedseed>1754291070</deployedseed> <deployedseed>1751932072</deployedseed> <deployedseed>1089076165</deployedseed> <deployedseed>215450400</deployedseed> <deployedseed>766534514</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-h Kettenregel II</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,5),3); power:rand_with_step(3,7,2); signs:makelist(rand([-1,1]),2); exercise:(nums[1]*myvar^2+signs[1]*nums[2]*myvar+signs[2]*nums[3])^power; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1676415387</deployedseed> <deployedseed>146672542</deployedseed> <deployedseed>1726255949</deployedseed> <deployedseed>1628089061</deployedseed> <deployedseed>633210403</deployedseed> <deployedseed>1850144475</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-i Gemischtes I</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,5),2); nums:rand_selection(makelist(i+1,i,58),2); exercise:(myvar^powers[1]+nums[1])^powers[2]*nums[2]*myvar; ta1:diff(exercise, myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>603470063</deployedseed> <deployedseed>1387533043</deployedseed> <deployedseed>820026169</deployedseed> <deployedseed>1884036955</deployedseed> <deployedseed>562165609</deployedseed> <deployedseed>931146921</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-j Gemischtes II</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,3),3); nums:rand_selection(makelist(i,i,5),2); exercise:(myvar^powers[1]-nums[1])^powers[2]*(myvar+nums[2])^powers[3]; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>949540891</deployedseed> <deployedseed>2032277992</deployedseed> <deployedseed>504654950</deployedseed> <deployedseed>906697601</deployedseed> <deployedseed>1241320418</deployedseed> <deployedseed>891184866</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-k Gemischtes III</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); terms:[rand_with_step(1,4,1)+myvar, myvar]; terms:random_permutation(terms); power:rand_with_step(3,7,1); exercise:(terms[1]/terms[2])^power; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1060600269</deployedseed> <deployedseed>1317786455</deployedseed> <deployedseed>2016195942</deployedseed> <deployedseed>79640143</deployedseed> <deployedseed>1481526612</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-l Gemischtes IV</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),2); power:rand_with_step(2,6,1); exercise:nums[1]*sqrt(nums[2]*myvar+myvar^power); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>63010318</deployedseed> <deployedseed>2022252790</deployedseed> <deployedseed>2032269463</deployedseed> <deployedseed>1301956355</deployedseed> <deployedseed>1085730060</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-m Gemischtes V</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),4); power:rand_with_step(2,5,1); terms:[(nums[1]*myvar+nums[2]), (nums[3]*myvar^power-nums[4])]; terms:random_permutation(terms); exercise:(terms[1]*terms[2])/myvar; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1627444094</deployedseed> <deployedseed>570947981</deployedseed> <deployedseed>1123631251</deployedseed> <deployedseed>566895213</deployedseed> <deployedseed>265672538</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/test/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-n Gemischtes VI</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<p>Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); root_power:rand_with_step(3,6,1); power:rand_with_prohib(2,5,[root_power]); nums:rand_selection(makelist(i+2,i,6),2);exercise:(nums[1]*myvar-nums[2])^(power/root_power); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>466316231</deployedseed> <deployedseed>73259082</deployedseed> <deployedseed>253364053</deployedseed> <deployedseed>1197047345</deployedseed> <deployedseed>873528357</deployedseed> <deployedseed>10923026</deployedseed> <deployedseed>1464509121</deployedseed></question>
+
+</quiz>
diff --git a/question-files/questions-pa-its_ger.xml b/question-files/questions-pa-its_ger.xml
new file mode 100644
index 0000000000000000000000000000000000000000..973cebcf472da36fa3911c1df9d356b0e6b008b4
--- /dev/null
+++ b/question-files/questions-pa-its_ger.xml
@@ -0,0 +1,8192 @@
+<quiz><question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/000 Start Elements</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>000 Start 0.2</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-instant-tutoring.js"></script>
+<script>
+ ALQuiz.setCurrentQuestionId("start");
+</script>
+<p class="hint">Hey! Ich helfe dir beim Lösen der Mathe-Aufgaben. In diesem Übungsraum leite ich dich durch 5 Mathe-Welten. Jede Mathe-Welt besteht aus mehreren Hilfsschritt-Leveln und einem Endgegner <img src="https://marvin.hs-bochum.de/~mneugebauer/skull.svg" style="width:1em">. Das Ziel ist, in jeder Welt die Endgegner-Aufgabe zu lösen. Du brauchst die Hilfsschritt-Level nicht unbedingt lösen. Doch wenn du sie löst, wird es dir leichter fallen, die Endgegner-Aufgabe zu lösen.<br><br>Nutze die <span class="show-on-mobile-only"><a href="javascript:;" onclick="let showsidebarbutton = document.getElementById('showsidebaricon'); if (showsidebarbutton != undefined) { showsidebarbutton.click(); return; } let questionCard = document.querySelector('[id*=quiznavbutton]'); let drawerParent = questionCard.closest('.drawer'); if (drawerParent != undefined) { let target = drawerParent.id; let drawerOpener = document.querySelector('button[data-target='+target+'][data-action=toggle]'); if (drawerOpener != undefined) { drawerOpener.click(); } }">Navigation</a></span><span class="show-on-desktop-only">Navigation (rechts)</span> um dich durch die Level und Welten zu bewegen.<br><br>Mit Klick auf <a href="javascript:;" onclick="tutorialFocusElement(document.querySelector('.submitbtns'));">"Nächste Frage"</a>
+ <!--liefere ich dir automatisch die nächste Frage, die zu deinem Lernstand passt.-->Geht es los.<br>Viel Erfolg!<br>
+ Hier kannst du schon einmal die Eingabe ausprobieren. Versuche doch einfach Mal, die Zahl {@tasklist[1]@} einzugeben und deine Eingabe mit "Enter" überprüfen zu lassen.<br>
+</p>
+
+<p></p>
+<p>Machen Sie sich mithilfe des untenstehenden Eingabefelds mit der mathematischen Eingabe per Tastatur vertraut. Probieren Sie zum Beispiel <code>42</code>, <code>2*x+1</code>, <code>3/5</code> oder <code>sqrt(2)</code>. Schreiben Sie einen Ausdruck pro Zeile.</p>
+Durch das Beginnen einer neuen Zeile (Enter) wird Ihre Eingabe vom Digitalen Mentor geprüft.<br>
+<p></p>
+<p>[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><br>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1</defaultgrade>
+ <penalty>0.1</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>tasklist:[42,2*x+1,3/5,sqrt(2)];
+i:1;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text/>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text>Richtige Antwort, gut gemacht!</text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text>Ihre Antwort ist teilweise korrekt.</text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text>Falsche Antwort.</text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>equiv</type>
+ <tans>tasklist</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options>hideequiv</options>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>tasklist[1]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Genau! So kannst du eine Eingabe machen und sie prüfen lassen. Gibt jetzt darunter {@tasklist[2]@} ein.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>+</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>tasklist[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Genau! So kannst du eine Eingabe machen und sie prüfen lassen. Gibt jetzt {@tasklist[3]@} ein.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>tasklist[3]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Genau! So kannst du eine Eingabe machen und sie prüfen lassen. Gibt jetzt {@tasklist[4]@} ein.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>+</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>tasklist[4]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Prima, das soll für den Einstieg reichen! Viel Erfolg! Mit Klick auf "Nächste Frage" geht es los.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.1</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Genau, so kannst du eine Eingabe machen und sie prüfen lassen. Versuche doch noch einmal, einen der folgenden Ausdrücke einzugeben.</p><p dir="ltr" style="text-align: left;">{@tasklist[1]@}</p><p dir="ltr" style="text-align: left;">{@tasklist[2]@}</p><p dir="ltr" style="text-align: left;">{@tasklist[3]@}</p><p dir="ltr" style="text-align: left;">{@tasklist[4]@}<br></p>]]></text>
+ </falsefeedback>
+ </node>
+ </prt>
+ </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-a Gleichung eingeben (Multiplikation)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t0_syn_1_a')</script><p class="bubble"><div class="hint">Okay! Hier eine leichte Aufgabe zur Eingabe. Benutze für jede Multiplikation das Symbol * (Stern).
+ <!--<span class="show-on-mobile-only"><br><br>Nutze die <a href="javascript:;" onclick="let userFocusTop = document.createElement('div');userFocusTop.classList.add('user-focus', 'hide-top');let pageHeight = document.documentElement.scrollHeight;userFocusTop.style.height=Math.ceil(pageHeight+window.pageYOffset)+'px';userFocusTop.onclick = removeTutorialFocus;document.body.appendChild(userFocusTop);">Buttons über deiner Tastatur</a>, um die wichtigsten Mathe-Operatoren schnell zu finden.</span>-->
+ <br><br>Falls du ohne Tastatur unterwegs bist, kannst du mithilfe des <a href="javascript:;" onclick="tutorialFocusElement(document.querySelector('.mathsbutton'));">Mathe-Operatoren-Buttons</a> zusätzliche Buttons aktivieren, um alle Mathe-Operatoren schnell zu finden.
+
+ <!--<br><br>Drücke jederzeit den "Prüfen"-Button, um zu sehen, wie deine Eingabe interpretiert wurde.<br>Erst wenn du nach dem "Prüfen"-Button deine Eingabe nicht änderst und
+ erneut "Prüfen" klickst, wird deine Eingabe als Antwort abgeschickt.-->
+<br><br>Neben dem Eingabefeld siehst du, wie deine Eingabe interpretiert wird.<br>Wenn du auf den "Prüfen"-Button klickst, wird deine Eingabe als Antwort abgeschickt.
+</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Geben Sie die Gleichung \({@ta1@}\) in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,y=3*x+5],[a2,y=4*x+3],[a3,y=2*x+1],[a4,y=2*x-5],[a5,y=5*x-3],[a6,y=4*x-6]];SYN_a:rand(SYN_A);ta1:SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>480757020</deployedseed><deployedseed>585237317</deployedseed><deployedseed>1798333349</deployedseed><deployedseed>2118152732</deployedseed><deployedseed>1988707695</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-b Gleichung eingeben (Division)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t0_syn_1_b')</script><p class="bubble"><div class="hint">Okay! Divisionen werden mit / (Slash) dargestellt. Hier erscheinen Sie als Brüche.<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Geben Sie die Gleichung \({@TA@}\) in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,y=5/3],[a2,y=4/7],[a3,y=1/3],[a4,y=2/5],[a5,y=3/10],[a6,y=1/4]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);TA:SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>TA</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Wir arbeiten hier nur wenn explizit danach gefragt wird mit Dezimalzahlen. Brüche stellen das Ergebnis in der Regel genauer dar.<br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>TA</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords>3x</forbidwords><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>2690042</deployedseed><deployedseed>300094393</deployedseed><deployedseed>765518486</deployedseed><deployedseed>17019212</deployedseed><deployedseed>1233892964</deployedseed><deployedseed>147932577</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-c Potenzen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t0_syn_1_c')</script><p class="bubble"><div class="hint"><p>Mit dem Zeichen ^ (Caret) kannst du Potenzen darstellen.</p><div> <ul> <li>\(x^2\) wird so eingegeben: <code>x^2</code></li> <li>\(x^{-2}\) wird so eingegeben: <code>x^(-2)</code></li> <li>\(x^{1/3}\) wird so eingegeben: <code>x^(1/3)</code></li> </ul></div></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Geben Sie die Gleichung \[{@ta@}\] in das Eingabefeld ein.</p>
+<p><p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,(4+b)^2],[a2,(5+b)^2],[a3,(3+b)^2],[a4,(2+b)^2],[a5,(3+2*b)^2],[a6,(4+2*b)^2]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:expand(SYN_a[2])=SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[Sehr gut. Hier wurde übrigens eine binomische Formel angewendet, um einen Term zu faktorisieren.<br><p dir="ltr" style="text-align: left;" <br=""></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Deine Antwort ist zwar äquivalent mit der dargestellten Gleichung, aber du hast nicht genau die gleiche Gleichung dargestellt.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>93323135</deployedseed><deployedseed>1032837775</deployedseed><deployedseed>680315517</deployedseed><deployedseed>838329017</deployedseed><deployedseed>162866526</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-d Rationale Ausdrücke</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t0_syn_1_d')</script><p class="bubble"><div class="hint">Okay! Machen wir es etwas komplizierter. Um Terme in Brüchen darzustellen, musst du besonders auf die Klammersetzung achten.<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Geben Sie die Gleichung \[{@ta@}\] in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:x^2;b:(x+1);c:(x-5);SYN_A:[[a1,a,b,c],[a2,b,a,c],[a3,c,a,b]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:SYN_a[2]/(SYN_a[3]*SYN_a[4]);wa:SYN_a[2]/SYN_a[3]*SYN_a[4];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;" <br=""></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Bitte beachte, dass du um den Nenner zusätzliche Klammern setzen musst, damit er als zusammenhängender Divisor interpretiert wird.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>82298515</deployedseed><deployedseed>1458249622</deployedseed><deployedseed>1731794639</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-e Wurzelzeichen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t0_syn_1_e')</script><p class="bubble"><div class="hint">Gut. Um eine Wurzel darzustellen nutze <code>sqrt(x)</code> für \(\sqrt{x}\;\).</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Geben Sie \[{@ta1@}\] in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,3],[a2,5],[a3,7],[a4,11],[a5,13],[a6,19]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta1:sqrt(SYN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1136692395</deployedseed><deployedseed>659595513</deployedseed><deployedseed>2040368424</deployedseed><deployedseed>262860513</deployedseed><deployedseed>592365331</deployedseed><deployedseed>1218846808</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-f Mehrere Lösungen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t0_syn_1_f')</script><p class="bubble"><div class="hint">Gelegentlich müssen Ausdrücke mit logischen Verbindungen verknüpft werden. Nutze dafür <code>and</code> oder <code>or</code>. <br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Lösen Sie nach \(x\) auf. Geben Sie die Lösung in der Form \(x=? \mbox{ or } x=?\) ein.</p>
+<p><p>\[{@task@}\]<br></p><p>[[input:ans]] [[validation:ans]][[feedback:prt1]]</p><p><em>Achtung: Bitte setzen Sie kein zusätzliches +-Symbol vor positive Zahlen.<br></em></p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,4],[a2,9],[a3,16],[a4,25],[a5,36]];/*SYN_a:SYN_A[1];*/SYN_a:rand(SYN_A);ta:x=sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);taalt:x=+sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);task:x^2=SYN_a[2];wa1:x=sqrt(SYN_a[2]);wa2:x=-sqrt(SYN_a[2]);wa3:x=sqrt(SYN_a[2]) nounand x=-sqrt(SYN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>4</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>4</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>5</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>4</name><answertest>AlgEquiv</answertest><sans>1</sans><tans>1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-5-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr">Du hast nur eine von zwei richtigen Lösungen eingegeben.<br>Beispiel: \(5 \cdot 5 = 25\) und \(-5 \cdot -5 = 25\) (Minus Mal Minus ergibt Plus).<br>Für \(x^2 = 25\) gilt deshalb \(x = 5\) oder \(x = -5\), was hier in der Form <code>x=5 or x=-5</code> aufgeschrieben wird.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-5-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>5</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa3</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-6-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast alle richtigen Lösungen angegeben, allerdings hast du sie mit <code>and</code> verknüpft. Korrekt ist, sie mit <code>or</code> zu verknüpfen. Man schreibt</p><ul><li>entweder \(x=?\; oder \;x=?\)</li><li>oder \(x_1=?\; und \;x_2 = ?\;\).</li></ul>Hier benutzen wir ausschließlich die erste Form, die mit <code>x=? or x=?</code> dargestellt wird.<br>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-6-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords>4x</forbidwords><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>1032259226</deployedseed><deployedseed>2071301041</deployedseed><deployedseed>668615301</deployedseed><deployedseed>1810103727</deployedseed><deployedseed>2047586646</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-g Gleichung mehrschrittig lösen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t0_syn_1_g')</script><p class="bubble"><div class="hint">Um einen Rechenweg darzustellen, tippe jeden Schritt deiner Rechnung in eine neue Zeile in das Eingabefeld ein.</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p><p>Lösen Sie \(\;\){@p@}\(\;\) nach x auf.</p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.</p><p>Sie brauchen kein Äquivalenz-Zeichen eingeben.<br></p></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;b:3;c:4;SYN_A:[[a1,a,b,c],[a2,b,a,c],[a3,c,a,b],[a4,a,c,b],[a5,b,c,a],[a6,c,b,a]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:[SYN_a[2]*(SYN_a[3]+x)=SYN_a[4],SYN_a[2]*SYN_a[3]+SYN_a[2]*x=SYN_a[4],SYN_a[2]*x=SYN_a[4]-SYN_a[2]*SYN_a[3],x=(SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]];/*ta:[2*(3+x)=-3,2*x+6=-3,2*x=-9,x=-9/2];*/p:first(ta);/*p:"\\(2 \\cdot (3 + x) = -3\\)";*/wa1:x=-((SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]);wa2:x=SYN_a[4]-SYN_a[2]*SYN_a[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last(ans1)</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Aber fast richtig. Du hast dich offenbar mit dem Vorzeichen vertan.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar ist dir ein Fehler beim Lösen der Klammer unterlaufen. Um die Klammer aufzulösen, musst du beide beide Summanden in der Klammer mit dem Faktor vor der Klammer multiplizieren.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Weiter so. Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>equiv</type><tans>ta</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint>firstline</syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options>hideequiv</options></input><deployedseed>668615301</deployedseed><deployedseed>1810103727</deployedseed><deployedseed>2047586646</deployedseed><deployedseed>1032259226</deployedseed><deployedseed>2071301041</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-h Griechische Buchstaben</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t0_syn_1_h')</script><p class="bubble"><div class="hint">Wenn griechische Buchstaben einzugeben sind, schreibe sie einfach aus. Beispiel: \(\alpha=\) <code>alpha</code> , \(\beta=\) <code>beta</code><code></code> ,\(\pi=\) <code>pi </code><code></code>.<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Geben Sie \[{@ta@}\] in das Eingebefeld ein.</p>
+<p><p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p><em>Achtung: Bitte kopieren Sie keine Unicode-Zeichen, sondern benutzen Sie einfach Ihre Tastatur. <br></em></p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:beta;b:pi;c:alpha;SYN_A:[[a1,a,b],[a2,b,a],[a3,a,c],[a4,c,a],[a5,b,c],[a6,c,b]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:SYN_a[2]*z^(SYN_a[3]*x)wa1:SYN_a[2]*z^SYN_a[3]*x</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offenbar vergessen, eine Klammer um die Potenz zu schreiben. Schreibe Potenzen in Klammern, wenn sie aus mehr als einer Zahl bestehen. Beispiel: \(x^{-2a}\) wird so eingegeben: <code>x^(-2*a)</code>.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>1516837293</deployedseed><deployedseed>911975771</deployedseed><deployedseed>742782033</deployedseed><deployedseed>1709130663</deployedseed><deployedseed>648468622</deployedseed><deployedseed>272609913</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-i Syntax-Endboss</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t0_syn_1_i')</script><p class="bubble"><div class="hint">Willkommen zum Endgegner dieser Mathe-Welt. Mit dem Lösen dieser Aufgabe hast du die erste Mathe-Welt bereits abgeschlossen. Viel Erfolg!<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p><p>Lösen Sie {@p@} nach \(x\) auf.<br></p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.<br></p></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]<p></p><p><em>Zur Erinnerung: Das Kommando für</em> \(\sqrt{x}\)<em> lautet </em><code>sqrt(x)</code><em>. Nutzen Sie </em><code>or</code><em> um mehrere Lösungen anzugeben.</em></p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;b:3;c:4;d:2;e:3;SYN_A:[[a1,a,d],[a2,b,d],[a3,c,d],[a4,a,e],[a5,b,e],[a6,c,e]];SYN_a:rand(SYN_A);pifactor:ev(SYN_a[2]*(SYN_a[3]^2),simp);ta:[/*(SYN_a[2]*x^2)/(pifactor*pi)=1,*/SYN_a[2]*x^2=pifactor*pi,x^2=(SYN_a[3]^2)*pi,x=SYN_a[3]*sqrt(pi) nounor x=-SYN_a[3]*sqrt(pi)];p:first(ta);wa1:x=SYN_a[3]*sqrt(pi);wa2:x=-SYN_a[3]*sqrt(pi);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last(ans1)</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text><![CDATA[]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>4</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>3</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>3</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>1</sans><tans>1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast nur eine von zwei richtigen Lösungen eingegeben.<br>Beispiel: \(5\,\sqrt{\pi} \cdot 5\,\sqrt{\pi} = 25\,\pi\) und \(-5\,\sqrt{\pi} \cdot -5\,\sqrt{\pi} = 25\,\pi\) (Minus Mal Minus ergibt Plus).<br>Für \(x^2 = 25\pi\) gilt deshalb \(x = 5\,\sqrt{\pi}\) oder \(x = -5\,\sqrt{\pi}\), was hier in der Form <code>x=5*sqrt(pi) or x=-5*sqrt(pi)</code> aufgeschrieben wird.</p><p dir="ltr" style="text-align: left;"></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>4</name><answertest>AlgEquiv</answertest><sans>last(ans1)</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-5-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-5-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>equiv</type><tans>ta</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint>firstline</syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options>hideequiv</options></input><deployedseed>1169120426</deployedseed><deployedseed>1624332195</deployedseed><deployedseed>1578649438</deployedseed><deployedseed>1629124203</deployedseed><deployedseed>2120835467</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-a Kürzen zweier einfacher Brüche</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_bi-a')</script><p class="bubble"><div class="hint">Tipp: Gekürzt wird, indem man Zähler & Nenner durch dieselbe Zahl teilt.</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\({@f@} \cdot {@g@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(2,8,1); b:rand_with_step(20,40,10); c:a*b; d:b/5; e:a*b/10; ta1:1/a; simp:false; f:5/e; g:d/10; wa1:(5+d)/(e+10);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@f@} \cdot {@g@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir="ltr" style="text-align: left;">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>423191525</deployedseed><deployedseed>1756629135</deployedseed><deployedseed>505485688</deployedseed><deployedseed>813830513</deployedseed><deployedseed>1619258121</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-b Kürzen zweier Brüche mit Variablen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_bi-b')</script><p class="bubble"><div class="hint">Tipp: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\,a\,a\,b\,b\,c}{a\,a\,a\,a\,a\,b\,c\,c\,c}\)</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); powers:makelist(rand(5)+1, 6); myvar1: mya^powers[1]; myvar2: myb^powers[2]; myvar3: myc^powers[3]; myvar4: mya^powers[4]; myvar5: myb^powers[5]; myvar6: myc^powers[6]; d:(myvar1*myvar2*myvar3)/(myvar4*myvar5*myvar6); ta1:d;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Beispiel: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,b\,b\mkern-5mu/\,c\mkern-5mu/}{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,a\,a\,b\mkern-5mu/\,c\mkern-5mu/\,c\,c} = \frac{b}{a^2\,c^2}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>194802941</deployedseed><deployedseed>1917875187</deployedseed><deployedseed>1931041228</deployedseed><deployedseed>928137609</deployedseed><deployedseed>264598581</deployedseed><deployedseed>1633750828</deployedseed><deployedseed>1318198792</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-c Kürzen zweier Brüche mit Variablen und Zahlen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_bi-c')</script><p class="bubble"><div class="hint">Tipp: Erst auf einen Bruchstrich sortieren. Beispiel: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} = \frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c}\)</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>num1:rand_with_step(5,8,1); varlist:[a,b,c,u,v,w,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1], varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); num2:rand_with_step(3,7,1); num3:rand_with_step(3,7,1); nom1:num1*num2*myvars[1]; denom1:num1*myvars[2]; nom2:num1*num3*myvars[1]*myvars[2]; denom2:num1*myvars[1]*myvars[3]; ta1:(nom1/denom1)*(nom2/denom2); /*Alle Variablen in den Zählern mit einer Variable im Nenner gekürzt.*/wa1:((nom1/myvars[1])*(nom2/myvars[1]))/((denom1*denom2)/myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich die Variable {@myvars[1]@} im Nenner gegen beide Variablen in den Zählern gekürzt. Bei der Multiplikation von Brüchen kannst du immer nur einen Faktor gegen den anderen kürzen. Beispiel: \(\frac{36}{6} = \frac{6\cdot6}{6} = \frac{6\mkern-5mu/\cdot6}{6\mkern-5mu/} = \frac{6}{1} = 6\) und nicht \(\frac{36}{6} = \frac{6\cdot6}{6} \ne \frac{6\mkern-5mu/\cdot6\mkern-5mu/}{6\mkern-5mu/} = 1\;\).<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>So lassen sich Produkte auf einem Bruchstrich sortieren und kürzen: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} =\frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c} =\frac{49^7\mkern-14mu\large/ \small \; \cdot 21^3\mkern-14mu\large/\small \; \cdot a\mkern-5mu/ \cdot a \cdot b\mkern-5mu/}{7\mkern-5.5mu/ \cdot7\mkern-5.5mu/ \cdot a\mkern-5mu/\cdot b\mkern-5mu/\cdot c} =\frac{21\,a}{c}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1842189518</deployedseed><deployedseed>1601667602</deployedseed><deployedseed>2136766316</deployedseed><deployedseed>1542661342</deployedseed><deployedseed>2072145258</deployedseed><deployedseed>328965971</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-d Kürzen zweier Brüche mit Termen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_bi-d')</script><p class="bubble"><div class="hint">Tipp: Kennst du noch den Ausspruch „Aus Summen kürzen nur die Dummen“?!</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([x,y,z]); term_summand1:rand_with_prohib(-3,3,[0]); term_summand2:rand_with_prohib(-3,3,[0,term_summand1]); term1:myvar+term_summand1; term2:myvar+term_summand2; ta1:term1/myvar*(myvar^2/(term1*term2*myvar)); /*wa1 means: naive shortened fraction*/ wa1:(term1-myvar)/1*(myvar^2/(term1*term2*myvar));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Offensichtlich hast du beim ersten Bruch die Variable {@myvar@} im Nenner gegen die Variable {@myvar@} im Zähler gekürzt. Das geht aber nicht, weil die Variable {@myvar@} im Zähler mit einem anderen Summanden eine Summe bildet. Beispiel: \(3 = \frac{6}{2} = \frac{4+2}{2} \ne \frac{4 + 2\mkern-5.5mu/}{2\mkern-5.5mu/} = \frac{4}{1} = 4\;\).]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p> Nur ganze Faktoren dürfen gekürzt werden. Zum Beispiel: \(\frac{\boldsymbol{(x-1)}\cdot 2}{x \cdot \boldsymbol{(x-1)}} = \frac{2}{x}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>837792651</deployedseed><deployedseed>528135820</deployedseed><deployedseed>879656886</deployedseed><deployedseed>1917537516</deployedseed><deployedseed>1617668401</deployedseed><deployedseed>159039633</deployedseed><deployedseed>1131743594</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-a Einfachen Bruch erweitern</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_bii-a')</script><p class="bubble">Viel Erfolg beim Lösen dieser Aufgabe!</p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\({@c@} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(4,9,1); b:a-1; c:a/b; d:a*5; e:b*5; simp:false; ta1:d/e;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@c@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>437845679</deployedseed><deployedseed>2092409135</deployedseed><deployedseed>1712748750</deployedseed><deployedseed>182980498</deployedseed><deployedseed>388683995</deployedseed><deployedseed>1561500176</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-b Bruch mit Variablen erweitern</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_bii-b')</script><p class="bubble">Viel Erfolg beim Lösen dieser Aufgabe!</p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@numerator@}}{{@denominator@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,4); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[1]^powers[3]; fac4:myvars[2]^powers[4]; numerator:fac1*fac2; denominator:fac3*fac4; d:numerator/denominator; tanumerator:5*num(d); tadenominator:5*denom(d); simp:false; ta1:tanumerator/tadenominator;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@numerator@}}{{@denominator@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>36209422</deployedseed><deployedseed>1000344719</deployedseed><deployedseed>1827440244</deployedseed><deployedseed>1291739138</deployedseed><deployedseed>825866743</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-c Bruch mit Variablen und Zahlen erweitern</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_bii-c')</script><p class="bubble">Viel Erfolg beim Lösen dieser Aufgabe!</p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,3); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[2]^powers[3]; rand1:rand(4); rand2:rand_with_prohib(0,3,[rand1]); number1:rand1*2+3; number2:rand2*2+3; number3:rand_with_step(2,8,2); numerator:fac1*fac2; denominator:fac3; d:numerator/denominator; tanumerator:5*number1*number2*num(d); tadenominator:5*number3*denom(d); simp:false; ta1:tanumerator/tadenominator;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
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+ <insertstars>5</insertstars>
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+ <requirelowestterms>0</requirelowestterms>
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+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
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+ <text/>
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+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
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+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1516326427</deployedseed><deployedseed>1341581403</deployedseed><deployedseed>79491835</deployedseed><deployedseed>1422333316</deployedseed><deployedseed>1757641065</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ca Einfache Addition von Brüchen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_ca')</script><p class="bubble"><div class="hint">Tipp: Beim Addieren und Subtrahieren müssen die Nenner der Brüche gleich sein. Kannst du dich noch an das kleinste gemeinsame Vielfache erinnern?</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(1,4,1)*2+1; fac1:rand_with_step(1,4,1); fac2:rand_with_prohib(1,4,[fac1]); denoms:[a, a*fac1,a*fac2]; nums:makelist(rand_with_step(1,denoms[i]-1,2),i,3); signs:makelist(rand_with_prohib(-1,1,[0]),3); fractions:makelist(signs[i]*nums[i]/denoms[i],i,3); fractions:random_permutation(fractions); ta1:fractions[1]+fractions[2]+fractions[3]; simp:false; exercise:fractions[1]+fractions[2]+fractions[3]; /*wa1 means: naive addition*/ wa1:(num(fractions[1])+num(fractions[2])+num(fractions[3]))/(denom(fractions[1])+denom(fractions[2])+denom(fractions[3]));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir="ltr" style="text-align: left;">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um die Nenner gleich zu machen, musst du sie so erweitern, dass sie den gleichen Nenner haben. Dann können die Zähler addiert werden. Das kleinste gemeinsame Vielfache von 5, 10 und 15 lässt sich zum Beispiel finden, indem man die jeweiligen Reihen notiert und die kleinste gemeinsame Zahl sucht.</p><table><tr><th>5er-Reihe</th><th>10er-Reihe</th><th>15er-Reihe</th></tr><tr><td>5</td><td>10</td><td>15</td></tr><tr><td>10</td><td>20</td><td><strong>30</strong></td></tr><tr><td>15</td><td><strong>30</strong></td><td>...</td></tr><tr><td>20</td><td>...</td><td>...</td></tr><tr><td>25</td><td>...</td><td>...</td></tr><tr><td><strong>30</strong></td><td>...</td><td>...</td></tr><tr><td>...</td><td>...</td><td>...</td></tr></table></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>311233457</deployedseed><deployedseed>584289189</deployedseed><deployedseed>1338253474</deployedseed><deployedseed>933392702</deployedseed><deployedseed>236951333</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cb Addition von Brüchen mit Variablen und gleichem Nenner</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_cb')</script><p class="bubble"><div class="hint">Tipp: Überlege genau, was ein Minus vor einem Bruch bedeutet.</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c]); fractions_correct_and_wa1:[[(myvar+1)/myvar, -myvar+1], [(myvar-1)/myvar, -myvar-1], [(1-myvar)/myvar, -1-myvar]]; fractions_correct_and_wa1:random_permutation(fractions_correct_and_wa1); fractions:makelist(fractions_correct_and_wa1[i][1],i,3); terms_wa1:makelist(fractions_correct_and_wa1[i][2],i,3); exercise:fractions[1]-fractions[2]-fractions[3]; ta1:combine(exercise); wa1:(num(fractions[1])+terms_wa1[2]+terms_wa1[3])/myvar;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@}-{@fractions[2]@}-{@fractions[3]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast offenbar die Minuszeichen nicht korrekt aufgelöst.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
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+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Ein Minus vor dem Bruch gehört zum ganzen Bruch: gilt also für den ganzen Zähler oder ganzen Nenner (häufig nimmt man den Zähler).</p><p>\(\Rightarrow -\frac{a-1}{a} = \frac{-\boldsymbol{(a-1)}}{a} = \frac{-a+1}{a}\)</p><p>Wichtig bei Summen im Zähler!!!</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
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+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cc Addition von Brüchen mit Variablen und unterschiedlichen Nennern</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_cc')</script><p class="bubble"><div class="hint">Tipp: Jeder Teilnenner (hier: {@myvars[1]@}, {@myvars[2]@}, {@myvars[3]@}) muss als Faktor im gemeinsamen Nenner vorkommen.</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); fractions:[(1+myvars[1])/myvars[1], rand_with_step(2,5,1)/myvars[2], myvars[1]/myvars[3]]; fractions:random_permutation(fractions); exercise:fractions[1]+fractions[2]+fractions[3]; common_denom:denom(fractions[1])*denom(fractions[2])*denom(fractions[3]); ta1:((num(fractions[1])*denom(fractions[2])*denom(fractions[3]))+(num(fractions[2])*denom(fractions[1])*denom(fractions[3]))+(num(fractions[3])*denom(fractions[1])*denom(fractions[2])))/common_denom; ta1alt:(expand((num(fractions[1])*denom(fractions[2])*denom(fractions[3])))+expand((num(fractions[2])*denom(fractions[1])*denom(fractions[3])))+expand((num(fractions[3])*denom(fractions[1])*denom(fractions[2]))))/common_denom;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{1+a}{a}+\frac{2}{b}+\frac{a}{c}\) ist der gemeinsame Nenner \(a \cdot b \cdot c\). So muss erweitert werden, damit die Zähler addiert werden können:</p><p>\(\frac{(1+a) \boldsymbol{\cdot b \cdot c} }{a \boldsymbol{\cdot b \cdot c}}+\frac{2 \boldsymbol{\cdot a \cdot c}}{\boldsymbol{a} \cdot b \boldsymbol{\cdot c}}+\frac{a \boldsymbol{\cdot a \cdot b}}{\boldsymbol{a \cdot b} \cdot c}\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(1+a\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>638235066</deployedseed><deployedseed>1053964038</deployedseed><deployedseed>625975426</deployedseed><deployedseed>1098133316</deployedseed><deployedseed>1880026849</deployedseed><deployedseed>1344755034</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cd Addition von Brüchen mit einer Variablen und unterschiedlichen Nennern</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_cd')</script><p class="bubble">Viel Erfolg beim Lösen dieser Aufgabe!</p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([x,y,z]); nums:makelist(rand_with_step(2,5,1),2); fractions:[(nums[1]+myvar)/myvar^2,(nums[2]-myvar^2)/myvar]; common_denom:myvar^2; ta1:(num(fractions[1])-num(fractions[2])*myvar)/common_denom; ta1alt:(num(fractions[1])-expand(num(fractions[2])*myvar))/common_denom; exercise:fractions[1]-fractions[2]; /*wa1 means: didn't consider minus sign before bracket*/ wa1:(num(fractions[1])+(-nums[2]-myvar^2)*myvar)/common_denom;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast offenbar die Minuszeichen nicht korrekt aufgelöst (siehe Tipp unten).]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um immer einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{3+x}{x^2}-\frac{5-x}{x}\) ist ein gemeinsame Nenner \(x^2 \cdot x = x^3\). Betrachtet man die Teilnenner \(x^2\) und \(x\) genauer, fällt auf, dass \(x\) bereits als Faktor in \(x^2\) vorkommt. Denn \(x^2 = x \cdot x\). Deswegen kann hier auch \(x^2\) als Hauptnenner gewählt werden.</p><p>Dazu muss so erweitert werden:</p><p>\(\frac{(3+x)}{x^{2}}-\frac{(5-x^2) \boldsymbol{ \cdot x}}{x \boldsymbol{\cdot x}} = \frac{3+x}{x^{2}}-\frac{5x-x^3}{x^{\boldsymbol{2}}} = \frac{3+x-(5x-x^3)}{x^2} = \dots\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(5-x^2\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>669633138</deployedseed><deployedseed>2093071884</deployedseed><deployedseed>1766326583</deployedseed><deployedseed>488830876</deployedseed><deployedseed>1210423031</deployedseed><deployedseed>158072256</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ce Addition von Brüchen mit Variablen und unterschiedlichen Nennern I (Update1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_ce')</script><p class="bubble"><div class="hint">Tipp: Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); numbers:makelist(rand_with_step(2,5,1), 5); factors:random_permutation([1,2,4]); /*only +*/ signs:makelist(rand_with_prohib(1,1,[0]),2); fractions:[(numbers[1]*myvars[1]-numbers[2]*myvars[2])/(factors[1]*5*myvars[1]*myvars[2]), (numbers[3]*myvars[3]-numbers[4]*myvars[1])/(factors[2]*5*myvars[1]*myvars[3]), (myvars[3]^2-numbers[5])/(factors[3]*5*myvars[2]*myvars[3])]; tanum:(num(fractions[1])*(4/factors[1])*myvars[3]+num(fractions[2])*(4/factors[2])*myvars[2]+num(fractions[3])*(4/factors[3])*myvars[1]); tanumalt:expand(tanum); tadenom:(5*4*myvars[1]*myvars[2]*myvars[3]); ta1:tanum/tadenom; /*fractions_to_show:random_permutation(fractions);*/ fractions_to_show:fractions; ta1alt:tanumalt/tadenom; fractions_to_show[2]:fractions_to_show[2]*signs[1]; fractions_to_show[3]:fractions_to_show[3]*signs[2]; exercise:fractions_to_show[1]+fractions_to_show[2]+fractions_to_show[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
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+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{5\,z-4\,x}{10\,x\,z}+\frac{7\,y-3\,z}{20\,y\,z}+\frac{y^2-2}{5\,x\,y}\) ist \(20\) das kleinste gemeinsame Vielfache (kgV) von \(10\), \(20\) und \(5\) und \(x \cdot y \cdot z\) ist das kgV von \(x \cdot z\), \(y \cdot z\) und \(x \cdot y\). Der Hauptnenner ist demnach \(20 \cdot x \cdot y \cdot z\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(20 \cdot x \cdot y \cdot z\;\) steht. \(\frac{5\,z-4\,x}{10\,x\,z}\) wird mit \(2 \cdot y\) erweitert, \(\frac{7\,y-3\,z}{20\,y\,z}\) wird mit \(x\) erweitert und \(\frac{y^2-2}{5\,x\,y}\) wird mit \(4 \cdot z\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(5\,z-4\,x)\boldsymbol{ \cdot 2\,y}}{10\,x\,z \boldsymbol{ \cdot 2\,y}}+\frac{(7\,y-3\,z) \boldsymbol{ \cdot x}}{20\,y\,z \boldsymbol{ \cdot x}}+\frac{(y^2-2) \boldsymbol{ \cdot 4\,z}}{5\,x\,y \boldsymbol{ \cdot 4\,z}}\)</p><p>\(= \frac{10\,y\,z-8\,x\,y}{20\,x\,y\,z}+\frac{7\,x\,y-3\,x\,z}{20\,x\,y\,z}+\frac{4\,y^2\,z-8\,z}{20\,x\,y\,z} = \dots\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1330316881</deployedseed><deployedseed>2007639052</deployedseed><deployedseed>846124380</deployedseed><deployedseed>520216901</deployedseed><deployedseed>1618486590</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cf Addition von Brüchen mit Variablen und unterschiedlichen Nennern II</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_cf')</script><p class="bubble"><div class="hint">Tipp: 1) Überlege genau, was ein Minus vor einem Bruch bedeutet. 2) Jeder Teilnenner (hier: {@denom(main_fraction)@}, {@denom(fractions[1])@}, {@denom(fractions[2])@}) muss als Faktor im gemeinsamen Nenner vorkommen. 3) Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); numbers:rand_selection(makelist(i,i,5),2); denom_nums_origin:rand_selection([18,12,6],1)[1]; denom_nums:[denom_nums_origin, denom_nums_origin/2, denom_nums_origin/3]; main_fraction:(numbers[1]-myvars[1])/(denom_nums[1]*myvars[1]^2); fractions:[(myvars[2])/(denom_nums[2]*myvars[1]), (myvars[2]+numbers[2])/(denom_nums[3]*myvars[1]*myvars[2])]; tanum:num(main_fraction)*myvars[2]-num(fractions[1])*2*myvars[1]*myvars[2]-num(fractions[2])*3*myvars[1]; tanumalt:expand(tanum); tadenom:denom_nums_origin*myvars[1]^2*myvars[2]; ta1:tanum/tadenom; ta1alt:tanumalt/tadenom; fractions:random_permutation(fractions); simp:false; exercise:main_fraction-fractions[1]-fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{1-x}{18\,x^2}-\frac{y}{9\,x}-\frac{x+3}{6\,x\,y}\) ist \(18\) das kleinste gemeinsame Vielfache (kgV) von \(18\), \(9\) und \(6\) und \(x^2 \cdot y\) ist das kgV von \(x^2\), \(x\) und \(x \cdot y\). Der Hauptnenner ist demnach \(18 \cdot x^2 \cdot y\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(18 \cdot x^2 \cdot y\;\) steht. \(\frac{1-x}{18\,x^2}\) wird mit \(y\) erweitert, \(\frac{y}{9\,x}\) wird mit \(2\,x\,y\) erweitert und \(\frac{x+3}{6\,x\,y}\) wird mit \(3 \cdot x\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(1-x) \boldsymbol{\cdot y}}{18\,x^2 \boldsymbol{\cdot y}}-\frac{y \boldsymbol{\cdot 2\,x\,y}}{9\,x \boldsymbol{\cdot 2\,x\,y}}-\frac{(x+3) \boldsymbol{\cdot 3\,x}}{6\,x\,y \boldsymbol{\cdot 3\,x}}\)</p><p>\(= \frac{y-x\,y}{18\,x^2\,y}-\frac{2\,x\,y^2}{18\,x^2\,y}-\frac{3\,x^2+9\,x}{18\,x^2\,y} = \dots\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>527686404</deployedseed><deployedseed>1918490776</deployedseed><deployedseed>2103547991</deployedseed><deployedseed>1091135158</deployedseed><deployedseed>1696865873</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-da Multiplikation zweier einfacher Brüche</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_da')</script><p class="bubble"><div class="hint">Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@}\cdot{@fractions[2]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8),4); fractions:[nums[1]/nums[2], nums[3]/nums[4]]; ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions*/ wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied*/ wa2:fractions[1]+fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@}\cdot{@fractions[2]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{2}{3} \cdot \frac{6}{5} = \frac{2 \cdot 6}{3 \cdot 5} = \frac{12}{15} = \frac{4}{5}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1088212423</deployedseed><deployedseed>1553109555</deployedseed><deployedseed>777390971</deployedseed><deployedseed>1688656099</deployedseed><deployedseed>1485690277</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-db Multiplikation zweier Brüche mit Variablen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_db')</script><p class="bubble"><div class="hint">Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); fractions:[mya/myb, mya^2/(mya*myb)]; fractions:random_permutation(fractions); ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions with previously shortened the larger fraction*/ wa1:(2*mya)/(2*myb); /*wa2 means: naively summed fractions without previously shortening the larger fraction*/ wa2:(mya+myb^2)/(mya+myb*mya); /*wa3 means: correctly summed fractions instead of multiplied*/ wa3:fractions[1]+fractions[2]; /*wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied wa2:fractions[1]+fractions[2];*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
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+ <options/>
+ </input>
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+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
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+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
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+ <truescoremode>=</truescoremode>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.]]></text>
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+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden. Du hast außerdem den Bruch \({@mya@}^2/({@mya@}*{@myb@})\) nicht ausreichend vereinfacht. Er kann zu \({@mya@}/{@myb@}\) gekürzt werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
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+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
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+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{a}{b} \cdot \frac{a^2}{a\,b} = \frac{a}{b} \cdot \frac{a \cdot a}{a\,b} = \frac{a \cdot a \cdot a}{a \cdot b \cdot b} = \frac{a^3}{a\,b^2}\)</p></p>]]></text>
+</truefeedback>
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+<falsepenalty/>
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+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>545658671</deployedseed><deployedseed>1228864607</deployedseed><deployedseed>806993602</deployedseed><deployedseed>1501016569</deployedseed><deployedseed>710282177</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dc Multiplikation Bruch mit Zahlen, Bruch mit Variablen, Ganzzahl</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_dc')</script><p class="bubble"><div class="hint">Tipp: Wie kann man eine ganze Zahl als Bruch schreiben?</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8),3); nums:sort(nums); varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); factors:[nums[1], (mya*myb)/myc, nums[2]/nums[3]]; factors:random_permutation(factors); ta1:factors[1]*factors[2]*factors[3]; simp:false; exercise:factors[1]*factors[2]*factors[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
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+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
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+ <falsefeedback format="html">
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+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
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+ <truepenalty/>
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+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
+ <falsenextnode>999</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
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+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Jede ganze Zahl kann als Bruch geschrieben werden, indem man sie durch 1 teilt. Beispiel: \(3 \cdot \frac{a\,b}{c} \cdot \frac{5}{6} = \frac{3}{1} \cdot \frac{a\,b}{c} \cdot \frac{5}{6}\)</p><p>\( = \frac{3 \cdot a \cdot b \cdot 5}{1 \cdot c \cdot 6} = \frac{15\,a\,b}{6\,c} = \frac{5\,a\,b}{2\,c}\)</p><p>Hinweis: Generellt gilt \(\cdot 1\) und \(:\,1\) geht immer.</p></p>]]></text>
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+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1569886884</deployedseed><deployedseed>1980675582</deployedseed><deployedseed>1601683210</deployedseed><deployedseed>51348788</deployedseed><deployedseed>726919830</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dd Multiplikation zweier Brüche mit Termen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_dd')</script><p class="bubble"><div class="hint">Tipp: Achtung: Summanden & Faktoren => Klammer!</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:rand_selection(varlist, 2); nums:rand_selection(makelist(i+1,i,9), 6); fractions:[(nums[1]*myvars[1]+nums[2]*myvars[2])/(nums[3]*myvars[2]+nums[4]*myvars[1]), (-nums[5]*myvars[1])/(nums[6]+myvars[1])]; ta1:fractions[1]*fractions[2]; taalt:combine(expand(ta1)); /*wa1 means: the multiplication of the numerator was done with only one summand of the first fraction’s numerator (the second one)*/ wa1:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(denom(fractions[1])*denom(fractions[2])); /*old_wa2 means the same as wa1 but with the first fraction numerator’s second summand*/ /*old_wa2: (nums[1]*myvars[1]*num(fractions[2])+nums[2]*myvars[2])/(denom(fractions[1])*denom(fractions[2]));*/ /*wa2 means the same as wa1 but with the denominators, so no brackets: first summand of second fraction is multiplied with last summand of first fraction*/ wa2:(num(fractions[1])*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]); /*wa3 is the combination of wa1 and wa2*/ wa3:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}= {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
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+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
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+ <showvalidation>3</showvalidation>
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+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Nenner richtig multipliziert, doch du hast den Faktor im Zähler des zweiten Bruches nur mit dem zweiten Summanden des Zählers im ersten Bruch multipliziert. Das heißt bei der Multiplikation der Zähler musst du Klammern um die Summe setzen und jeden Summanden des ersten Zählers mit dem Faktor des anderen Zählers multiplizieren.]]></text>
+</truefeedback>
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+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
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+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Zähler richtig multipliziert, hast jedoch im Nenner nicht beachtet, dass Summen als Ganzes multipliziert werden. Das heißt bei der Multiplikation der Nenner musst du Klammern um die Summen setzen und jeden Summanden des einen Nenners mit jedem Summanden des anderen Nenners multiplizieren.]]></text>
+</truefeedback>
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+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>5</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-6-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Summen nicht als Ganzes multipliziert. Das betrifft eine Summe im Zähler und die Summen im Nenner. Du musst jeweils Klammern setzen, damit jeder Summand mit jedem anderen Summanden multipliziert wird. ]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-6-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{4\,x+10\,y}{5\,y+2\,x} \cdot \frac{-4\,x}{3+x} = \)\(\frac{\boldsymbol{(4\,x+10\,y)} \cdot -4\,x}{\boldsymbol{(5\,y+2\,x)} \cdot \boldsymbol{(3+x)}} = \dots\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>783029466</deployedseed><deployedseed>1177445020</deployedseed><deployedseed>1009895582</deployedseed><deployedseed>1167689465</deployedseed><deployedseed>1922827729</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-de Einfacher Doppelbruch</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_de')</script><p class="bubble"><div class="hint">Tipp: Achtung: Doppelbruch</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8), 4); nums:sort(nums); ta1:((nums[1])/(nums[4]))/((nums[2])/(nums[3])); /*wa1 means: multiplied fractions instead of division*/ wa1:((nums[1])/(nums[4]))*((nums[2])/(nums[3])); /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:((nums[4])/(nums[1]))*((nums[2])/(nums[3]));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>352990161</deployedseed><deployedseed>467670994</deployedseed><deployedseed>1747402747</deployedseed><deployedseed>2135608811</deployedseed><deployedseed>460810681</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-df Bruch und Geteilt-Rechnung</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_df')</script><p class="bubble"><div class="hint">Achtung: Auch ein Doppelbruch ;)</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@dividend@}:{@divisor@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>power:rand_with_step(2,4,1); myvars:rand_selection([a,b,c,x,y,z],2); dividend:myvars[1]/myvars[2]; num:rand_with_step(1,5,1); divisor:(num-myvars[1])/(myvars[2]^power); ta1: dividend/divisor; /*wa1 means: multiplied fractions instead of division*/ wa1:dividend*divisor; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:dividend^(-1)*divisor; /*wa3 means: didn’t consider to multiply the denominator of the first fraction with the sum of the second fraction’s numerator as a whole*/ wa3:(num(dividend)*denom(divisor))/(myvars[2]*num-myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@dividend@}:{@divisor@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast den richtigen Kehrwert gebildet um die Brüche dann zu multiplizieren, jedoch hast du dann die Klammersetzung bei der Mutliplikation nicht beachtet.</p><p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{x}{a} : \frac{1-x}{a^2} = \frac{x}{a} \cdot \frac{a^2}{1-x}\)\(= \frac{x \cdot a^2}{a \cdot \boldsymbol{(1-x)}} = \dots\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: \(\boldsymbol{:}\) ist dasselbe wir ein Doppelbruchstrich.</p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>68495326</deployedseed><deployedseed>83279259</deployedseed><deployedseed>1848999895</deployedseed><deployedseed>1656521999</deployedseed><deployedseed>333378154</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dg Doppelbruch mit Zahlen und Variablen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_dg')</script><p class="bubble"><div class="hint">Tipp: Achtung: Doppelbruch</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:rand_selection(makelist(i+1,i,3),2); nums:rand_selection(makelist(i+1,i,4),2); myvars:rand_selection([a,b,c,x,y,z],2); fractions:[nums[1]/myvars[1]^powers[1], (nums[2]*myvars[2]^powers[2])/myvars[1]]; fractions:random_permutation(fractions); ta1:fractions[1]/fractions[2]; /*wa1 means: multiplied fractions instead of division*/ wa1:fractions[1]*fractions[2]; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:fractions[1]^(-1)*fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{2}{a^2}}{\frac{3\,b^2}{a}} = \frac{2}{a^2} \cdot \frac{a}{3\,b^2} = \frac{2\,a}{3\,a^2\,b^2}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1783639635</deployedseed><deployedseed>863915904</deployedseed><deployedseed>446314797</deployedseed><deployedseed>1562297660</deployedseed><deployedseed>1172377010</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dh Doppelbruch mit Termen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_dh')</script><p class="bubble"><div class="hint">Tipp: Achtung: Doppelbruch</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8), 3); nums:sort(nums); myvars:rand_selection([a,b,c,x,y,z],2); terms:[nums[1]*((1-myvars[1])/myvars[2]), (nums[2]/nums[3])*(myvars[2]^2/myvars[1])]; /*terms:random_permutation(terms);*/ ta1:terms[1]/terms[2]; taalt:combine(expand(ta1)); /*wa1 means: didn't consider to multiple first factor in the numerator with both summands of the fraction's numerator*/ wa1:((nums[1]*1-myvars[1])/myvars[2])/terms[2]; wa2:terms[1]*terms[2]; wa3:terms[1]^(-1)*terms[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Beim Multiplizieren des Faktors {@nums[1]@} und des Bruchs \(\frac{1-{@myvars[1]@}}{{@myvars[2]@}}\) im Zähler des Doppelbruchs musst du beachten, dass Summen als Ganzes multipliziert werden.</p><p>Beispiel: \(5 \cdot \frac{1-a}{b} = \frac{5 \cdot \boldsymbol{(1-a)}}{b} = \dots\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>5</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>5</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-6-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-6-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Lösungsweg für eine Beispielaufgabe:</p><p>\(\large\frac{5 \cdot \frac{1-a}{b}}{\frac{1}{3} \cdot \frac{b^2}{a}}\)\(\large = \frac{\frac{5 \cdot \boldsymbol{(1-a)}}{b}}{\frac{b^2}{3\,a}} = \frac{5 - 5\,a}{b} \cdot \frac{3\,a}{b^2}\)</p><p>\(\large = \frac{3\,a \cdot \boldsymbol{(5-5\,a)}}{b \cdot b^2} = \frac{15\,a - 15\,a^2}{b^3}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>611281053</deployedseed><deployedseed>439766047</deployedseed><deployedseed>725695831</deployedseed><deployedseed>1029360039</deployedseed><deployedseed>1825759080</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ea Bruchrechnung Kombination I</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_ea')</script><p class="bubble"><div class="hint">Tipp: Achtung: Doppelbrüche und Summanden => Punkt-vor-Strich-Rechnung</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(2,4,1); nums_real_frac:sort(rand_selection(makelist(i,i,9),4)); nums_unreal_frac:sort(rand_selection(makelist(i+3,i,7),6)); main_summand:((nums_real_frac[1])/(nums_real_frac[4]))/((nums_real_frac[2])/(nums_real_frac[3])); summands:[int*(nums_unreal_frac[6]/nums_unreal_frac[1]), ((nums_unreal_frac[5])/(nums_unreal_frac[2]))/((nums_unreal_frac[4])/(nums_unreal_frac[3]))]; ta1:main_summand+summands[1]-summands[2]; wa1:(main_summand+int)*summands[1]/int-summands[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast offensichtlich die Punkt-vor-Strich-Regel nicht beachtet.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6} = \frac{\frac{5}{6}}{\frac{1}{3}}+(2 \cdot \frac{9}{6}) \ne (\frac{\frac{5}{6}}{\frac{1}{3}}+2) \cdot \frac{9}{6}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Jeden Summanden einzeln betrachten und ausrechnen: Doppelbrüche auflösen und zusammenfassen.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6}-\frac{\frac{13}{4}}{\frac{6}{5}} = \frac{5}{6} \cdot \frac{3}{1}+\frac{2}{1} \cdot \frac{9}{6}-\frac{13}{5} \cdot \frac{5}{6}\)</p><p>\(= (\frac{5}{6\mkern-5mu/^2} \cdot \frac{3\mkern-5mu/^1}{1})+(\frac{2\mkern-5mu/^1}{1} \cdot \frac{9}{6\mkern-5mu/^2})-(\frac{13}{5\mkern-5mu/^1} \cdot \frac{5\mkern-5mu/^1}{6})\)</p><p>\(= \frac{5}{2} + \frac{9}{2} - \frac{13}{6} = \frac{5 \cdot 3}{2 \cdot 3} + \frac{9 \cdot 3}{2 \cdot 3} - \frac{13}{6} = \frac{15}{6} + \frac{27}{6} - \frac{13}{6}\)</p><p>\(= \frac{15+27+13}{6} = \frac{55}{6}\)<\p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>2022519868</deployedseed><deployedseed>2007714528</deployedseed><deployedseed>1652468809</deployedseed><deployedseed>1890021691</deployedseed><deployedseed>1160555762</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-eb Bruchrechnung Kombination II</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_eb')</script><p class="bubble"><div class="hint">Tipp: Sorgfältig ausmultiplizieren</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(3,7,1); nums:sort(rand_selection(makelist(i,i,9),6)); factors:[int, (nums[1]/nums[6]+nums[2]/nums[5]), (1-nums[3]/nums[4])]; ta1:factors[1]*factors[2]*factors[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})= {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>999</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Hier hast du zwei Möglichkeiten: Alles sauber ausmultiplizieren oder vor dem Multiplizieren die Klammern ausrechnen (Empfehlung!)</p><p>Beispiel: \(6 \cdot (\frac{3}{4}+\frac{1}{8}) \cdot (1-\frac{1}{4}) = 6 \cdot (\frac{3 \cdot 2}{4 \cdot 2}+\frac{1}{8}) \cdot (\frac{1 \cdot 4}{1 \cdot 4}-\frac{1}{4})\) </p><p>\(= 6 \cdot (\frac{6}{8}+\frac{1}{8}) \cdot (\frac{4}{4}-\frac{1}{4}) = 6 \cdot (\frac{7}{8}) \cdot (\frac{3}{4})\)</p><p>\( = \frac{6}{1} \cdot \frac{7}{8} \cdot \frac{3}{4} = \frac{6\mkern-5mu/^3 \cdot 7 \cdot 3}{1 \cdot 8\mkern-5mu/^4 \cdot 4} = \frac{63}{16}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>382901616</deployedseed><deployedseed>1683089904</deployedseed><deployedseed>724792720</deployedseed><deployedseed>857106597</deployedseed><deployedseed>2126061360</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ec Bruchrechnung Kombination III</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t1_fra_1_ec')</script><p class="bubble"><div class="hint">Tipp: Achtung: Doppelbruch und gemischter Bruch vs. unechter Bruch</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(2,4,1); myvar:rand_selection([a,b,c,x,y,z],1)[1]; nums:sort(rand_selection(makelist(i,i,9),6)); summands:[(int+(nums[1]/nums[4]))*(myvar/nums[5]),1-((nums[6]-myvar)/((nums[4])/(nums[3])))]; ta1:combine(expand(summands[1]+summands[2])); wa1:(int*(nums[1]/nums[4]))*(myvar/nums[5])+summands[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast offenbar den gemischten Bruch \({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\) als Multiplikation \({@int@} \cdot \frac{{@nums[1]@}}{{@nums[4]@}}\) interpretiert. Allerdings meint der gemischte Bruch hier \({@int@}\) Ganze und \(\frac{{@nums[1]@}}{{@nums[4]@}}\) Anteil. Empfehlung: Gemischte Brüche als unechte Brüche umschreiben. Beispiel:\(2\frac{1}{6} = 2+\frac{1}{6} = \frac{2 \cdot 6}{1 \cdot 6} + \frac{1}{6} = \frac{12}{6}+\frac{1}{6} = \frac{13}{6}\)]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: \(\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}}\) ist auch ein Doppelbruch.</p><p>Achte darauf, dann die Klammer richtig zu setzen.</p><p>Beispiel: \(\frac{2-a}{\frac{7}{8}} = \boldsymbol{(}2-a\boldsymbol{)} \cdot \frac{8}{7}\)</p><p>Beachte: 1) Ganze Zahlen zum Bruch umschreiben. 2) Doppelbrüche umschreiben (Beispiel oben). 3) Gemischte Brüche umschreiben (Beispiel \(2\frac{1}{6}\) sind \(\frac{13}{6}\;\)). 4) Punkt-vor-Strich-Regel.</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>2024587341</deployedseed><deployedseed>1597148134</deployedseed><deployedseed>899831950</deployedseed><deployedseed>29495097</deployedseed><deployedseed>97014366</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-j Binomische Formeln I - Anwendungsaufgabe</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t3_frabin_1_j')</script><p class="bubble"><div class="hint">Um diese Aufgabe zu lösen, musst du mehrere binomische Formeln anwenden.<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen und faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.</div>
+</div>
+<p></p>
+<p>\(\frac{{@expand(BIN_a[2])@}}{{@expand(BIN_a[3])@}} \cdot {@BIN_a[3]@}\)\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p><br></p>
+<p><br></p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>aa:4;
+bb:5;
+c:3;
+d:2;
+
+u:(c*a-d*b)^2;
+ualt:(d*b-c*a)^2;
+v:(aa*a+d*b)^2;
+w:(bb*a-c*b)*(bb*a+c*b);
+
+x:(aa*a-d*b)^2;
+xalt:(d*b-aa*a)^2;
+y:(bb*a+c*b)^2;
+z:(c*a+d*b)*(c*a-d*b);
+
+/*BIN_A:[
+[a1,(2*a+5*b)^2,"\\(\\frac{4\\,a^2+20\\,a\\,b+25\\,b^2}{16\\,a^2-9\\,b^2}\\cdot(4\\,a-3\\,b)\\cdot(4\\,a+3\\,b)\\)"]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];*/
+
+BIN_A:[
+[a1,u,v,ualt],
+[a2,v,w,v],
+[a3,w,u,w],
+[a4,x,y,xalt],
+[a5,y,z,y],
+[a6,z,y,z]
+];
+BIN_a:rand(BIN_A);
+
+ta:BIN_a[2];
+taalt:BIN_a[4];
+
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>534740616</deployedseed> <deployedseed>47766652</deployedseed> <deployedseed>1657775726</deployedseed> <deployedseed>931829986</deployedseed> <deployedseed>1703936373</deployedseed> <deployedseed>151644710</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-g Binomische Formeln Ia - Erste binomische Formel</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t3_frabin_1_g')</script><p class="bubble"><div class="hint">Um den Bruch aus der Endgegner-Aufgabe zu vereinfachen, musst du binomische Formeln anwenden. Deshalb kommen wir nun zu den binomischen Formeln. Die erste binomische Formel besagt: \((a + b)^2 = a^2 + 2\,a\,b + b^2\;\).</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,(4+b)^2],
+[a2,(5+b)^2],
+[a3,(3+b)^2],
+[a4,(2+b)^2],
+[a5,(3+2*b)^2],
+[a6,(4+2*b)^2]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];
+task:expand(BIN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die erste binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1994312303</deployedseed> <deployedseed>1744518788</deployedseed> <deployedseed>1627526666</deployedseed> <deployedseed>1566276649</deployedseed> <deployedseed>1138479794</deployedseed> <deployedseed>806677520</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-h Binomische Formeln Ib - Zweite binomische Formel</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t3_frabin_1_h')</script><p class="bubble"><div class="hint">Die zweite binomische Formel besagt:\((a - b)^2 = a^2 - 2\,a\,b + b^2\;\).<!--Diesmal musst du den Term erst umformen, damit er in der richtigen Form erscheint.--><br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:4;
+b:5;
+c:3;
+d:2;
+
+e:1;
+f:2;
+
+BIN_A:[
+[a1,a,e],
+[a2,b,e],
+[a3,c,e],
+[a4,d,e],
+[a5,a,f],
+[a6,c,f]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]-BIN_a[3]*y)^2;
+taalt:(BIN_a[3]*y-BIN_a[2])^2;
+task:expand(ta);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>893674818</deployedseed> <deployedseed>675538571</deployedseed> <deployedseed>985713485</deployedseed> <deployedseed>1039647874</deployedseed> <deployedseed>1781202861</deployedseed> <deployedseed>824682247</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-i Binomische Formeln Ic - Dritte binomische Formel</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t3_frabin_1_i')</script><p class="bubble"><div class="hint">Die dritte binomische Formel besagt: \((a + b)\,(a - b) = a^2 - b^2\;\).<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p></p>
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>aa:4;
+bb:5;
+c:3;
+d:2;
+
+
+BIN_A:[
+[a1,aa,bb],
+[a2,c,d],
+[a3,d,aa],
+[a4,d,bb],
+[a5,d,c],
+[a6,aa,c]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]*x-BIN_a[3]*y)*(BIN_a[2]*x+BIN_a[3]*y);
+task:expand(ta);
+wa:(BIN_a[2]^2*x-BIN_a[3]^2*y)*(BIN_a[2]^2*x+BIN_a[3]^2*y);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die dritte binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast zwar die Unbekannten x und y korrekt faktorisiert, aber die sie begleitenden Faktoren unverändert in die Klammern geschrieben. Um diese korrekt zu faktorisieren, musst du ihre Wurzeln berechnen. Richtig wäre {@ta@}.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>455750255</deployedseed> <deployedseed>970764179</deployedseed> <deployedseed>1971560923</deployedseed> <deployedseed>987956614</deployedseed> <deployedseed>533447380</deployedseed> <deployedseed>299284489</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-k Bruchrechenregeln Ig2 - Bruch mit binomischem Term erweitern 2 (copy)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t3_frabin_1_k')</script><p class="bubble"><div class="hint">Dies ist der Endgegner zur Mathe-Welt <strong>Bruchrechenregeln und binomische Formeln</strong>. Wenn du diese Aufgabe schaffst, hast du diese Welt schon gemeistert. Wende zuerst die binomischen Formeln an, um die Nenner zu vereinfachen. Um die Brüche dann zu addieren, musst du mit einem Term erweitern.<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen und faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;
+b:3;
+c:4;
+
+aa:x-a;
+bb:x-b;
+cc:x-c;
+
+/*FRA_A:[
+[a1,(x^2-3)/(x^2-4),"\\(\\frac{x + 3}{x^2 - 4} + \\frac{x - 3}{x - 2}\\)",(x^2-3)/((x+2)*(x-2))]
+];*/
+
+FRA_A:[
+[a1,aa, a],
+[a2,bb, b],
+[a3,cc, c]
+];
+FRA_a:rand(FRA_A);
+task:(3*FRA_a[3]*x+FRA_a[3]^2)/expand(FRA_a[2]^2)+x/FRA_a[2];
+ta:(x+FRA_a[3])^2/(FRA_a[2])^2;
+
+simp:false;
+taalt:((x+FRA_a[3])/(FRA_a[2]))^2;
+simp:true;
+
+wa1:expand((x+FRA_a[3])^2)/(FRA_a[2])^2;
+wa2:(x+FRA_a[3])^2/expand((FRA_a[2])^2);
+wa3:expand((x+FRA_a[3])^2)/expand(FRA_a[2]^2);
+wa4:(3*FRA_a[3]*x+FRA_a[3]^2)/expand(FRA_a[2]^2)+x^2/FRA_a[2]^2; /*naively expanded fraction by squaring numerator and denominator*/
+wa5:(3*FRA_a[3]*x+FRA_a[3]^2+x)/(expand(FRA_a[2]^2)+FRA_a[2]); /*naively summed fractions, keeping the denominators*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@FRA_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>2</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die erste binomische Formel an, um den Zähler zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa2</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die zweite binomische Formel an, um den Nenner zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>4</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa3</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die erste binomische Formel an, um den Zähler zu faktorisieren und
+ wende die zweite binomische Formel an, um den Nenner zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa4</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich den zweiten Summanden mit sich selbst multipliziert (quadriert), damit die Nenner gleich sind. Allerdings wird ein Bruch so nicht erweitert. Der quadrierte Bruch ist nicht mehr äquivalent mit dem vorherigen Bruch. Beispiel: \((\frac{2}{5})^2 = \frac{4}{25} \ne \frac{2}{5}\;\) wohingegen \(\frac{2}{5} = \frac{2 \cdot 5}{5 \cdot 5} = \frac{10}{25}\;\). Bitte überlege erneut, womit der zweite Summand erweitert werden muss, damit die Nenner gleich sind.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa5</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich die beiden Brüche addiert, indem du Zähler plus Zähler (oben) und Nenner plus Nenner (unten) gerechnet hast. So können Brüche nicht addiert werden. Beispiel: \( \frac{1}{2} + \frac{1}{4} \ne \frac{1+1}{2+4}\;\) . Brüche müssen so erweitert werden, dass sie den gleichen Nenner haben. Dann können die Zähler addiert werden: \(\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}\).</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>2099085786</deployedseed> <deployedseed>245667775</deployedseed> <deployedseed>1806806387</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-a p-q-Formal Ia - Termumformung</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t4_pq_1_a')</script><p class="bubble"><div class="hint">Um die p-q-Formel anzuwenden, müssen wir zunächst den Term in die richtige Form bringen. Um den folgenden Term wie gewünscht umzuformen, subtrahiere und dividiere auf beiden Seiten der Gleichung.<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p>Formen Sie den Term so um, dass er in der Form \(x^2+px+q = 0\) erscheint. Sie können dies Zeile für Zeile tun.<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[6*x+3*x^2-2=10,x^2+2*x-4=0],6*x+3*x^2-2=10],
+[a2,[15*x+5*x^2=20,x^2+3*x-4=0],15*x+5*x^2=20],
+[a3,[8*x+2*x^2-2=12,x^2+4*x-7=0],8*x+2*x^2-2=12],
+[a4,[20*x+4*x^2=-16,x^2+5*x+4=0],20*x+4*x^2=-16]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Gut gemacht! Wenn ein Term auf diese Weise umgeformt ist, kannst du mit der p-q-Formel die möglichen Werte für \(x\) bestimmen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Weiter so! Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>equiv</type>
+ <tans>BIN_a[2]</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint>firstline</syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options>firstline</options>
+ </input><deployedseed>1126686893</deployedseed> <deployedseed>1832581792</deployedseed> <deployedseed>1406889611</deployedseed> <deployedseed>511391873</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-c p-q-Formel I - Endboss</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t4_pq_1_c')</script><p class="bubble"><div class="hint">Forme den Term um und wende dann die p-q-Formel an, um diese Endgegner-Aufgabe zu lösen. Dann bist du mit dieser Mathe-Welt fertig.<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p>Bestimmen Sie alle reellen Lösungen der quadratischen Gleichung in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\(= ?\;\). Sie können Ihren Rechenweg angeben.<br></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[-2*y^2+6*y=4, -2*y^2+6*y-4=0,y^2-3*y-2=0,stackeq(y=3/2+sqrt(9/4-2) nounor y=3/2-sqrt(9/4-2)),y=1 nounor y=2],-2*y^2+6*y=4,y,1,2,y=3/2+sqrt(9/4+2),y=3/2-sqrt(9/4+2)],
+[a2,[2*y^2-16=-4*y,2*y^2+4*y-16=0,y^2+2*y-8=0,stackeq(y=-1+sqrt((1)^2+8) nounor y=-1-sqrt((1)^2+8)),y=-4 nounor y=2],2*y^2-16=-4*y,y,-4,2,y=-1+sqrt((1)^2-8),y=-1-sqrt((1)^2-8)],
+[a3,[-2*d^2+2*d=-24,-2*d^2+2*d+24=0,d^2-d-12=0,d=1/2+sqrt((1/2)^2+12) nounor d=1/2-sqrt((1/2)^2+12),d=-3 nounor d=4],-2*d^2+2*d=-24,d,-3,4,d=1/2+sqrt((1/2)^2-12),d=1/2-sqrt((1/2)^2-12)],
+[a4,[-2*u^2-14*u=24,-2*u^2-14*u-24=0,u^2+7*u+12=0,u=-7/2+sqrt((7/2)^2-12) nounor u=-7/2-sqrt((7/2)^2-12),u=-4 nounor u=-3],-2*u^2-14*u=24,u,-4,-3,u=-7/2+sqrt((7/2)^2+12), u=-7/2-sqrt((7/2)^2+12)]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.</p><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast!
+ Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel
+in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2}
+\boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir="ltr">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir="ltr">Versuche es erneut und gib beide Lösungen an.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast! Offenbar hast du dich beim
+\(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet
+ \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil
+ am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du
+das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr">Außerdem
+ hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel
+ bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+}
+\sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-}
+\sqrt{...}\) gibt.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast!
+ Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>equiv</type>
+ <tans>BIN_a[2]</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint>firstline</syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options>firstline</options>
+ </input><deployedseed>1183308849</deployedseed> <deployedseed>1817300183</deployedseed> <deployedseed>1556042756</deployedseed> <deployedseed>493079990</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-b p-q-Formel Ib - pq-Formel</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t4_pq_1_b')</script><p class="bubble"><div class="hint">Erinnerst du dich noch an die pq-Formel? Für \(\;x^2 + p\,x + q = 0\;\) gilt \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\).<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p>Bestimmen Sie den Wert der Variable in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\( = ?\;\).<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[h^2+3*h-4=0,h=-3/2+sqrt((3/2)^2+4) nounor h=-3/2-sqrt((3/2)^2+4),h=-3/2+sqrt(25/4) nounor h=-3/2-sqrt(25/4),h=-3/2+5/2 nounor h=-3/2-5/2,h=-4 nounor h=1],"\\(h^2+3\\,h-4=0\\)",h,1,-4,h=-3/2+sqrt(9/4-4),h=-3/2-sqrt(9/4-4)],
+[a2,[y^2-2*y-8=0,y=1+sqrt((-1)^2+8) nounor y=1-sqrt((-1)^2+8),y=-2 nounor y=4],"\\(y^2-2\\,y-8=0\\)",y,-2,4,y=1-sqrt(1-8),y=1+sqrt(1-8)],
+[a3,[z^2-4*z-5=0,z=2+sqrt((-2)^2+5) nounor z=2-sqrt((-2)^2+5),z=5 nounor z=-1],"\\(z^2-4\\,z-5=0\\)",z,5,-1,z=2+sqrt(4-5),z=2-sqrt(4-5)],
+[a4,[a^2-10*a+9=0,a=5+sqrt((-5)^2-9) nounor a=5-sqrt((-5)^2-9),a=9 nounor a=1],"\\(a^2-10\\,a+9=0\\)",a,9,1,a=5+sqrt(25+9),a=5-sqrt(25+9)]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr" style="text-align: left;">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2} \boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir="ltr" style="text-align: left;">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir="ltr" style="text-align: left;">Versuche es erneut und gib beide Lösungen an.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr" style="text-align: left;">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last(ans1)</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\) gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>equiv</type>
+ <tans>BIN_a[2]</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint>firstline</syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options>firstline</options>
+ </input><deployedseed>1183616185</deployedseed> <deployedseed>1771539896</deployedseed> <deployedseed>1420701792</deployedseed> <deployedseed>1009534997</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-f Potenzrechenregeln I - Endboss</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t5_rul_1_f')</script><p class="bubble"><div class="hint">Dies ist die Endgegner-Aufgabe dieser Mathe-Welt <strong>Potenzrechenrelgen</strong>. Wenn du diese Aufgabe schaffst, hast du diese Mathe-Welt gemeistert. Viel Erfolg!</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie folgenden Ausdruck; hierbei sind \(x,y \in \mathbb{R_{> 0}}\).</div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,stackeq(y^(-1/6)),"\\(\\frac{1}{\\sqrt[3]{y \\, \\sqrt x}} \\, \\sqrt[6]{x \\, y}\\)"],
+[a2,a^20*x^8,"\\(\\left( \\frac{a^3 x^5}{a^{-2} x^3} \\right)^4\\)"]
+];
+RUL_a:rand(RUL_A);
+
+/*ans1 is evaluated by ev(ans1,simp) to accept e. g. 1/(y^(1/6)) and y^(-1/6) and y^(-(1/6))*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ev(ans1,simp)</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1167231517</deployedseed> <deployedseed>1313491755</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-a Potenzrechenregeln Ia – Exponenten addieren</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t5_rul_1_a')</script><p class="bubble"><div class="hint">Fangen wir damit an, die Exponenten zu addieren, wenn die Basis gleich ist und multipliziert wird.<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^a*c^b,"\\(c^{\\,a}\\cdot c^{\\,b}\\)"],
+[a2,x^a*x^b,"\\(x^{\\,a}\\cdot x^{\\,b}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1724483596</deployedseed> <deployedseed>337440314</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-b Potenzrechenregeln Ib – Exponenten subtrahieren</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t5_rul_1_b')</script><p class="bubble"><div class="hint">Das funktioniert auch in die andere Richtung.<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^a/c^b,"\\(\\frac{c^{\\,a}}{c^{\\,b}}\\)"],
+[a2,x^a/x^b,"\\(\\frac{x^{\\,a}}{x^{\\,b}}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>29351489</deployedseed> <deployedseed>1996084793</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-c Potenzrechenregeln Ic - Wurzel als Potenz darstellen</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t5_rul_1_c')</script><p class="bubble"><div class="hint">Mithilfe von Potenzen der Form \(c^{\frac{1}{n}}\) lässt sich die n-te Wurzel von \(c\), also \(\;\sqrt[n]{c}\;\), darstellen.</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p></p>
+<div>
+ <div>Stellen Sie den Ausdruck in der Form \(c^{\frac{1}{n}}\) dar.<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(1/6),"\\(\\sqrt[6]{c}\\)"],
+[a2,c^(1/5),"\\(\\sqrt[5]{c}\\)"],
+[a3,c^(1/4),"\\(\\sqrt[4]{c}\\)"],
+[a4,c^(1/3),"\\(\\sqrt[3]{c}\\)"],
+[a5,c^(1/7),"\\(\\sqrt[7]{c}\\)"],
+[a6,c^(1/8),"\\(\\sqrt[8]{c}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Sie können noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1074873352</deployedseed> <deployedseed>460473552</deployedseed> <deployedseed>771365681</deployedseed> <deployedseed>1250006169</deployedseed> <deployedseed>259744359</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-d Potenzrechenregeln Id – Exponenten multiplizieren</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t5_rul_1_d')</script><p class="bubble"><div class="hint">Wird ein Ausdruck, der eine Potenz enthält, potenziert, lassen sich die Exponenten miteinander multiplizieren.<br></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(a*b),"\\((c^a)^b\\)",c^a*b],
+[a2,x^(a*b),"\\((x^a)^b\\)",x^a*b]
+];
+RUL_a:rand(RUL_A);
+wa:RUL_a[4];
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast die Klammer falsch gesetzt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1495340815</deployedseed> <deployedseed>1196787611</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-e Potenzrechenregeln Ie - Potenzrechenregeln anwenden</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t5_rul_1_e')</script><p class="bubble"><div class="hint">Um diese Aufgabe zu lösen, kannst du mehrere der gerade erläuterten Regeln kombinieren. </div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>
+
+
+<p></p>
+<div>Nutzen Sie die Potenzrechenregeln, um folgenden Ausdruck zu vereinfachen.<br></div>
+<p>
+</p>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p>
+<div class="bubble in-modal no-arrow">
+ <div>Hier zur Erinnerung die wichtigsten Potenzrechenregeln. Für \(x, y \neq 0\) und \(n, m \in \mathbb{Z}\) gilt:</div>
+<div>
+ <div>
+ <div>
+ <ul>
+ <li>\(x^{n+m} = x^n\,x^m\;\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \(2^5 = 2^{2+3} = 2^2 \cdot 2^3 = 4 \cdot 8 = 32\)</span></div></li></ul><ul>
+ <li>
+ <div>
+ <div>\(\left( x^n \right)^m = x^{n\,m}\;\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \(\left( 2^2 \right)^3 = 2^6 = 64\)</span></div></div>
+ </div>
+ </li>
+ <li>
+ <div>
+ <div>
+ <div>
+ <div>\((x\,y)^n = x^n\,y^n\;\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \(6^2 = (2 \cdot 3)^2 = 2^2 \cdot 3^2 = 4 \cdot 9 = 36\)</span></div></div>
+ </div>
+ </div>
+ </div>
+ </li>
+ <li>\(\frac{1}{x^n} = x^{-n}\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \( \frac{1}{x^2} \cdot x^2 = x^{-2} \cdot x^2 = x^{-2+2} = x^0 = 1\)</span><br></div></li>
+ <li>\(\sqrt[n]{x} = x^{\frac{1}{n}}\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \( \sqrt[3]{x} \cdot x^3 = x^{\frac{1}{3}} \cdot x^3 = x^{\frac{1}{3}+3} = x^1 = x\)</span></div></li>
+ </ul>
+ </div>
+ </div>
+</div>
+<p></p>
+<div>
+ <div>
+ <div>
+ <ul></ul>
+ </div>
+ </div>
+</div>
+</div></p>
+]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(13/6),"\\(\\sqrt[6]{c} \\cdot c^2\\)"],
+[a2,x^10,"\\(\\frac{x^5}{x^{-5}}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Richtig, aber du kannst noch weiter vereinfachen.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1602709371</deployedseed> <deployedseed>547016054</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-a Ganzzahlige Summanden ableiten</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_a')</script><p class="bubble"><div class="hint">Tipp: Leite jeden Summanden einzeln ab.</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i,i,10),4); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; exercise:nums[1]*myvar^powers[1]+nums[2]*myvar^powers[2]+nums[3]*myvar+nums[4]; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>351097132</deployedseed> <deployedseed>1047509677</deployedseed> <deployedseed>442872926</deployedseed> <deployedseed>286970886</deployedseed> <deployedseed>999400432</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-b Gebrochenrationale Summanden ableiten</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_b')</script><p class="bubble"><div class="hint">Tipp: Leite jeden Summanden einzeln ab.</div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})={@fractions[1]@} \cdot {@myvar@}^{@powers[1]@}+{@fractions[2]@} \cdot {@myvar@}^{@powers[2]@}+{@fractions[3]@} \cdot {@myvar@}+{@myint@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myint:rand_with_step(1,10,1); numerators:rand_selection(makelist(i+2,i,6),3); denominators:makelist(rand_with_step(numerators[i]+1,numerators[i]+5,1),i,3); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; fractions:makelist(numerators[i]/denominators[i],i,3); exercise:fractions[1]*myvar^powers[1]+fractions[2]*myvar^powers[2]+fractions[3]*myvar+myint; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>857840145</deployedseed> <deployedseed>1543126498</deployedseed> <deployedseed>1871228756</deployedseed> <deployedseed>318121367</deployedseed> <deployedseed>2127933990</deployedseed> <deployedseed>484803571</deployedseed> <deployedseed>1056868370</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-c Produkte ableiten I</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_c')</script><p class="bubble"><div class="hint"><p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:rand_selection(makelist(i+1,i,4),2); myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,4),2); exercise:(myvar^powers[1]+nums[1])*(myvar^powers[2]-nums[2]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1213180404</deployedseed> <deployedseed>1876101711</deployedseed> <deployedseed>1520468669</deployedseed> <deployedseed>1233734487</deployedseed> <deployedseed>1329784126</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-d Produkte ableiten II</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_d')</script><p class="bubble"><div class="hint"><p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>num:rand_with_step(1,5,2); denom:rand_with_step(num+2, num+5,2); fraction:num/denom; nums:rand_selection(append(makelist(i-7,i,6),makelist(i,i,6)),4); myvar:rand([a,b,c,x,y,z]); power:rand([3,4]); exercise:(fraction*myvar+nums[1])*(nums[2]*myvar^power+nums[3]*myvar+nums[4]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>290055394</deployedseed> <deployedseed>1877259825</deployedseed> <deployedseed>1027269811</deployedseed> <deployedseed>1906880472</deployedseed> <deployedseed>1551769121</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-e Division ableiten I</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_e')</script><p class="bubble"><div class="hint"><p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:[rand_with_step(3,4,1), 2]; nums:rand_selection(makelist(i,i,12),5); myvar:rand([a,b,c,x,y,z]); exercise:(myvar^powers[1]+nums[1]*myvar^powers[2]+myvar)/(nums[2]*myvar^2+nums[3]*myvar+nums[4]); ta1:diff(exercise, myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1439694172</deployedseed> <deployedseed>1028579078</deployedseed> <deployedseed>1454088108</deployedseed> <deployedseed>1063999325</deployedseed> <deployedseed>1974598074</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-f Division ableiten II</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_f')</script><p class="bubble"><div class="hint"><p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:[rand([3,5,7,11]), rand_with_step(2,5,1)]; myvar:rand([a,b,c,x,y,z]); terms:[sqrt(nums[1])*myvar-nums[2], nums[1]*myvar^2-nums[2]]; terms:random_permutation(terms); exercise:terms[1]/terms[2]; ta1:diff(exercise, myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>525681144</deployedseed> <deployedseed>1447367624</deployedseed> <deployedseed>435810786</deployedseed> <deployedseed>1421496847</deployedseed> <deployedseed>918279888</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-g Kettenregel I</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_g')</script><p class="bubble"><div class="hint"><p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root@}]{{@myvar@}^2-{@num@}}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); root:rand([3,5]); num:rand_with_step(3,9,1); exercise:(myvar^2-num)^(1/root); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1079586531</deployedseed> <deployedseed>1754291070</deployedseed> <deployedseed>1751932072</deployedseed> <deployedseed>1089076165</deployedseed> <deployedseed>215450400</deployedseed> <deployedseed>766534514</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-h Kettenregel II</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_h')</script><p class="bubble"><div class="hint"><p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p></div></p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,5),3); power:rand_with_step(3,7,2); signs:makelist(rand([-1,1]),2); exercise:(nums[1]*myvar^2+signs[1]*nums[2]*myvar+signs[2]*nums[3])^power; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1676415387</deployedseed> <deployedseed>146672542</deployedseed> <deployedseed>1726255949</deployedseed> <deployedseed>1628089061</deployedseed> <deployedseed>633210403</deployedseed> <deployedseed>1850144475</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-i Gemischtes I</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_i')</script><p class="bubble">Viel Erfolg beim Lösen dieser Aufgabe!</p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,5),2); nums:rand_selection(makelist(i+1,i,58),2); exercise:(myvar^powers[1]+nums[1])^powers[2]*nums[2]*myvar; ta1:diff(exercise, myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>603470063</deployedseed> <deployedseed>1387533043</deployedseed> <deployedseed>820026169</deployedseed> <deployedseed>1884036955</deployedseed> <deployedseed>562165609</deployedseed> <deployedseed>931146921</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-j Gemischtes II</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_j')</script><p class="bubble">Viel Erfolg beim Lösen dieser Aufgabe!</p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,3),3); nums:rand_selection(makelist(i,i,5),2); exercise:(myvar^powers[1]-nums[1])^powers[2]*(myvar+nums[2])^powers[3]; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>949540891</deployedseed> <deployedseed>2032277992</deployedseed> <deployedseed>504654950</deployedseed> <deployedseed>906697601</deployedseed> <deployedseed>1241320418</deployedseed> <deployedseed>891184866</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-k Gemischtes III</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_k')</script><p class="bubble">Viel Erfolg beim Lösen dieser Aufgabe!</p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); terms:[rand_with_step(1,4,1)+myvar, myvar]; terms:random_permutation(terms); power:rand_with_step(3,7,1); exercise:(terms[1]/terms[2])^power; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1060600269</deployedseed> <deployedseed>1317786455</deployedseed> <deployedseed>2016195942</deployedseed> <deployedseed>79640143</deployedseed> <deployedseed>1481526612</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-l Gemischtes IV</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_l')</script><p class="bubble">Viel Erfolg beim Lösen dieser Aufgabe!</p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),2); power:rand_with_step(2,6,1); exercise:nums[1]*sqrt(nums[2]*myvar+myvar^power); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>63010318</deployedseed> <deployedseed>2022252790</deployedseed> <deployedseed>2032269463</deployedseed> <deployedseed>1301956355</deployedseed> <deployedseed>1085730060</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-m Gemischtes V</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_m')</script><p class="bubble">Viel Erfolg beim Lösen dieser Aufgabe!</p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),4); power:rand_with_step(2,5,1); terms:[(nums[1]*myvar+nums[2]), (nums[3]*myvar^power-nums[4])]; terms:random_permutation(terms); exercise:(terms[1]*terms[2])/myvar; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1627444094</deployedseed> <deployedseed>570947981</deployedseed> <deployedseed>1123631251</deployedseed> <deployedseed>566895213</deployedseed> <deployedseed>265672538</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-n Gemischtes VI</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-qpool-pa.js"></script><script>ALQuiz.setCurrentQuestionId('t7_der_1_n')</script><p class="bubble">Viel Erfolg beim Lösen dieser Aufgabe!</p><img class="dm-icon" src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg"><p>Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); root_power:rand_with_step(3,6,1); power:rand_with_prohib(2,5,[root_power]); nums:rand_selection(makelist(i+2,i,6),2);exercise:(nums[1]*myvar-nums[2])^(power/root_power); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>466316231</deployedseed> <deployedseed>73259082</deployedseed> <deployedseed>253364053</deployedseed> <deployedseed>1197047345</deployedseed> <deployedseed>873528357</deployedseed> <deployedseed>10923026</deployedseed> <deployedseed>1464509121</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/pa/zzz Config Elements</text><info><text/></info></category><idnumber/></question><question type="description">
+ <name>
+ <text>zzz INSTANT TUTORING default-config</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href;</script>
+<p>Sie sind in der Konfigurationsdatei vom Digitalen Mentor gelandet. Klicken sie bitte auf eine der anderen Fragen in der Test-Navigation, um zurück zum Übungsraum zu gelangen.</p>
+{"groups": {"start": "Start", "t0_syn_1": "Syntax", "t1_fra_1": "Bruchrechnung", "t3_frabin_1": "Binom. Formeln", "t4_pq_1": "pq-Formel", "t5_rul_1": "Potenzrechenregeln", "t7_der_1": "Ableitungen"}, "questions": {"start": {"name": "Start", "group": "start"}, "t0_syn_1_a": {"name": "Gleichung eingeben (Multiplikation)", "variants": 5}, "t0_syn_1_b": {"name": "Gleichung eingeben (Division)", "variants": 6}, "t0_syn_1_c": {"name": "Potenzen", "variants": 5}, "t0_syn_1_d": {"name": "Rationale Ausdr\u00fccke", "variants": 3}, "t0_syn_1_e": {"name": "Wurzelzeichen", "variants": 6}, "t0_syn_1_f": {"name": "Mehrere L\u00f6sungen", "variants": 5}, "t0_syn_1_g": {"name": "Gleichung mehrschrittig l\u00f6sen", "variants": 5}, "t0_syn_1_h": {"name": "Griechische Buchstaben", "variants": 6}, "t0_syn_1_i": {"name": "Syntax-Endboss", "variants": 5}, "t1_fra_1_bi-a": {"name": "K\u00fcrzen zweier einfacher Br\u00fcche", "variants": 5}, "t1_fra_1_bi-b": {"name": "K\u00fcrzen zweier Br\u00fcche mit Variablen", "variants": 7}, "t1_fra_1_bi-c": {"name": "K\u00fcrzen zweier Br\u00fcche mit Variablen und Zahlen", "variants": 6}, "t1_fra_1_bi-d": {"name": "K\u00fcrzen zweier Br\u00fcche mit Termen", "variants": 7}, "t1_fra_1_bii-a": {"name": "Einfachen Bruch erweitern", "variants": 6}, "t1_fra_1_bii-b": {"name": "Bruch mit Variablen erweitern", "variants": 5}, "t1_fra_1_bii-c": {"name": "Bruch mit Variablen und Zahlen erweitern", "variants": 5}, "t1_fra_1_ca": {"name": "Einfache Addition von Br\u00fcchen", "variants": 5}, "t1_fra_1_cb": {"name": "Addition von Br\u00fcchen mit Variablen und gleichem Nenner", "variants": 5}, "t1_fra_1_cc": {"name": "Addition von Br\u00fcchen mit Variablen und unterschiedlichen Nennern", "variants": 6}, "t1_fra_1_cd": {"name": "Addition von Br\u00fcchen mit einer Variablen und unterschiedlichen Nennern", "variants": 6}, "t1_fra_1_ce": {"name": "Addition von Br\u00fcchen mit Variablen und unterschiedlichen Nennern I (Update1)", "variants": 5}, "t1_fra_1_cf": {"name": "Addition von Br\u00fcchen mit Variablen und unterschiedlichen Nennern II", "variants": 5}, "t1_fra_1_da": {"name": "Multiplikation zweier einfacher Br\u00fcche", "variants": 5}, "t1_fra_1_db": {"name": "Multiplikation zweier Br\u00fcche mit Variablen", "variants": 5}, "t1_fra_1_dc": {"name": "Multiplikation Bruch mit Zahlen, Bruch mit Variablen, Ganzzahl", "variants": 5}, "t1_fra_1_dd": {"name": "Multiplikation zweier Br\u00fcche mit Termen", "variants": 5}, "t1_fra_1_de": {"name": "Einfacher Doppelbruch", "variants": 5}, "t1_fra_1_df": {"name": "Bruch und Geteilt-Rechnung", "variants": 5}, "t1_fra_1_dg": {"name": "Doppelbruch mit Zahlen und Variablen", "variants": 5}, "t1_fra_1_dh": {"name": "Doppelbruch mit Termen", "variants": 5}, "t1_fra_1_ea": {"name": "Bruchrechnung Kombination I", "variants": 5}, "t1_fra_1_eb": {"name": "Bruchrechnung Kombination II", "variants": 5}, "t1_fra_1_ec": {"name": "Bruchrechnung Kombination III", "variants": 5}, "t3_frabin_1_g": {"name": "Binomische Formeln Ia - Erste binomische Formel", "variants": 6}, "t3_frabin_1_h": {"name": "Binomische Formeln Ib - Zweite binomische Formel", "variants": 6}, "t3_frabin_1_i": {"name": "Binomische Formeln Ic - Dritte binomische Formel", "variants": 6}, "t3_frabin_1_j": {"name": "Binomische Formeln I - Anwendungsaufgabe", "variants": 6}, "t3_frabin_1_k": {"name": "Bruchrechenregeln Ig2 - Bruch mit binomischem Term erweitern 2 (copy)", "variants": 3}, "t4_pq_1_a": {"name": "p-q-Formal Ia - Termumformung", "variants": 4}, "t4_pq_1_b": {"name": "p-q-Formel Ib - pq-Formel", "variants": 4}, "t4_pq_1_c": {"name": "p-q-Formel I - Endboss", "variants": 4}, "t5_rul_1_a": {"name": "Potenzrechenregeln Ia \u2013 Exponenten addieren", "variants": 2}, "t5_rul_1_b": {"name": "Potenzrechenregeln Ib \u2013 Exponenten subtrahieren", "variants": 2}, "t5_rul_1_c": {"name": "Potenzrechenregeln Ic - Wurzel als Potenz darstellen", "variants": 5}, "t5_rul_1_d": {"name": "Potenzrechenregeln Id \u2013 Exponenten multiplizieren", "variants": 2}, "t5_rul_1_e": {"name": "Potenzrechenregeln Ie - Potenzrechenregeln anwenden", "variants": 2}, "t5_rul_1_f": {"name": "Potenzrechenregeln I - Endboss", "variants": 2}, "t7_der_1_a": {"name": "Ganzzahlige Summanden ableiten", "variants": 5}, "t7_der_1_b": {"name": "Gebrochenrationale Summanden ableiten", "variants": 7}, "t7_der_1_c": {"name": "Produkte ableiten I", "variants": 5}, "t7_der_1_d": {"name": "Produkte ableiten II", "variants": 5}, "t7_der_1_e": {"name": "Division ableiten I", "variants": 5}, "t7_der_1_f": {"name": "Division ableiten II", "variants": 5}, "t7_der_1_g": {"name": "Kettenregel I", "variants": 6}, "t7_der_1_h": {"name": "Kettenregel II", "variants": 6}, "t7_der_1_i": {"name": "Gemischtes I", "variants": 6}, "t7_der_1_j": {"name": "Gemischtes II", "variants": 6}, "t7_der_1_k": {"name": "Gemischtes III", "variants": 5}, "t7_der_1_l": {"name": "Gemischtes IV", "variants": 5}, "t7_der_1_m": {"name": "Gemischtes V", "variants": 5}, "t7_der_1_n": {"name": "Gemischtes VI", "variants": 7}}}]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>0</defaultgrade>
+ <penalty>0</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ </question>
+
+</quiz>
diff --git a/question-files/questions-rpg_ger.xml b/question-files/questions-rpg_ger.xml
new file mode 100644
index 0000000000000000000000000000000000000000..a5873ec106a0a2d85376028e916676b66e2836cc
--- /dev/null
+++ b/question-files/questions-rpg_ger.xml
@@ -0,0 +1,30740 @@
+<quiz><question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/000 Start Elements</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>Start GamiExamPrep 0.8 (Einstiegsakademie)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[
+<script src="https://marvin.hs-bochum.de/~mneugebauer/alquiz-fantasy-bg-ver3.js"></script>
+<script>
+ let quizObjectAsString = '{"groups": {"start": "Start", "t0_syn_1": "Syntax", "t1_fra_1": "Bruchrechnung", "t3_frabin_1": "Binom. Formeln", "t4_pq_1": "pq-Formel", "t5_rul_1": "Potenzrechenregeln", "t7_der_1": "Ableitungen"}, "questions": {"start": {"name": "Start", "group": "start"}, "t0_syn_1_a": {"name": "Gleichung eingeben (Multiplikation)", "variants": 4, "color": "#573036", "filter": "invert(20%) sepia(11%) saturate(2292%) hue-rotate(301deg) brightness(88%) contrast(87%)"}, "t0_syn_1_b": {"name": "Gleichung eingeben (Division)", "variants": 4, "color": "#1BA1C7", "filter": "invert(46%) sepia(89%) saturate(419%) hue-rotate(147deg) brightness(97%) contrast(96%)"}, "t0_syn_1_c": {"name": "Potenzen", "variants": 4, "color": "#B38ABB", "filter": "invert(67%) sepia(28%) saturate(423%) hue-rotate(244deg) brightness(85%) contrast(89%)"}, "t0_syn_1_d": {"name": "Rationale Ausdr\u00fccke", "variants": 3, "color": "#D558A8", "filter": "invert(50%) sepia(90%) saturate(907%) hue-rotate(290deg) brightness(87%) contrast(90%)"}, "t0_syn_1_e": {"name": "Wurzelzeichen", "variants": 4, "color": "#1B5658", "filter": "invert(26%) sepia(12%) saturate(2407%) hue-rotate(133deg) brightness(95%) contrast(86%)"}, "t0_syn_1_f": {"name": "Mehrere L\u00f6sungen", "variants": 4, "color": "#810311", "filter": "invert(8%) sepia(64%) saturate(6140%) hue-rotate(346deg) brightness(93%) contrast(104%)"}, "t0_syn_1_g": {"name": "Gleichung mehrschrittig l\u00f6sen", "variants": 4, "color": "#74CD27", "filter": "invert(68%) sepia(76%) saturate(507%) hue-rotate(42deg) brightness(95%) contrast(83%)"}, "t0_syn_1_h": {"name": "Griechische Buchstaben", "variants": 4, "color": "#3CF48A", "filter": "invert(72%) sepia(40%) saturate(699%) hue-rotate(89deg) brightness(101%) contrast(98%)"}, "t0_syn_1_i": {"name": "Syntax-Endboss", "variants": 4, "color": "#77B211", "filter": "invert(64%) sepia(52%) saturate(5261%) hue-rotate(48deg) brightness(107%) contrast(87%)"}, "t1_fra_1_bi-a": {"name": "K\u00fcrzen zweier einfacher Br\u00fcche", "variants": 4, "color": "#FD9C80", "filter": "invert(84%) sepia(53%) saturate(4565%) hue-rotate(313deg) brightness(115%) contrast(108%)"}, "t1_fra_1_bi-b": {"name": "K\u00fcrzen zweier Br\u00fcche mit Variablen", "variants": 4, "color": "#E249B2", "filter": "invert(52%) sepia(64%) saturate(4425%) hue-rotate(292deg) brightness(93%) contrast(90%)"}, "t1_fra_1_bi-c": {"name": "K\u00fcrzen zweier Br\u00fcche mit Variablen und Zahlen", "variants": 4, "color": "#D57774", "filter": "invert(81%) sepia(50%) saturate(3032%) hue-rotate(305deg) brightness(86%) contrast(94%)"}, "t1_fra_1_bi-d": {"name": "K\u00fcrzen zweier Br\u00fcche mit Termen", "variants": 4, "color": "#944A6C", "filter": "invert(34%) sepia(25%) saturate(1028%) hue-rotate(280deg) brightness(96%) contrast(89%)"}, "t1_fra_1_bii-a": {"name": "Einfachen Bruch erweitern", "variants": 4, "color": "#9B49A2", "filter": "invert(35%) sepia(65%) saturate(573%) hue-rotate(248deg) brightness(92%) contrast(92%)"}, "t1_fra_1_bii-b": {"name": "Bruch mit Variablen erweitern", "variants": 4, "color": "#FA00D1", "filter": "invert(54%) sepia(100%) saturate(7435%) hue-rotate(298deg) brightness(97%) contrast(127%)"}, "t1_fra_1_bii-c": {"name": "Bruch mit Variablen und Zahlen erweitern", "variants": 4, "color": "#E2AFDA", "filter": "invert(96%) sepia(86%) saturate(2059%) hue-rotate(203deg) brightness(96%) contrast(83%)"}, "t1_fra_1_ca": {"name": "Einfache Addition von Br\u00fcchen", "variants": 4, "color": "#EB3E57", "filter": "invert(33%) sepia(19%) saturate(6570%) hue-rotate(328deg) brightness(97%) contrast(89%)"}, "t1_fra_1_cb": {"name": "Addition von Br\u00fcchen mit Variablen und gleichem Nenner", "variants": 4, "color": "#7E182C", "filter": "invert(14%) sepia(27%) saturate(5843%) hue-rotate(328deg) brightness(98%) contrast(98%)"}, "t1_fra_1_cc": {"name": "Addition von Br\u00fcchen mit Variablen und unterschiedlichen Nennern", "variants": 4, "color": "#3960A7", "filter": "invert(33%) sepia(56%) saturate(621%) hue-rotate(180deg) brightness(96%) contrast(95%)"}, "t1_fra_1_cd": {"name": "Addition von 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4, "color": "#E39FB2", "filter": "invert(78%) sepia(4%) saturate(2863%) hue-rotate(296deg) brightness(88%) contrast(102%)"}, "t1_fra_1_dh": {"name": "Doppelbruch mit Termen", "variants": 4, "color": "#23F5CC", "filter": "invert(100%) sepia(72%) saturate(2181%) hue-rotate(84deg) brightness(106%) contrast(91%)"}, "t1_fra_1_ea": {"name": "Bruchrechnung Kombination I", "variants": 4, "color": "#01D504", "filter": "invert(43%) sepia(74%) saturate(1175%) hue-rotate(89deg) brightness(106%) contrast(114%)"}, "t1_fra_1_eb": {"name": "Bruchrechnung Kombination II", "variants": 4, "color": "#C6F237", "filter": "invert(96%) sepia(38%) saturate(4597%) hue-rotate(13deg) brightness(104%) contrast(89%)"}, "t1_fra_1_ec": {"name": "Bruchrechnung Kombination III", "variants": 4, "color": "#B64537", "filter": "invert(36%) sepia(12%) saturate(4301%) hue-rotate(324deg) brightness(93%) contrast(92%)"}, "t3_frabin_1_g": {"name": "Binomische Formeln Ia - Erste binomische Formel", "variants": 4, "color": 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+ let quizObject = JSON.parse(quizObjectAsString)
+ let ALQuiz = new FantasyQuiz(quizObject);
+ ALQuiz.setCurrentQuestionId("start");
+ document.addEventListener("DOMContentLoaded", function() {
+ ALQuiz.init();
+ });
+</script>
+<p dir="ltr" style="text-align: left;display:none;">Some formula to load Mathjax \(x=1\)<br></p>
+
+<p>[[input:ans1]] [[validation:ans1]]</p>
+<p>[[input:ans2]] [[validation:ans2]]<br></p>
+ ]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1</defaultgrade>
+ <penalty>0.1</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>ta1:x=42;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text><![CDATA[<p>[[feedback:prt1]]</p>]]></text>
+ </specificfeedback>
+ <questionnote>
+ <text/>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text>Richtige Antwort, gut gemacht!</text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text>Ihre Antwort ist teilweise korrekt.</text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text>Falsche Antwort.</text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <input>
+ <name>ans2</name>
+ <type>string</type>
+ <tans><![CDATA["Filled by Javascript"]]></tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>0</mustverify>
+ <showvalidation>0</showvalidation>
+ <options>hideanswer</options>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-a Gleichung eingeben (Multiplikation) (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \({@ta1@}\) in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Hier eine leichte Aufgabe zur Eingabe. Benutze für jede Multiplikation das Symbol * (Stern).
+ <!--<span class="show-on-mobile-only"><br><br>Nutze die <a href="javascript:;" onclick="let userFocusTop = document.createElement('div');userFocusTop.classList.add('user-focus', 'hide-top');let pageHeight = document.documentElement.scrollHeight;userFocusTop.style.height=Math.ceil(pageHeight+window.pageYOffset)+'px';userFocusTop.onclick = removeTutorialFocus;document.body.appendChild(userFocusTop);">Buttons über deiner Tastatur</a>, um die wichtigsten Mathe-Operatoren schnell zu finden.</span>-->
+ <br><br>Falls du ohne Tastatur unterwegs bist, kannst du mithilfe des <a href="javascript:;" onclick="tutorialFocusElement(document.querySelector('.mathsbutton'));">Mathe-Operatoren-Buttons</a> zusätzliche Buttons aktivieren, um alle Mathe-Operatoren schnell zu finden.
+
+ <!--<br><br>Drücke jederzeit den "Prüfen"-Button, um zu sehen, wie deine Eingabe interpretiert wurde.<br>Erst wenn du nach dem "Prüfen"-Button deine Eingabe nicht änderst und
+ erneut "Prüfen" klickst, wird deine Eingabe als Antwort abgeschickt.-->
+<br><br>Neben dem Eingabefeld siehst du, wie deine Eingabe interpretiert wird.<br>Wenn du auf den "Prüfen"-Button klickst, wird deine Eingabe als Antwort abgeschickt.
+</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,y=3*x+5],[a2,y=4*x+3],[a3,y=2*x+1],[a4,y=2*x-5],[a5,y=5*x-3],[a6,y=4*x-6]];SYN_a:rand(SYN_A);ta1:SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>480757020</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-a Gleichung eingeben (Multiplikation) (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \({@ta1@}\) in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Hier eine leichte Aufgabe zur Eingabe. Benutze für jede Multiplikation das Symbol * (Stern).
+ <!--<span class="show-on-mobile-only"><br><br>Nutze die <a href="javascript:;" onclick="let userFocusTop = document.createElement('div');userFocusTop.classList.add('user-focus', 'hide-top');let pageHeight = document.documentElement.scrollHeight;userFocusTop.style.height=Math.ceil(pageHeight+window.pageYOffset)+'px';userFocusTop.onclick = removeTutorialFocus;document.body.appendChild(userFocusTop);">Buttons über deiner Tastatur</a>, um die wichtigsten Mathe-Operatoren schnell zu finden.</span>-->
+ <br><br>Falls du ohne Tastatur unterwegs bist, kannst du mithilfe des <a href="javascript:;" onclick="tutorialFocusElement(document.querySelector('.mathsbutton'));">Mathe-Operatoren-Buttons</a> zusätzliche Buttons aktivieren, um alle Mathe-Operatoren schnell zu finden.
+
+ <!--<br><br>Drücke jederzeit den "Prüfen"-Button, um zu sehen, wie deine Eingabe interpretiert wurde.<br>Erst wenn du nach dem "Prüfen"-Button deine Eingabe nicht änderst und
+ erneut "Prüfen" klickst, wird deine Eingabe als Antwort abgeschickt.-->
+<br><br>Neben dem Eingabefeld siehst du, wie deine Eingabe interpretiert wird.<br>Wenn du auf den "Prüfen"-Button klickst, wird deine Eingabe als Antwort abgeschickt.
+</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,y=3*x+5],[a2,y=4*x+3],[a3,y=2*x+1],[a4,y=2*x-5],[a5,y=5*x-3],[a6,y=4*x-6]];SYN_a:rand(SYN_A);ta1:SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>585237317</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-a Gleichung eingeben (Multiplikation) (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \({@ta1@}\) in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Hier eine leichte Aufgabe zur Eingabe. Benutze für jede Multiplikation das Symbol * (Stern).
+ <!--<span class="show-on-mobile-only"><br><br>Nutze die <a href="javascript:;" onclick="let userFocusTop = document.createElement('div');userFocusTop.classList.add('user-focus', 'hide-top');let pageHeight = document.documentElement.scrollHeight;userFocusTop.style.height=Math.ceil(pageHeight+window.pageYOffset)+'px';userFocusTop.onclick = removeTutorialFocus;document.body.appendChild(userFocusTop);">Buttons über deiner Tastatur</a>, um die wichtigsten Mathe-Operatoren schnell zu finden.</span>-->
+ <br><br>Falls du ohne Tastatur unterwegs bist, kannst du mithilfe des <a href="javascript:;" onclick="tutorialFocusElement(document.querySelector('.mathsbutton'));">Mathe-Operatoren-Buttons</a> zusätzliche Buttons aktivieren, um alle Mathe-Operatoren schnell zu finden.
+
+ <!--<br><br>Drücke jederzeit den "Prüfen"-Button, um zu sehen, wie deine Eingabe interpretiert wurde.<br>Erst wenn du nach dem "Prüfen"-Button deine Eingabe nicht änderst und
+ erneut "Prüfen" klickst, wird deine Eingabe als Antwort abgeschickt.-->
+<br><br>Neben dem Eingabefeld siehst du, wie deine Eingabe interpretiert wird.<br>Wenn du auf den "Prüfen"-Button klickst, wird deine Eingabe als Antwort abgeschickt.
+</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,y=3*x+5],[a2,y=4*x+3],[a3,y=2*x+1],[a4,y=2*x-5],[a5,y=5*x-3],[a6,y=4*x-6]];SYN_a:rand(SYN_A);ta1:SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1798333349</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-a Gleichung eingeben (Multiplikation) (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \({@ta1@}\) in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Hier eine leichte Aufgabe zur Eingabe. Benutze für jede Multiplikation das Symbol * (Stern).
+ <!--<span class="show-on-mobile-only"><br><br>Nutze die <a href="javascript:;" onclick="let userFocusTop = document.createElement('div');userFocusTop.classList.add('user-focus', 'hide-top');let pageHeight = document.documentElement.scrollHeight;userFocusTop.style.height=Math.ceil(pageHeight+window.pageYOffset)+'px';userFocusTop.onclick = removeTutorialFocus;document.body.appendChild(userFocusTop);">Buttons über deiner Tastatur</a>, um die wichtigsten Mathe-Operatoren schnell zu finden.</span>-->
+ <br><br>Falls du ohne Tastatur unterwegs bist, kannst du mithilfe des <a href="javascript:;" onclick="tutorialFocusElement(document.querySelector('.mathsbutton'));">Mathe-Operatoren-Buttons</a> zusätzliche Buttons aktivieren, um alle Mathe-Operatoren schnell zu finden.
+
+ <!--<br><br>Drücke jederzeit den "Prüfen"-Button, um zu sehen, wie deine Eingabe interpretiert wurde.<br>Erst wenn du nach dem "Prüfen"-Button deine Eingabe nicht änderst und
+ erneut "Prüfen" klickst, wird deine Eingabe als Antwort abgeschickt.-->
+<br><br>Neben dem Eingabefeld siehst du, wie deine Eingabe interpretiert wird.<br>Wenn du auf den "Prüfen"-Button klickst, wird deine Eingabe als Antwort abgeschickt.
+</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,y=3*x+5],[a2,y=4*x+3],[a3,y=2*x+1],[a4,y=2*x-5],[a5,y=5*x-3],[a6,y=4*x-6]];SYN_a:rand(SYN_A);ta1:SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>2118152732</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-b Gleichung eingeben (Division) (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \({@TA@}\) in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Divisionen werden mit / (Slash) dargestellt. Hier erscheinen Sie als Brüche.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,y=5/3],[a2,y=4/7],[a3,y=1/3],[a4,y=2/5],[a5,y=3/10],[a6,y=1/4]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);TA:SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>TA</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Wir arbeiten hier nur wenn explizit danach gefragt wird mit Dezimalzahlen. Brüche stellen das Ergebnis in der Regel genauer dar.<br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>TA</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords>3x</forbidwords><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>2690042</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-b Gleichung eingeben (Division) (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \({@TA@}\) in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Divisionen werden mit / (Slash) dargestellt. Hier erscheinen Sie als Brüche.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,y=5/3],[a2,y=4/7],[a3,y=1/3],[a4,y=2/5],[a5,y=3/10],[a6,y=1/4]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);TA:SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>TA</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Wir arbeiten hier nur wenn explizit danach gefragt wird mit Dezimalzahlen. Brüche stellen das Ergebnis in der Regel genauer dar.<br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>TA</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords>3x</forbidwords><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>300094393</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-b Gleichung eingeben (Division) (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \({@TA@}\) in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Divisionen werden mit / (Slash) dargestellt. Hier erscheinen Sie als Brüche.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,y=5/3],[a2,y=4/7],[a3,y=1/3],[a4,y=2/5],[a5,y=3/10],[a6,y=1/4]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);TA:SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>TA</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Wir arbeiten hier nur wenn explizit danach gefragt wird mit Dezimalzahlen. Brüche stellen das Ergebnis in der Regel genauer dar.<br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>TA</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords>3x</forbidwords><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>765518486</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-b Gleichung eingeben (Division) (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \({@TA@}\) in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Divisionen werden mit / (Slash) dargestellt. Hier erscheinen Sie als Brüche.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,y=5/3],[a2,y=4/7],[a3,y=1/3],[a4,y=2/5],[a5,y=3/10],[a6,y=1/4]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);TA:SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>TA</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Wir arbeiten hier nur wenn explizit danach gefragt wird mit Dezimalzahlen. Brüche stellen das Ergebnis in der Regel genauer dar.<br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>TA</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords>3x</forbidwords><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>17019212</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-c Potenzen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \[{@ta@}\] in das Eingabefeld ein.</p>
+<p><p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p><p class="hint"><p>Mit dem Zeichen ^ (Caret) kannst du Potenzen darstellen.</p><div> <ul> <li>\(x^2\) wird so eingegeben: <code>x^2</code></li> <li>\(x^{-2}\) wird so eingegeben: <code>x^(-2)</code></li> <li>\(x^{1/3}\) wird so eingegeben: <code>x^(1/3)</code></li> </ul></div></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,(4+b)^2],[a2,(5+b)^2],[a3,(3+b)^2],[a4,(2+b)^2],[a5,(3+2*b)^2],[a6,(4+2*b)^2]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:expand(SYN_a[2])=SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[Sehr gut. Hier wurde übrigens eine binomische Formel angewendet, um einen Term zu faktorisieren.<br><p dir="ltr" style="text-align: left;" <br=""></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Deine Antwort ist zwar äquivalent mit der dargestellten Gleichung, aber du hast nicht genau die gleiche Gleichung dargestellt.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>93323135</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-c Potenzen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \[{@ta@}\] in das Eingabefeld ein.</p>
+<p><p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p><p class="hint"><p>Mit dem Zeichen ^ (Caret) kannst du Potenzen darstellen.</p><div> <ul> <li>\(x^2\) wird so eingegeben: <code>x^2</code></li> <li>\(x^{-2}\) wird so eingegeben: <code>x^(-2)</code></li> <li>\(x^{1/3}\) wird so eingegeben: <code>x^(1/3)</code></li> </ul></div></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,(4+b)^2],[a2,(5+b)^2],[a3,(3+b)^2],[a4,(2+b)^2],[a5,(3+2*b)^2],[a6,(4+2*b)^2]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:expand(SYN_a[2])=SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[Sehr gut. Hier wurde übrigens eine binomische Formel angewendet, um einen Term zu faktorisieren.<br><p dir="ltr" style="text-align: left;" <br=""></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Deine Antwort ist zwar äquivalent mit der dargestellten Gleichung, aber du hast nicht genau die gleiche Gleichung dargestellt.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>1032837775</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-c Potenzen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \[{@ta@}\] in das Eingabefeld ein.</p>
+<p><p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p><p class="hint"><p>Mit dem Zeichen ^ (Caret) kannst du Potenzen darstellen.</p><div> <ul> <li>\(x^2\) wird so eingegeben: <code>x^2</code></li> <li>\(x^{-2}\) wird so eingegeben: <code>x^(-2)</code></li> <li>\(x^{1/3}\) wird so eingegeben: <code>x^(1/3)</code></li> </ul></div></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,(4+b)^2],[a2,(5+b)^2],[a3,(3+b)^2],[a4,(2+b)^2],[a5,(3+2*b)^2],[a6,(4+2*b)^2]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:expand(SYN_a[2])=SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[Sehr gut. Hier wurde übrigens eine binomische Formel angewendet, um einen Term zu faktorisieren.<br><p dir="ltr" style="text-align: left;" <br=""></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Deine Antwort ist zwar äquivalent mit der dargestellten Gleichung, aber du hast nicht genau die gleiche Gleichung dargestellt.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>680315517</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-c Potenzen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \[{@ta@}\] in das Eingabefeld ein.</p>
+<p><p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p><p class="hint"><p>Mit dem Zeichen ^ (Caret) kannst du Potenzen darstellen.</p><div> <ul> <li>\(x^2\) wird so eingegeben: <code>x^2</code></li> <li>\(x^{-2}\) wird so eingegeben: <code>x^(-2)</code></li> <li>\(x^{1/3}\) wird so eingegeben: <code>x^(1/3)</code></li> </ul></div></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,(4+b)^2],[a2,(5+b)^2],[a3,(3+b)^2],[a4,(2+b)^2],[a5,(3+2*b)^2],[a6,(4+2*b)^2]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:expand(SYN_a[2])=SYN_a[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[Sehr gut. Hier wurde übrigens eine binomische Formel angewendet, um einen Term zu faktorisieren.<br><p dir="ltr" style="text-align: left;" <br=""></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Deine Antwort ist zwar äquivalent mit der dargestellten Gleichung, aber du hast nicht genau die gleiche Gleichung dargestellt.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>838329017</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-d Rationale Ausdrücke (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \[{@ta@}\] in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Machen wir es etwas komplizierter. Um Terme in Brüchen darzustellen, musst du besonders auf die Klammersetzung achten.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:x^2;b:(x+1);c:(x-5);SYN_A:[[a1,a,b,c],[a2,b,a,c],[a3,c,a,b]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:SYN_a[2]/(SYN_a[3]*SYN_a[4]);wa:SYN_a[2]/SYN_a[3]*SYN_a[4];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;" <br=""></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Bitte beachte, dass du um den Nenner zusätzliche Klammern setzen musst, damit er als zusammenhängender Divisor interpretiert wird.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>82298515</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-d Rationale Ausdrücke (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \[{@ta@}\] in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Machen wir es etwas komplizierter. Um Terme in Brüchen darzustellen, musst du besonders auf die Klammersetzung achten.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:x^2;b:(x+1);c:(x-5);SYN_A:[[a1,a,b,c],[a2,b,a,c],[a3,c,a,b]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:SYN_a[2]/(SYN_a[3]*SYN_a[4]);wa:SYN_a[2]/SYN_a[3]*SYN_a[4];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;" <br=""></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Bitte beachte, dass du um den Nenner zusätzliche Klammern setzen musst, damit er als zusammenhängender Divisor interpretiert wird.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>1458249622</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-d Rationale Ausdrücke (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie die Gleichung \[{@ta@}\] in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Okay! Machen wir es etwas komplizierter. Um Terme in Brüchen darzustellen, musst du besonders auf die Klammersetzung achten.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:x^2;b:(x+1);c:(x-5);SYN_A:[[a1,a,b,c],[a2,b,a,c],[a3,c,a,b]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:SYN_a[2]/(SYN_a[3]*SYN_a[4]);wa:SYN_a[2]/SYN_a[3]*SYN_a[4];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;" <br=""></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Bitte beachte, dass du um den Nenner zusätzliche Klammern setzen musst, damit er als zusammenhängender Divisor interpretiert wird.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>1731794639</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-e Wurzelzeichen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie \[{@ta1@}\] in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Gut. Um eine Wurzel darzustellen nutze <code>sqrt(x)</code> für \(\sqrt{x}\;\).</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,3],[a2,5],[a3,7],[a4,11],[a5,13],[a6,19]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta1:sqrt(SYN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1136692395</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-e Wurzelzeichen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie \[{@ta1@}\] in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Gut. Um eine Wurzel darzustellen nutze <code>sqrt(x)</code> für \(\sqrt{x}\;\).</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,3],[a2,5],[a3,7],[a4,11],[a5,13],[a6,19]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta1:sqrt(SYN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>659595513</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-e Wurzelzeichen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie \[{@ta1@}\] in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Gut. Um eine Wurzel darzustellen nutze <code>sqrt(x)</code> für \(\sqrt{x}\;\).</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,3],[a2,5],[a3,7],[a4,11],[a5,13],[a6,19]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta1:sqrt(SYN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>2040368424</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-e Wurzelzeichen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie \[{@ta1@}\] in das Eingabefeld ein.</p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Gut. Um eine Wurzel darzustellen nutze <code>sqrt(x)</code> für \(\sqrt{x}\;\).</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,3],[a2,5],[a3,7],[a4,11],[a5,13],[a6,19]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta1:sqrt(SYN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>262860513</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-f Mehrere Lösungen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Lösen Sie nach \(x\) auf. Geben Sie die Lösung in der Form \(x=? \mbox{ or } x=?\) ein.</p>
+<p><p>\[{@task@}\]<br></p><p>[[input:ans]] [[validation:ans]][[feedback:prt1]]</p><p><em>Achtung: Bitte setzen Sie kein zusätzliches +-Symbol vor positive Zahlen.<br></em></p></p><p class="hint">Gelegentlich müssen Ausdrücke mit logischen Verbindungen verknüpft werden. Nutze dafür <code>and</code> oder <code>or</code>. <br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,4],[a2,9],[a3,16],[a4,25],[a5,36]];/*SYN_a:SYN_A[1];*/SYN_a:rand(SYN_A);ta:x=sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);taalt:x=+sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);task:x^2=SYN_a[2];wa1:x=sqrt(SYN_a[2]);wa2:x=-sqrt(SYN_a[2]);wa3:x=sqrt(SYN_a[2]) nounand x=-sqrt(SYN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>4</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>4</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>5</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>4</name><answertest>AlgEquiv</answertest><sans>1</sans><tans>1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-5-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr">Du hast nur eine von zwei richtigen Lösungen eingegeben.<br>Beispiel: \(5 \cdot 5 = 25\) und \(-5 \cdot -5 = 25\) (Minus Mal Minus ergibt Plus).<br>Für \(x^2 = 25\) gilt deshalb \(x = 5\) oder \(x = -5\), was hier in der Form <code>x=5 or x=-5</code> aufgeschrieben wird.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-5-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>5</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa3</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-6-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast alle richtigen Lösungen angegeben, allerdings hast du sie mit <code>and</code> verknüpft. Korrekt ist, sie mit <code>or</code> zu verknüpfen. Man schreibt</p><ul><li>entweder \(x=?\; oder \;x=?\)</li><li>oder \(x_1=?\; und \;x_2 = ?\;\).</li></ul>Hier benutzen wir ausschließlich die erste Form, die mit <code>x=? or x=?</code> dargestellt wird.<br>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-6-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords>4x</forbidwords><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>1032259226</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-f Mehrere Lösungen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Lösen Sie nach \(x\) auf. Geben Sie die Lösung in der Form \(x=? \mbox{ or } x=?\) ein.</p>
+<p><p>\[{@task@}\]<br></p><p>[[input:ans]] [[validation:ans]][[feedback:prt1]]</p><p><em>Achtung: Bitte setzen Sie kein zusätzliches +-Symbol vor positive Zahlen.<br></em></p></p><p class="hint">Gelegentlich müssen Ausdrücke mit logischen Verbindungen verknüpft werden. Nutze dafür <code>and</code> oder <code>or</code>. <br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
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+ <text>SYN_A:[[a1,4],[a2,9],[a3,16],[a4,25],[a5,36]];/*SYN_a:SYN_A[1];*/SYN_a:rand(SYN_A);ta:x=sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);taalt:x=+sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);task:x^2=SYN_a[2];wa1:x=sqrt(SYN_a[2]);wa2:x=-sqrt(SYN_a[2]);wa3:x=sqrt(SYN_a[2]) nounand x=-sqrt(SYN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
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+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
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+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-f Mehrere Lösungen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Lösen Sie nach \(x\) auf. Geben Sie die Lösung in der Form \(x=? \mbox{ or } x=?\) ein.</p>
+<p><p>\[{@task@}\]<br></p><p>[[input:ans]] [[validation:ans]][[feedback:prt1]]</p><p><em>Achtung: Bitte setzen Sie kein zusätzliches +-Symbol vor positive Zahlen.<br></em></p></p><p class="hint">Gelegentlich müssen Ausdrücke mit logischen Verbindungen verknüpft werden. Nutze dafür <code>and</code> oder <code>or</code>. <br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,4],[a2,9],[a3,16],[a4,25],[a5,36]];/*SYN_a:SYN_A[1];*/SYN_a:rand(SYN_A);ta:x=sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);taalt:x=+sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);task:x^2=SYN_a[2];wa1:x=sqrt(SYN_a[2]);wa2:x=-sqrt(SYN_a[2]);wa3:x=sqrt(SYN_a[2]) nounand x=-sqrt(SYN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
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+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
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+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>4</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>4</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>5</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>4</name><answertest>AlgEquiv</answertest><sans>1</sans><tans>1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-5-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr">Du hast nur eine von zwei richtigen Lösungen eingegeben.<br>Beispiel: \(5 \cdot 5 = 25\) und \(-5 \cdot -5 = 25\) (Minus Mal Minus ergibt Plus).<br>Für \(x^2 = 25\) gilt deshalb \(x = 5\) oder \(x = -5\), was hier in der Form <code>x=5 or x=-5</code> aufgeschrieben wird.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-5-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>5</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa3</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-6-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast alle richtigen Lösungen angegeben, allerdings hast du sie mit <code>and</code> verknüpft. Korrekt ist, sie mit <code>or</code> zu verknüpfen. Man schreibt</p><ul><li>entweder \(x=?\; oder \;x=?\)</li><li>oder \(x_1=?\; und \;x_2 = ?\;\).</li></ul>Hier benutzen wir ausschließlich die erste Form, die mit <code>x=? or x=?</code> dargestellt wird.<br>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-6-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords>4x</forbidwords><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>668615301</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-f Mehrere Lösungen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Lösen Sie nach \(x\) auf. Geben Sie die Lösung in der Form \(x=? \mbox{ or } x=?\) ein.</p>
+<p><p>\[{@task@}\]<br></p><p>[[input:ans]] [[validation:ans]][[feedback:prt1]]</p><p><em>Achtung: Bitte setzen Sie kein zusätzliches +-Symbol vor positive Zahlen.<br></em></p></p><p class="hint">Gelegentlich müssen Ausdrücke mit logischen Verbindungen verknüpft werden. Nutze dafür <code>and</code> oder <code>or</code>. <br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>SYN_A:[[a1,4],[a2,9],[a3,16],[a4,25],[a5,36]];/*SYN_a:SYN_A[1];*/SYN_a:rand(SYN_A);ta:x=sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);taalt:x=+sqrt(SYN_a[2]) nounor x=-sqrt(SYN_a[2]);task:x^2=SYN_a[2];wa1:x=sqrt(SYN_a[2]);wa2:x=-sqrt(SYN_a[2]);wa3:x=sqrt(SYN_a[2]) nounand x=-sqrt(SYN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>4</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>4</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>5</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>4</name><answertest>AlgEquiv</answertest><sans>1</sans><tans>1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-5-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr">Du hast nur eine von zwei richtigen Lösungen eingegeben.<br>Beispiel: \(5 \cdot 5 = 25\) und \(-5 \cdot -5 = 25\) (Minus Mal Minus ergibt Plus).<br>Für \(x^2 = 25\) gilt deshalb \(x = 5\) oder \(x = -5\), was hier in der Form <code>x=5 or x=-5</code> aufgeschrieben wird.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-5-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>5</name><answertest>AlgEquiv</answertest><sans>ans</sans><tans>wa3</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-6-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast alle richtigen Lösungen angegeben, allerdings hast du sie mit <code>and</code> verknüpft. Korrekt ist, sie mit <code>or</code> zu verknüpfen. Man schreibt</p><ul><li>entweder \(x=?\; oder \;x=?\)</li><li>oder \(x_1=?\; und \;x_2 = ?\;\).</li></ul>Hier benutzen wir ausschließlich die erste Form, die mit <code>x=? or x=?</code> dargestellt wird.<br>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-6-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords>4x</forbidwords><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>1810103727</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-g Gleichung mehrschrittig lösen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p><p>Lösen Sie \(\;\){@p@}\(\;\) nach x auf.</p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.</p><p>Sie brauchen kein Äquivalenz-Zeichen eingeben.<br></p></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Um einen Rechenweg darzustellen, tippe jeden Schritt deiner Rechnung in eine neue Zeile in das Eingabefeld ein.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;b:3;c:4;SYN_A:[[a1,a,b,c],[a2,b,a,c],[a3,c,a,b],[a4,a,c,b],[a5,b,c,a],[a6,c,b,a]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:[SYN_a[2]*(SYN_a[3]+x)=SYN_a[4],SYN_a[2]*SYN_a[3]+SYN_a[2]*x=SYN_a[4],SYN_a[2]*x=SYN_a[4]-SYN_a[2]*SYN_a[3],x=(SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]];/*ta:[2*(3+x)=-3,2*x+6=-3,2*x=-9,x=-9/2];*/p:first(ta);/*p:"\\(2 \\cdot (3 + x) = -3\\)";*/wa1:x=-((SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]);wa2:x=SYN_a[4]-SYN_a[2]*SYN_a[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Aber fast richtig. Du hast dich offenbar mit dem Vorzeichen vertan.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar ist dir ein Fehler beim Lösen der Klammer unterlaufen. Um die Klammer aufzulösen, musst du beide beide Summanden in der Klammer mit dem Faktor vor der Klammer multiplizieren.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Weiter so. Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>last(ta)</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint></syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options></options></input><deployedseed>668615301</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-g Gleichung mehrschrittig lösen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p><p>Lösen Sie \(\;\){@p@}\(\;\) nach x auf.</p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.</p><p>Sie brauchen kein Äquivalenz-Zeichen eingeben.<br></p></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Um einen Rechenweg darzustellen, tippe jeden Schritt deiner Rechnung in eine neue Zeile in das Eingabefeld ein.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;b:3;c:4;SYN_A:[[a1,a,b,c],[a2,b,a,c],[a3,c,a,b],[a4,a,c,b],[a5,b,c,a],[a6,c,b,a]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:[SYN_a[2]*(SYN_a[3]+x)=SYN_a[4],SYN_a[2]*SYN_a[3]+SYN_a[2]*x=SYN_a[4],SYN_a[2]*x=SYN_a[4]-SYN_a[2]*SYN_a[3],x=(SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]];/*ta:[2*(3+x)=-3,2*x+6=-3,2*x=-9,x=-9/2];*/p:first(ta);/*p:"\\(2 \\cdot (3 + x) = -3\\)";*/wa1:x=-((SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]);wa2:x=SYN_a[4]-SYN_a[2]*SYN_a[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Aber fast richtig. Du hast dich offenbar mit dem Vorzeichen vertan.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar ist dir ein Fehler beim Lösen der Klammer unterlaufen. Um die Klammer aufzulösen, musst du beide beide Summanden in der Klammer mit dem Faktor vor der Klammer multiplizieren.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Weiter so. Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>last(ta)</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint></syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options></options></input><deployedseed>1810103727</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-g Gleichung mehrschrittig lösen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p><p>Lösen Sie \(\;\){@p@}\(\;\) nach x auf.</p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.</p><p>Sie brauchen kein Äquivalenz-Zeichen eingeben.<br></p></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Um einen Rechenweg darzustellen, tippe jeden Schritt deiner Rechnung in eine neue Zeile in das Eingabefeld ein.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;b:3;c:4;SYN_A:[[a1,a,b,c],[a2,b,a,c],[a3,c,a,b],[a4,a,c,b],[a5,b,c,a],[a6,c,b,a]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:[SYN_a[2]*(SYN_a[3]+x)=SYN_a[4],SYN_a[2]*SYN_a[3]+SYN_a[2]*x=SYN_a[4],SYN_a[2]*x=SYN_a[4]-SYN_a[2]*SYN_a[3],x=(SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]];/*ta:[2*(3+x)=-3,2*x+6=-3,2*x=-9,x=-9/2];*/p:first(ta);/*p:"\\(2 \\cdot (3 + x) = -3\\)";*/wa1:x=-((SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]);wa2:x=SYN_a[4]-SYN_a[2]*SYN_a[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Aber fast richtig. Du hast dich offenbar mit dem Vorzeichen vertan.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar ist dir ein Fehler beim Lösen der Klammer unterlaufen. Um die Klammer aufzulösen, musst du beide beide Summanden in der Klammer mit dem Faktor vor der Klammer multiplizieren.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Weiter so. Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>last(ta)</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint></syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options></options></input><deployedseed>2047586646</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-g Gleichung mehrschrittig lösen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p><p>Lösen Sie \(\;\){@p@}\(\;\) nach x auf.</p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.</p><p>Sie brauchen kein Äquivalenz-Zeichen eingeben.<br></p></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Um einen Rechenweg darzustellen, tippe jeden Schritt deiner Rechnung in eine neue Zeile in das Eingabefeld ein.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;b:3;c:4;SYN_A:[[a1,a,b,c],[a2,b,a,c],[a3,c,a,b],[a4,a,c,b],[a5,b,c,a],[a6,c,b,a]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:[SYN_a[2]*(SYN_a[3]+x)=SYN_a[4],SYN_a[2]*SYN_a[3]+SYN_a[2]*x=SYN_a[4],SYN_a[2]*x=SYN_a[4]-SYN_a[2]*SYN_a[3],x=(SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]];/*ta:[2*(3+x)=-3,2*x+6=-3,2*x=-9,x=-9/2];*/p:first(ta);/*p:"\\(2 \\cdot (3 + x) = -3\\)";*/wa1:x=-((SYN_a[4]-SYN_a[2]*SYN_a[3])/SYN_a[2]);wa2:x=SYN_a[4]-SYN_a[2]*SYN_a[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Aber fast richtig. Du hast dich offenbar mit dem Vorzeichen vertan.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar ist dir ein Fehler beim Lösen der Klammer unterlaufen. Um die Klammer aufzulösen, musst du beide beide Summanden in der Klammer mit dem Faktor vor der Klammer multiplizieren.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Weiter so. Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>last(ta)</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint></syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options></options></input><deployedseed>1032259226</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-h Griechische Buchstaben (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie \[{@ta@}\] in das Eingebefeld ein.</p>
+<p><p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p><em>Achtung: Bitte kopieren Sie keine Unicode-Zeichen, sondern benutzen Sie einfach Ihre Tastatur. <br></em></p></p><p class="hint">Wenn griechische Buchstaben einzugeben sind, schreibe sie einfach aus. Beispiel: \(\alpha=\) <code>alpha</code> , \(\beta=\) <code>beta</code><code></code> ,\(\pi=\) <code>pi </code><code></code>.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:beta;b:pi;c:alpha;SYN_A:[[a1,a,b],[a2,b,a],[a3,a,c],[a4,c,a],[a5,b,c],[a6,c,b]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:SYN_a[2]*z^(SYN_a[3]*x)wa1:SYN_a[2]*z^SYN_a[3]*x</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offenbar vergessen, eine Klammer um die Potenz zu schreiben. Schreibe Potenzen in Klammern, wenn sie aus mehr als einer Zahl bestehen. Beispiel: \(x^{-2a}\) wird so eingegeben: <code>x^(-2*a)</code>.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>1516837293</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-h Griechische Buchstaben (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie \[{@ta@}\] in das Eingebefeld ein.</p>
+<p><p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p><em>Achtung: Bitte kopieren Sie keine Unicode-Zeichen, sondern benutzen Sie einfach Ihre Tastatur. <br></em></p></p><p class="hint">Wenn griechische Buchstaben einzugeben sind, schreibe sie einfach aus. Beispiel: \(\alpha=\) <code>alpha</code> , \(\beta=\) <code>beta</code><code></code> ,\(\pi=\) <code>pi </code><code></code>.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:beta;b:pi;c:alpha;SYN_A:[[a1,a,b],[a2,b,a],[a3,a,c],[a4,c,a],[a5,b,c],[a6,c,b]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:SYN_a[2]*z^(SYN_a[3]*x)wa1:SYN_a[2]*z^SYN_a[3]*x</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offenbar vergessen, eine Klammer um die Potenz zu schreiben. Schreibe Potenzen in Klammern, wenn sie aus mehr als einer Zahl bestehen. Beispiel: \(x^{-2a}\) wird so eingegeben: <code>x^(-2*a)</code>.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>911975771</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-h Griechische Buchstaben (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie \[{@ta@}\] in das Eingebefeld ein.</p>
+<p><p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p><em>Achtung: Bitte kopieren Sie keine Unicode-Zeichen, sondern benutzen Sie einfach Ihre Tastatur. <br></em></p></p><p class="hint">Wenn griechische Buchstaben einzugeben sind, schreibe sie einfach aus. Beispiel: \(\alpha=\) <code>alpha</code> , \(\beta=\) <code>beta</code><code></code> ,\(\pi=\) <code>pi </code><code></code>.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:beta;b:pi;c:alpha;SYN_A:[[a1,a,b],[a2,b,a],[a3,a,c],[a4,c,a],[a5,b,c],[a6,c,b]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:SYN_a[2]*z^(SYN_a[3]*x)wa1:SYN_a[2]*z^SYN_a[3]*x</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offenbar vergessen, eine Klammer um die Potenz zu schreiben. Schreibe Potenzen in Klammern, wenn sie aus mehr als einer Zahl bestehen. Beispiel: \(x^{-2a}\) wird so eingegeben: <code>x^(-2*a)</code>.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>742782033</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-h Griechische Buchstaben (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Geben Sie \[{@ta@}\] in das Eingebefeld ein.</p>
+<p><p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p><em>Achtung: Bitte kopieren Sie keine Unicode-Zeichen, sondern benutzen Sie einfach Ihre Tastatur. <br></em></p></p><p class="hint">Wenn griechische Buchstaben einzugeben sind, schreibe sie einfach aus. Beispiel: \(\alpha=\) <code>alpha</code> , \(\beta=\) <code>beta</code><code></code> ,\(\pi=\) <code>pi </code><code></code>.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:beta;b:pi;c:alpha;SYN_A:[[a1,a,b],[a2,b,a],[a3,a,c],[a4,c,a],[a5,b,c],[a6,c,b]];/*SYN_a:rand(SYN_A);*/SYN_a:rand(SYN_A);ta:SYN_a[2]*z^(SYN_a[3]*x)wa1:SYN_a[2]*z^SYN_a[3]*x</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-0-T </trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"><br></p>]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-0-F </falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offenbar vergessen, eine Klammer um die Potenz zu schreiben. Schreibe Potenzen in Klammern, wenn sie aus mehr als einer Zahl bestehen. Beispiel: \(x^{-2a}\) wird so eingegeben: <code>x^(-2*a)</code>.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>ta</tans><boxsize>20</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint/><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>1</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options/></input><deployedseed>1709130663</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-i Syntax-Endboss (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p><p>Lösen Sie {@p@} nach \(x\) auf.<br></p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.<br></p></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]<p></p><p><em>Zur Erinnerung: Das Kommando für</em> \(\sqrt{x}\)<em> lautet </em><code>sqrt(x)</code><em>. Nutzen Sie </em><code>or</code><em> um mehrere Lösungen anzugeben.</em></p></p><p class="hint">Willkommen zum Endgegner dieser Mathe-Welt. Mit dem Lösen dieser Aufgabe hast du die erste Mathe-Welt bereits abgeschlossen. Viel Erfolg!<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;b:3;c:4;d:2;e:3;SYN_A:[[a1,a,d],[a2,b,d],[a3,c,d],[a4,a,e],[a5,b,e],[a6,c,e]];SYN_a:rand(SYN_A);pifactor:ev(SYN_a[2]*(SYN_a[3]^2),simp);ta:[/*(SYN_a[2]*x^2)/(pifactor*pi)=1,*/SYN_a[2]*x^2=pifactor*pi,x^2=(SYN_a[3]^2)*pi,x=SYN_a[3]*sqrt(pi) nounor x=-SYN_a[3]*sqrt(pi)];p:first(ta);wa1:x=SYN_a[3]*sqrt(pi);wa2:x=-SYN_a[3]*sqrt(pi);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text><![CDATA[]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>4</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>3</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>3</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>1</sans><tans>1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast nur eine von zwei richtigen Lösungen eingegeben.<br>Beispiel: \(5\,\sqrt{\pi} \cdot 5\,\sqrt{\pi} = 25\,\pi\) und \(-5\,\sqrt{\pi} \cdot -5\,\sqrt{\pi} = 25\,\pi\) (Minus Mal Minus ergibt Plus).<br>Für \(x^2 = 25\pi\) gilt deshalb \(x = 5\,\sqrt{\pi}\) oder \(x = -5\,\sqrt{\pi}\), was hier in der Form <code>x=5*sqrt(pi) or x=-5*sqrt(pi)</code> aufgeschrieben wird.</p><p dir="ltr" style="text-align: left;"></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>4</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-5-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-5-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>last(ta)</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint></syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options></options></input><deployedseed>1169120426</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-i Syntax-Endboss (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p><p>Lösen Sie {@p@} nach \(x\) auf.<br></p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.<br></p></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]<p></p><p><em>Zur Erinnerung: Das Kommando für</em> \(\sqrt{x}\)<em> lautet </em><code>sqrt(x)</code><em>. Nutzen Sie </em><code>or</code><em> um mehrere Lösungen anzugeben.</em></p></p><p class="hint">Willkommen zum Endgegner dieser Mathe-Welt. Mit dem Lösen dieser Aufgabe hast du die erste Mathe-Welt bereits abgeschlossen. Viel Erfolg!<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;b:3;c:4;d:2;e:3;SYN_A:[[a1,a,d],[a2,b,d],[a3,c,d],[a4,a,e],[a5,b,e],[a6,c,e]];SYN_a:rand(SYN_A);pifactor:ev(SYN_a[2]*(SYN_a[3]^2),simp);ta:[/*(SYN_a[2]*x^2)/(pifactor*pi)=1,*/SYN_a[2]*x^2=pifactor*pi,x^2=(SYN_a[3]^2)*pi,x=SYN_a[3]*sqrt(pi) nounor x=-SYN_a[3]*sqrt(pi)];p:first(ta);wa1:x=SYN_a[3]*sqrt(pi);wa2:x=-SYN_a[3]*sqrt(pi);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text><![CDATA[]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>4</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>3</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>3</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>1</sans><tans>1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast nur eine von zwei richtigen Lösungen eingegeben.<br>Beispiel: \(5\,\sqrt{\pi} \cdot 5\,\sqrt{\pi} = 25\,\pi\) und \(-5\,\sqrt{\pi} \cdot -5\,\sqrt{\pi} = 25\,\pi\) (Minus Mal Minus ergibt Plus).<br>Für \(x^2 = 25\pi\) gilt deshalb \(x = 5\,\sqrt{\pi}\) oder \(x = -5\,\sqrt{\pi}\), was hier in der Form <code>x=5*sqrt(pi) or x=-5*sqrt(pi)</code> aufgeschrieben wird.</p><p dir="ltr" style="text-align: left;"></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>4</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-5-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-5-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>last(ta)</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint></syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options></options></input><deployedseed>1624332195</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-i Syntax-Endboss (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p><p>Lösen Sie {@p@} nach \(x\) auf.<br></p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.<br></p></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]<p></p><p><em>Zur Erinnerung: Das Kommando für</em> \(\sqrt{x}\)<em> lautet </em><code>sqrt(x)</code><em>. Nutzen Sie </em><code>or</code><em> um mehrere Lösungen anzugeben.</em></p></p><p class="hint">Willkommen zum Endgegner dieser Mathe-Welt. Mit dem Lösen dieser Aufgabe hast du die erste Mathe-Welt bereits abgeschlossen. Viel Erfolg!<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;b:3;c:4;d:2;e:3;SYN_A:[[a1,a,d],[a2,b,d],[a3,c,d],[a4,a,e],[a5,b,e],[a6,c,e]];SYN_a:rand(SYN_A);pifactor:ev(SYN_a[2]*(SYN_a[3]^2),simp);ta:[/*(SYN_a[2]*x^2)/(pifactor*pi)=1,*/SYN_a[2]*x^2=pifactor*pi,x^2=(SYN_a[3]^2)*pi,x=SYN_a[3]*sqrt(pi) nounor x=-SYN_a[3]*sqrt(pi)];p:first(ta);wa1:x=SYN_a[3]*sqrt(pi);wa2:x=-SYN_a[3]*sqrt(pi);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text><![CDATA[]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>4</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>3</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>3</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>1</sans><tans>1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast nur eine von zwei richtigen Lösungen eingegeben.<br>Beispiel: \(5\,\sqrt{\pi} \cdot 5\,\sqrt{\pi} = 25\,\pi\) und \(-5\,\sqrt{\pi} \cdot -5\,\sqrt{\pi} = 25\,\pi\) (Minus Mal Minus ergibt Plus).<br>Für \(x^2 = 25\pi\) gilt deshalb \(x = 5\,\sqrt{\pi}\) oder \(x = -5\,\sqrt{\pi}\), was hier in der Form <code>x=5*sqrt(pi) or x=-5*sqrt(pi)</code> aufgeschrieben wird.</p><p dir="ltr" style="text-align: left;"></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>4</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-5-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-5-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>last(ta)</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint></syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options></options></input><deployedseed>1578649438</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t0_syn Syntax</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t0-01-i Syntax-Endboss (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p><p>Lösen Sie {@p@} nach \(x\) auf.<br></p><p>Zeigen Sie Ihren Rechenweg, indem Sie diese Aufgabe Zeile für Zeile lösen.<br></p></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]<p></p><p><em>Zur Erinnerung: Das Kommando für</em> \(\sqrt{x}\)<em> lautet </em><code>sqrt(x)</code><em>. Nutzen Sie </em><code>or</code><em> um mehrere Lösungen anzugeben.</em></p></p><p class="hint">Willkommen zum Endgegner dieser Mathe-Welt. Mit dem Lösen dieser Aufgabe hast du die erste Mathe-Welt bereits abgeschlossen. Viel Erfolg!<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;b:3;c:4;d:2;e:3;SYN_A:[[a1,a,d],[a2,b,d],[a3,c,d],[a4,a,e],[a5,b,e],[a6,c,e]];SYN_a:rand(SYN_A);pifactor:ev(SYN_a[2]*(SYN_a[3]^2),simp);ta:[/*(SYN_a[2]*x^2)/(pifactor*pi)=1,*/SYN_a[2]*x^2=pifactor*pi,x^2=(SYN_a[3]^2)*pi,x=SYN_a[3]*sqrt(pi) nounor x=-SYN_a[3]*sqrt(pi)];p:first(ta);wa1:x=SYN_a[3]*sqrt(pi);wa2:x=-SYN_a[3]*sqrt(pi);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@SYN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text><![CDATA[]]></text></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>4</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>3</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>wa2</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>3</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>3</name><answertest>AlgEquiv</answertest><sans>1</sans><tans>1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-4-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast nur eine von zwei richtigen Lösungen eingegeben.<br>Beispiel: \(5\,\sqrt{\pi} \cdot 5\,\sqrt{\pi} = 25\,\pi\) und \(-5\,\sqrt{\pi} \cdot -5\,\sqrt{\pi} = 25\,\pi\) (Minus Mal Minus ergibt Plus).<br>Für \(x^2 = 25\pi\) gilt deshalb \(x = 5\,\sqrt{\pi}\) oder \(x = -5\,\sqrt{\pi}\), was hier in der Form <code>x=5*sqrt(pi) or x=-5*sqrt(pi)</code> aufgeschrieben wird.</p><p dir="ltr" style="text-align: left;"></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-4-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>4</name><answertest>AlgEquiv</answertest><sans>last([ans1])</sans><tans>last(ta)</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-5-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-5-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><input><name>ans1</name><type>algebraic</type><tans>last(ta)</tans><boxsize>15</boxsize><strictsyntax>1</strictsyntax><insertstars>5</insertstars><syntaxhint></syntaxhint><syntaxattribute>0</syntaxattribute><forbidwords/><allowwords/><forbidfloat>1</forbidfloat><requirelowestterms>0</requirelowestterms><checkanswertype>1</checkanswertype><mustverify>1</mustverify><showvalidation>3</showvalidation><options></options></input><deployedseed>1629124203</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-a Kürzen zweier einfacher Brüche (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\({@f@} \cdot {@g@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Gekürzt wird, indem man Zähler & Nenner durch dieselbe Zahl teilt.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(2,8,1); b:rand_with_step(20,40,10); c:a*b; d:b/5; e:a*b/10; ta1:1/a; simp:false; f:5/e; g:d/10; wa1:(5+d)/(e+10);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@f@} \cdot {@g@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir="ltr" style="text-align: left;">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>423191525</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-a Kürzen zweier einfacher Brüche (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\({@f@} \cdot {@g@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Gekürzt wird, indem man Zähler & Nenner durch dieselbe Zahl teilt.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(2,8,1); b:rand_with_step(20,40,10); c:a*b; d:b/5; e:a*b/10; ta1:1/a; simp:false; f:5/e; g:d/10; wa1:(5+d)/(e+10);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@f@} \cdot {@g@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
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+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir="ltr" style="text-align: left;">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1756629135</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-a Kürzen zweier einfacher Brüche (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\({@f@} \cdot {@g@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Gekürzt wird, indem man Zähler & Nenner durch dieselbe Zahl teilt.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(2,8,1); b:rand_with_step(20,40,10); c:a*b; d:b/5; e:a*b/10; ta1:1/a; simp:false; f:5/e; g:d/10; wa1:(5+d)/(e+10);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@f@} \cdot {@g@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
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+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
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+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir="ltr" style="text-align: left;">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>505485688</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-a Kürzen zweier einfacher Brüche (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\({@f@} \cdot {@g@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Gekürzt wird, indem man Zähler & Nenner durch dieselbe Zahl teilt.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(2,8,1); b:rand_with_step(20,40,10); c:a*b; d:b/5; e:a*b/10; ta1:1/a; simp:false; f:5/e; g:d/10; wa1:(5+d)/(e+10);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@f@} \cdot {@g@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir="ltr" style="text-align: left;">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>813830513</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-b Kürzen zweier Brüche mit Variablen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\,a\,a\,b\,b\,c}{a\,a\,a\,a\,a\,b\,c\,c\,c}\)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); powers:makelist(rand(5)+1, 6); myvar1: mya^powers[1]; myvar2: myb^powers[2]; myvar3: myc^powers[3]; myvar4: mya^powers[4]; myvar5: myb^powers[5]; myvar6: myc^powers[6]; d:(myvar1*myvar2*myvar3)/(myvar4*myvar5*myvar6); ta1:d;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Beispiel: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,b\,b\mkern-5mu/\,c\mkern-5mu/}{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,a\,a\,b\mkern-5mu/\,c\mkern-5mu/\,c\,c} = \frac{b}{a^2\,c^2}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>194802941</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-b Kürzen zweier Brüche mit Variablen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\,a\,a\,b\,b\,c}{a\,a\,a\,a\,a\,b\,c\,c\,c}\)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); powers:makelist(rand(5)+1, 6); myvar1: mya^powers[1]; myvar2: myb^powers[2]; myvar3: myc^powers[3]; myvar4: mya^powers[4]; myvar5: myb^powers[5]; myvar6: myc^powers[6]; d:(myvar1*myvar2*myvar3)/(myvar4*myvar5*myvar6); ta1:d;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Beispiel: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,b\,b\mkern-5mu/\,c\mkern-5mu/}{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,a\,a\,b\mkern-5mu/\,c\mkern-5mu/\,c\,c} = \frac{b}{a^2\,c^2}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1917875187</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-b Kürzen zweier Brüche mit Variablen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\,a\,a\,b\,b\,c}{a\,a\,a\,a\,a\,b\,c\,c\,c}\)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); powers:makelist(rand(5)+1, 6); myvar1: mya^powers[1]; myvar2: myb^powers[2]; myvar3: myc^powers[3]; myvar4: mya^powers[4]; myvar5: myb^powers[5]; myvar6: myc^powers[6]; d:(myvar1*myvar2*myvar3)/(myvar4*myvar5*myvar6); ta1:d;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Beispiel: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,b\,b\mkern-5mu/\,c\mkern-5mu/}{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,a\,a\,b\mkern-5mu/\,c\mkern-5mu/\,c\,c} = \frac{b}{a^2\,c^2}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1931041228</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-b Kürzen zweier Brüche mit Variablen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\,a\,a\,b\,b\,c}{a\,a\,a\,a\,a\,b\,c\,c\,c}\)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); powers:makelist(rand(5)+1, 6); myvar1: mya^powers[1]; myvar2: myb^powers[2]; myvar3: myc^powers[3]; myvar4: mya^powers[4]; myvar5: myb^powers[5]; myvar6: myc^powers[6]; d:(myvar1*myvar2*myvar3)/(myvar4*myvar5*myvar6); ta1:d;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@myvar1@}\cdot{@myvar2@}\cdot{@myvar3@}}{{@myvar4@}\cdot{@myvar5@}\cdot{@myvar6@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Beispiel: \(\frac{a^3\,b^2\,c}{a^5\,b\,c^3} = \frac{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,b\,b\mkern-5mu/\,c\mkern-5mu/}{a\mkern-5mu/\,a\mkern-5mu/\,a\mkern-5mu/\,a\,a\,b\mkern-5mu/\,c\mkern-5mu/\,c\,c} = \frac{b}{a^2\,c^2}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>928137609</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-c Kürzen zweier Brüche mit Variablen und Zahlen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Erst auf einen Bruchstrich sortieren. Beispiel: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} = \frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c}\)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>num1:rand_with_step(5,8,1); varlist:[a,b,c,u,v,w,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1], varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); num2:rand_with_step(3,7,1); num3:rand_with_step(3,7,1); nom1:num1*num2*myvars[1]; denom1:num1*myvars[2]; nom2:num1*num3*myvars[1]*myvars[2]; denom2:num1*myvars[1]*myvars[3]; ta1:(nom1/denom1)*(nom2/denom2); /*Alle Variablen in den Zählern mit einer Variable im Nenner gekürzt.*/wa1:((nom1/myvars[1])*(nom2/myvars[1]))/((denom1*denom2)/myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich die Variable {@myvars[1]@} im Nenner gegen beide Variablen in den Zählern gekürzt. Bei der Multiplikation von Brüchen kannst du immer nur einen Faktor gegen den anderen kürzen. Beispiel: \(\frac{36}{6} = \frac{6\cdot6}{6} = \frac{6\mkern-5mu/\cdot6}{6\mkern-5mu/} = \frac{6}{1} = 6\) und nicht \(\frac{36}{6} = \frac{6\cdot6}{6} \ne \frac{6\mkern-5mu/\cdot6\mkern-5mu/}{6\mkern-5mu/} = 1\;\).<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>So lassen sich Produkte auf einem Bruchstrich sortieren und kürzen: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} =\frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c} =\frac{49^7\mkern-14mu\large/ \small \; \cdot 21^3\mkern-14mu\large/\small \; \cdot a\mkern-5mu/ \cdot a \cdot b\mkern-5mu/}{7\mkern-5.5mu/ \cdot7\mkern-5.5mu/ \cdot a\mkern-5mu/\cdot b\mkern-5mu/\cdot c} =\frac{21\,a}{c}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1842189518</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-c Kürzen zweier Brüche mit Variablen und Zahlen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Erst auf einen Bruchstrich sortieren. Beispiel: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} = \frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c}\)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>num1:rand_with_step(5,8,1); varlist:[a,b,c,u,v,w,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1], varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); num2:rand_with_step(3,7,1); num3:rand_with_step(3,7,1); nom1:num1*num2*myvars[1]; denom1:num1*myvars[2]; nom2:num1*num3*myvars[1]*myvars[2]; denom2:num1*myvars[1]*myvars[3]; ta1:(nom1/denom1)*(nom2/denom2); /*Alle Variablen in den Zählern mit einer Variable im Nenner gekürzt.*/wa1:((nom1/myvars[1])*(nom2/myvars[1]))/((denom1*denom2)/myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich die Variable {@myvars[1]@} im Nenner gegen beide Variablen in den Zählern gekürzt. Bei der Multiplikation von Brüchen kannst du immer nur einen Faktor gegen den anderen kürzen. Beispiel: \(\frac{36}{6} = \frac{6\cdot6}{6} = \frac{6\mkern-5mu/\cdot6}{6\mkern-5mu/} = \frac{6}{1} = 6\) und nicht \(\frac{36}{6} = \frac{6\cdot6}{6} \ne \frac{6\mkern-5mu/\cdot6\mkern-5mu/}{6\mkern-5mu/} = 1\;\).<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>So lassen sich Produkte auf einem Bruchstrich sortieren und kürzen: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} =\frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c} =\frac{49^7\mkern-14mu\large/ \small \; \cdot 21^3\mkern-14mu\large/\small \; \cdot a\mkern-5mu/ \cdot a \cdot b\mkern-5mu/}{7\mkern-5.5mu/ \cdot7\mkern-5.5mu/ \cdot a\mkern-5mu/\cdot b\mkern-5mu/\cdot c} =\frac{21\,a}{c}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1601667602</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-c Kürzen zweier Brüche mit Variablen und Zahlen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Erst auf einen Bruchstrich sortieren. Beispiel: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} = \frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c}\)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>num1:rand_with_step(5,8,1); varlist:[a,b,c,u,v,w,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1], varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); num2:rand_with_step(3,7,1); num3:rand_with_step(3,7,1); nom1:num1*num2*myvars[1]; denom1:num1*myvars[2]; nom2:num1*num3*myvars[1]*myvars[2]; denom2:num1*myvars[1]*myvars[3]; ta1:(nom1/denom1)*(nom2/denom2); /*Alle Variablen in den Zählern mit einer Variable im Nenner gekürzt.*/wa1:((nom1/myvars[1])*(nom2/myvars[1]))/((denom1*denom2)/myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich die Variable {@myvars[1]@} im Nenner gegen beide Variablen in den Zählern gekürzt. Bei der Multiplikation von Brüchen kannst du immer nur einen Faktor gegen den anderen kürzen. Beispiel: \(\frac{36}{6} = \frac{6\cdot6}{6} = \frac{6\mkern-5mu/\cdot6}{6\mkern-5mu/} = \frac{6}{1} = 6\) und nicht \(\frac{36}{6} = \frac{6\cdot6}{6} \ne \frac{6\mkern-5mu/\cdot6\mkern-5mu/}{6\mkern-5mu/} = 1\;\).<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>So lassen sich Produkte auf einem Bruchstrich sortieren und kürzen: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} =\frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c} =\frac{49^7\mkern-14mu\large/ \small \; \cdot 21^3\mkern-14mu\large/\small \; \cdot a\mkern-5mu/ \cdot a \cdot b\mkern-5mu/}{7\mkern-5.5mu/ \cdot7\mkern-5.5mu/ \cdot a\mkern-5mu/\cdot b\mkern-5mu/\cdot c} =\frac{21\,a}{c}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>2136766316</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-c Kürzen zweier Brüche mit Variablen und Zahlen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Erst auf einen Bruchstrich sortieren. Beispiel: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} = \frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c}\)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>num1:rand_with_step(5,8,1); varlist:[a,b,c,u,v,w,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1], varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); num2:rand_with_step(3,7,1); num3:rand_with_step(3,7,1); nom1:num1*num2*myvars[1]; denom1:num1*myvars[2]; nom2:num1*num3*myvars[1]*myvars[2]; denom2:num1*myvars[1]*myvars[3]; ta1:(nom1/denom1)*(nom2/denom2); /*Alle Variablen in den Zählern mit einer Variable im Nenner gekürzt.*/wa1:((nom1/myvars[1])*(nom2/myvars[1]))/((denom1*denom2)/myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@nom1@}}{{@denom1@}} \cdot \frac{{@nom2@}}{{@denom2@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>wa1</tans><testoptions/><quiet>0</quiet><truescoremode>+</truescoremode><truescore>0</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich die Variable {@myvars[1]@} im Nenner gegen beide Variablen in den Zählern gekürzt. Bei der Multiplikation von Brüchen kannst du immer nur einen Faktor gegen den anderen kürzen. Beispiel: \(\frac{36}{6} = \frac{6\cdot6}{6} = \frac{6\mkern-5mu/\cdot6}{6\mkern-5mu/} = \frac{6}{1} = 6\) und nicht \(\frac{36}{6} = \frac{6\cdot6}{6} \ne \frac{6\mkern-5mu/\cdot6\mkern-5mu/}{6\mkern-5mu/} = 1\;\).<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>So lassen sich Produkte auf einem Bruchstrich sortieren und kürzen: \(\frac{49\,a}{7\,b} \cdot \frac{21\,a\,b}{7\,a\,c} =\frac{49\,a\cdot 21\,a\,b}{7\,b \cdot 7\,a\,c} = \frac{49 \cdot 21 \cdot a \cdot b}{7 \cdot 7 \cdot a\cdot b\cdot c} =\frac{49^7\mkern-14mu\large/ \small \; \cdot 21^3\mkern-14mu\large/\small \; \cdot a\mkern-5mu/ \cdot a \cdot b\mkern-5mu/}{7\mkern-5.5mu/ \cdot7\mkern-5.5mu/ \cdot a\mkern-5mu/\cdot b\mkern-5mu/\cdot c} =\frac{21\,a}{c}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1542661342</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-d Kürzen zweier Brüche mit Termen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Kennst du noch den Ausspruch „Aus Summen kürzen nur die Dummen“?!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([x,y,z]); term_summand1:rand_with_prohib(-3,3,[0]); term_summand2:rand_with_prohib(-3,3,[0,term_summand1]); term1:myvar+term_summand1; term2:myvar+term_summand2; ta1:term1/myvar*(myvar^2/(term1*term2*myvar)); /*wa1 means: naive shortened fraction*/ wa1:(term1-myvar)/1*(myvar^2/(term1*term2*myvar));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Offensichtlich hast du beim ersten Bruch die Variable {@myvar@} im Nenner gegen die Variable {@myvar@} im Zähler gekürzt. Das geht aber nicht, weil die Variable {@myvar@} im Zähler mit einem anderen Summanden eine Summe bildet. Beispiel: \(3 = \frac{6}{2} = \frac{4+2}{2} \ne \frac{4 + 2\mkern-5.5mu/}{2\mkern-5.5mu/} = \frac{4}{1} = 4\;\).]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p> Nur ganze Faktoren dürfen gekürzt werden. Zum Beispiel: \(\frac{\boldsymbol{(x-1)}\cdot 2}{x \cdot \boldsymbol{(x-1)}} = \frac{2}{x}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>837792651</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-d Kürzen zweier Brüche mit Termen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Kennst du noch den Ausspruch „Aus Summen kürzen nur die Dummen“?!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([x,y,z]); term_summand1:rand_with_prohib(-3,3,[0]); term_summand2:rand_with_prohib(-3,3,[0,term_summand1]); term1:myvar+term_summand1; term2:myvar+term_summand2; ta1:term1/myvar*(myvar^2/(term1*term2*myvar)); /*wa1 means: naive shortened fraction*/ wa1:(term1-myvar)/1*(myvar^2/(term1*term2*myvar));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Offensichtlich hast du beim ersten Bruch die Variable {@myvar@} im Nenner gegen die Variable {@myvar@} im Zähler gekürzt. Das geht aber nicht, weil die Variable {@myvar@} im Zähler mit einem anderen Summanden eine Summe bildet. Beispiel: \(3 = \frac{6}{2} = \frac{4+2}{2} \ne \frac{4 + 2\mkern-5.5mu/}{2\mkern-5.5mu/} = \frac{4}{1} = 4\;\).]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p> Nur ganze Faktoren dürfen gekürzt werden. Zum Beispiel: \(\frac{\boldsymbol{(x-1)}\cdot 2}{x \cdot \boldsymbol{(x-1)}} = \frac{2}{x}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>528135820</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-d Kürzen zweier Brüche mit Termen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Kennst du noch den Ausspruch „Aus Summen kürzen nur die Dummen“?!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([x,y,z]); term_summand1:rand_with_prohib(-3,3,[0]); term_summand2:rand_with_prohib(-3,3,[0,term_summand1]); term1:myvar+term_summand1; term2:myvar+term_summand2; ta1:term1/myvar*(myvar^2/(term1*term2*myvar)); /*wa1 means: naive shortened fraction*/ wa1:(term1-myvar)/1*(myvar^2/(term1*term2*myvar));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Offensichtlich hast du beim ersten Bruch die Variable {@myvar@} im Nenner gegen die Variable {@myvar@} im Zähler gekürzt. Das geht aber nicht, weil die Variable {@myvar@} im Zähler mit einem anderen Summanden eine Summe bildet. Beispiel: \(3 = \frac{6}{2} = \frac{4+2}{2} \ne \frac{4 + 2\mkern-5.5mu/}{2\mkern-5.5mu/} = \frac{4}{1} = 4\;\).]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p> Nur ganze Faktoren dürfen gekürzt werden. Zum Beispiel: \(\frac{\boldsymbol{(x-1)}\cdot 2}{x \cdot \boldsymbol{(x-1)}} = \frac{2}{x}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>879656886</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bi-d Kürzen zweier Brüche mit Termen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Kürze und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Kennst du noch den Ausspruch „Aus Summen kürzen nur die Dummen“?!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([x,y,z]); term_summand1:rand_with_prohib(-3,3,[0]); term_summand2:rand_with_prohib(-3,3,[0,term_summand1]); term1:myvar+term_summand1; term2:myvar+term_summand2; ta1:term1/myvar*(myvar^2/(term1*term2*myvar)); /*wa1 means: naive shortened fraction*/ wa1:(term1-myvar)/1*(myvar^2/(term1*term2*myvar));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@term1@}}{{@myvar@}}\cdot\frac{{@myvar@}^2}{({@term1@})({@term2@}){@myvar@}}={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Offensichtlich hast du beim ersten Bruch die Variable {@myvar@} im Nenner gegen die Variable {@myvar@} im Zähler gekürzt. Das geht aber nicht, weil die Variable {@myvar@} im Zähler mit einem anderen Summanden eine Summe bildet. Beispiel: \(3 = \frac{6}{2} = \frac{4+2}{2} \ne \frac{4 + 2\mkern-5.5mu/}{2\mkern-5.5mu/} = \frac{4}{1} = 4\;\).]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p> Nur ganze Faktoren dürfen gekürzt werden. Zum Beispiel: \(\frac{\boldsymbol{(x-1)}\cdot 2}{x \cdot \boldsymbol{(x-1)}} = \frac{2}{x}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1917537516</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-a Einfachen Bruch erweitern (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\({@c@} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(4,9,1); b:a-1; c:a/b; d:a*5; e:b*5; simp:false; ta1:d/e;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@c@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>437845679</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-a Einfachen Bruch erweitern (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\({@c@} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(4,9,1); b:a-1; c:a/b; d:a*5; e:b*5; simp:false; ta1:d/e;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@c@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>2092409135</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-a Einfachen Bruch erweitern (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\({@c@} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(4,9,1); b:a-1; c:a/b; d:a*5; e:b*5; simp:false; ta1:d/e;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@c@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1712748750</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-a Einfachen Bruch erweitern (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\({@c@} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(4,9,1); b:a-1; c:a/b; d:a*5; e:b*5; simp:false; ta1:d/e;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@c@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
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+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>182980498</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-b Bruch mit Variablen erweitern (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@numerator@}}{{@denominator@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,4); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[1]^powers[3]; fac4:myvars[2]^powers[4]; numerator:fac1*fac2; denominator:fac3*fac4; d:numerator/denominator; tanumerator:5*num(d); tadenominator:5*denom(d); simp:false; ta1:tanumerator/tadenominator;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@numerator@}}{{@denominator@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>36209422</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-b Bruch mit Variablen erweitern (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@numerator@}}{{@denominator@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,4); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[1]^powers[3]; fac4:myvars[2]^powers[4]; numerator:fac1*fac2; denominator:fac3*fac4; d:numerator/denominator; tanumerator:5*num(d); tadenominator:5*denom(d); simp:false; ta1:tanumerator/tadenominator;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@numerator@}}{{@denominator@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1000344719</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-b Bruch mit Variablen erweitern (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@numerator@}}{{@denominator@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,4); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[1]^powers[3]; fac4:myvars[2]^powers[4]; numerator:fac1*fac2; denominator:fac3*fac4; d:numerator/denominator; tanumerator:5*num(d); tadenominator:5*denom(d); simp:false; ta1:tanumerator/tadenominator;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@numerator@}}{{@denominator@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1827440244</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-b Bruch mit Variablen erweitern (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@numerator@}}{{@denominator@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,4); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[1]^powers[3]; fac4:myvars[2]^powers[4]; numerator:fac1*fac2; denominator:fac3*fac4; d:numerator/denominator; tanumerator:5*num(d); tadenominator:5*denom(d); simp:false; ta1:tanumerator/tadenominator;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@numerator@}}{{@denominator@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1291739138</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-c Bruch mit Variablen und Zahlen erweitern (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,3); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[2]^powers[3]; rand1:rand(4); rand2:rand_with_prohib(0,3,[rand1]); number1:rand1*2+3; number2:rand2*2+3; number3:rand_with_step(2,8,2); numerator:fac1*fac2; denominator:fac3; d:numerator/denominator; tanumerator:5*number1*number2*num(d); tadenominator:5*number3*denom(d); simp:false; ta1:tanumerator/tadenominator;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1516326427</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-c Bruch mit Variablen und Zahlen erweitern (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,3); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[2]^powers[3]; rand1:rand(4); rand2:rand_with_prohib(0,3,[rand1]); number1:rand1*2+3; number2:rand2*2+3; number3:rand_with_step(2,8,2); numerator:fac1*fac2; denominator:fac3; d:numerator/denominator; tanumerator:5*number1*number2*num(d); tadenominator:5*number3*denom(d); simp:false; ta1:tanumerator/tadenominator;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1341581403</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-c Bruch mit Variablen und Zahlen erweitern (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,3); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[2]^powers[3]; rand1:rand(4); rand2:rand_with_prohib(0,3,[rand1]); number1:rand1*2+3; number2:rand2*2+3; number3:rand_with_step(2,8,2); numerator:fac1*fac2; denominator:fac3; d:numerator/denominator; tanumerator:5*number1*number2*num(d); tadenominator:5*number3*denom(d); simp:false; ta1:tanumerator/tadenominator;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>79491835</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-bii-c Bruch mit Variablen und Zahlen erweitern (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Erweitere jeweils mit der Zahl 5 und fasse so weit wie möglich zusammen.</p>
+<p>\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = \)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); powers:makelist(rand(5)+1,3); fac1:myvars[1]^powers[1]; fac2:myvars[2]^powers[2]; fac3:myvars[2]^powers[3]; rand1:rand(4); rand2:rand_with_prohib(0,3,[rand1]); number1:rand1*2+3; number2:rand2*2+3; number3:rand_with_step(2,8,2); numerator:fac1*fac2; denominator:fac3; d:numerator/denominator; tanumerator:5*number1*number2*num(d); tadenominator:5*number3*denom(d); simp:false; ta1:tanumerator/tadenominator;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\frac{{@number1@}\,{@fac1@}\,{@number2@}\,{@fac2@}}{{@number3@}\,{@fac3@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
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+ <deployedseed>1422333316</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ca Einfache Addition von Brüchen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Addieren und Subtrahieren müssen die Nenner der Brüche gleich sein. Kannst du dich noch an das kleinste gemeinsame Vielfache erinnern?</p>]]></text>
+ </questiontext>
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+ <text>2023010400</text>
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+ <questionvariables>
+ <text>a:rand_with_step(1,4,1)*2+1; fac1:rand_with_step(1,4,1); fac2:rand_with_prohib(1,4,[fac1]); denoms:[a, a*fac1,a*fac2]; nums:makelist(rand_with_step(1,denoms[i]-1,2),i,3); signs:makelist(rand_with_prohib(-1,1,[0]),3); fractions:makelist(signs[i]*nums[i]/denoms[i],i,3); fractions:random_permutation(fractions); ta1:fractions[1]+fractions[2]+fractions[3]; simp:false; exercise:fractions[1]+fractions[2]+fractions[3]; /*wa1 means: naive addition*/ wa1:(num(fractions[1])+num(fractions[2])+num(fractions[3]))/(denom(fractions[1])+denom(fractions[2])+denom(fractions[3]));</text>
+ </questionvariables>
+ <specificfeedback format="html">
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+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
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+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
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+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
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+ <falseanswernote>prt1-2-F</falseanswernote>
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+ <node>
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+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir="ltr" style="text-align: left;">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>]]></text>
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+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um die Nenner gleich zu machen, musst du sie so erweitern, dass sie den gleichen Nenner haben. Dann können die Zähler addiert werden. Das kleinste gemeinsame Vielfache von 5, 10 und 15 lässt sich zum Beispiel finden, indem man die jeweiligen Reihen notiert und die kleinste gemeinsame Zahl sucht.</p><table><tr><th>5er-Reihe</th><th>10er-Reihe</th><th>15er-Reihe</th></tr><tr><td>5</td><td>10</td><td>15</td></tr><tr><td>10</td><td>20</td><td><strong>30</strong></td></tr><tr><td>15</td><td><strong>30</strong></td><td>...</td></tr><tr><td>20</td><td>...</td><td>...</td></tr><tr><td>25</td><td>...</td><td>...</td></tr><tr><td><strong>30</strong></td><td>...</td><td>...</td></tr><tr><td>...</td><td>...</td><td>...</td></tr></table></p>]]></text>
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+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ca Einfache Addition von Brüchen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Addieren und Subtrahieren müssen die Nenner der Brüche gleich sein. Kannst du dich noch an das kleinste gemeinsame Vielfache erinnern?</p>]]></text>
+ </questiontext>
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+ </questionvariables>
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+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
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+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir="ltr" style="text-align: left;">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>]]></text>
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+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um die Nenner gleich zu machen, musst du sie so erweitern, dass sie den gleichen Nenner haben. Dann können die Zähler addiert werden. Das kleinste gemeinsame Vielfache von 5, 10 und 15 lässt sich zum Beispiel finden, indem man die jeweiligen Reihen notiert und die kleinste gemeinsame Zahl sucht.</p><table><tr><th>5er-Reihe</th><th>10er-Reihe</th><th>15er-Reihe</th></tr><tr><td>5</td><td>10</td><td>15</td></tr><tr><td>10</td><td>20</td><td><strong>30</strong></td></tr><tr><td>15</td><td><strong>30</strong></td><td>...</td></tr><tr><td>20</td><td>...</td><td>...</td></tr><tr><td>25</td><td>...</td><td>...</td></tr><tr><td><strong>30</strong></td><td>...</td><td>...</td></tr><tr><td>...</td><td>...</td><td>...</td></tr></table></p>]]></text>
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+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ca Einfache Addition von Brüchen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Addieren und Subtrahieren müssen die Nenner der Brüche gleich sein. Kannst du dich noch an das kleinste gemeinsame Vielfache erinnern?</p>]]></text>
+ </questiontext>
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+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
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+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
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+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir="ltr" style="text-align: left;">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um die Nenner gleich zu machen, musst du sie so erweitern, dass sie den gleichen Nenner haben. Dann können die Zähler addiert werden. Das kleinste gemeinsame Vielfache von 5, 10 und 15 lässt sich zum Beispiel finden, indem man die jeweiligen Reihen notiert und die kleinste gemeinsame Zahl sucht.</p><table><tr><th>5er-Reihe</th><th>10er-Reihe</th><th>15er-Reihe</th></tr><tr><td>5</td><td>10</td><td>15</td></tr><tr><td>10</td><td>20</td><td><strong>30</strong></td></tr><tr><td>15</td><td><strong>30</strong></td><td>...</td></tr><tr><td>20</td><td>...</td><td>...</td></tr><tr><td>25</td><td>...</td><td>...</td></tr><tr><td><strong>30</strong></td><td>...</td><td>...</td></tr><tr><td>...</td><td>...</td><td>...</td></tr></table></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1338253474</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ca Einfache Addition von Brüchen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Addieren und Subtrahieren müssen die Nenner der Brüche gleich sein. Kannst du dich noch an das kleinste gemeinsame Vielfache erinnern?</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:rand_with_step(1,4,1)*2+1; fac1:rand_with_step(1,4,1); fac2:rand_with_prohib(1,4,[fac1]); denoms:[a, a*fac1,a*fac2]; nums:makelist(rand_with_step(1,denoms[i]-1,2),i,3); signs:makelist(rand_with_prohib(-1,1,[0]),3); fractions:makelist(signs[i]*nums[i]/denoms[i],i,3); fractions:random_permutation(fractions); ta1:fractions[1]+fractions[2]+fractions[3]; simp:false; exercise:fractions[1]+fractions[2]+fractions[3]; /*wa1 means: naive addition*/ wa1:(num(fractions[1])+num(fractions[2])+num(fractions[3]))/(denom(fractions[1])+denom(fractions[2])+denom(fractions[3]));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
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+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
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+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
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+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. So können Brüche aber nicht addiert werden. Beispiel: \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\). Zunächst müssen die Brüche so erweitert werden, dass die Nenner gleich sind. Dann werden die Zähler addiert. Beispiel:</p><p dir="ltr" style="text-align: left;">\(\frac{1}{2}+\frac{1}{4}=\frac{1\cdot2}{2\cdot2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}\)<br></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um die Nenner gleich zu machen, musst du sie so erweitern, dass sie den gleichen Nenner haben. Dann können die Zähler addiert werden. Das kleinste gemeinsame Vielfache von 5, 10 und 15 lässt sich zum Beispiel finden, indem man die jeweiligen Reihen notiert und die kleinste gemeinsame Zahl sucht.</p><table><tr><th>5er-Reihe</th><th>10er-Reihe</th><th>15er-Reihe</th></tr><tr><td>5</td><td>10</td><td>15</td></tr><tr><td>10</td><td>20</td><td><strong>30</strong></td></tr><tr><td>15</td><td><strong>30</strong></td><td>...</td></tr><tr><td>20</td><td>...</td><td>...</td></tr><tr><td>25</td><td>...</td><td>...</td></tr><tr><td><strong>30</strong></td><td>...</td><td>...</td></tr><tr><td>...</td><td>...</td><td>...</td></tr></table></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>933392702</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cb Addition von Brüchen mit Variablen und gleichem Nenner (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Überlege genau, was ein Minus vor einem Bruch bedeutet.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c]); fractions_correct_and_wa1:[[(myvar+1)/myvar, -myvar+1], [(myvar-1)/myvar, -myvar-1], [(1-myvar)/myvar, -1-myvar]]; fractions_correct_and_wa1:random_permutation(fractions_correct_and_wa1); fractions:makelist(fractions_correct_and_wa1[i][1],i,3); terms_wa1:makelist(fractions_correct_and_wa1[i][2],i,3); exercise:fractions[1]-fractions[2]-fractions[3]; ta1:combine(exercise); wa1:(num(fractions[1])+terms_wa1[2]+terms_wa1[3])/myvar;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@}-{@fractions[2]@}-{@fractions[3]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
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+ <checkanswertype>0</checkanswertype>
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+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
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+ <feedbackvariables>
+ <text/>
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+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast offenbar die Minuszeichen nicht korrekt aufgelöst.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Ein Minus vor dem Bruch gehört zum ganzen Bruch: gilt also für den ganzen Zähler oder ganzen Nenner (häufig nimmt man den Zähler).</p><p>\(\Rightarrow -\frac{a-1}{a} = \frac{-\boldsymbol{(a-1)}}{a} = \frac{-a+1}{a}\)</p><p>Wichtig bei Summen im Zähler!!!</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>471812117</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cb Addition von Brüchen mit Variablen und gleichem Nenner (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Überlege genau, was ein Minus vor einem Bruch bedeutet.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c]); fractions_correct_and_wa1:[[(myvar+1)/myvar, -myvar+1], [(myvar-1)/myvar, -myvar-1], [(1-myvar)/myvar, -1-myvar]]; fractions_correct_and_wa1:random_permutation(fractions_correct_and_wa1); fractions:makelist(fractions_correct_and_wa1[i][1],i,3); terms_wa1:makelist(fractions_correct_and_wa1[i][2],i,3); exercise:fractions[1]-fractions[2]-fractions[3]; ta1:combine(exercise); wa1:(num(fractions[1])+terms_wa1[2]+terms_wa1[3])/myvar;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@}-{@fractions[2]@}-{@fractions[3]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast offenbar die Minuszeichen nicht korrekt aufgelöst.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Ein Minus vor dem Bruch gehört zum ganzen Bruch: gilt also für den ganzen Zähler oder ganzen Nenner (häufig nimmt man den Zähler).</p><p>\(\Rightarrow -\frac{a-1}{a} = \frac{-\boldsymbol{(a-1)}}{a} = \frac{-a+1}{a}\)</p><p>Wichtig bei Summen im Zähler!!!</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>416709956</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cb Addition von Brüchen mit Variablen und gleichem Nenner (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Überlege genau, was ein Minus vor einem Bruch bedeutet.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c]); fractions_correct_and_wa1:[[(myvar+1)/myvar, -myvar+1], [(myvar-1)/myvar, -myvar-1], [(1-myvar)/myvar, -1-myvar]]; fractions_correct_and_wa1:random_permutation(fractions_correct_and_wa1); fractions:makelist(fractions_correct_and_wa1[i][1],i,3); terms_wa1:makelist(fractions_correct_and_wa1[i][2],i,3); exercise:fractions[1]-fractions[2]-fractions[3]; ta1:combine(exercise); wa1:(num(fractions[1])+terms_wa1[2]+terms_wa1[3])/myvar;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@}-{@fractions[2]@}-{@fractions[3]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast offenbar die Minuszeichen nicht korrekt aufgelöst.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Ein Minus vor dem Bruch gehört zum ganzen Bruch: gilt also für den ganzen Zähler oder ganzen Nenner (häufig nimmt man den Zähler).</p><p>\(\Rightarrow -\frac{a-1}{a} = \frac{-\boldsymbol{(a-1)}}{a} = \frac{-a+1}{a}\)</p><p>Wichtig bei Summen im Zähler!!!</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>743127794</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cb Addition von Brüchen mit Variablen und gleichem Nenner (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Überlege genau, was ein Minus vor einem Bruch bedeutet.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c]); fractions_correct_and_wa1:[[(myvar+1)/myvar, -myvar+1], [(myvar-1)/myvar, -myvar-1], [(1-myvar)/myvar, -1-myvar]]; fractions_correct_and_wa1:random_permutation(fractions_correct_and_wa1); fractions:makelist(fractions_correct_and_wa1[i][1],i,3); terms_wa1:makelist(fractions_correct_and_wa1[i][2],i,3); exercise:fractions[1]-fractions[2]-fractions[3]; ta1:combine(exercise); wa1:(num(fractions[1])+terms_wa1[2]+terms_wa1[3])/myvar;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@}-{@fractions[2]@}-{@fractions[3]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast offenbar die Minuszeichen nicht korrekt aufgelöst.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Ein Minus vor dem Bruch gehört zum ganzen Bruch: gilt also für den ganzen Zähler oder ganzen Nenner (häufig nimmt man den Zähler).</p><p>\(\Rightarrow -\frac{a-1}{a} = \frac{-\boldsymbol{(a-1)}}{a} = \frac{-a+1}{a}\)</p><p>Wichtig bei Summen im Zähler!!!</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>2005900637</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cc Addition von Brüchen mit Variablen und unterschiedlichen Nennern (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Jeder Teilnenner (hier: {@myvars[1]@}, {@myvars[2]@}, {@myvars[3]@}) muss als Faktor im gemeinsamen Nenner vorkommen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); fractions:[(1+myvars[1])/myvars[1], rand_with_step(2,5,1)/myvars[2], myvars[1]/myvars[3]]; fractions:random_permutation(fractions); exercise:fractions[1]+fractions[2]+fractions[3]; common_denom:denom(fractions[1])*denom(fractions[2])*denom(fractions[3]); ta1:((num(fractions[1])*denom(fractions[2])*denom(fractions[3]))+(num(fractions[2])*denom(fractions[1])*denom(fractions[3]))+(num(fractions[3])*denom(fractions[1])*denom(fractions[2])))/common_denom; ta1alt:(expand((num(fractions[1])*denom(fractions[2])*denom(fractions[3])))+expand((num(fractions[2])*denom(fractions[1])*denom(fractions[3])))+expand((num(fractions[3])*denom(fractions[1])*denom(fractions[2]))))/common_denom;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
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+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
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+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{1+a}{a}+\frac{2}{b}+\frac{a}{c}\) ist der gemeinsame Nenner \(a \cdot b \cdot c\). So muss erweitert werden, damit die Zähler addiert werden können:</p><p>\(\frac{(1+a) \boldsymbol{\cdot b \cdot c} }{a \boldsymbol{\cdot b \cdot c}}+\frac{2 \boldsymbol{\cdot a \cdot c}}{\boldsymbol{a} \cdot b \boldsymbol{\cdot c}}+\frac{a \boldsymbol{\cdot a \cdot b}}{\boldsymbol{a \cdot b} \cdot c}\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(1+a\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>638235066</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cc Addition von Brüchen mit Variablen und unterschiedlichen Nennern (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Jeder Teilnenner (hier: {@myvars[1]@}, {@myvars[2]@}, {@myvars[3]@}) muss als Faktor im gemeinsamen Nenner vorkommen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); fractions:[(1+myvars[1])/myvars[1], rand_with_step(2,5,1)/myvars[2], myvars[1]/myvars[3]]; fractions:random_permutation(fractions); exercise:fractions[1]+fractions[2]+fractions[3]; common_denom:denom(fractions[1])*denom(fractions[2])*denom(fractions[3]); ta1:((num(fractions[1])*denom(fractions[2])*denom(fractions[3]))+(num(fractions[2])*denom(fractions[1])*denom(fractions[3]))+(num(fractions[3])*denom(fractions[1])*denom(fractions[2])))/common_denom; ta1alt:(expand((num(fractions[1])*denom(fractions[2])*denom(fractions[3])))+expand((num(fractions[2])*denom(fractions[1])*denom(fractions[3])))+expand((num(fractions[3])*denom(fractions[1])*denom(fractions[2]))))/common_denom;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
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+ <forbidwords/>
+ <allowwords/>
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+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{1+a}{a}+\frac{2}{b}+\frac{a}{c}\) ist der gemeinsame Nenner \(a \cdot b \cdot c\). So muss erweitert werden, damit die Zähler addiert werden können:</p><p>\(\frac{(1+a) \boldsymbol{\cdot b \cdot c} }{a \boldsymbol{\cdot b \cdot c}}+\frac{2 \boldsymbol{\cdot a \cdot c}}{\boldsymbol{a} \cdot b \boldsymbol{\cdot c}}+\frac{a \boldsymbol{\cdot a \cdot b}}{\boldsymbol{a \cdot b} \cdot c}\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(1+a\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1053964038</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cc Addition von Brüchen mit Variablen und unterschiedlichen Nennern (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Jeder Teilnenner (hier: {@myvars[1]@}, {@myvars[2]@}, {@myvars[3]@}) muss als Faktor im gemeinsamen Nenner vorkommen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); fractions:[(1+myvars[1])/myvars[1], rand_with_step(2,5,1)/myvars[2], myvars[1]/myvars[3]]; fractions:random_permutation(fractions); exercise:fractions[1]+fractions[2]+fractions[3]; common_denom:denom(fractions[1])*denom(fractions[2])*denom(fractions[3]); ta1:((num(fractions[1])*denom(fractions[2])*denom(fractions[3]))+(num(fractions[2])*denom(fractions[1])*denom(fractions[3]))+(num(fractions[3])*denom(fractions[1])*denom(fractions[2])))/common_denom; ta1alt:(expand((num(fractions[1])*denom(fractions[2])*denom(fractions[3])))+expand((num(fractions[2])*denom(fractions[1])*denom(fractions[3])))+expand((num(fractions[3])*denom(fractions[1])*denom(fractions[2]))))/common_denom;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
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+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
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+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{1+a}{a}+\frac{2}{b}+\frac{a}{c}\) ist der gemeinsame Nenner \(a \cdot b \cdot c\). So muss erweitert werden, damit die Zähler addiert werden können:</p><p>\(\frac{(1+a) \boldsymbol{\cdot b \cdot c} }{a \boldsymbol{\cdot b \cdot c}}+\frac{2 \boldsymbol{\cdot a \cdot c}}{\boldsymbol{a} \cdot b \boldsymbol{\cdot c}}+\frac{a \boldsymbol{\cdot a \cdot b}}{\boldsymbol{a \cdot b} \cdot c}\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(1+a\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>625975426</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cc Addition von Brüchen mit Variablen und unterschiedlichen Nennern (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Jeder Teilnenner (hier: {@myvars[1]@}, {@myvars[2]@}, {@myvars[3]@}) muss als Faktor im gemeinsamen Nenner vorkommen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); fractions:[(1+myvars[1])/myvars[1], rand_with_step(2,5,1)/myvars[2], myvars[1]/myvars[3]]; fractions:random_permutation(fractions); exercise:fractions[1]+fractions[2]+fractions[3]; common_denom:denom(fractions[1])*denom(fractions[2])*denom(fractions[3]); ta1:((num(fractions[1])*denom(fractions[2])*denom(fractions[3]))+(num(fractions[2])*denom(fractions[1])*denom(fractions[3]))+(num(fractions[3])*denom(fractions[1])*denom(fractions[2])))/common_denom; ta1alt:(expand((num(fractions[1])*denom(fractions[2])*denom(fractions[3])))+expand((num(fractions[2])*denom(fractions[1])*denom(fractions[3])))+expand((num(fractions[3])*denom(fractions[1])*denom(fractions[2]))))/common_denom;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
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+ <checkanswertype>0</checkanswertype>
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+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{1+a}{a}+\frac{2}{b}+\frac{a}{c}\) ist der gemeinsame Nenner \(a \cdot b \cdot c\). So muss erweitert werden, damit die Zähler addiert werden können:</p><p>\(\frac{(1+a) \boldsymbol{\cdot b \cdot c} }{a \boldsymbol{\cdot b \cdot c}}+\frac{2 \boldsymbol{\cdot a \cdot c}}{\boldsymbol{a} \cdot b \boldsymbol{\cdot c}}+\frac{a \boldsymbol{\cdot a \cdot b}}{\boldsymbol{a \cdot b} \cdot c}\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(1+a\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p></p>]]></text>
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+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
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+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
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+</node></prt><deployedseed>1098133316</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cd Addition von Brüchen mit einer Variablen und unterschiedlichen Nennern (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([x,y,z]); nums:makelist(rand_with_step(2,5,1),2); fractions:[(nums[1]+myvar)/myvar^2,(nums[2]-myvar^2)/myvar]; common_denom:myvar^2; ta1:(num(fractions[1])-num(fractions[2])*myvar)/common_denom; ta1alt:(num(fractions[1])-expand(num(fractions[2])*myvar))/common_denom; exercise:fractions[1]-fractions[2]; /*wa1 means: didn't consider minus sign before bracket*/ wa1:(num(fractions[1])+(-nums[2]-myvar^2)*myvar)/common_denom;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
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+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast offenbar die Minuszeichen nicht korrekt aufgelöst (siehe Tipp unten).]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um immer einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{3+x}{x^2}-\frac{5-x}{x}\) ist ein gemeinsame Nenner \(x^2 \cdot x = x^3\). Betrachtet man die Teilnenner \(x^2\) und \(x\) genauer, fällt auf, dass \(x\) bereits als Faktor in \(x^2\) vorkommt. Denn \(x^2 = x \cdot x\). Deswegen kann hier auch \(x^2\) als Hauptnenner gewählt werden.</p><p>Dazu muss so erweitert werden:</p><p>\(\frac{(3+x)}{x^{2}}-\frac{(5-x^2) \boldsymbol{ \cdot x}}{x \boldsymbol{\cdot x}} = \frac{3+x}{x^{2}}-\frac{5x-x^3}{x^{\boldsymbol{2}}} = \frac{3+x-(5x-x^3)}{x^2} = \dots\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(5-x^2\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p></p>]]></text>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>669633138</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cd Addition von Brüchen mit einer Variablen und unterschiedlichen Nennern (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([x,y,z]); nums:makelist(rand_with_step(2,5,1),2); fractions:[(nums[1]+myvar)/myvar^2,(nums[2]-myvar^2)/myvar]; common_denom:myvar^2; ta1:(num(fractions[1])-num(fractions[2])*myvar)/common_denom; ta1alt:(num(fractions[1])-expand(num(fractions[2])*myvar))/common_denom; exercise:fractions[1]-fractions[2]; /*wa1 means: didn't consider minus sign before bracket*/ wa1:(num(fractions[1])+(-nums[2]-myvar^2)*myvar)/common_denom;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
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+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast offenbar die Minuszeichen nicht korrekt aufgelöst (siehe Tipp unten).]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um immer einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{3+x}{x^2}-\frac{5-x}{x}\) ist ein gemeinsame Nenner \(x^2 \cdot x = x^3\). Betrachtet man die Teilnenner \(x^2\) und \(x\) genauer, fällt auf, dass \(x\) bereits als Faktor in \(x^2\) vorkommt. Denn \(x^2 = x \cdot x\). Deswegen kann hier auch \(x^2\) als Hauptnenner gewählt werden.</p><p>Dazu muss so erweitert werden:</p><p>\(\frac{(3+x)}{x^{2}}-\frac{(5-x^2) \boldsymbol{ \cdot x}}{x \boldsymbol{\cdot x}} = \frac{3+x}{x^{2}}-\frac{5x-x^3}{x^{\boldsymbol{2}}} = \frac{3+x-(5x-x^3)}{x^2} = \dots\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(5-x^2\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
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+</node></prt><deployedseed>2093071884</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cd Addition von Brüchen mit einer Variablen und unterschiedlichen Nennern (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([x,y,z]); nums:makelist(rand_with_step(2,5,1),2); fractions:[(nums[1]+myvar)/myvar^2,(nums[2]-myvar^2)/myvar]; common_denom:myvar^2; ta1:(num(fractions[1])-num(fractions[2])*myvar)/common_denom; ta1alt:(num(fractions[1])-expand(num(fractions[2])*myvar))/common_denom; exercise:fractions[1]-fractions[2]; /*wa1 means: didn't consider minus sign before bracket*/ wa1:(num(fractions[1])+(-nums[2]-myvar^2)*myvar)/common_denom;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast offenbar die Minuszeichen nicht korrekt aufgelöst (siehe Tipp unten).]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um immer einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{3+x}{x^2}-\frac{5-x}{x}\) ist ein gemeinsame Nenner \(x^2 \cdot x = x^3\). Betrachtet man die Teilnenner \(x^2\) und \(x\) genauer, fällt auf, dass \(x\) bereits als Faktor in \(x^2\) vorkommt. Denn \(x^2 = x \cdot x\). Deswegen kann hier auch \(x^2\) als Hauptnenner gewählt werden.</p><p>Dazu muss so erweitert werden:</p><p>\(\frac{(3+x)}{x^{2}}-\frac{(5-x^2) \boldsymbol{ \cdot x}}{x \boldsymbol{\cdot x}} = \frac{3+x}{x^{2}}-\frac{5x-x^3}{x^{\boldsymbol{2}}} = \frac{3+x-(5x-x^3)}{x^2} = \dots\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(5-x^2\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1766326583</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cd Addition von Brüchen mit einer Variablen und unterschiedlichen Nennern (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([x,y,z]); nums:makelist(rand_with_step(2,5,1),2); fractions:[(nums[1]+myvar)/myvar^2,(nums[2]-myvar^2)/myvar]; common_denom:myvar^2; ta1:(num(fractions[1])-num(fractions[2])*myvar)/common_denom; ta1alt:(num(fractions[1])-expand(num(fractions[2])*myvar))/common_denom; exercise:fractions[1]-fractions[2]; /*wa1 means: didn't consider minus sign before bracket*/ wa1:(num(fractions[1])+(-nums[2]-myvar^2)*myvar)/common_denom;</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast offenbar die Minuszeichen nicht korrekt aufgelöst (siehe Tipp unten).]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Um immer einen gemeinsamen Nenner bei Brüchen mit Variablen im Nenner zu bekommen, können alle Teilnenner miteinander multipliziert werden.</p><p>Beispiel: Im Term \(\frac{3+x}{x^2}-\frac{5-x}{x}\) ist ein gemeinsame Nenner \(x^2 \cdot x = x^3\). Betrachtet man die Teilnenner \(x^2\) und \(x\) genauer, fällt auf, dass \(x\) bereits als Faktor in \(x^2\) vorkommt. Denn \(x^2 = x \cdot x\). Deswegen kann hier auch \(x^2\) als Hauptnenner gewählt werden.</p><p>Dazu muss so erweitert werden:</p><p>\(\frac{(3+x)}{x^{2}}-\frac{(5-x^2) \boldsymbol{ \cdot x}}{x \boldsymbol{\cdot x}} = \frac{3+x}{x^{2}}-\frac{5x-x^3}{x^{\boldsymbol{2}}} = \frac{3+x-(5x-x^3)}{x^2} = \dots\)</p><p>Bedenke: Beim Erweitern wird nur multipliziert. Der Ausdruck \(5-x^2\) ist eine Summe. \(\Rightarrow\) Klammer drum beim Erweitern!</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>488830876</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ce Addition von Brüchen mit Variablen und unterschiedlichen Nennern I (Update1) (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); numbers:makelist(rand_with_step(2,5,1), 5); factors:random_permutation([1,2,4]); /*only +*/ signs:makelist(rand_with_prohib(1,1,[0]),2); fractions:[(numbers[1]*myvars[1]-numbers[2]*myvars[2])/(factors[1]*5*myvars[1]*myvars[2]), (numbers[3]*myvars[3]-numbers[4]*myvars[1])/(factors[2]*5*myvars[1]*myvars[3]), (myvars[3]^2-numbers[5])/(factors[3]*5*myvars[2]*myvars[3])]; tanum:(num(fractions[1])*(4/factors[1])*myvars[3]+num(fractions[2])*(4/factors[2])*myvars[2]+num(fractions[3])*(4/factors[3])*myvars[1]); tanumalt:expand(tanum); tadenom:(5*4*myvars[1]*myvars[2]*myvars[3]); ta1:tanum/tadenom; /*fractions_to_show:random_permutation(fractions);*/ fractions_to_show:fractions; ta1alt:tanumalt/tadenom; fractions_to_show[2]:fractions_to_show[2]*signs[1]; fractions_to_show[3]:fractions_to_show[3]*signs[2]; exercise:fractions_to_show[1]+fractions_to_show[2]+fractions_to_show[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{5\,z-4\,x}{10\,x\,z}+\frac{7\,y-3\,z}{20\,y\,z}+\frac{y^2-2}{5\,x\,y}\) ist \(20\) das kleinste gemeinsame Vielfache (kgV) von \(10\), \(20\) und \(5\) und \(x \cdot y \cdot z\) ist das kgV von \(x \cdot z\), \(y \cdot z\) und \(x \cdot y\). Der Hauptnenner ist demnach \(20 \cdot x \cdot y \cdot z\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(20 \cdot x \cdot y \cdot z\;\) steht. \(\frac{5\,z-4\,x}{10\,x\,z}\) wird mit \(2 \cdot y\) erweitert, \(\frac{7\,y-3\,z}{20\,y\,z}\) wird mit \(x\) erweitert und \(\frac{y^2-2}{5\,x\,y}\) wird mit \(4 \cdot z\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(5\,z-4\,x)\boldsymbol{ \cdot 2\,y}}{10\,x\,z \boldsymbol{ \cdot 2\,y}}+\frac{(7\,y-3\,z) \boldsymbol{ \cdot x}}{20\,y\,z \boldsymbol{ \cdot x}}+\frac{(y^2-2) \boldsymbol{ \cdot 4\,z}}{5\,x\,y \boldsymbol{ \cdot 4\,z}}\)</p><p>\(= \frac{10\,y\,z-8\,x\,y}{20\,x\,y\,z}+\frac{7\,x\,y-3\,x\,z}{20\,x\,y\,z}+\frac{4\,y^2\,z-8\,z}{20\,x\,y\,z} = \dots\)</p></p>]]></text>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1330316881</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ce Addition von Brüchen mit Variablen und unterschiedlichen Nennern I (Update1) (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); numbers:makelist(rand_with_step(2,5,1), 5); factors:random_permutation([1,2,4]); /*only +*/ signs:makelist(rand_with_prohib(1,1,[0]),2); fractions:[(numbers[1]*myvars[1]-numbers[2]*myvars[2])/(factors[1]*5*myvars[1]*myvars[2]), (numbers[3]*myvars[3]-numbers[4]*myvars[1])/(factors[2]*5*myvars[1]*myvars[3]), (myvars[3]^2-numbers[5])/(factors[3]*5*myvars[2]*myvars[3])]; tanum:(num(fractions[1])*(4/factors[1])*myvars[3]+num(fractions[2])*(4/factors[2])*myvars[2]+num(fractions[3])*(4/factors[3])*myvars[1]); tanumalt:expand(tanum); tadenom:(5*4*myvars[1]*myvars[2]*myvars[3]); ta1:tanum/tadenom; /*fractions_to_show:random_permutation(fractions);*/ fractions_to_show:fractions; ta1alt:tanumalt/tadenom; fractions_to_show[2]:fractions_to_show[2]*signs[1]; fractions_to_show[3]:fractions_to_show[3]*signs[2]; exercise:fractions_to_show[1]+fractions_to_show[2]+fractions_to_show[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
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+ <type>algebraic</type>
+ <tans>ta1</tans>
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+<name>999</name>
+<answertest>AlgEquiv</answertest>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{5\,z-4\,x}{10\,x\,z}+\frac{7\,y-3\,z}{20\,y\,z}+\frac{y^2-2}{5\,x\,y}\) ist \(20\) das kleinste gemeinsame Vielfache (kgV) von \(10\), \(20\) und \(5\) und \(x \cdot y \cdot z\) ist das kgV von \(x \cdot z\), \(y \cdot z\) und \(x \cdot y\). Der Hauptnenner ist demnach \(20 \cdot x \cdot y \cdot z\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(20 \cdot x \cdot y \cdot z\;\) steht. \(\frac{5\,z-4\,x}{10\,x\,z}\) wird mit \(2 \cdot y\) erweitert, \(\frac{7\,y-3\,z}{20\,y\,z}\) wird mit \(x\) erweitert und \(\frac{y^2-2}{5\,x\,y}\) wird mit \(4 \cdot z\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(5\,z-4\,x)\boldsymbol{ \cdot 2\,y}}{10\,x\,z \boldsymbol{ \cdot 2\,y}}+\frac{(7\,y-3\,z) \boldsymbol{ \cdot x}}{20\,y\,z \boldsymbol{ \cdot x}}+\frac{(y^2-2) \boldsymbol{ \cdot 4\,z}}{5\,x\,y \boldsymbol{ \cdot 4\,z}}\)</p><p>\(= \frac{10\,y\,z-8\,x\,y}{20\,x\,y\,z}+\frac{7\,x\,y-3\,x\,z}{20\,x\,y\,z}+\frac{4\,y^2\,z-8\,z}{20\,x\,y\,z} = \dots\)</p></p>]]></text>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>2007639052</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ce Addition von Brüchen mit Variablen und unterschiedlichen Nennern I (Update1) (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); numbers:makelist(rand_with_step(2,5,1), 5); factors:random_permutation([1,2,4]); /*only +*/ signs:makelist(rand_with_prohib(1,1,[0]),2); fractions:[(numbers[1]*myvars[1]-numbers[2]*myvars[2])/(factors[1]*5*myvars[1]*myvars[2]), (numbers[3]*myvars[3]-numbers[4]*myvars[1])/(factors[2]*5*myvars[1]*myvars[3]), (myvars[3]^2-numbers[5])/(factors[3]*5*myvars[2]*myvars[3])]; tanum:(num(fractions[1])*(4/factors[1])*myvars[3]+num(fractions[2])*(4/factors[2])*myvars[2]+num(fractions[3])*(4/factors[3])*myvars[1]); tanumalt:expand(tanum); tadenom:(5*4*myvars[1]*myvars[2]*myvars[3]); ta1:tanum/tadenom; /*fractions_to_show:random_permutation(fractions);*/ fractions_to_show:fractions; ta1alt:tanumalt/tadenom; fractions_to_show[2]:fractions_to_show[2]*signs[1]; fractions_to_show[3]:fractions_to_show[3]*signs[2]; exercise:fractions_to_show[1]+fractions_to_show[2]+fractions_to_show[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
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+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
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+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
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+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
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+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{5\,z-4\,x}{10\,x\,z}+\frac{7\,y-3\,z}{20\,y\,z}+\frac{y^2-2}{5\,x\,y}\) ist \(20\) das kleinste gemeinsame Vielfache (kgV) von \(10\), \(20\) und \(5\) und \(x \cdot y \cdot z\) ist das kgV von \(x \cdot z\), \(y \cdot z\) und \(x \cdot y\). Der Hauptnenner ist demnach \(20 \cdot x \cdot y \cdot z\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(20 \cdot x \cdot y \cdot z\;\) steht. \(\frac{5\,z-4\,x}{10\,x\,z}\) wird mit \(2 \cdot y\) erweitert, \(\frac{7\,y-3\,z}{20\,y\,z}\) wird mit \(x\) erweitert und \(\frac{y^2-2}{5\,x\,y}\) wird mit \(4 \cdot z\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(5\,z-4\,x)\boldsymbol{ \cdot 2\,y}}{10\,x\,z \boldsymbol{ \cdot 2\,y}}+\frac{(7\,y-3\,z) \boldsymbol{ \cdot x}}{20\,y\,z \boldsymbol{ \cdot x}}+\frac{(y^2-2) \boldsymbol{ \cdot 4\,z}}{5\,x\,y \boldsymbol{ \cdot 4\,z}}\)</p><p>\(= \frac{10\,y\,z-8\,x\,y}{20\,x\,y\,z}+\frac{7\,x\,y-3\,x\,z}{20\,x\,y\,z}+\frac{4\,y^2\,z-8\,z}{20\,x\,y\,z} = \dots\)</p></p>]]></text>
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+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>846124380</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ce Addition von Brüchen mit Variablen und unterschiedlichen Nennern I (Update1) (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[2],varlist); myvars:append(myvars,[rand(varlist)]); numbers:makelist(rand_with_step(2,5,1), 5); factors:random_permutation([1,2,4]); /*only +*/ signs:makelist(rand_with_prohib(1,1,[0]),2); fractions:[(numbers[1]*myvars[1]-numbers[2]*myvars[2])/(factors[1]*5*myvars[1]*myvars[2]), (numbers[3]*myvars[3]-numbers[4]*myvars[1])/(factors[2]*5*myvars[1]*myvars[3]), (myvars[3]^2-numbers[5])/(factors[3]*5*myvars[2]*myvars[3])]; tanum:(num(fractions[1])*(4/factors[1])*myvars[3]+num(fractions[2])*(4/factors[2])*myvars[2]+num(fractions[3])*(4/factors[3])*myvars[1]); tanumalt:expand(tanum); tadenom:(5*4*myvars[1]*myvars[2]*myvars[3]); ta1:tanum/tadenom; /*fractions_to_show:random_permutation(fractions);*/ fractions_to_show:fractions; ta1alt:tanumalt/tadenom; fractions_to_show[2]:fractions_to_show[2]*signs[1]; fractions_to_show[3]:fractions_to_show[3]*signs[2]; exercise:fractions_to_show[1]+fractions_to_show[2]+fractions_to_show[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
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+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
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+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{5\,z-4\,x}{10\,x\,z}+\frac{7\,y-3\,z}{20\,y\,z}+\frac{y^2-2}{5\,x\,y}\) ist \(20\) das kleinste gemeinsame Vielfache (kgV) von \(10\), \(20\) und \(5\) und \(x \cdot y \cdot z\) ist das kgV von \(x \cdot z\), \(y \cdot z\) und \(x \cdot y\). Der Hauptnenner ist demnach \(20 \cdot x \cdot y \cdot z\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(20 \cdot x \cdot y \cdot z\;\) steht. \(\frac{5\,z-4\,x}{10\,x\,z}\) wird mit \(2 \cdot y\) erweitert, \(\frac{7\,y-3\,z}{20\,y\,z}\) wird mit \(x\) erweitert und \(\frac{y^2-2}{5\,x\,y}\) wird mit \(4 \cdot z\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(5\,z-4\,x)\boldsymbol{ \cdot 2\,y}}{10\,x\,z \boldsymbol{ \cdot 2\,y}}+\frac{(7\,y-3\,z) \boldsymbol{ \cdot x}}{20\,y\,z \boldsymbol{ \cdot x}}+\frac{(y^2-2) \boldsymbol{ \cdot 4\,z}}{5\,x\,y \boldsymbol{ \cdot 4\,z}}\)</p><p>\(= \frac{10\,y\,z-8\,x\,y}{20\,x\,y\,z}+\frac{7\,x\,y-3\,x\,z}{20\,x\,y\,z}+\frac{4\,y^2\,z-8\,z}{20\,x\,y\,z} = \dots\)</p></p>]]></text>
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+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>520216901</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cf Addition von Brüchen mit Variablen und unterschiedlichen Nennern II (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: 1) Überlege genau, was ein Minus vor einem Bruch bedeutet. 2) Jeder Teilnenner (hier: {@denom(main_fraction)@}, {@denom(fractions[1])@}, {@denom(fractions[2])@}) muss als Faktor im gemeinsamen Nenner vorkommen. 3) Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); numbers:rand_selection(makelist(i,i,5),2); denom_nums_origin:rand_selection([18,12,6],1)[1]; denom_nums:[denom_nums_origin, denom_nums_origin/2, denom_nums_origin/3]; main_fraction:(numbers[1]-myvars[1])/(denom_nums[1]*myvars[1]^2); fractions:[(myvars[2])/(denom_nums[2]*myvars[1]), (myvars[2]+numbers[2])/(denom_nums[3]*myvars[1]*myvars[2])]; tanum:num(main_fraction)*myvars[2]-num(fractions[1])*2*myvars[1]*myvars[2]-num(fractions[2])*3*myvars[1]; tanumalt:expand(tanum); tadenom:denom_nums_origin*myvars[1]^2*myvars[2]; ta1:tanum/tadenom; ta1alt:tanumalt/tadenom; fractions:random_permutation(fractions); simp:false; exercise:main_fraction-fractions[1]-fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
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+ <forbidfloat>1</forbidfloat>
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+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{1-x}{18\,x^2}-\frac{y}{9\,x}-\frac{x+3}{6\,x\,y}\) ist \(18\) das kleinste gemeinsame Vielfache (kgV) von \(18\), \(9\) und \(6\) und \(x^2 \cdot y\) ist das kgV von \(x^2\), \(x\) und \(x \cdot y\). Der Hauptnenner ist demnach \(18 \cdot x^2 \cdot y\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(18 \cdot x^2 \cdot y\;\) steht. \(\frac{1-x}{18\,x^2}\) wird mit \(y\) erweitert, \(\frac{y}{9\,x}\) wird mit \(2\,x\,y\) erweitert und \(\frac{x+3}{6\,x\,y}\) wird mit \(3 \cdot x\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(1-x) \boldsymbol{\cdot y}}{18\,x^2 \boldsymbol{\cdot y}}-\frac{y \boldsymbol{\cdot 2\,x\,y}}{9\,x \boldsymbol{\cdot 2\,x\,y}}-\frac{(x+3) \boldsymbol{\cdot 3\,x}}{6\,x\,y \boldsymbol{\cdot 3\,x}}\)</p><p>\(= \frac{y-x\,y}{18\,x^2\,y}-\frac{2\,x\,y^2}{18\,x^2\,y}-\frac{3\,x^2+9\,x}{18\,x^2\,y} = \dots\)</p></p>]]></text>
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+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
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+</node></prt><deployedseed>527686404</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cf Addition von Brüchen mit Variablen und unterschiedlichen Nennern II (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: 1) Überlege genau, was ein Minus vor einem Bruch bedeutet. 2) Jeder Teilnenner (hier: {@denom(main_fraction)@}, {@denom(fractions[1])@}, {@denom(fractions[2])@}) muss als Faktor im gemeinsamen Nenner vorkommen. 3) Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); numbers:rand_selection(makelist(i,i,5),2); denom_nums_origin:rand_selection([18,12,6],1)[1]; denom_nums:[denom_nums_origin, denom_nums_origin/2, denom_nums_origin/3]; main_fraction:(numbers[1]-myvars[1])/(denom_nums[1]*myvars[1]^2); fractions:[(myvars[2])/(denom_nums[2]*myvars[1]), (myvars[2]+numbers[2])/(denom_nums[3]*myvars[1]*myvars[2])]; tanum:num(main_fraction)*myvars[2]-num(fractions[1])*2*myvars[1]*myvars[2]-num(fractions[2])*3*myvars[1]; tanumalt:expand(tanum); tadenom:denom_nums_origin*myvars[1]^2*myvars[2]; ta1:tanum/tadenom; ta1alt:tanumalt/tadenom; fractions:random_permutation(fractions); simp:false; exercise:main_fraction-fractions[1]-fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
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+ <insertstars>5</insertstars>
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+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{1-x}{18\,x^2}-\frac{y}{9\,x}-\frac{x+3}{6\,x\,y}\) ist \(18\) das kleinste gemeinsame Vielfache (kgV) von \(18\), \(9\) und \(6\) und \(x^2 \cdot y\) ist das kgV von \(x^2\), \(x\) und \(x \cdot y\). Der Hauptnenner ist demnach \(18 \cdot x^2 \cdot y\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(18 \cdot x^2 \cdot y\;\) steht. \(\frac{1-x}{18\,x^2}\) wird mit \(y\) erweitert, \(\frac{y}{9\,x}\) wird mit \(2\,x\,y\) erweitert und \(\frac{x+3}{6\,x\,y}\) wird mit \(3 \cdot x\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(1-x) \boldsymbol{\cdot y}}{18\,x^2 \boldsymbol{\cdot y}}-\frac{y \boldsymbol{\cdot 2\,x\,y}}{9\,x \boldsymbol{\cdot 2\,x\,y}}-\frac{(x+3) \boldsymbol{\cdot 3\,x}}{6\,x\,y \boldsymbol{\cdot 3\,x}}\)</p><p>\(= \frac{y-x\,y}{18\,x^2\,y}-\frac{2\,x\,y^2}{18\,x^2\,y}-\frac{3\,x^2+9\,x}{18\,x^2\,y} = \dots\)</p></p>]]></text>
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+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
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+</node></prt><deployedseed>1918490776</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cf Addition von Brüchen mit Variablen und unterschiedlichen Nennern II (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: 1) Überlege genau, was ein Minus vor einem Bruch bedeutet. 2) Jeder Teilnenner (hier: {@denom(main_fraction)@}, {@denom(fractions[1])@}, {@denom(fractions[2])@}) muss als Faktor im gemeinsamen Nenner vorkommen. 3) Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); numbers:rand_selection(makelist(i,i,5),2); denom_nums_origin:rand_selection([18,12,6],1)[1]; denom_nums:[denom_nums_origin, denom_nums_origin/2, denom_nums_origin/3]; main_fraction:(numbers[1]-myvars[1])/(denom_nums[1]*myvars[1]^2); fractions:[(myvars[2])/(denom_nums[2]*myvars[1]), (myvars[2]+numbers[2])/(denom_nums[3]*myvars[1]*myvars[2])]; tanum:num(main_fraction)*myvars[2]-num(fractions[1])*2*myvars[1]*myvars[2]-num(fractions[2])*3*myvars[1]; tanumalt:expand(tanum); tadenom:denom_nums_origin*myvars[1]^2*myvars[2]; ta1:tanum/tadenom; ta1alt:tanumalt/tadenom; fractions:random_permutation(fractions); simp:false; exercise:main_fraction-fractions[1]-fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{1-x}{18\,x^2}-\frac{y}{9\,x}-\frac{x+3}{6\,x\,y}\) ist \(18\) das kleinste gemeinsame Vielfache (kgV) von \(18\), \(9\) und \(6\) und \(x^2 \cdot y\) ist das kgV von \(x^2\), \(x\) und \(x \cdot y\). Der Hauptnenner ist demnach \(18 \cdot x^2 \cdot y\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(18 \cdot x^2 \cdot y\;\) steht. \(\frac{1-x}{18\,x^2}\) wird mit \(y\) erweitert, \(\frac{y}{9\,x}\) wird mit \(2\,x\,y\) erweitert und \(\frac{x+3}{6\,x\,y}\) wird mit \(3 \cdot x\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(1-x) \boldsymbol{\cdot y}}{18\,x^2 \boldsymbol{\cdot y}}-\frac{y \boldsymbol{\cdot 2\,x\,y}}{9\,x \boldsymbol{\cdot 2\,x\,y}}-\frac{(x+3) \boldsymbol{\cdot 3\,x}}{6\,x\,y \boldsymbol{\cdot 3\,x}}\)</p><p>\(= \frac{y-x\,y}{18\,x^2\,y}-\frac{2\,x\,y^2}{18\,x^2\,y}-\frac{3\,x^2+9\,x}{18\,x^2\,y} = \dots\)</p></p>]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>2103547991</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-cf Addition von Brüchen mit Variablen und unterschiedlichen Nennern II (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Addiere bzw. subtrahiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@exercise@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: 1) Überlege genau, was ein Minus vor einem Bruch bedeutet. 2) Jeder Teilnenner (hier: {@denom(main_fraction)@}, {@denom(fractions[1])@}, {@denom(fractions[2])@}) muss als Faktor im gemeinsamen Nenner vorkommen. 3) Zahlen und Variablen zunächst getrennt behandeln, um den gemeinsamen Nenner zu finden.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:[]; myvars:append(myvars,[rand(varlist)]); varlist:delete(myvars[1],varlist); myvars:append(myvars,[rand(varlist)]); numbers:rand_selection(makelist(i,i,5),2); denom_nums_origin:rand_selection([18,12,6],1)[1]; denom_nums:[denom_nums_origin, denom_nums_origin/2, denom_nums_origin/3]; main_fraction:(numbers[1]-myvars[1])/(denom_nums[1]*myvars[1]^2); fractions:[(myvars[2])/(denom_nums[2]*myvars[1]), (myvars[2]+numbers[2])/(denom_nums[3]*myvars[1]*myvars[2])]; tanum:num(main_fraction)*myvars[2]-num(fractions[1])*2*myvars[1]*myvars[2]-num(fractions[2])*3*myvars[1]; tanumalt:expand(tanum); tadenom:denom_nums_origin*myvars[1]^2*myvars[2]; ta1:tanum/tadenom; ta1alt:tanumalt/tadenom; fractions:random_permutation(fractions); simp:false; exercise:main_fraction-fractions[1]-fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@exercise@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>999</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Zur Bildung eines gemeinsamen Nenners können Zahlen und Variablen getrennt bearbeitet werden.</p><p>Beispiel: Im Term \(\frac{1-x}{18\,x^2}-\frac{y}{9\,x}-\frac{x+3}{6\,x\,y}\) ist \(18\) das kleinste gemeinsame Vielfache (kgV) von \(18\), \(9\) und \(6\) und \(x^2 \cdot y\) ist das kgV von \(x^2\), \(x\) und \(x \cdot y\). Der Hauptnenner ist demnach \(18 \cdot x^2 \cdot y\;\).</p><p>Die Brüche müssen nun so erweitert werden, dass in jedem der Nenner \(18 \cdot x^2 \cdot y\;\) steht. \(\frac{1-x}{18\,x^2}\) wird mit \(y\) erweitert, \(\frac{y}{9\,x}\) wird mit \(2\,x\,y\) erweitert und \(\frac{x+3}{6\,x\,y}\) wird mit \(3 \cdot x\) erweitert. Daraus ergibt sich:</p><p>\(\frac{(1-x) \boldsymbol{\cdot y}}{18\,x^2 \boldsymbol{\cdot y}}-\frac{y \boldsymbol{\cdot 2\,x\,y}}{9\,x \boldsymbol{\cdot 2\,x\,y}}-\frac{(x+3) \boldsymbol{\cdot 3\,x}}{6\,x\,y \boldsymbol{\cdot 3\,x}}\)</p><p>\(= \frac{y-x\,y}{18\,x^2\,y}-\frac{2\,x\,y^2}{18\,x^2\,y}-\frac{3\,x^2+9\,x}{18\,x^2\,y} = \dots\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1091135158</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-da Multiplikation zweier einfacher Brüche (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@}\cdot{@fractions[2]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8),4); fractions:[nums[1]/nums[2], nums[3]/nums[4]]; ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions*/ wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied*/ wa2:fractions[1]+fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@}\cdot{@fractions[2]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{2}{3} \cdot \frac{6}{5} = \frac{2 \cdot 6}{3 \cdot 5} = \frac{12}{15} = \frac{4}{5}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1088212423</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-da Multiplikation zweier einfacher Brüche (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@}\cdot{@fractions[2]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8),4); fractions:[nums[1]/nums[2], nums[3]/nums[4]]; ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions*/ wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied*/ wa2:fractions[1]+fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@}\cdot{@fractions[2]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
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+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
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+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
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+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{2}{3} \cdot \frac{6}{5} = \frac{2 \cdot 6}{3 \cdot 5} = \frac{12}{15} = \frac{4}{5}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1553109555</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-da Multiplikation zweier einfacher Brüche (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@}\cdot{@fractions[2]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8),4); fractions:[nums[1]/nums[2], nums[3]/nums[4]]; ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions*/ wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied*/ wa2:fractions[1]+fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@}\cdot{@fractions[2]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
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+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
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+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
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+ <autosimplify>1</autosimplify>
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+ <truepenalty/>
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+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
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+ <falsepenalty/>
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+ <falseanswernote>prt1-1-F</falseanswernote>
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+ </falsefeedback>
+ </node>
+ <node>
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+ <sans>ans1</sans>
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+ <truepenalty/>
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+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
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+ <node>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.]]></text>
+</truefeedback>
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+<falsepenalty/>
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+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{2}{3} \cdot \frac{6}{5} = \frac{2 \cdot 6}{3 \cdot 5} = \frac{12}{15} = \frac{4}{5}\)</p></p>]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>777390971</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-da Multiplikation zweier einfacher Brüche (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@}\cdot{@fractions[2]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8),4); fractions:[nums[1]/nums[2], nums[3]/nums[4]]; ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions*/ wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied*/ wa2:fractions[1]+fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@}\cdot{@fractions[2]@} = {@ta1@}\)</text>
+ </questionnote>
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+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
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+ <complexno>i</complexno>
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+ <type>algebraic</type>
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+ <trueanswernote>prt1-1-T</trueanswernote>
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+ <falsescore>0</falsescore>
+ <falsepenalty/>
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+ <falseanswernote>prt1-1-F</falseanswernote>
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+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.]]></text>
+</truefeedback>
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+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
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+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{2}{3} \cdot \frac{6}{5} = \frac{2 \cdot 6}{3 \cdot 5} = \frac{12}{15} = \frac{4}{5}\)</p></p>]]></text>
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+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1688656099</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-db Multiplikation zweier Brüche mit Variablen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
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+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); fractions:[mya/myb, mya^2/(mya*myb)]; fractions:random_permutation(fractions); ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions with previously shortened the larger fraction*/ wa1:(2*mya)/(2*myb); /*wa2 means: naively summed fractions without previously shortening the larger fraction*/ wa2:(mya+myb^2)/(mya+myb*mya); /*wa3 means: correctly summed fractions instead of multiplied*/ wa3:fractions[1]+fractions[2]; /*wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied wa2:fractions[1]+fractions[2];*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
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+ <prt>
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+ <value>1.0000000</value>
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+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
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+ <falsescore>0</falsescore>
+ <falsepenalty/>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
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+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.]]></text>
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+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden. Du hast außerdem den Bruch \({@mya@}^2/({@mya@}*{@myb@})\) nicht ausreichend vereinfacht. Er kann zu \({@mya@}/{@myb@}\) gekürzt werden.]]></text>
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+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{a}{b} \cdot \frac{a^2}{a\,b} = \frac{a}{b} \cdot \frac{a \cdot a}{a\,b} = \frac{a \cdot a \cdot a}{a \cdot b \cdot b} = \frac{a^3}{a\,b^2}\)</p></p>]]></text>
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+ <deployedseed>545658671</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-db Multiplikation zweier Brüche mit Variablen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); fractions:[mya/myb, mya^2/(mya*myb)]; fractions:random_permutation(fractions); ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions with previously shortened the larger fraction*/ wa1:(2*mya)/(2*myb); /*wa2 means: naively summed fractions without previously shortening the larger fraction*/ wa2:(mya+myb^2)/(mya+myb*mya); /*wa3 means: correctly summed fractions instead of multiplied*/ wa3:fractions[1]+fractions[2]; /*wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied wa2:fractions[1]+fractions[2];*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} = {@ta1@}\)</text>
+ </questionnote>
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+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
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+ <tans>ta1</tans>
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+ <node>
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+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
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+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.]]></text>
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+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
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+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden. Du hast außerdem den Bruch \({@mya@}^2/({@mya@}*{@myb@})\) nicht ausreichend vereinfacht. Er kann zu \({@mya@}/{@myb@}\) gekürzt werden.]]></text>
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+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
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+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{a}{b} \cdot \frac{a^2}{a\,b} = \frac{a}{b} \cdot \frac{a \cdot a}{a\,b} = \frac{a \cdot a \cdot a}{a \cdot b \cdot b} = \frac{a^3}{a\,b^2}\)</p></p>]]></text>
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+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1228864607</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-db Multiplikation zweier Brüche mit Variablen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
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+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); fractions:[mya/myb, mya^2/(mya*myb)]; fractions:random_permutation(fractions); ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions with previously shortened the larger fraction*/ wa1:(2*mya)/(2*myb); /*wa2 means: naively summed fractions without previously shortening the larger fraction*/ wa2:(mya+myb^2)/(mya+myb*mya); /*wa3 means: correctly summed fractions instead of multiplied*/ wa3:fractions[1]+fractions[2]; /*wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied wa2:fractions[1]+fractions[2];*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} = {@ta1@}\)</text>
+ </questionnote>
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+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
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+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
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+ <value>1.0000000</value>
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+ <trueanswernote>prt1-1-T</trueanswernote>
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+ <text/>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.]]></text>
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+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
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+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden. Du hast außerdem den Bruch \({@mya@}^2/({@mya@}*{@myb@})\) nicht ausreichend vereinfacht. Er kann zu \({@mya@}/{@myb@}\) gekürzt werden.]]></text>
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+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{a}{b} \cdot \frac{a^2}{a\,b} = \frac{a}{b} \cdot \frac{a \cdot a}{a\,b} = \frac{a \cdot a \cdot a}{a \cdot b \cdot b} = \frac{a^3}{a\,b^2}\)</p></p>]]></text>
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+ <deployedseed>806993602</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-db Multiplikation zweier Brüche mit Variablen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Beim Multiplizieren immer: Zähler Mal Zähler und Nenner Mal Nenner rechnen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); fractions:[mya/myb, mya^2/(mya*myb)]; fractions:random_permutation(fractions); ta1:fractions[1]*fractions[2]; simp:false; exercise:fractions[1]*fractions[2]; /*wa1 means: naively summed fractions with previously shortened the larger fraction*/ wa1:(2*mya)/(2*myb); /*wa2 means: naively summed fractions without previously shortening the larger fraction*/ wa2:(mya+myb^2)/(mya+myb*mya); /*wa3 means: correctly summed fractions instead of multiplied*/ wa3:fractions[1]+fractions[2]; /*wa1:num((fractions[1])+num(fractions[2]))/(denom(fractions[2])+denom(fractions[2])); /*wa2 means: summed fractions instead of multiplied wa2:fractions[1]+fractions[2];*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@} \cdot \frac{{@mya@}^2}{{@mya@}\cdot{@myb@}} = {@ta1@}\)</text>
+ </questionnote>
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+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
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+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
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+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
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+ <falsescore>0</falsescore>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
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+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
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+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden.]]></text>
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+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Die Brüche sollten multipliziert werden. Du hast die Brüche addiert, indem du Zähler plus Zähler und Nenner plus Nenner gerechnet hast. Abgesehen davon, dass Brüche so nicht addiert werden können, sollten die Brüche multipliziert werden. Du hast außerdem den Bruch \({@mya@}^2/({@mya@}*{@myb@})\) nicht ausreichend vereinfacht. Er kann zu \({@mya@}/{@myb@}\) gekürzt werden.]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche wunderbar <strong>addiert</strong>, aber die Brüche sollten <strong>multipliziert</strong> werden.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Zwei Brüche lassen sich multiplizieren, indem Zähler mal Zähler und Nenner mal Nenner gerechnet wird. Beispiel: \(\frac{a}{b} \cdot \frac{a^2}{a\,b} = \frac{a}{b} \cdot \frac{a \cdot a}{a\,b} = \frac{a \cdot a \cdot a}{a \cdot b \cdot b} = \frac{a^3}{a\,b^2}\)</p></p>]]></text>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1501016569</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dc Multiplikation Bruch mit Zahlen, Bruch mit Variablen, Ganzzahl (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Wie kann man eine ganze Zahl als Bruch schreiben?</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
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+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8),3); nums:sort(nums); varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); factors:[nums[1], (mya*myb)/myc, nums[2]/nums[3]]; factors:random_permutation(factors); ta1:factors[1]*factors[2]*factors[3]; simp:false; exercise:factors[1]*factors[2]*factors[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} = {@ta1@}\)</text>
+ </questionnote>
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+ <assumepositive>0</assumepositive>
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+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
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+ <inversetrig>cos-1</inversetrig>
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+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
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+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
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+ <falsescore>0</falsescore>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>999</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Jede ganze Zahl kann als Bruch geschrieben werden, indem man sie durch 1 teilt. Beispiel: \(3 \cdot \frac{a\,b}{c} \cdot \frac{5}{6} = \frac{3}{1} \cdot \frac{a\,b}{c} \cdot \frac{5}{6}\)</p><p>\( = \frac{3 \cdot a \cdot b \cdot 5}{1 \cdot c \cdot 6} = \frac{15\,a\,b}{6\,c} = \frac{5\,a\,b}{2\,c}\)</p><p>Hinweis: Generellt gilt \(\cdot 1\) und \(:\,1\) geht immer.</p></p>]]></text>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1569886884</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dc Multiplikation Bruch mit Zahlen, Bruch mit Variablen, Ganzzahl (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Wie kann man eine ganze Zahl als Bruch schreiben?</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8),3); nums:sort(nums); varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); factors:[nums[1], (mya*myb)/myc, nums[2]/nums[3]]; factors:random_permutation(factors); ta1:factors[1]*factors[2]*factors[3]; simp:false; exercise:factors[1]*factors[2]*factors[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
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+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
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+ <text/>
+ </feedbackvariables>
+ <node>
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+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
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+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
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+ </falsefeedback>
+ </node>
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+ <answertest>AlgEquiv</answertest>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>999</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Jede ganze Zahl kann als Bruch geschrieben werden, indem man sie durch 1 teilt. Beispiel: \(3 \cdot \frac{a\,b}{c} \cdot \frac{5}{6} = \frac{3}{1} \cdot \frac{a\,b}{c} \cdot \frac{5}{6}\)</p><p>\( = \frac{3 \cdot a \cdot b \cdot 5}{1 \cdot c \cdot 6} = \frac{15\,a\,b}{6\,c} = \frac{5\,a\,b}{2\,c}\)</p><p>Hinweis: Generellt gilt \(\cdot 1\) und \(:\,1\) geht immer.</p></p>]]></text>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1980675582</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dc Multiplikation Bruch mit Zahlen, Bruch mit Variablen, Ganzzahl (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Wie kann man eine ganze Zahl als Bruch schreiben?</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8),3); nums:sort(nums); varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); factors:[nums[1], (mya*myb)/myc, nums[2]/nums[3]]; factors:random_permutation(factors); ta1:factors[1]*factors[2]*factors[3]; simp:false; exercise:factors[1]*factors[2]*factors[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
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+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
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+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>999</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Jede ganze Zahl kann als Bruch geschrieben werden, indem man sie durch 1 teilt. Beispiel: \(3 \cdot \frac{a\,b}{c} \cdot \frac{5}{6} = \frac{3}{1} \cdot \frac{a\,b}{c} \cdot \frac{5}{6}\)</p><p>\( = \frac{3 \cdot a \cdot b \cdot 5}{1 \cdot c \cdot 6} = \frac{15\,a\,b}{6\,c} = \frac{5\,a\,b}{2\,c}\)</p><p>Hinweis: Generellt gilt \(\cdot 1\) und \(:\,1\) geht immer.</p></p>]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1601683210</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dc Multiplikation Bruch mit Zahlen, Bruch mit Variablen, Ganzzahl (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Wie kann man eine ganze Zahl als Bruch schreiben?</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8),3); nums:sort(nums); varlist:[a,b,c,x,y,z]; mya:rand(varlist); varlist:delete(mya,varlist); myb:rand(varlist); varlist:delete(myb,varlist); myc:rand(varlist); factors:[nums[1], (mya*myb)/myc, nums[2]/nums[3]]; factors:random_permutation(factors); ta1:factors[1]*factors[2]*factors[3]; simp:false; exercise:factors[1]*factors[2]*factors[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@factors[1]@}\cdot{@factors[2]@}\cdot{@factors[3]@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
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+ <insertstars>5</insertstars>
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+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
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+ <truepenalty/>
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+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
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+ <truescoremode>=</truescoremode>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Jede ganze Zahl kann als Bruch geschrieben werden, indem man sie durch 1 teilt. Beispiel: \(3 \cdot \frac{a\,b}{c} \cdot \frac{5}{6} = \frac{3}{1} \cdot \frac{a\,b}{c} \cdot \frac{5}{6}\)</p><p>\( = \frac{3 \cdot a \cdot b \cdot 5}{1 \cdot c \cdot 6} = \frac{15\,a\,b}{6\,c} = \frac{5\,a\,b}{2\,c}\)</p><p>Hinweis: Generellt gilt \(\cdot 1\) und \(:\,1\) geht immer.</p></p>]]></text>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>51348788</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dd Multiplikation zweier Brüche mit Termen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Summanden & Faktoren => Klammer!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:rand_selection(varlist, 2); nums:rand_selection(makelist(i+1,i,9), 6); fractions:[(nums[1]*myvars[1]+nums[2]*myvars[2])/(nums[3]*myvars[2]+nums[4]*myvars[1]), (-nums[5]*myvars[1])/(nums[6]+myvars[1])]; ta1:fractions[1]*fractions[2]; taalt:combine(expand(ta1)); /*wa1 means: the multiplication of the numerator was done with only one summand of the first fraction’s numerator (the second one)*/ wa1:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(denom(fractions[1])*denom(fractions[2])); /*old_wa2 means the same as wa1 but with the first fraction numerator’s second summand*/ /*old_wa2: (nums[1]*myvars[1]*num(fractions[2])+nums[2]*myvars[2])/(denom(fractions[1])*denom(fractions[2]));*/ /*wa2 means the same as wa1 but with the denominators, so no brackets: first summand of second fraction is multiplied with last summand of first fraction*/ wa2:(num(fractions[1])*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]); /*wa3 is the combination of wa1 and wa2*/ wa3:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}= {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
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+ <mustverify>1</mustverify>
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+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Nenner richtig multipliziert, doch du hast den Faktor im Zähler des zweiten Bruches nur mit dem zweiten Summanden des Zählers im ersten Bruch multipliziert. Das heißt bei der Multiplikation der Zähler musst du Klammern um die Summe setzen und jeden Summanden des ersten Zählers mit dem Faktor des anderen Zählers multiplizieren.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Zähler richtig multipliziert, hast jedoch im Nenner nicht beachtet, dass Summen als Ganzes multipliziert werden. Das heißt bei der Multiplikation der Nenner musst du Klammern um die Summen setzen und jeden Summanden des einen Nenners mit jedem Summanden des anderen Nenners multiplizieren.]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>5</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>5</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
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+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-6-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Summen nicht als Ganzes multipliziert. Das betrifft eine Summe im Zähler und die Summen im Nenner. Du musst jeweils Klammern setzen, damit jeder Summand mit jedem anderen Summanden multipliziert wird. ]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
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+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-6-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
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+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{4\,x+10\,y}{5\,y+2\,x} \cdot \frac{-4\,x}{3+x} = \)\(\frac{\boldsymbol{(4\,x+10\,y)} \cdot -4\,x}{\boldsymbol{(5\,y+2\,x)} \cdot \boldsymbol{(3+x)}} = \dots\)</p></p>]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>783029466</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dd Multiplikation zweier Brüche mit Termen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Summanden & Faktoren => Klammer!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:rand_selection(varlist, 2); nums:rand_selection(makelist(i+1,i,9), 6); fractions:[(nums[1]*myvars[1]+nums[2]*myvars[2])/(nums[3]*myvars[2]+nums[4]*myvars[1]), (-nums[5]*myvars[1])/(nums[6]+myvars[1])]; ta1:fractions[1]*fractions[2]; taalt:combine(expand(ta1)); /*wa1 means: the multiplication of the numerator was done with only one summand of the first fraction’s numerator (the second one)*/ wa1:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(denom(fractions[1])*denom(fractions[2])); /*old_wa2 means the same as wa1 but with the first fraction numerator’s second summand*/ /*old_wa2: (nums[1]*myvars[1]*num(fractions[2])+nums[2]*myvars[2])/(denom(fractions[1])*denom(fractions[2]));*/ /*wa2 means the same as wa1 but with the denominators, so no brackets: first summand of second fraction is multiplied with last summand of first fraction*/ wa2:(num(fractions[1])*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]); /*wa3 is the combination of wa1 and wa2*/ wa3:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}= {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
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+ <name>ans1</name>
+ <type>algebraic</type>
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+ <boxsize>15</boxsize>
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+ <insertstars>5</insertstars>
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+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
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+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Nenner richtig multipliziert, doch du hast den Faktor im Zähler des zweiten Bruches nur mit dem zweiten Summanden des Zählers im ersten Bruch multipliziert. Das heißt bei der Multiplikation der Zähler musst du Klammern um die Summe setzen und jeden Summanden des ersten Zählers mit dem Faktor des anderen Zählers multiplizieren.]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Zähler richtig multipliziert, hast jedoch im Nenner nicht beachtet, dass Summen als Ganzes multipliziert werden. Das heißt bei der Multiplikation der Nenner musst du Klammern um die Summen setzen und jeden Summanden des einen Nenners mit jedem Summanden des anderen Nenners multiplizieren.]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>5</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>5</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-6-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Summen nicht als Ganzes multipliziert. Das betrifft eine Summe im Zähler und die Summen im Nenner. Du musst jeweils Klammern setzen, damit jeder Summand mit jedem anderen Summanden multipliziert wird. ]]></text>
+</truefeedback>
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+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-6-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{4\,x+10\,y}{5\,y+2\,x} \cdot \frac{-4\,x}{3+x} = \)\(\frac{\boldsymbol{(4\,x+10\,y)} \cdot -4\,x}{\boldsymbol{(5\,y+2\,x)} \cdot \boldsymbol{(3+x)}} = \dots\)</p></p>]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1177445020</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dd Multiplikation zweier Brüche mit Termen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Summanden & Faktoren => Klammer!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:rand_selection(varlist, 2); nums:rand_selection(makelist(i+1,i,9), 6); fractions:[(nums[1]*myvars[1]+nums[2]*myvars[2])/(nums[3]*myvars[2]+nums[4]*myvars[1]), (-nums[5]*myvars[1])/(nums[6]+myvars[1])]; ta1:fractions[1]*fractions[2]; taalt:combine(expand(ta1)); /*wa1 means: the multiplication of the numerator was done with only one summand of the first fraction’s numerator (the second one)*/ wa1:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(denom(fractions[1])*denom(fractions[2])); /*old_wa2 means the same as wa1 but with the first fraction numerator’s second summand*/ /*old_wa2: (nums[1]*myvars[1]*num(fractions[2])+nums[2]*myvars[2])/(denom(fractions[1])*denom(fractions[2]));*/ /*wa2 means the same as wa1 but with the denominators, so no brackets: first summand of second fraction is multiplied with last summand of first fraction*/ wa2:(num(fractions[1])*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]); /*wa3 is the combination of wa1 and wa2*/ wa3:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}= {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
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+ <insertstars>5</insertstars>
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+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Nenner richtig multipliziert, doch du hast den Faktor im Zähler des zweiten Bruches nur mit dem zweiten Summanden des Zählers im ersten Bruch multipliziert. Das heißt bei der Multiplikation der Zähler musst du Klammern um die Summe setzen und jeden Summanden des ersten Zählers mit dem Faktor des anderen Zählers multiplizieren.]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Zähler richtig multipliziert, hast jedoch im Nenner nicht beachtet, dass Summen als Ganzes multipliziert werden. Das heißt bei der Multiplikation der Nenner musst du Klammern um die Summen setzen und jeden Summanden des einen Nenners mit jedem Summanden des anderen Nenners multiplizieren.]]></text>
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+<falsepenalty/>
+<falsenextnode>5</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>5</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-6-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Summen nicht als Ganzes multipliziert. Das betrifft eine Summe im Zähler und die Summen im Nenner. Du musst jeweils Klammern setzen, damit jeder Summand mit jedem anderen Summanden multipliziert wird. ]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-6-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
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+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{4\,x+10\,y}{5\,y+2\,x} \cdot \frac{-4\,x}{3+x} = \)\(\frac{\boldsymbol{(4\,x+10\,y)} \cdot -4\,x}{\boldsymbol{(5\,y+2\,x)} \cdot \boldsymbol{(3+x)}} = \dots\)</p></p>]]></text>
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+<falsepenalty/>
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+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1009895582</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dd Multiplikation zweier Brüche mit Termen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Summanden & Faktoren => Klammer!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>varlist:[a,b,c,x,y,z]; myvars:rand_selection(varlist, 2); nums:rand_selection(makelist(i+1,i,9), 6); fractions:[(nums[1]*myvars[1]+nums[2]*myvars[2])/(nums[3]*myvars[2]+nums[4]*myvars[1]), (-nums[5]*myvars[1])/(nums[6]+myvars[1])]; ta1:fractions[1]*fractions[2]; taalt:combine(expand(ta1)); /*wa1 means: the multiplication of the numerator was done with only one summand of the first fraction’s numerator (the second one)*/ wa1:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(denom(fractions[1])*denom(fractions[2])); /*old_wa2 means the same as wa1 but with the first fraction numerator’s second summand*/ /*old_wa2: (nums[1]*myvars[1]*num(fractions[2])+nums[2]*myvars[2])/(denom(fractions[1])*denom(fractions[2]));*/ /*wa2 means the same as wa1 but with the denominators, so no brackets: first summand of second fraction is multiplied with last summand of first fraction*/ wa2:(num(fractions[1])*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]); /*wa3 is the combination of wa1 and wa2*/ wa3:(nums[1]*myvars[1]+nums[2]*myvars[2]*num(fractions[2]))/(nums[3]*myvars[2]+nums[4]*myvars[1]*nums[6]+myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@fractions[1]@} \cdot \frac{-{@nums[5]@}\cdot{@myvars[1]@}}{{@nums[6]@}+{@myvars[1]@}}= {@ta1@}\)</text>
+ </questionnote>
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+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
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+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Nenner richtig multipliziert, doch du hast den Faktor im Zähler des zweiten Bruches nur mit dem zweiten Summanden des Zählers im ersten Bruch multipliziert. Das heißt bei der Multiplikation der Zähler musst du Klammern um die Summe setzen und jeden Summanden des ersten Zählers mit dem Faktor des anderen Zählers multiplizieren.]]></text>
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+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
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+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Zähler richtig multipliziert, hast jedoch im Nenner nicht beachtet, dass Summen als Ganzes multipliziert werden. Das heißt bei der Multiplikation der Nenner musst du Klammern um die Summen setzen und jeden Summanden des einen Nenners mit jedem Summanden des anderen Nenners multiplizieren.]]></text>
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+<name>5</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-6-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Summen nicht als Ganzes multipliziert. Das betrifft eine Summe im Zähler und die Summen im Nenner. Du musst jeweils Klammern setzen, damit jeder Summand mit jedem anderen Summanden multipliziert wird. ]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-6-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{4\,x+10\,y}{5\,y+2\,x} \cdot \frac{-4\,x}{3+x} = \)\(\frac{\boldsymbol{(4\,x+10\,y)} \cdot -4\,x}{\boldsymbol{(5\,y+2\,x)} \cdot \boldsymbol{(3+x)}} = \dots\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1167689465</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-de Einfacher Doppelbruch (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8), 4); nums:sort(nums); ta1:((nums[1])/(nums[4]))/((nums[2])/(nums[3])); /*wa1 means: multiplied fractions instead of division*/ wa1:((nums[1])/(nums[4]))*((nums[2])/(nums[3])); /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:((nums[4])/(nums[1]))*((nums[2])/(nums[3]));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>352990161</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-de Einfacher Doppelbruch (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8), 4); nums:sort(nums); ta1:((nums[1])/(nums[4]))/((nums[2])/(nums[3])); /*wa1 means: multiplied fractions instead of division*/ wa1:((nums[1])/(nums[4]))*((nums[2])/(nums[3])); /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:((nums[4])/(nums[1]))*((nums[2])/(nums[3]));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>467670994</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-de Einfacher Doppelbruch (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8), 4); nums:sort(nums); ta1:((nums[1])/(nums[4]))/((nums[2])/(nums[3])); /*wa1 means: multiplied fractions instead of division*/ wa1:((nums[1])/(nums[4]))*((nums[2])/(nums[3])); /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:((nums[4])/(nums[1]))*((nums[2])/(nums[3]));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
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+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1747402747</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-de Einfacher Doppelbruch (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8), 4); nums:sort(nums); ta1:((nums[1])/(nums[4]))/((nums[2])/(nums[3])); /*wa1 means: multiplied fractions instead of division*/ wa1:((nums[1])/(nums[4]))*((nums[2])/(nums[3])); /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:((nums[4])/(nums[1]))*((nums[2])/(nums[3]));</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{\frac{{@nums[1]@}}{{@nums[4]@}}}{\frac{{@nums[2]@}}{{@nums[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>2135608811</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-df Bruch und Geteilt-Rechnung (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@dividend@}:{@divisor@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Achtung: Auch ein Doppelbruch ;)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>power:rand_with_step(2,4,1); myvars:rand_selection([a,b,c,x,y,z],2); dividend:myvars[1]/myvars[2]; num:rand_with_step(1,5,1); divisor:(num-myvars[1])/(myvars[2]^power); ta1: dividend/divisor; /*wa1 means: multiplied fractions instead of division*/ wa1:dividend*divisor; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:dividend^(-1)*divisor; /*wa3 means: didn’t consider to multiply the denominator of the first fraction with the sum of the second fraction’s numerator as a whole*/ wa3:(num(dividend)*denom(divisor))/(myvars[2]*num-myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@dividend@}:{@divisor@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast den richtigen Kehrwert gebildet um die Brüche dann zu multiplizieren, jedoch hast du dann die Klammersetzung bei der Mutliplikation nicht beachtet.</p><p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{x}{a} : \frac{1-x}{a^2} = \frac{x}{a} \cdot \frac{a^2}{1-x}\)\(= \frac{x \cdot a^2}{a \cdot \boldsymbol{(1-x)}} = \dots\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: \(\boldsymbol{:}\) ist dasselbe wir ein Doppelbruchstrich.</p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p></p>]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>68495326</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-df Bruch und Geteilt-Rechnung (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@dividend@}:{@divisor@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Achtung: Auch ein Doppelbruch ;)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>power:rand_with_step(2,4,1); myvars:rand_selection([a,b,c,x,y,z],2); dividend:myvars[1]/myvars[2]; num:rand_with_step(1,5,1); divisor:(num-myvars[1])/(myvars[2]^power); ta1: dividend/divisor; /*wa1 means: multiplied fractions instead of division*/ wa1:dividend*divisor; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:dividend^(-1)*divisor; /*wa3 means: didn’t consider to multiply the denominator of the first fraction with the sum of the second fraction’s numerator as a whole*/ wa3:(num(dividend)*denom(divisor))/(myvars[2]*num-myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@dividend@}:{@divisor@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
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+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
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+ <node>
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+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
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+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
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+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
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+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast den richtigen Kehrwert gebildet um die Brüche dann zu multiplizieren, jedoch hast du dann die Klammersetzung bei der Mutliplikation nicht beachtet.</p><p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{x}{a} : \frac{1-x}{a^2} = \frac{x}{a} \cdot \frac{a^2}{1-x}\)\(= \frac{x \cdot a^2}{a \cdot \boldsymbol{(1-x)}} = \dots\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: \(\boldsymbol{:}\) ist dasselbe wir ein Doppelbruchstrich.</p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p></p>]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>83279259</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-df Bruch und Geteilt-Rechnung (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@dividend@}:{@divisor@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Achtung: Auch ein Doppelbruch ;)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>power:rand_with_step(2,4,1); myvars:rand_selection([a,b,c,x,y,z],2); dividend:myvars[1]/myvars[2]; num:rand_with_step(1,5,1); divisor:(num-myvars[1])/(myvars[2]^power); ta1: dividend/divisor; /*wa1 means: multiplied fractions instead of division*/ wa1:dividend*divisor; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:dividend^(-1)*divisor; /*wa3 means: didn’t consider to multiply the denominator of the first fraction with the sum of the second fraction’s numerator as a whole*/ wa3:(num(dividend)*denom(divisor))/(myvars[2]*num-myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@dividend@}:{@divisor@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
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+ <variantsselectionseed/>
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+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
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+ <insertstars>5</insertstars>
+ <syntaxhint/>
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+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
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+ <mustverify>1</mustverify>
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+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
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+ <node>
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+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
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+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
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+ <tans>ta1</tans>
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+ <truepenalty/>
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+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
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+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
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+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast den richtigen Kehrwert gebildet um die Brüche dann zu multiplizieren, jedoch hast du dann die Klammersetzung bei der Mutliplikation nicht beachtet.</p><p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{x}{a} : \frac{1-x}{a^2} = \frac{x}{a} \cdot \frac{a^2}{1-x}\)\(= \frac{x \cdot a^2}{a \cdot \boldsymbol{(1-x)}} = \dots\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: \(\boldsymbol{:}\) ist dasselbe wir ein Doppelbruchstrich.</p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p></p>]]></text>
+</truefeedback>
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+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1848999895</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-df Bruch und Geteilt-Rechnung (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\({@dividend@}:{@divisor@} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Achtung: Auch ein Doppelbruch ;)</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>power:rand_with_step(2,4,1); myvars:rand_selection([a,b,c,x,y,z],2); dividend:myvars[1]/myvars[2]; num:rand_with_step(1,5,1); divisor:(num-myvars[1])/(myvars[2]^power); ta1: dividend/divisor; /*wa1 means: multiplied fractions instead of division*/ wa1:dividend*divisor; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:dividend^(-1)*divisor; /*wa3 means: didn’t consider to multiply the denominator of the first fraction with the sum of the second fraction’s numerator as a whole*/ wa3:(num(dividend)*denom(divisor))/(myvars[2]*num-myvars[1]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@dividend@}:{@divisor@} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
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+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
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+ <node>
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+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
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+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
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+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
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+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
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+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
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+<falseanswernote>prt1-4-F</falseanswernote>
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+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast den richtigen Kehrwert gebildet um die Brüche dann zu multiplizieren, jedoch hast du dann die Klammersetzung bei der Mutliplikation nicht beachtet.</p><p>Wenn Brüche multipliziert werden, werden die Summen als Ganzes multipliziert.</p><p>Beispiel: \(\frac{x}{a} : \frac{1-x}{a^2} = \frac{x}{a} \cdot \frac{a^2}{1-x}\)\(= \frac{x \cdot a^2}{a \cdot \boldsymbol{(1-x)}} = \dots\)</p>]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: \(\boldsymbol{:}\) ist dasselbe wir ein Doppelbruchstrich.</p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{1}{3}}{\frac{3}{5}} = \frac{1}{3} \cdot \frac{5}{3} = \frac{5}{9}\)</p></p>]]></text>
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+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1656521999</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dg Doppelbruch mit Zahlen und Variablen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:rand_selection(makelist(i+1,i,3),2); nums:rand_selection(makelist(i+1,i,4),2); myvars:rand_selection([a,b,c,x,y,z],2); fractions:[nums[1]/myvars[1]^powers[1], (nums[2]*myvars[2]^powers[2])/myvars[1]]; fractions:random_permutation(fractions); ta1:fractions[1]/fractions[2]; /*wa1 means: multiplied fractions instead of division*/ wa1:fractions[1]*fractions[2]; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:fractions[1]^(-1)*fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
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+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
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+ <node>
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+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
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+ <falsescore>0</falsescore>
+ <falsepenalty/>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
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+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
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+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
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+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
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+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
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+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{2}{a^2}}{\frac{3\,b^2}{a}} = \frac{2}{a^2} \cdot \frac{a}{3\,b^2} = \frac{2\,a}{3\,a^2\,b^2}\)</p></p>]]></text>
+</truefeedback>
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+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1783639635</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dg Doppelbruch mit Zahlen und Variablen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:rand_selection(makelist(i+1,i,3),2); nums:rand_selection(makelist(i+1,i,4),2); myvars:rand_selection([a,b,c,x,y,z],2); fractions:[nums[1]/myvars[1]^powers[1], (nums[2]*myvars[2]^powers[2])/myvars[1]]; fractions:random_permutation(fractions); ta1:fractions[1]/fractions[2]; /*wa1 means: multiplied fractions instead of division*/ wa1:fractions[1]*fractions[2]; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:fractions[1]^(-1)*fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
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+ <boxsize>15</boxsize>
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+ <options/>
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+ <prt>
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+ <truepenalty/>
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+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
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+ <falsescore>0</falsescore>
+ <falsepenalty/>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
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+ <truepenalty/>
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+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
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+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
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+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
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+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
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+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{2}{a^2}}{\frac{3\,b^2}{a}} = \frac{2}{a^2} \cdot \frac{a}{3\,b^2} = \frac{2\,a}{3\,a^2\,b^2}\)</p></p>]]></text>
+</truefeedback>
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+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>863915904</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dg Doppelbruch mit Zahlen und Variablen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:rand_selection(makelist(i+1,i,3),2); nums:rand_selection(makelist(i+1,i,4),2); myvars:rand_selection([a,b,c,x,y,z],2); fractions:[nums[1]/myvars[1]^powers[1], (nums[2]*myvars[2]^powers[2])/myvars[1]]; fractions:random_permutation(fractions); ta1:fractions[1]/fractions[2]; /*wa1 means: multiplied fractions instead of division*/ wa1:fractions[1]*fractions[2]; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:fractions[1]^(-1)*fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{2}{a^2}}{\frac{3\,b^2}{a}} = \frac{2}{a^2} \cdot \frac{a}{3\,b^2} = \frac{2\,a}{3\,a^2\,b^2}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>446314797</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dg Doppelbruch mit Zahlen und Variablen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:rand_selection(makelist(i+1,i,3),2); nums:rand_selection(makelist(i+1,i,4),2); myvars:rand_selection([a,b,c,x,y,z],2); fractions:[nums[1]/myvars[1]^powers[1], (nums[2]*myvars[2]^powers[2])/myvars[1]]; fractions:random_permutation(fractions); ta1:fractions[1]/fractions[2]; /*wa1 means: multiplied fractions instead of division*/ wa1:fractions[1]*fractions[2]; /*wa2 means: multiplicative inversed the dividend instead of the divisor*/ wa2:fractions[1]^(-1)*fractions[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{{@fractions[1]@}}{{@fractions[2]@}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>3</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Wenn zwei Brüche dividiert werden, wird der erste Bruch (Dividend) mit dem Kehrwert des zweiten Bruchs (Divisor) multipliziert.</p><p>Beispiel: \(\large\frac{\frac{2}{a^2}}{\frac{3\,b^2}{a}} = \frac{2}{a^2} \cdot \frac{a}{3\,b^2} = \frac{2\,a}{3\,a^2\,b^2}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1562297660</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dh Doppelbruch mit Termen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8), 3); nums:sort(nums); myvars:rand_selection([a,b,c,x,y,z],2); terms:[nums[1]*((1-myvars[1])/myvars[2]), (nums[2]/nums[3])*(myvars[2]^2/myvars[1])]; /*terms:random_permutation(terms);*/ ta1:terms[1]/terms[2]; taalt:combine(expand(ta1)); /*wa1 means: didn't consider to multiple first factor in the numerator with both summands of the fraction's numerator*/ wa1:((nums[1]*1-myvars[1])/myvars[2])/terms[2]; wa2:terms[1]*terms[2]; wa3:terms[1]^(-1)*terms[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Beim Multiplizieren des Faktors {@nums[1]@} und des Bruchs \(\frac{1-{@myvars[1]@}}{{@myvars[2]@}}\) im Zähler des Doppelbruchs musst du beachten, dass Summen als Ganzes multipliziert werden.</p><p>Beispiel: \(5 \cdot \frac{1-a}{b} = \frac{5 \cdot \boldsymbol{(1-a)}}{b} = \dots\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>5</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>5</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-6-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-6-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Lösungsweg für eine Beispielaufgabe:</p><p>\(\large\frac{5 \cdot \frac{1-a}{b}}{\frac{1}{3} \cdot \frac{b^2}{a}}\)\(\large = \frac{\frac{5 \cdot \boldsymbol{(1-a)}}{b}}{\frac{b^2}{3\,a}} = \frac{5 - 5\,a}{b} \cdot \frac{3\,a}{b^2}\)</p><p>\(\large = \frac{3\,a \cdot \boldsymbol{(5-5\,a)}}{b \cdot b^2} = \frac{15\,a - 15\,a^2}{b^3}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>611281053</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dh Doppelbruch mit Termen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8), 3); nums:sort(nums); myvars:rand_selection([a,b,c,x,y,z],2); terms:[nums[1]*((1-myvars[1])/myvars[2]), (nums[2]/nums[3])*(myvars[2]^2/myvars[1])]; /*terms:random_permutation(terms);*/ ta1:terms[1]/terms[2]; taalt:combine(expand(ta1)); /*wa1 means: didn't consider to multiple first factor in the numerator with both summands of the fraction's numerator*/ wa1:((nums[1]*1-myvars[1])/myvars[2])/terms[2]; wa2:terms[1]*terms[2]; wa3:terms[1]^(-1)*terms[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Beim Multiplizieren des Faktors {@nums[1]@} und des Bruchs \(\frac{1-{@myvars[1]@}}{{@myvars[2]@}}\) im Zähler des Doppelbruchs musst du beachten, dass Summen als Ganzes multipliziert werden.</p><p>Beispiel: \(5 \cdot \frac{1-a}{b} = \frac{5 \cdot \boldsymbol{(1-a)}}{b} = \dots\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>5</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>5</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-6-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-6-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Lösungsweg für eine Beispielaufgabe:</p><p>\(\large\frac{5 \cdot \frac{1-a}{b}}{\frac{1}{3} \cdot \frac{b^2}{a}}\)\(\large = \frac{\frac{5 \cdot \boldsymbol{(1-a)}}{b}}{\frac{b^2}{3\,a}} = \frac{5 - 5\,a}{b} \cdot \frac{3\,a}{b^2}\)</p><p>\(\large = \frac{3\,a \cdot \boldsymbol{(5-5\,a)}}{b \cdot b^2} = \frac{15\,a - 15\,a^2}{b^3}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>439766047</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dh Doppelbruch mit Termen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8), 3); nums:sort(nums); myvars:rand_selection([a,b,c,x,y,z],2); terms:[nums[1]*((1-myvars[1])/myvars[2]), (nums[2]/nums[3])*(myvars[2]^2/myvars[1])]; /*terms:random_permutation(terms);*/ ta1:terms[1]/terms[2]; taalt:combine(expand(ta1)); /*wa1 means: didn't consider to multiple first factor in the numerator with both summands of the fraction's numerator*/ wa1:((nums[1]*1-myvars[1])/myvars[2])/terms[2]; wa2:terms[1]*terms[2]; wa3:terms[1]^(-1)*terms[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Beim Multiplizieren des Faktors {@nums[1]@} und des Bruchs \(\frac{1-{@myvars[1]@}}{{@myvars[2]@}}\) im Zähler des Doppelbruchs musst du beachten, dass Summen als Ganzes multipliziert werden.</p><p>Beispiel: \(5 \cdot \frac{1-a}{b} = \frac{5 \cdot \boldsymbol{(1-a)}}{b} = \dots\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>5</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>5</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-6-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-6-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Lösungsweg für eine Beispielaufgabe:</p><p>\(\large\frac{5 \cdot \frac{1-a}{b}}{\frac{1}{3} \cdot \frac{b^2}{a}}\)\(\large = \frac{\frac{5 \cdot \boldsymbol{(1-a)}}{b}}{\frac{b^2}{3\,a}} = \frac{5 - 5\,a}{b} \cdot \frac{3\,a}{b^2}\)</p><p>\(\large = \frac{3\,a \cdot \boldsymbol{(5-5\,a)}}{b \cdot b^2} = \frac{15\,a - 15\,a^2}{b^3}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>725695831</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-dh Doppelbruch mit Termen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Multipliziere bzw. dividiere und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i+1,i,8), 3); nums:sort(nums); myvars:rand_selection([a,b,c,x,y,z],2); terms:[nums[1]*((1-myvars[1])/myvars[2]), (nums[2]/nums[3])*(myvars[2]^2/myvars[1])]; /*terms:random_permutation(terms);*/ ta1:terms[1]/terms[2]; taalt:combine(expand(ta1)); /*wa1 means: didn't consider to multiple first factor in the numerator with both summands of the fraction's numerator*/ wa1:((nums[1]*1-myvars[1])/myvars[2])/terms[2]; wa2:terms[1]*terms[2]; wa3:terms[1]^(-1)*terms[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{{@nums[1]@} \cdot \frac{1-{@myvars[1]@}}{{@myvars[2]@}}}{\frac{@nums[2]@}{{@nums[3]@}} \cdot \frac{{@myvars[2]@}^2}{{@myvars[1]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>999</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>3</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node>
+<name>3</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-4-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Beim Multiplizieren des Faktors {@nums[1]@} und des Bruchs \(\frac{1-{@myvars[1]@}}{{@myvars[2]@}}\) im Zähler des Doppelbruchs musst du beachten, dass Summen als Ganzes multipliziert werden.</p><p>Beispiel: \(5 \cdot \frac{1-a}{b} = \frac{5 \cdot \boldsymbol{(1-a)}}{b} = \dots\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>4</falsenextnode>
+<falseanswernote>prt1-4-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>4</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa2</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-5-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast die Brüche <strong>multipliziert</strong> statt sie zu <strong>dividieren</strong>.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>5</falsenextnode>
+<falseanswernote>prt1-5-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>5</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa3</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-6-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[Du hast den Kehrwert vom ersten Bruch (Dividend) gebildet, allerdings muss man den Kehrwert vom zweiten Bruch (Divisor) bilden und die Brüche dann multiplizieren, um eine Division zu erhalten.]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-6-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Lösungsweg für eine Beispielaufgabe:</p><p>\(\large\frac{5 \cdot \frac{1-a}{b}}{\frac{1}{3} \cdot \frac{b^2}{a}}\)\(\large = \frac{\frac{5 \cdot \boldsymbol{(1-a)}}{b}}{\frac{b^2}{3\,a}} = \frac{5 - 5\,a}{b} \cdot \frac{3\,a}{b^2}\)</p><p>\(\large = \frac{3\,a \cdot \boldsymbol{(5-5\,a)}}{b \cdot b^2} = \frac{15\,a - 15\,a^2}{b^3}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt><deployedseed>1029360039</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ea Bruchrechnung Kombination I (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbrüche und Summanden => Punkt-vor-Strich-Rechnung</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(2,4,1); nums_real_frac:sort(rand_selection(makelist(i,i,9),4)); nums_unreal_frac:sort(rand_selection(makelist(i+3,i,7),6)); main_summand:((nums_real_frac[1])/(nums_real_frac[4]))/((nums_real_frac[2])/(nums_real_frac[3])); summands:[int*(nums_unreal_frac[6]/nums_unreal_frac[1]), ((nums_unreal_frac[5])/(nums_unreal_frac[2]))/((nums_unreal_frac[4])/(nums_unreal_frac[3]))]; ta1:main_summand+summands[1]-summands[2]; wa1:(main_summand+int)*summands[1]/int-summands[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast offensichtlich die Punkt-vor-Strich-Regel nicht beachtet.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6} = \frac{\frac{5}{6}}{\frac{1}{3}}+(2 \cdot \frac{9}{6}) \ne (\frac{\frac{5}{6}}{\frac{1}{3}}+2) \cdot \frac{9}{6}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Jeden Summanden einzeln betrachten und ausrechnen: Doppelbrüche auflösen und zusammenfassen.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6}-\frac{\frac{13}{4}}{\frac{6}{5}} = \frac{5}{6} \cdot \frac{3}{1}+\frac{2}{1} \cdot \frac{9}{6}-\frac{13}{5} \cdot \frac{5}{6}\)</p><p>\(= (\frac{5}{6\mkern-5mu/^2} \cdot \frac{3\mkern-5mu/^1}{1})+(\frac{2\mkern-5mu/^1}{1} \cdot \frac{9}{6\mkern-5mu/^2})-(\frac{13}{5\mkern-5mu/^1} \cdot \frac{5\mkern-5mu/^1}{6})\)</p><p>\(= \frac{5}{2} + \frac{9}{2} - \frac{13}{6} = \frac{5 \cdot 3}{2 \cdot 3} + \frac{9 \cdot 3}{2 \cdot 3} - \frac{13}{6} = \frac{15}{6} + \frac{27}{6} - \frac{13}{6}\)</p><p>\(= \frac{15+27+13}{6} = \frac{55}{6}\)<\p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>2022519868</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ea Bruchrechnung Kombination I (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbrüche und Summanden => Punkt-vor-Strich-Rechnung</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(2,4,1); nums_real_frac:sort(rand_selection(makelist(i,i,9),4)); nums_unreal_frac:sort(rand_selection(makelist(i+3,i,7),6)); main_summand:((nums_real_frac[1])/(nums_real_frac[4]))/((nums_real_frac[2])/(nums_real_frac[3])); summands:[int*(nums_unreal_frac[6]/nums_unreal_frac[1]), ((nums_unreal_frac[5])/(nums_unreal_frac[2]))/((nums_unreal_frac[4])/(nums_unreal_frac[3]))]; ta1:main_summand+summands[1]-summands[2]; wa1:(main_summand+int)*summands[1]/int-summands[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast offensichtlich die Punkt-vor-Strich-Regel nicht beachtet.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6} = \frac{\frac{5}{6}}{\frac{1}{3}}+(2 \cdot \frac{9}{6}) \ne (\frac{\frac{5}{6}}{\frac{1}{3}}+2) \cdot \frac{9}{6}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Jeden Summanden einzeln betrachten und ausrechnen: Doppelbrüche auflösen und zusammenfassen.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6}-\frac{\frac{13}{4}}{\frac{6}{5}} = \frac{5}{6} \cdot \frac{3}{1}+\frac{2}{1} \cdot \frac{9}{6}-\frac{13}{5} \cdot \frac{5}{6}\)</p><p>\(= (\frac{5}{6\mkern-5mu/^2} \cdot \frac{3\mkern-5mu/^1}{1})+(\frac{2\mkern-5mu/^1}{1} \cdot \frac{9}{6\mkern-5mu/^2})-(\frac{13}{5\mkern-5mu/^1} \cdot \frac{5\mkern-5mu/^1}{6})\)</p><p>\(= \frac{5}{2} + \frac{9}{2} - \frac{13}{6} = \frac{5 \cdot 3}{2 \cdot 3} + \frac{9 \cdot 3}{2 \cdot 3} - \frac{13}{6} = \frac{15}{6} + \frac{27}{6} - \frac{13}{6}\)</p><p>\(= \frac{15+27+13}{6} = \frac{55}{6}\)<\p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>2007714528</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ea Bruchrechnung Kombination I (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbrüche und Summanden => Punkt-vor-Strich-Rechnung</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(2,4,1); nums_real_frac:sort(rand_selection(makelist(i,i,9),4)); nums_unreal_frac:sort(rand_selection(makelist(i+3,i,7),6)); main_summand:((nums_real_frac[1])/(nums_real_frac[4]))/((nums_real_frac[2])/(nums_real_frac[3])); summands:[int*(nums_unreal_frac[6]/nums_unreal_frac[1]), ((nums_unreal_frac[5])/(nums_unreal_frac[2]))/((nums_unreal_frac[4])/(nums_unreal_frac[3]))]; ta1:main_summand+summands[1]-summands[2]; wa1:(main_summand+int)*summands[1]/int-summands[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast offensichtlich die Punkt-vor-Strich-Regel nicht beachtet.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6} = \frac{\frac{5}{6}}{\frac{1}{3}}+(2 \cdot \frac{9}{6}) \ne (\frac{\frac{5}{6}}{\frac{1}{3}}+2) \cdot \frac{9}{6}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Jeden Summanden einzeln betrachten und ausrechnen: Doppelbrüche auflösen und zusammenfassen.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6}-\frac{\frac{13}{4}}{\frac{6}{5}} = \frac{5}{6} \cdot \frac{3}{1}+\frac{2}{1} \cdot \frac{9}{6}-\frac{13}{5} \cdot \frac{5}{6}\)</p><p>\(= (\frac{5}{6\mkern-5mu/^2} \cdot \frac{3\mkern-5mu/^1}{1})+(\frac{2\mkern-5mu/^1}{1} \cdot \frac{9}{6\mkern-5mu/^2})-(\frac{13}{5\mkern-5mu/^1} \cdot \frac{5\mkern-5mu/^1}{6})\)</p><p>\(= \frac{5}{2} + \frac{9}{2} - \frac{13}{6} = \frac{5 \cdot 3}{2 \cdot 3} + \frac{9 \cdot 3}{2 \cdot 3} - \frac{13}{6} = \frac{15}{6} + \frac{27}{6} - \frac{13}{6}\)</p><p>\(= \frac{15+27+13}{6} = \frac{55}{6}\)<\p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1652468809</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ea Bruchrechnung Kombination I (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbrüche und Summanden => Punkt-vor-Strich-Rechnung</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(2,4,1); nums_real_frac:sort(rand_selection(makelist(i,i,9),4)); nums_unreal_frac:sort(rand_selection(makelist(i+3,i,7),6)); main_summand:((nums_real_frac[1])/(nums_real_frac[4]))/((nums_real_frac[2])/(nums_real_frac[3])); summands:[int*(nums_unreal_frac[6]/nums_unreal_frac[1]), ((nums_unreal_frac[5])/(nums_unreal_frac[2]))/((nums_unreal_frac[4])/(nums_unreal_frac[3]))]; ta1:main_summand+summands[1]-summands[2]; wa1:(main_summand+int)*summands[1]/int-summands[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(\large\frac{\frac{{@nums_real_frac[1]@}}{{@nums_real_frac[4]@}}}{\frac{{@nums_real_frac[2]@}}{{@nums_real_frac[3]@}}}+{@int@} \cdot \frac{{@nums_unreal_frac[6]@}}{{@nums_unreal_frac[1]@}}-\frac{\frac{{@nums_unreal_frac[5]@}}{{@nums_unreal_frac[2]@}}}{\frac{{@nums_unreal_frac[4]@}}{{@nums_unreal_frac[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast offensichtlich die Punkt-vor-Strich-Regel nicht beachtet.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6} = \frac{\frac{5}{6}}{\frac{1}{3}}+(2 \cdot \frac{9}{6}) \ne (\frac{\frac{5}{6}}{\frac{1}{3}}+2) \cdot \frac{9}{6}\)</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: Jeden Summanden einzeln betrachten und ausrechnen: Doppelbrüche auflösen und zusammenfassen.</p><p>Beispiel: \(\large \frac{\frac{5}{6}}{\frac{1}{3}}+2 \cdot \frac{9}{6}-\frac{\frac{13}{4}}{\frac{6}{5}} = \frac{5}{6} \cdot \frac{3}{1}+\frac{2}{1} \cdot \frac{9}{6}-\frac{13}{5} \cdot \frac{5}{6}\)</p><p>\(= (\frac{5}{6\mkern-5mu/^2} \cdot \frac{3\mkern-5mu/^1}{1})+(\frac{2\mkern-5mu/^1}{1} \cdot \frac{9}{6\mkern-5mu/^2})-(\frac{13}{5\mkern-5mu/^1} \cdot \frac{5\mkern-5mu/^1}{6})\)</p><p>\(= \frac{5}{2} + \frac{9}{2} - \frac{13}{6} = \frac{5 \cdot 3}{2 \cdot 3} + \frac{9 \cdot 3}{2 \cdot 3} - \frac{13}{6} = \frac{15}{6} + \frac{27}{6} - \frac{13}{6}\)</p><p>\(= \frac{15+27+13}{6} = \frac{55}{6}\)<\p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1890021691</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-eb Bruchrechnung Kombination II (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Sorgfältig ausmultiplizieren</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(3,7,1); nums:sort(rand_selection(makelist(i,i,9),6)); factors:[int, (nums[1]/nums[6]+nums[2]/nums[5]), (1-nums[3]/nums[4])]; ta1:factors[1]*factors[2]*factors[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})= {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>999</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Hier hast du zwei Möglichkeiten: Alles sauber ausmultiplizieren oder vor dem Multiplizieren die Klammern ausrechnen (Empfehlung!)</p><p>Beispiel: \(6 \cdot (\frac{3}{4}+\frac{1}{8}) \cdot (1-\frac{1}{4}) = 6 \cdot (\frac{3 \cdot 2}{4 \cdot 2}+\frac{1}{8}) \cdot (\frac{1 \cdot 4}{1 \cdot 4}-\frac{1}{4})\) </p><p>\(= 6 \cdot (\frac{6}{8}+\frac{1}{8}) \cdot (\frac{4}{4}-\frac{1}{4}) = 6 \cdot (\frac{7}{8}) \cdot (\frac{3}{4})\)</p><p>\( = \frac{6}{1} \cdot \frac{7}{8} \cdot \frac{3}{4} = \frac{6\mkern-5mu/^3 \cdot 7 \cdot 3}{1 \cdot 8\mkern-5mu/^4 \cdot 4} = \frac{63}{16}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>382901616</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-eb Bruchrechnung Kombination II (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Sorgfältig ausmultiplizieren</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(3,7,1); nums:sort(rand_selection(makelist(i,i,9),6)); factors:[int, (nums[1]/nums[6]+nums[2]/nums[5]), (1-nums[3]/nums[4])]; ta1:factors[1]*factors[2]*factors[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})= {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>999</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Hier hast du zwei Möglichkeiten: Alles sauber ausmultiplizieren oder vor dem Multiplizieren die Klammern ausrechnen (Empfehlung!)</p><p>Beispiel: \(6 \cdot (\frac{3}{4}+\frac{1}{8}) \cdot (1-\frac{1}{4}) = 6 \cdot (\frac{3 \cdot 2}{4 \cdot 2}+\frac{1}{8}) \cdot (\frac{1 \cdot 4}{1 \cdot 4}-\frac{1}{4})\) </p><p>\(= 6 \cdot (\frac{6}{8}+\frac{1}{8}) \cdot (\frac{4}{4}-\frac{1}{4}) = 6 \cdot (\frac{7}{8}) \cdot (\frac{3}{4})\)</p><p>\( = \frac{6}{1} \cdot \frac{7}{8} \cdot \frac{3}{4} = \frac{6\mkern-5mu/^3 \cdot 7 \cdot 3}{1 \cdot 8\mkern-5mu/^4 \cdot 4} = \frac{63}{16}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1683089904</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-eb Bruchrechnung Kombination II (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Sorgfältig ausmultiplizieren</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(3,7,1); nums:sort(rand_selection(makelist(i,i,9),6)); factors:[int, (nums[1]/nums[6]+nums[2]/nums[5]), (1-nums[3]/nums[4])]; ta1:factors[1]*factors[2]*factors[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})= {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>999</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Hier hast du zwei Möglichkeiten: Alles sauber ausmultiplizieren oder vor dem Multiplizieren die Klammern ausrechnen (Empfehlung!)</p><p>Beispiel: \(6 \cdot (\frac{3}{4}+\frac{1}{8}) \cdot (1-\frac{1}{4}) = 6 \cdot (\frac{3 \cdot 2}{4 \cdot 2}+\frac{1}{8}) \cdot (\frac{1 \cdot 4}{1 \cdot 4}-\frac{1}{4})\) </p><p>\(= 6 \cdot (\frac{6}{8}+\frac{1}{8}) \cdot (\frac{4}{4}-\frac{1}{4}) = 6 \cdot (\frac{7}{8}) \cdot (\frac{3}{4})\)</p><p>\( = \frac{6}{1} \cdot \frac{7}{8} \cdot \frac{3}{4} = \frac{6\mkern-5mu/^3 \cdot 7 \cdot 3}{1 \cdot 8\mkern-5mu/^4 \cdot 4} = \frac{63}{16}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>724792720</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-eb Bruchrechnung Kombination II (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})=\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Sorgfältig ausmultiplizieren</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(3,7,1); nums:sort(rand_selection(makelist(i,i,9),6)); factors:[int, (nums[1]/nums[6]+nums[2]/nums[5]), (1-nums[3]/nums[4])]; ta1:factors[1]*factors[2]*factors[3];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@factors[1]@}\cdot(\frac{{@nums[1]@}}{{@nums[6]@}}+\frac{{@nums[2]@}}{{@nums[5]@}})\cdot (1-\frac{{@nums[3]@}}{{@nums[4]@}})= {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>999</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Hier hast du zwei Möglichkeiten: Alles sauber ausmultiplizieren oder vor dem Multiplizieren die Klammern ausrechnen (Empfehlung!)</p><p>Beispiel: \(6 \cdot (\frac{3}{4}+\frac{1}{8}) \cdot (1-\frac{1}{4}) = 6 \cdot (\frac{3 \cdot 2}{4 \cdot 2}+\frac{1}{8}) \cdot (\frac{1 \cdot 4}{1 \cdot 4}-\frac{1}{4})\) </p><p>\(= 6 \cdot (\frac{6}{8}+\frac{1}{8}) \cdot (\frac{4}{4}-\frac{1}{4}) = 6 \cdot (\frac{7}{8}) \cdot (\frac{3}{4})\)</p><p>\( = \frac{6}{1} \cdot \frac{7}{8} \cdot \frac{3}{4} = \frac{6\mkern-5mu/^3 \cdot 7 \cdot 3}{1 \cdot 8\mkern-5mu/^4 \cdot 4} = \frac{63}{16}\)</p></p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>857106597</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ec Bruchrechnung Kombination III (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch und gemischter Bruch vs. unechter Bruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(2,4,1); myvar:rand_selection([a,b,c,x,y,z],1)[1]; nums:sort(rand_selection(makelist(i,i,9),6)); summands:[(int+(nums[1]/nums[4]))*(myvar/nums[5]),1-((nums[6]-myvar)/((nums[4])/(nums[3])))]; ta1:combine(expand(summands[1]+summands[2])); wa1:(int*(nums[1]/nums[4]))*(myvar/nums[5])+summands[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast offenbar den gemischten Bruch \({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\) als Multiplikation \({@int@} \cdot \frac{{@nums[1]@}}{{@nums[4]@}}\) interpretiert. Allerdings meint der gemischte Bruch hier \({@int@}\) Ganze und \(\frac{{@nums[1]@}}{{@nums[4]@}}\) Anteil. Empfehlung: Gemischte Brüche als unechte Brüche umschreiben. Beispiel:\(2\frac{1}{6} = 2+\frac{1}{6} = \frac{2 \cdot 6}{1 \cdot 6} + \frac{1}{6} = \frac{12}{6}+\frac{1}{6} = \frac{13}{6}\)]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: \(\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}}\) ist auch ein Doppelbruch.</p><p>Achte darauf, dann die Klammer richtig zu setzen.</p><p>Beispiel: \(\frac{2-a}{\frac{7}{8}} = \boldsymbol{(}2-a\boldsymbol{)} \cdot \frac{8}{7}\)</p><p>Beachte: 1) Ganze Zahlen zum Bruch umschreiben. 2) Doppelbrüche umschreiben (Beispiel oben). 3) Gemischte Brüche umschreiben (Beispiel \(2\frac{1}{6}\) sind \(\frac{13}{6}\;\)). 4) Punkt-vor-Strich-Regel.</p>]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>2024587341</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ec Bruchrechnung Kombination III (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch und gemischter Bruch vs. unechter Bruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(2,4,1); myvar:rand_selection([a,b,c,x,y,z],1)[1]; nums:sort(rand_selection(makelist(i,i,9),6)); summands:[(int+(nums[1]/nums[4]))*(myvar/nums[5]),1-((nums[6]-myvar)/((nums[4])/(nums[3])))]; ta1:combine(expand(summands[1]+summands[2])); wa1:(int*(nums[1]/nums[4]))*(myvar/nums[5])+summands[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
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+ <checkanswertype>0</checkanswertype>
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+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
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+ <falsescore>0</falsescore>
+ <falsepenalty/>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast offenbar den gemischten Bruch \({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\) als Multiplikation \({@int@} \cdot \frac{{@nums[1]@}}{{@nums[4]@}}\) interpretiert. Allerdings meint der gemischte Bruch hier \({@int@}\) Ganze und \(\frac{{@nums[1]@}}{{@nums[4]@}}\) Anteil. Empfehlung: Gemischte Brüche als unechte Brüche umschreiben. Beispiel:\(2\frac{1}{6} = 2+\frac{1}{6} = \frac{2 \cdot 6}{1 \cdot 6} + \frac{1}{6} = \frac{12}{6}+\frac{1}{6} = \frac{13}{6}\)]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
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+<truescoremode>+</truescoremode>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: \(\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}}\) ist auch ein Doppelbruch.</p><p>Achte darauf, dann die Klammer richtig zu setzen.</p><p>Beispiel: \(\frac{2-a}{\frac{7}{8}} = \boldsymbol{(}2-a\boldsymbol{)} \cdot \frac{8}{7}\)</p><p>Beachte: 1) Ganze Zahlen zum Bruch umschreiben. 2) Doppelbrüche umschreiben (Beispiel oben). 3) Gemischte Brüche umschreiben (Beispiel \(2\frac{1}{6}\) sind \(\frac{13}{6}\;\)). 4) Punkt-vor-Strich-Regel.</p>]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>1597148134</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ec Bruchrechnung Kombination III (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch und gemischter Bruch vs. unechter Bruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(2,4,1); myvar:rand_selection([a,b,c,x,y,z],1)[1]; nums:sort(rand_selection(makelist(i,i,9),6)); summands:[(int+(nums[1]/nums[4]))*(myvar/nums[5]),1-((nums[6]-myvar)/((nums[4])/(nums[3])))]; ta1:combine(expand(summands[1]+summands[2])); wa1:(int*(nums[1]/nums[4]))*(myvar/nums[5])+summands[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
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+ <options/>
+ </input>
+ <prt>
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+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
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+ <text/>
+ </feedbackvariables>
+ <node>
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+ <tans>ta1</tans>
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+ <truescoremode>=</truescoremode>
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+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
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+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
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+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
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+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast offenbar den gemischten Bruch \({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\) als Multiplikation \({@int@} \cdot \frac{{@nums[1]@}}{{@nums[4]@}}\) interpretiert. Allerdings meint der gemischte Bruch hier \({@int@}\) Ganze und \(\frac{{@nums[1]@}}{{@nums[4]@}}\) Anteil. Empfehlung: Gemischte Brüche als unechte Brüche umschreiben. Beispiel:\(2\frac{1}{6} = 2+\frac{1}{6} = \frac{2 \cdot 6}{1 \cdot 6} + \frac{1}{6} = \frac{12}{6}+\frac{1}{6} = \frac{13}{6}\)]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
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+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: \(\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}}\) ist auch ein Doppelbruch.</p><p>Achte darauf, dann die Klammer richtig zu setzen.</p><p>Beispiel: \(\frac{2-a}{\frac{7}{8}} = \boldsymbol{(}2-a\boldsymbol{)} \cdot \frac{8}{7}\)</p><p>Beachte: 1) Ganze Zahlen zum Bruch umschreiben. 2) Doppelbrüche umschreiben (Beispiel oben). 3) Gemischte Brüche umschreiben (Beispiel \(2\frac{1}{6}\) sind \(\frac{13}{6}\;\)). 4) Punkt-vor-Strich-Regel.</p>]]></text>
+</truefeedback>
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+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>899831950</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t1_fra Bruchrechnung</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t1-01-ec Bruchrechnung Kombination III (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Berechne und fasse soweit wie möglich zusammen.</p>
+<p>\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} =\)[[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Achtung: Doppelbruch und gemischter Bruch vs. unechter Bruch</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>int:rand_with_step(2,4,1); myvar:rand_selection([a,b,c,x,y,z],1)[1]; nums:sort(rand_selection(makelist(i,i,9),6)); summands:[(int+(nums[1]/nums[4]))*(myvar/nums[5]),1-((nums[6]-myvar)/((nums[4])/(nums[3])))]; ta1:combine(expand(summands[1]+summands[2])); wa1:(int*(nums[1]/nums[4]))*(myvar/nums[5])+summands[2];</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\cdot\frac{{@myvar@}}{{@nums[5]@}}+1-\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}} = {@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
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+ </input>
+ <prt>
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+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>999</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+<name>2</name>
+<answertest>AlgEquiv</answertest>
+<sans>ans1</sans>
+<tans>wa1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>999</truenextnode>
+<trueanswernote>prt1-3-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p>Du hast offenbar den gemischten Bruch \({@int@}\frac{{@nums[1]@}}{{@nums[4]@}}\) als Multiplikation \({@int@} \cdot \frac{{@nums[1]@}}{{@nums[4]@}}\) interpretiert. Allerdings meint der gemischte Bruch hier \({@int@}\) Ganze und \(\frac{{@nums[1]@}}{{@nums[4]@}}\) Anteil. Empfehlung: Gemischte Brüche als unechte Brüche umschreiben. Beispiel:\(2\frac{1}{6} = 2+\frac{1}{6} = \frac{2 \cdot 6}{1 \cdot 6} + \frac{1}{6} = \frac{12}{6}+\frac{1}{6} = \frac{13}{6}\)]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>999</falsenextnode>
+<falseanswernote>prt1-3-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node><node>
+<name>999</name>
+<answertest>AlgEquiv</answertest>
+<sans>1</sans>
+<tans>1</tans>
+<testoptions/>
+<quiet>0</quiet>
+<truescoremode>+</truescoremode>
+<truescore>0</truescore>
+<truepenalty/>
+<truenextnode>-1</truenextnode>
+<trueanswernote>prt1-1000-T</trueanswernote>
+<truefeedback format="html">
+ <text><![CDATA[<p><p>Tipp: \(\frac{{@nums[6]@}-{@myvar@}}{\frac{{@nums[4]@}}{{@nums[3]@}}}\) ist auch ein Doppelbruch.</p><p>Achte darauf, dann die Klammer richtig zu setzen.</p><p>Beispiel: \(\frac{2-a}{\frac{7}{8}} = \boldsymbol{(}2-a\boldsymbol{)} \cdot \frac{8}{7}\)</p><p>Beachte: 1) Ganze Zahlen zum Bruch umschreiben. 2) Doppelbrüche umschreiben (Beispiel oben). 3) Gemischte Brüche umschreiben (Beispiel \(2\frac{1}{6}\) sind \(\frac{13}{6}\;\)). 4) Punkt-vor-Strich-Regel.</p>]]></text>
+</truefeedback>
+<falsescoremode>-</falsescoremode>
+<falsescore>0</falsescore>
+<falsepenalty/>
+<falsenextnode>-1</falsenextnode>
+<falseanswernote>prt1-1000-F</falseanswernote>
+<falsefeedback format="html">
+ <text/>
+</falsefeedback>
+</node></prt>
+ <deployedseed>29495097</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-j Binomische Formeln I - Anwendungsaufgabe (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen und faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.</div>
+</div>
+<p></p>
+<p>\(\frac{{@expand(BIN_a[2])@}}{{@expand(BIN_a[3])@}} \cdot {@BIN_a[3]@}\)\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p><br></p>
+<p><br></p></p>
+<p class="hint">Um diese Aufgabe zu lösen, musst du mehrere binomische Formeln anwenden.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>aa:4;
+bb:5;
+c:3;
+d:2;
+
+u:(c*a-d*b)^2;
+ualt:(d*b-c*a)^2;
+v:(aa*a+d*b)^2;
+w:(bb*a-c*b)*(bb*a+c*b);
+
+x:(aa*a-d*b)^2;
+xalt:(d*b-aa*a)^2;
+y:(bb*a+c*b)^2;
+z:(c*a+d*b)*(c*a-d*b);
+
+/*BIN_A:[
+[a1,(2*a+5*b)^2,"\\(\\frac{4\\,a^2+20\\,a\\,b+25\\,b^2}{16\\,a^2-9\\,b^2}\\cdot(4\\,a-3\\,b)\\cdot(4\\,a+3\\,b)\\)"]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];*/
+
+BIN_A:[
+[a1,u,v,ualt],
+[a2,v,w,v],
+[a3,w,u,w],
+[a4,x,y,xalt],
+[a5,y,z,y],
+[a6,z,y,z]
+];
+BIN_a:rand(BIN_A);
+
+ta:BIN_a[2];
+taalt:BIN_a[4];
+
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>534740616</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-j Binomische Formeln I - Anwendungsaufgabe (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen und faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.</div>
+</div>
+<p></p>
+<p>\(\frac{{@expand(BIN_a[2])@}}{{@expand(BIN_a[3])@}} \cdot {@BIN_a[3]@}\)\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p><br></p>
+<p><br></p></p>
+<p class="hint">Um diese Aufgabe zu lösen, musst du mehrere binomische Formeln anwenden.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>aa:4;
+bb:5;
+c:3;
+d:2;
+
+u:(c*a-d*b)^2;
+ualt:(d*b-c*a)^2;
+v:(aa*a+d*b)^2;
+w:(bb*a-c*b)*(bb*a+c*b);
+
+x:(aa*a-d*b)^2;
+xalt:(d*b-aa*a)^2;
+y:(bb*a+c*b)^2;
+z:(c*a+d*b)*(c*a-d*b);
+
+/*BIN_A:[
+[a1,(2*a+5*b)^2,"\\(\\frac{4\\,a^2+20\\,a\\,b+25\\,b^2}{16\\,a^2-9\\,b^2}\\cdot(4\\,a-3\\,b)\\cdot(4\\,a+3\\,b)\\)"]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];*/
+
+BIN_A:[
+[a1,u,v,ualt],
+[a2,v,w,v],
+[a3,w,u,w],
+[a4,x,y,xalt],
+[a5,y,z,y],
+[a6,z,y,z]
+];
+BIN_a:rand(BIN_A);
+
+ta:BIN_a[2];
+taalt:BIN_a[4];
+
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>47766652</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-j Binomische Formeln I - Anwendungsaufgabe (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen und faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.</div>
+</div>
+<p></p>
+<p>\(\frac{{@expand(BIN_a[2])@}}{{@expand(BIN_a[3])@}} \cdot {@BIN_a[3]@}\)\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p><br></p>
+<p><br></p></p>
+<p class="hint">Um diese Aufgabe zu lösen, musst du mehrere binomische Formeln anwenden.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>aa:4;
+bb:5;
+c:3;
+d:2;
+
+u:(c*a-d*b)^2;
+ualt:(d*b-c*a)^2;
+v:(aa*a+d*b)^2;
+w:(bb*a-c*b)*(bb*a+c*b);
+
+x:(aa*a-d*b)^2;
+xalt:(d*b-aa*a)^2;
+y:(bb*a+c*b)^2;
+z:(c*a+d*b)*(c*a-d*b);
+
+/*BIN_A:[
+[a1,(2*a+5*b)^2,"\\(\\frac{4\\,a^2+20\\,a\\,b+25\\,b^2}{16\\,a^2-9\\,b^2}\\cdot(4\\,a-3\\,b)\\cdot(4\\,a+3\\,b)\\)"]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];*/
+
+BIN_A:[
+[a1,u,v,ualt],
+[a2,v,w,v],
+[a3,w,u,w],
+[a4,x,y,xalt],
+[a5,y,z,y],
+[a6,z,y,z]
+];
+BIN_a:rand(BIN_A);
+
+ta:BIN_a[2];
+taalt:BIN_a[4];
+
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1657775726</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-j Binomische Formeln I - Anwendungsaufgabe (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen und faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.</div>
+</div>
+<p></p>
+<p>\(\frac{{@expand(BIN_a[2])@}}{{@expand(BIN_a[3])@}} \cdot {@BIN_a[3]@}\)\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p><p><br></p>
+<p><br></p></p>
+<p class="hint">Um diese Aufgabe zu lösen, musst du mehrere binomische Formeln anwenden.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>aa:4;
+bb:5;
+c:3;
+d:2;
+
+u:(c*a-d*b)^2;
+ualt:(d*b-c*a)^2;
+v:(aa*a+d*b)^2;
+w:(bb*a-c*b)*(bb*a+c*b);
+
+x:(aa*a-d*b)^2;
+xalt:(d*b-aa*a)^2;
+y:(bb*a+c*b)^2;
+z:(c*a+d*b)*(c*a-d*b);
+
+/*BIN_A:[
+[a1,(2*a+5*b)^2,"\\(\\frac{4\\,a^2+20\\,a\\,b+25\\,b^2}{16\\,a^2-9\\,b^2}\\cdot(4\\,a-3\\,b)\\cdot(4\\,a+3\\,b)\\)"]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];*/
+
+BIN_A:[
+[a1,u,v,ualt],
+[a2,v,w,v],
+[a3,w,u,w],
+[a4,x,y,xalt],
+[a5,y,z,y],
+[a6,z,y,z]
+];
+BIN_a:rand(BIN_A);
+
+ta:BIN_a[2];
+taalt:BIN_a[4];
+
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Du kannst noch weiter vereinfachen.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>931829986</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-g Binomische Formeln Ia - Erste binomische Formel (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Um den Bruch aus der Endgegner-Aufgabe zu vereinfachen, musst du binomische Formeln anwenden. Deshalb kommen wir nun zu den binomischen Formeln. Die erste binomische Formel besagt: \((a + b)^2 = a^2 + 2\,a\,b + b^2\;\).</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,(4+b)^2],
+[a2,(5+b)^2],
+[a3,(3+b)^2],
+[a4,(2+b)^2],
+[a5,(3+2*b)^2],
+[a6,(4+2*b)^2]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];
+task:expand(BIN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die erste binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1994312303</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-g Binomische Formeln Ia - Erste binomische Formel (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Um den Bruch aus der Endgegner-Aufgabe zu vereinfachen, musst du binomische Formeln anwenden. Deshalb kommen wir nun zu den binomischen Formeln. Die erste binomische Formel besagt: \((a + b)^2 = a^2 + 2\,a\,b + b^2\;\).</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,(4+b)^2],
+[a2,(5+b)^2],
+[a3,(3+b)^2],
+[a4,(2+b)^2],
+[a5,(3+2*b)^2],
+[a6,(4+2*b)^2]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];
+task:expand(BIN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die erste binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1744518788</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-g Binomische Formeln Ia - Erste binomische Formel (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Um den Bruch aus der Endgegner-Aufgabe zu vereinfachen, musst du binomische Formeln anwenden. Deshalb kommen wir nun zu den binomischen Formeln. Die erste binomische Formel besagt: \((a + b)^2 = a^2 + 2\,a\,b + b^2\;\).</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,(4+b)^2],
+[a2,(5+b)^2],
+[a3,(3+b)^2],
+[a4,(2+b)^2],
+[a5,(3+2*b)^2],
+[a6,(4+2*b)^2]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];
+task:expand(BIN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die erste binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1627526666</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-g Binomische Formeln Ia - Erste binomische Formel (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Um den Bruch aus der Endgegner-Aufgabe zu vereinfachen, musst du binomische Formeln anwenden. Deshalb kommen wir nun zu den binomischen Formeln. Die erste binomische Formel besagt: \((a + b)^2 = a^2 + 2\,a\,b + b^2\;\).</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,(4+b)^2],
+[a2,(5+b)^2],
+[a3,(3+b)^2],
+[a4,(2+b)^2],
+[a5,(3+2*b)^2],
+[a6,(4+2*b)^2]
+];
+BIN_a:rand(BIN_A);
+ta:BIN_a[2];
+task:expand(BIN_a[2]);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die erste binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1566276649</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-h Binomische Formeln Ib - Zweite binomische Formel (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Die zweite binomische Formel besagt:\((a - b)^2 = a^2 - 2\,a\,b + b^2\;\).<!--Diesmal musst du den Term erst umformen, damit er in der richtigen Form erscheint.--><br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:4;
+b:5;
+c:3;
+d:2;
+
+e:1;
+f:2;
+
+BIN_A:[
+[a1,a,e],
+[a2,b,e],
+[a3,c,e],
+[a4,d,e],
+[a5,a,f],
+[a6,c,f]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]-BIN_a[3]*y)^2;
+taalt:(BIN_a[3]*y-BIN_a[2])^2;
+task:expand(ta);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>893674818</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-h Binomische Formeln Ib - Zweite binomische Formel (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Die zweite binomische Formel besagt:\((a - b)^2 = a^2 - 2\,a\,b + b^2\;\).<!--Diesmal musst du den Term erst umformen, damit er in der richtigen Form erscheint.--><br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:4;
+b:5;
+c:3;
+d:2;
+
+e:1;
+f:2;
+
+BIN_A:[
+[a1,a,e],
+[a2,b,e],
+[a3,c,e],
+[a4,d,e],
+[a5,a,f],
+[a6,c,f]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]-BIN_a[3]*y)^2;
+taalt:(BIN_a[3]*y-BIN_a[2])^2;
+task:expand(ta);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>675538571</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-h Binomische Formeln Ib - Zweite binomische Formel (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Die zweite binomische Formel besagt:\((a - b)^2 = a^2 - 2\,a\,b + b^2\;\).<!--Diesmal musst du den Term erst umformen, damit er in der richtigen Form erscheint.--><br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:4;
+b:5;
+c:3;
+d:2;
+
+e:1;
+f:2;
+
+BIN_A:[
+[a1,a,e],
+[a2,b,e],
+[a3,c,e],
+[a4,d,e],
+[a5,a,f],
+[a6,c,f]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]-BIN_a[3]*y)^2;
+taalt:(BIN_a[3]*y-BIN_a[2])^2;
+task:expand(ta);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>985713485</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-h Binomische Formeln Ib - Zweite binomische Formel (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Die zweite binomische Formel besagt:\((a - b)^2 = a^2 - 2\,a\,b + b^2\;\).<!--Diesmal musst du den Term erst umformen, damit er in der richtigen Form erscheint.--><br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:4;
+b:5;
+c:3;
+d:2;
+
+e:1;
+f:2;
+
+BIN_A:[
+[a1,a,e],
+[a2,b,e],
+[a3,c,e],
+[a4,d,e],
+[a5,a,f],
+[a6,c,f]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]-BIN_a[3]*y)^2;
+taalt:(BIN_a[3]*y-BIN_a[2])^2;
+task:expand(ta);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die zweite binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1039647874</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-i Binomische Formeln Ic - Dritte binomische Formel (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Die dritte binomische Formel besagt: \((a + b)\,(a - b) = a^2 - b^2\;\).<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>aa:4;
+bb:5;
+c:3;
+d:2;
+
+
+BIN_A:[
+[a1,aa,bb],
+[a2,c,d],
+[a3,d,aa],
+[a4,d,bb],
+[a5,d,c],
+[a6,aa,c]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]*x-BIN_a[3]*y)*(BIN_a[2]*x+BIN_a[3]*y);
+task:expand(ta);
+wa:(BIN_a[2]^2*x-BIN_a[3]^2*y)*(BIN_a[2]^2*x+BIN_a[3]^2*y);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die dritte binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast zwar die Unbekannten x und y korrekt faktorisiert, aber die sie begleitenden Faktoren unverändert in die Klammern geschrieben. Um diese korrekt zu faktorisieren, musst du ihre Wurzeln berechnen. Richtig wäre {@ta@}.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>455750255</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-i Binomische Formeln Ic - Dritte binomische Formel (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Die dritte binomische Formel besagt: \((a + b)\,(a - b) = a^2 - b^2\;\).<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>aa:4;
+bb:5;
+c:3;
+d:2;
+
+
+BIN_A:[
+[a1,aa,bb],
+[a2,c,d],
+[a3,d,aa],
+[a4,d,bb],
+[a5,d,c],
+[a6,aa,c]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]*x-BIN_a[3]*y)*(BIN_a[2]*x+BIN_a[3]*y);
+task:expand(ta);
+wa:(BIN_a[2]^2*x-BIN_a[3]^2*y)*(BIN_a[2]^2*x+BIN_a[3]^2*y);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die dritte binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast zwar die Unbekannten x und y korrekt faktorisiert, aber die sie begleitenden Faktoren unverändert in die Klammern geschrieben. Um diese korrekt zu faktorisieren, musst du ihre Wurzeln berechnen. Richtig wäre {@ta@}.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>970764179</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-i Binomische Formeln Ic - Dritte binomische Formel (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Die dritte binomische Formel besagt: \((a + b)\,(a - b) = a^2 - b^2\;\).<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>aa:4;
+bb:5;
+c:3;
+d:2;
+
+
+BIN_A:[
+[a1,aa,bb],
+[a2,c,d],
+[a3,d,aa],
+[a4,d,bb],
+[a5,d,c],
+[a6,aa,c]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]*x-BIN_a[3]*y)*(BIN_a[2]*x+BIN_a[3]*y);
+task:expand(ta);
+wa:(BIN_a[2]^2*x-BIN_a[3]^2*y)*(BIN_a[2]^2*x+BIN_a[3]^2*y);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die dritte binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast zwar die Unbekannten x und y korrekt faktorisiert, aber die sie begleitenden Faktoren unverändert in die Klammern geschrieben. Um diese korrekt zu faktorisieren, musst du ihre Wurzeln berechnen. Richtig wäre {@ta@}.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1971560923</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-i Binomische Formeln Ic - Dritte binomische Formel (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<p></p>
+<p></p>
+<p></p>
+<div>
+ <div>Faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Die dritte binomische Formel besagt: \((a + b)\,(a - b) = a^2 - b^2\;\).<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>aa:4;
+bb:5;
+c:3;
+d:2;
+
+
+BIN_A:[
+[a1,aa,bb],
+[a2,c,d],
+[a3,d,aa],
+[a4,d,bb],
+[a5,d,c],
+[a6,aa,c]
+];
+BIN_a:rand(BIN_A);
+ta:(BIN_a[2]*x-BIN_a[3]*y)*(BIN_a[2]*x+BIN_a[3]*y);
+task:expand(ta);
+wa:(BIN_a[2]^2*x-BIN_a[3]^2*y)*(BIN_a[2]^2*x+BIN_a[3]^2*y);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du hast die dritte binomische Formel angewendet.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast zwar die Unbekannten x und y korrekt faktorisiert, aber die sie begleitenden Faktoren unverändert in die Klammern geschrieben. Um diese korrekt zu faktorisieren, musst du ihre Wurzeln berechnen. Richtig wäre {@ta@}.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>987956614</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-k Bruchrechenregeln Ig2 - Bruch mit binomischem Term erweitern 2 (copy) (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen und faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Dies ist der Endgegner zur Mathe-Welt <strong>Bruchrechenregeln und binomische Formeln</strong>. Wenn du diese Aufgabe schaffst, hast du diese Welt schon gemeistert. Wende zuerst die binomischen Formeln an, um die Nenner zu vereinfachen. Um die Brüche dann zu addieren, musst du mit einem Term erweitern.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;
+b:3;
+c:4;
+
+aa:x-a;
+bb:x-b;
+cc:x-c;
+
+/*FRA_A:[
+[a1,(x^2-3)/(x^2-4),"\\(\\frac{x + 3}{x^2 - 4} + \\frac{x - 3}{x - 2}\\)",(x^2-3)/((x+2)*(x-2))]
+];*/
+
+FRA_A:[
+[a1,aa, a],
+[a2,bb, b],
+[a3,cc, c]
+];
+FRA_a:rand(FRA_A);
+task:(3*FRA_a[3]*x+FRA_a[3]^2)/expand(FRA_a[2]^2)+x/FRA_a[2];
+ta:(x+FRA_a[3])^2/(FRA_a[2])^2;
+
+simp:false;
+taalt:((x+FRA_a[3])/(FRA_a[2]))^2;
+simp:true;
+
+wa1:expand((x+FRA_a[3])^2)/(FRA_a[2])^2;
+wa2:(x+FRA_a[3])^2/expand((FRA_a[2])^2);
+wa3:expand((x+FRA_a[3])^2)/expand(FRA_a[2]^2);
+wa4:(3*FRA_a[3]*x+FRA_a[3]^2)/expand(FRA_a[2]^2)+x^2/FRA_a[2]^2; /*naively expanded fraction by squaring numerator and denominator*/
+wa5:(3*FRA_a[3]*x+FRA_a[3]^2+x)/(expand(FRA_a[2]^2)+FRA_a[2]); /*naively summed fractions, keeping the denominators*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@FRA_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>2</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die erste binomische Formel an, um den Zähler zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa2</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die zweite binomische Formel an, um den Nenner zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>4</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa3</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die erste binomische Formel an, um den Zähler zu faktorisieren und
+ wende die zweite binomische Formel an, um den Nenner zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa4</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich den zweiten Summanden mit sich selbst multipliziert (quadriert), damit die Nenner gleich sind. Allerdings wird ein Bruch so nicht erweitert. Der quadrierte Bruch ist nicht mehr äquivalent mit dem vorherigen Bruch. Beispiel: \((\frac{2}{5})^2 = \frac{4}{25} \ne \frac{2}{5}\;\) wohingegen \(\frac{2}{5} = \frac{2 \cdot 5}{5 \cdot 5} = \frac{10}{25}\;\). Bitte überlege erneut, womit der zweite Summand erweitert werden muss, damit die Nenner gleich sind.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa5</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich die beiden Brüche addiert, indem du Zähler plus Zähler (oben) und Nenner plus Nenner (unten) gerechnet hast. So können Brüche nicht addiert werden. Beispiel: \( \frac{1}{2} + \frac{1}{4} \ne \frac{1+1}{2+4}\;\) . Brüche müssen so erweitert werden, dass sie den gleichen Nenner haben. Dann können die Zähler addiert werden: \(\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}\).</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>2099085786</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-k Bruchrechenregeln Ig2 - Bruch mit binomischem Term erweitern 2 (copy) (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen und faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Dies ist der Endgegner zur Mathe-Welt <strong>Bruchrechenregeln und binomische Formeln</strong>. Wenn du diese Aufgabe schaffst, hast du diese Welt schon gemeistert. Wende zuerst die binomischen Formeln an, um die Nenner zu vereinfachen. Um die Brüche dann zu addieren, musst du mit einem Term erweitern.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;
+b:3;
+c:4;
+
+aa:x-a;
+bb:x-b;
+cc:x-c;
+
+/*FRA_A:[
+[a1,(x^2-3)/(x^2-4),"\\(\\frac{x + 3}{x^2 - 4} + \\frac{x - 3}{x - 2}\\)",(x^2-3)/((x+2)*(x-2))]
+];*/
+
+FRA_A:[
+[a1,aa, a],
+[a2,bb, b],
+[a3,cc, c]
+];
+FRA_a:rand(FRA_A);
+task:(3*FRA_a[3]*x+FRA_a[3]^2)/expand(FRA_a[2]^2)+x/FRA_a[2];
+ta:(x+FRA_a[3])^2/(FRA_a[2])^2;
+
+simp:false;
+taalt:((x+FRA_a[3])/(FRA_a[2]))^2;
+simp:true;
+
+wa1:expand((x+FRA_a[3])^2)/(FRA_a[2])^2;
+wa2:(x+FRA_a[3])^2/expand((FRA_a[2])^2);
+wa3:expand((x+FRA_a[3])^2)/expand(FRA_a[2]^2);
+wa4:(3*FRA_a[3]*x+FRA_a[3]^2)/expand(FRA_a[2]^2)+x^2/FRA_a[2]^2; /*naively expanded fraction by squaring numerator and denominator*/
+wa5:(3*FRA_a[3]*x+FRA_a[3]^2+x)/(expand(FRA_a[2]^2)+FRA_a[2]); /*naively summed fractions, keeping the denominators*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@FRA_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>2</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die erste binomische Formel an, um den Zähler zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa2</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die zweite binomische Formel an, um den Nenner zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>4</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa3</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die erste binomische Formel an, um den Zähler zu faktorisieren und
+ wende die zweite binomische Formel an, um den Nenner zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa4</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich den zweiten Summanden mit sich selbst multipliziert (quadriert), damit die Nenner gleich sind. Allerdings wird ein Bruch so nicht erweitert. Der quadrierte Bruch ist nicht mehr äquivalent mit dem vorherigen Bruch. Beispiel: \((\frac{2}{5})^2 = \frac{4}{25} \ne \frac{2}{5}\;\) wohingegen \(\frac{2}{5} = \frac{2 \cdot 5}{5 \cdot 5} = \frac{10}{25}\;\). Bitte überlege erneut, womit der zweite Summand erweitert werden muss, damit die Nenner gleich sind.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa5</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich die beiden Brüche addiert, indem du Zähler plus Zähler (oben) und Nenner plus Nenner (unten) gerechnet hast. So können Brüche nicht addiert werden. Beispiel: \( \frac{1}{2} + \frac{1}{4} \ne \frac{1+1}{2+4}\;\) . Brüche müssen so erweitert werden, dass sie den gleichen Nenner haben. Dann können die Zähler addiert werden: \(\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}\).</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>245667775</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t3_frabin Binom. Formeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t3-01-k Bruchrechenregeln Ig2 - Bruch mit binomischem Term erweitern 2 (copy) (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen und faktorisieren Sie folgenden Term mithilfe der binomischen Formeln.<br></div>
+</div>
+<p></p>
+<p>{@task@}\(\,=\,\) [[input:ans1]][[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p></p>
+<p class="hint">Dies ist der Endgegner zur Mathe-Welt <strong>Bruchrechenregeln und binomische Formeln</strong>. Wenn du diese Aufgabe schaffst, hast du diese Welt schon gemeistert. Wende zuerst die binomischen Formeln an, um die Nenner zu vereinfachen. Um die Brüche dann zu addieren, musst du mit einem Term erweitern.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>a:2;
+b:3;
+c:4;
+
+aa:x-a;
+bb:x-b;
+cc:x-c;
+
+/*FRA_A:[
+[a1,(x^2-3)/(x^2-4),"\\(\\frac{x + 3}{x^2 - 4} + \\frac{x - 3}{x - 2}\\)",(x^2-3)/((x+2)*(x-2))]
+];*/
+
+FRA_A:[
+[a1,aa, a],
+[a2,bb, b],
+[a3,cc, c]
+];
+FRA_a:rand(FRA_A);
+task:(3*FRA_a[3]*x+FRA_a[3]^2)/expand(FRA_a[2]^2)+x/FRA_a[2];
+ta:(x+FRA_a[3])^2/(FRA_a[2])^2;
+
+simp:false;
+taalt:((x+FRA_a[3])/(FRA_a[2]))^2;
+simp:true;
+
+wa1:expand((x+FRA_a[3])^2)/(FRA_a[2])^2;
+wa2:(x+FRA_a[3])^2/expand((FRA_a[2])^2);
+wa3:expand((x+FRA_a[3])^2)/expand(FRA_a[2]^2);
+wa4:(3*FRA_a[3]*x+FRA_a[3]^2)/expand(FRA_a[2]^2)+x^2/FRA_a[2]^2; /*naively expanded fraction by squaring numerator and denominator*/
+wa5:(3*FRA_a[3]*x+FRA_a[3]^2+x)/(expand(FRA_a[2]^2)+FRA_a[2]); /*naively summed fractions, keeping the denominators*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@FRA_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>2</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die erste binomische Formel an, um den Zähler zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa2</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die zweite binomische Formel an, um den Nenner zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>4</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa3</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Wende die erste binomische Formel an, um den Zähler zu faktorisieren und
+ wende die zweite binomische Formel an, um den Nenner zu faktorisieren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>taalt</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa4</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich den zweiten Summanden mit sich selbst multipliziert (quadriert), damit die Nenner gleich sind. Allerdings wird ein Bruch so nicht erweitert. Der quadrierte Bruch ist nicht mehr äquivalent mit dem vorherigen Bruch. Beispiel: \((\frac{2}{5})^2 = \frac{4}{25} \ne \frac{2}{5}\;\) wohingegen \(\frac{2}{5} = \frac{2 \cdot 5}{5 \cdot 5} = \frac{10}{25}\;\). Bitte überlege erneut, womit der zweite Summand erweitert werden muss, damit die Nenner gleich sind.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>wa5</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast offensichtlich die beiden Brüche addiert, indem du Zähler plus Zähler (oben) und Nenner plus Nenner (unten) gerechnet hast. So können Brüche nicht addiert werden. Beispiel: \( \frac{1}{2} + \frac{1}{4} \ne \frac{1+1}{2+4}\;\) . Brüche müssen so erweitert werden, dass sie den gleichen Nenner haben. Dann können die Zähler addiert werden: \(\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}\).</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1806806387</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-a p-q-Formal Ia - Termumformung (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p>Formen Sie den Term so um, dass er in der Form \(x^2+px+q = 0\) erscheint. Sie können dies Zeile für Zeile tun.<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Um die p-q-Formel anzuwenden, müssen wir zunächst den Term in die richtige Form bringen. Um den folgenden Term wie gewünscht umzuformen, subtrahiere und dividiere auf beiden Seiten der Gleichung.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[6*x+3*x^2-2=10,x^2+2*x-4=0],6*x+3*x^2-2=10],
+[a2,[15*x+5*x^2=20,x^2+3*x-4=0],15*x+5*x^2=20],
+[a3,[8*x+2*x^2-2=12,x^2+4*x-7=0],8*x+2*x^2-2=12],
+[a4,[20*x+4*x^2=-16,x^2+5*x+4=0],20*x+4*x^2=-16]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Gut gemacht! Wenn ein Term auf diese Weise umgeformt ist, kannst du mit der p-q-Formel die möglichen Werte für \(x\) bestimmen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Weiter so! Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>last(BIN_a[2])</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint></syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options></options>
+ </input><deployedseed>1126686893</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-a p-q-Formal Ia - Termumformung (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p>Formen Sie den Term so um, dass er in der Form \(x^2+px+q = 0\) erscheint. Sie können dies Zeile für Zeile tun.<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Um die p-q-Formel anzuwenden, müssen wir zunächst den Term in die richtige Form bringen. Um den folgenden Term wie gewünscht umzuformen, subtrahiere und dividiere auf beiden Seiten der Gleichung.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[6*x+3*x^2-2=10,x^2+2*x-4=0],6*x+3*x^2-2=10],
+[a2,[15*x+5*x^2=20,x^2+3*x-4=0],15*x+5*x^2=20],
+[a3,[8*x+2*x^2-2=12,x^2+4*x-7=0],8*x+2*x^2-2=12],
+[a4,[20*x+4*x^2=-16,x^2+5*x+4=0],20*x+4*x^2=-16]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Gut gemacht! Wenn ein Term auf diese Weise umgeformt ist, kannst du mit der p-q-Formel die möglichen Werte für \(x\) bestimmen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Weiter so! Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>last(BIN_a[2])</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint></syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options></options>
+ </input><deployedseed>1832581792</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-a p-q-Formal Ia - Termumformung (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p>Formen Sie den Term so um, dass er in der Form \(x^2+px+q = 0\) erscheint. Sie können dies Zeile für Zeile tun.<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Um die p-q-Formel anzuwenden, müssen wir zunächst den Term in die richtige Form bringen. Um den folgenden Term wie gewünscht umzuformen, subtrahiere und dividiere auf beiden Seiten der Gleichung.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[6*x+3*x^2-2=10,x^2+2*x-4=0],6*x+3*x^2-2=10],
+[a2,[15*x+5*x^2=20,x^2+3*x-4=0],15*x+5*x^2=20],
+[a3,[8*x+2*x^2-2=12,x^2+4*x-7=0],8*x+2*x^2-2=12],
+[a4,[20*x+4*x^2=-16,x^2+5*x+4=0],20*x+4*x^2=-16]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Gut gemacht! Wenn ein Term auf diese Weise umgeformt ist, kannst du mit der p-q-Formel die möglichen Werte für \(x\) bestimmen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Weiter so! Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>last(BIN_a[2])</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint></syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options></options>
+ </input><deployedseed>1406889611</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-a p-q-Formal Ia - Termumformung (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p>Formen Sie den Term so um, dass er in der Form \(x^2+px+q = 0\) erscheint. Sie können dies Zeile für Zeile tun.<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Um die p-q-Formel anzuwenden, müssen wir zunächst den Term in die richtige Form bringen. Um den folgenden Term wie gewünscht umzuformen, subtrahiere und dividiere auf beiden Seiten der Gleichung.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[6*x+3*x^2-2=10,x^2+2*x-4=0],6*x+3*x^2-2=10],
+[a2,[15*x+5*x^2=20,x^2+3*x-4=0],15*x+5*x^2=20],
+[a3,[8*x+2*x^2-2=12,x^2+4*x-7=0],8*x+2*x^2-2=12],
+[a4,[20*x+4*x^2=-16,x^2+5*x+4=0],20*x+4*x^2=-16]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Gut gemacht! Wenn ein Term auf diese Weise umgeformt ist, kannst du mit der p-q-Formel die möglichen Werte für \(x\) bestimmen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Weiter so! Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>last(BIN_a[2])</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint></syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options></options>
+ </input><deployedseed>511391873</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-c p-q-Formel I - Endboss (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p>Bestimmen Sie alle reellen Lösungen der quadratischen Gleichung in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\(= ?\;\). Sie können Ihren Rechenweg angeben.<br></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Forme den Term um und wende dann die p-q-Formel an, um diese Endgegner-Aufgabe zu lösen. Dann bist du mit dieser Mathe-Welt fertig.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[-2*y^2+6*y=4, -2*y^2+6*y-4=0,y^2-3*y-2=0,stackeq(y=3/2+sqrt(9/4-2) nounor y=3/2-sqrt(9/4-2)),y=1 nounor y=2],-2*y^2+6*y=4,y,1,2,y=3/2+sqrt(9/4+2),y=3/2-sqrt(9/4+2)],
+[a2,[2*y^2-16=-4*y,2*y^2+4*y-16=0,y^2+2*y-8=0,stackeq(y=-1+sqrt((1)^2+8) nounor y=-1-sqrt((1)^2+8)),y=-4 nounor y=2],2*y^2-16=-4*y,y,-4,2,y=-1+sqrt((1)^2-8),y=-1-sqrt((1)^2-8)],
+[a3,[-2*d^2+2*d=-24,-2*d^2+2*d+24=0,d^2-d-12=0,d=1/2+sqrt((1/2)^2+12) nounor d=1/2-sqrt((1/2)^2+12),d=-3 nounor d=4],-2*d^2+2*d=-24,d,-3,4,d=1/2+sqrt((1/2)^2-12),d=1/2-sqrt((1/2)^2-12)],
+[a4,[-2*u^2-14*u=24,-2*u^2-14*u-24=0,u^2+7*u+12=0,u=-7/2+sqrt((7/2)^2-12) nounor u=-7/2-sqrt((7/2)^2-12),u=-4 nounor u=-3],-2*u^2-14*u=24,u,-4,-3,u=-7/2+sqrt((7/2)^2+12), u=-7/2-sqrt((7/2)^2+12)]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.</p><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast!
+ Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel
+in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2}
+\boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir="ltr">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir="ltr">Versuche es erneut und gib beide Lösungen an.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast! Offenbar hast du dich beim
+\(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet
+ \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil
+ am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du
+das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr">Außerdem
+ hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel
+ bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+}
+\sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-}
+\sqrt{...}\) gibt.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast!
+ Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>last(BIN_a[2])</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint></syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options></options>
+ </input><deployedseed>1183308849</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-c p-q-Formel I - Endboss (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p>Bestimmen Sie alle reellen Lösungen der quadratischen Gleichung in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\(= ?\;\). Sie können Ihren Rechenweg angeben.<br></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Forme den Term um und wende dann die p-q-Formel an, um diese Endgegner-Aufgabe zu lösen. Dann bist du mit dieser Mathe-Welt fertig.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[-2*y^2+6*y=4, -2*y^2+6*y-4=0,y^2-3*y-2=0,stackeq(y=3/2+sqrt(9/4-2) nounor y=3/2-sqrt(9/4-2)),y=1 nounor y=2],-2*y^2+6*y=4,y,1,2,y=3/2+sqrt(9/4+2),y=3/2-sqrt(9/4+2)],
+[a2,[2*y^2-16=-4*y,2*y^2+4*y-16=0,y^2+2*y-8=0,stackeq(y=-1+sqrt((1)^2+8) nounor y=-1-sqrt((1)^2+8)),y=-4 nounor y=2],2*y^2-16=-4*y,y,-4,2,y=-1+sqrt((1)^2-8),y=-1-sqrt((1)^2-8)],
+[a3,[-2*d^2+2*d=-24,-2*d^2+2*d+24=0,d^2-d-12=0,d=1/2+sqrt((1/2)^2+12) nounor d=1/2-sqrt((1/2)^2+12),d=-3 nounor d=4],-2*d^2+2*d=-24,d,-3,4,d=1/2+sqrt((1/2)^2-12),d=1/2-sqrt((1/2)^2-12)],
+[a4,[-2*u^2-14*u=24,-2*u^2-14*u-24=0,u^2+7*u+12=0,u=-7/2+sqrt((7/2)^2-12) nounor u=-7/2-sqrt((7/2)^2-12),u=-4 nounor u=-3],-2*u^2-14*u=24,u,-4,-3,u=-7/2+sqrt((7/2)^2+12), u=-7/2-sqrt((7/2)^2+12)]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
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+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
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+ <name>prt1</name>
+ <value>1.0000000</value>
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+ </feedbackvariables>
+ <node>
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+ <answertest>EqualComAss</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
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+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
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+ <truepenalty/>
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+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
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+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
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+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.</p><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
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+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast!
+ Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel
+in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2}
+\boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir="ltr">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir="ltr">Versuche es erneut und gib beide Lösungen an.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast! Offenbar hast du dich beim
+\(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet
+ \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil
+ am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du
+das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr">Außerdem
+ hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel
+ bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+}
+\sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-}
+\sqrt{...}\) gibt.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast!
+ Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>last(BIN_a[2])</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint></syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options></options>
+ </input><deployedseed>1817300183</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-c p-q-Formel I - Endboss (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p>Bestimmen Sie alle reellen Lösungen der quadratischen Gleichung in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\(= ?\;\). Sie können Ihren Rechenweg angeben.<br></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Forme den Term um und wende dann die p-q-Formel an, um diese Endgegner-Aufgabe zu lösen. Dann bist du mit dieser Mathe-Welt fertig.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[-2*y^2+6*y=4, -2*y^2+6*y-4=0,y^2-3*y-2=0,stackeq(y=3/2+sqrt(9/4-2) nounor y=3/2-sqrt(9/4-2)),y=1 nounor y=2],-2*y^2+6*y=4,y,1,2,y=3/2+sqrt(9/4+2),y=3/2-sqrt(9/4+2)],
+[a2,[2*y^2-16=-4*y,2*y^2+4*y-16=0,y^2+2*y-8=0,stackeq(y=-1+sqrt((1)^2+8) nounor y=-1-sqrt((1)^2+8)),y=-4 nounor y=2],2*y^2-16=-4*y,y,-4,2,y=-1+sqrt((1)^2-8),y=-1-sqrt((1)^2-8)],
+[a3,[-2*d^2+2*d=-24,-2*d^2+2*d+24=0,d^2-d-12=0,d=1/2+sqrt((1/2)^2+12) nounor d=1/2-sqrt((1/2)^2+12),d=-3 nounor d=4],-2*d^2+2*d=-24,d,-3,4,d=1/2+sqrt((1/2)^2-12),d=1/2-sqrt((1/2)^2-12)],
+[a4,[-2*u^2-14*u=24,-2*u^2-14*u-24=0,u^2+7*u+12=0,u=-7/2+sqrt((7/2)^2-12) nounor u=-7/2-sqrt((7/2)^2-12),u=-4 nounor u=-3],-2*u^2-14*u=24,u,-4,-3,u=-7/2+sqrt((7/2)^2+12), u=-7/2-sqrt((7/2)^2+12)]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.</p><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast!
+ Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel
+in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2}
+\boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir="ltr">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir="ltr">Versuche es erneut und gib beide Lösungen an.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast! Offenbar hast du dich beim
+\(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet
+ \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil
+ am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du
+das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr">Außerdem
+ hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel
+ bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+}
+\sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-}
+\sqrt{...}\) gibt.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast!
+ Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>last(BIN_a[2])</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint></syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options></options>
+ </input><deployedseed>1556042756</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-c p-q-Formel I - Endboss (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p>Bestimmen Sie alle reellen Lösungen der quadratischen Gleichung in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\(= ?\;\). Sie können Ihren Rechenweg angeben.<br></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Forme den Term um und wende dann die p-q-Formel an, um diese Endgegner-Aufgabe zu lösen. Dann bist du mit dieser Mathe-Welt fertig.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[-2*y^2+6*y=4, -2*y^2+6*y-4=0,y^2-3*y-2=0,stackeq(y=3/2+sqrt(9/4-2) nounor y=3/2-sqrt(9/4-2)),y=1 nounor y=2],-2*y^2+6*y=4,y,1,2,y=3/2+sqrt(9/4+2),y=3/2-sqrt(9/4+2)],
+[a2,[2*y^2-16=-4*y,2*y^2+4*y-16=0,y^2+2*y-8=0,stackeq(y=-1+sqrt((1)^2+8) nounor y=-1-sqrt((1)^2+8)),y=-4 nounor y=2],2*y^2-16=-4*y,y,-4,2,y=-1+sqrt((1)^2-8),y=-1-sqrt((1)^2-8)],
+[a3,[-2*d^2+2*d=-24,-2*d^2+2*d+24=0,d^2-d-12=0,d=1/2+sqrt((1/2)^2+12) nounor d=1/2-sqrt((1/2)^2+12),d=-3 nounor d=4],-2*d^2+2*d=-24,d,-3,4,d=1/2+sqrt((1/2)^2-12),d=1/2-sqrt((1/2)^2-12)],
+[a4,[-2*u^2-14*u=24,-2*u^2-14*u-24=0,u^2+7*u+12=0,u=-7/2+sqrt((7/2)^2-12) nounor u=-7/2-sqrt((7/2)^2-12),u=-4 nounor u=-3],-2*u^2-14*u=24,u,-4,-3,u=-7/2+sqrt((7/2)^2+12), u=-7/2-sqrt((7/2)^2+12)]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.</p><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast!
+ Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel
+in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2}
+\boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir="ltr">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir="ltr">Versuche es erneut und gib beide Lösungen an.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast! Offenbar hast du dich beim
+\(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet
+ \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil
+ am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du
+das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr">Außerdem
+ hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel
+ bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+}
+\sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-}
+\sqrt{...}\) gibt.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;"></p><p dir="ltr">Fast!
+ Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p><br><p></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>last(BIN_a[2])</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint></syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options></options>
+ </input><deployedseed>493079990</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-b p-q-Formel Ib - pq-Formel (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p>Bestimmen Sie den Wert der Variable in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\( = ?\;\).<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Erinnerst du dich noch an die pq-Formel? Für \(\;x^2 + p\,x + q = 0\;\) gilt \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\).<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[h^2+3*h-4=0,h=-3/2+sqrt((3/2)^2+4) nounor h=-3/2-sqrt((3/2)^2+4),h=-3/2+sqrt(25/4) nounor h=-3/2-sqrt(25/4),h=-3/2+5/2 nounor h=-3/2-5/2,h=-4 nounor h=1],"\\(h^2+3\\,h-4=0\\)",h,1,-4,h=-3/2+sqrt(9/4-4),h=-3/2-sqrt(9/4-4)],
+[a2,[y^2-2*y-8=0,y=1+sqrt((-1)^2+8) nounor y=1-sqrt((-1)^2+8),y=-2 nounor y=4],"\\(y^2-2\\,y-8=0\\)",y,-2,4,y=1-sqrt(1-8),y=1+sqrt(1-8)],
+[a3,[z^2-4*z-5=0,z=2+sqrt((-2)^2+5) nounor z=2-sqrt((-2)^2+5),z=5 nounor z=-1],"\\(z^2-4\\,z-5=0\\)",z,5,-1,z=2+sqrt(4-5),z=2-sqrt(4-5)],
+[a4,[a^2-10*a+9=0,a=5+sqrt((-5)^2-9) nounor a=5-sqrt((-5)^2-9),a=9 nounor a=1],"\\(a^2-10\\,a+9=0\\)",a,9,1,a=5+sqrt(25+9),a=5-sqrt(25+9)]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr" style="text-align: left;">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2} \boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir="ltr" style="text-align: left;">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir="ltr" style="text-align: left;">Versuche es erneut und gib beide Lösungen an.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr" style="text-align: left;">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\) gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>last(BIN_a[2])</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint></syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options></options>
+ </input><deployedseed>1183616185</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-b p-q-Formel Ib - pq-Formel (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p>Bestimmen Sie den Wert der Variable in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\( = ?\;\).<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Erinnerst du dich noch an die pq-Formel? Für \(\;x^2 + p\,x + q = 0\;\) gilt \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\).<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[h^2+3*h-4=0,h=-3/2+sqrt((3/2)^2+4) nounor h=-3/2-sqrt((3/2)^2+4),h=-3/2+sqrt(25/4) nounor h=-3/2-sqrt(25/4),h=-3/2+5/2 nounor h=-3/2-5/2,h=-4 nounor h=1],"\\(h^2+3\\,h-4=0\\)",h,1,-4,h=-3/2+sqrt(9/4-4),h=-3/2-sqrt(9/4-4)],
+[a2,[y^2-2*y-8=0,y=1+sqrt((-1)^2+8) nounor y=1-sqrt((-1)^2+8),y=-2 nounor y=4],"\\(y^2-2\\,y-8=0\\)",y,-2,4,y=1-sqrt(1-8),y=1+sqrt(1-8)],
+[a3,[z^2-4*z-5=0,z=2+sqrt((-2)^2+5) nounor z=2-sqrt((-2)^2+5),z=5 nounor z=-1],"\\(z^2-4\\,z-5=0\\)",z,5,-1,z=2+sqrt(4-5),z=2-sqrt(4-5)],
+[a4,[a^2-10*a+9=0,a=5+sqrt((-5)^2-9) nounor a=5-sqrt((-5)^2-9),a=9 nounor a=1],"\\(a^2-10\\,a+9=0\\)",a,9,1,a=5+sqrt(25+9),a=5-sqrt(25+9)]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr" style="text-align: left;">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2} \boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir="ltr" style="text-align: left;">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir="ltr" style="text-align: left;">Versuche es erneut und gib beide Lösungen an.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr" style="text-align: left;">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\) gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>last(BIN_a[2])</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint></syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options></options>
+ </input><deployedseed>1771539896</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-b p-q-Formel Ib - pq-Formel (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p>Bestimmen Sie den Wert der Variable in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\( = ?\;\).<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Erinnerst du dich noch an die pq-Formel? Für \(\;x^2 + p\,x + q = 0\;\) gilt \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\).<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[h^2+3*h-4=0,h=-3/2+sqrt((3/2)^2+4) nounor h=-3/2-sqrt((3/2)^2+4),h=-3/2+sqrt(25/4) nounor h=-3/2-sqrt(25/4),h=-3/2+5/2 nounor h=-3/2-5/2,h=-4 nounor h=1],"\\(h^2+3\\,h-4=0\\)",h,1,-4,h=-3/2+sqrt(9/4-4),h=-3/2-sqrt(9/4-4)],
+[a2,[y^2-2*y-8=0,y=1+sqrt((-1)^2+8) nounor y=1-sqrt((-1)^2+8),y=-2 nounor y=4],"\\(y^2-2\\,y-8=0\\)",y,-2,4,y=1-sqrt(1-8),y=1+sqrt(1-8)],
+[a3,[z^2-4*z-5=0,z=2+sqrt((-2)^2+5) nounor z=2-sqrt((-2)^2+5),z=5 nounor z=-1],"\\(z^2-4\\,z-5=0\\)",z,5,-1,z=2+sqrt(4-5),z=2-sqrt(4-5)],
+[a4,[a^2-10*a+9=0,a=5+sqrt((-5)^2-9) nounor a=5-sqrt((-5)^2-9),a=9 nounor a=1],"\\(a^2-10\\,a+9=0\\)",a,9,1,a=5+sqrt(25+9),a=5-sqrt(25+9)]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
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+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr" style="text-align: left;">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2} \boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir="ltr" style="text-align: left;">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir="ltr" style="text-align: left;">Versuche es erneut und gib beide Lösungen an.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr" style="text-align: left;">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\) gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>last(BIN_a[2])</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint></syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options></options>
+ </input><deployedseed>1420701792</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t4_pq pq-Formel</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t4-01-b p-q-Formel Ib - pq-Formel (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p>Bestimmen Sie den Wert der Variable in der Form {@BIN_a[4]@}\( = ? \mbox{ or }\) {@BIN_a[4]@}\( = ?\;\).<br></p>
+<p></p>
+<p></p>
+<p>{@BIN_a[3]@}<br></p>
+<p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Erinnerst du dich noch an die pq-Formel? Für \(\;x^2 + p\,x + q = 0\;\) gilt \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\).<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>BIN_A:[
+[a1,[h^2+3*h-4=0,h=-3/2+sqrt((3/2)^2+4) nounor h=-3/2-sqrt((3/2)^2+4),h=-3/2+sqrt(25/4) nounor h=-3/2-sqrt(25/4),h=-3/2+5/2 nounor h=-3/2-5/2,h=-4 nounor h=1],"\\(h^2+3\\,h-4=0\\)",h,1,-4,h=-3/2+sqrt(9/4-4),h=-3/2-sqrt(9/4-4)],
+[a2,[y^2-2*y-8=0,y=1+sqrt((-1)^2+8) nounor y=1-sqrt((-1)^2+8),y=-2 nounor y=4],"\\(y^2-2\\,y-8=0\\)",y,-2,4,y=1-sqrt(1-8),y=1+sqrt(1-8)],
+[a3,[z^2-4*z-5=0,z=2+sqrt((-2)^2+5) nounor z=2-sqrt((-2)^2+5),z=5 nounor z=-1],"\\(z^2-4\\,z-5=0\\)",z,5,-1,z=2+sqrt(4-5),z=2-sqrt(4-5)],
+[a4,[a^2-10*a+9=0,a=5+sqrt((-5)^2-9) nounor a=5-sqrt((-5)^2-9),a=9 nounor a=1],"\\(a^2-10\\,a+9=0\\)",a,9,1,a=5+sqrt(25+9),a=5-sqrt(25+9)]
+];
+
+BIN_a:rand(BIN_A);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@BIN_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>last(BIN_a[2])</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>2</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>10</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-11-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>11</falsenextnode>
+ <falseanswernote>prt1-11-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>11</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>12</truenextnode>
+ <trueanswernote>prt1-12-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-12-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>12</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-13-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm
+\sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\)
+ gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr" style="text-align: left;">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der
+p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2}
+\boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-13-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>2</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-3-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>3</falsenextnode>
+ <falseanswernote>prt1-3-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>3</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>4</truenextnode>
+ <trueanswernote>prt1-4-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>5</falsenextnode>
+ <falseanswernote>prt1-4-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>4</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-5-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Du hast nur eine von zwei richtigen Lösungen angegeben. Vor der Wurzel in der p-q-Formel steht ein \(\pm\)-Symbol: \(x= -\frac{p}{2} \boldsymbol{\pm} \sqrt{(\frac{p}{2})^2-q}\;\).</p><p dir="ltr" style="text-align: left;">Das bedeutet, dass es eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{+} \sqrt{(\frac{p}{2})^2-q}\)<br>und eine Lösung mit<br>\(x = -\frac{p}{2} \boldsymbol{-} \sqrt{(\frac{p}{2})^2-q}\)<br>für \(x\) gibt.</p><p dir="ltr" style="text-align: left;">Versuche es erneut und gib beide Lösungen an.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-5-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>5</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5] nounor BIN_a[4]=-1*BIN_a[6] </tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-6-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem Vorzeichen vertan. Die p-q-Formel lautet \(\;x= \boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>6</falsenextnode>
+ <falseanswernote>prt1-6-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>6</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[5]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-7-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>7</falsenextnode>
+ <falseanswernote>prt1-7-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>7</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[4]=-1*BIN_a[6]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>8</truenextnode>
+ <trueanswernote>prt1-8-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-8-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>8</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>1</sans>
+ <tans>1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-9-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Offenbar hast du dich beim \(p\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x=
+\boldsymbol{-}\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2-q}\;\). Weil am
+Anfang mit \(\boldsymbol{-}\frac{p}{2}\) gerechnet wird, musst du das
+Vorzeichen von \(p\) in \(x^2 + p\,x + q = 0\;\) umkehren.</p><p dir="ltr" style="text-align: left;">Außerdem hast du nur eine Lösung angegeben. Das \(\pm\)-Symbol in der p-q-Formel bedeutet, dass es eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{+} \sqrt{...}\) und eine Lösung mit \(x=-\frac{p}{2} \boldsymbol{-} \sqrt{...}\) gibt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>9</falsenextnode>
+ <falseanswernote>prt1-9-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>9</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>last([ans1])</sans>
+ <tans>BIN_a[7] nounor BIN_a[8]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-10-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Fast! Offenbar hast du dich beim \(q\) in der p-q-Formel mit dem
+Vorzeichen vertan. Die p-q-Formel lautet \(\;x= -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2\boldsymbol{-}q}\;\). Weil in der Wurzel mit \(-q\) gerechnet wird, musst du das
+Vorzeichen von \(q\) in \(x^2 + p\,x + q = 0\;\) umkehren.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>10</falsenextnode>
+ <falseanswernote>prt1-10-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>last(BIN_a[2])</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint></syntaxhint>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>0</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options></options>
+ </input><deployedseed>1009534997</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-f Potenzrechenregeln I - Endboss (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie folgenden Ausdruck; hierbei sind \(x,y \in \mathbb{R_{> 0}}\).</div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Dies ist die Endgegner-Aufgabe dieser Mathe-Welt <strong>Potenzrechenrelgen</strong>. Wenn du diese Aufgabe schaffst, hast du diese Mathe-Welt gemeistert. Viel Erfolg!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,stackeq(y^(-1/6)),"\\(\\frac{1}{\\sqrt[3]{y \\, \\sqrt x}} \\, \\sqrt[6]{x \\, y}\\)"],
+[a2,a^20*x^8,"\\(\\left( \\frac{a^3 x^5}{a^{-2} x^3} \\right)^4\\)"]
+];
+RUL_a:rand(RUL_A);
+
+/*ans1 is evaluated by ev(ans1,simp) to accept e. g. 1/(y^(1/6)) and y^(-1/6) and y^(-(1/6))*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ev(ans1,simp)</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1167231517</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-f Potenzrechenregeln I - Endboss (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie folgenden Ausdruck; hierbei sind \(x,y \in \mathbb{R_{> 0}}\).</div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Dies ist die Endgegner-Aufgabe dieser Mathe-Welt <strong>Potenzrechenrelgen</strong>. Wenn du diese Aufgabe schaffst, hast du diese Mathe-Welt gemeistert. Viel Erfolg!</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,stackeq(y^(-1/6)),"\\(\\frac{1}{\\sqrt[3]{y \\, \\sqrt x}} \\, \\sqrt[6]{x \\, y}\\)"],
+[a2,a^20*x^8,"\\(\\left( \\frac{a^3 x^5}{a^{-2} x^3} \\right)^4\\)"]
+];
+RUL_a:rand(RUL_A);
+
+/*ans1 is evaluated by ev(ans1,simp) to accept e. g. 1/(y^(1/6)) and y^(-1/6) and y^(-(1/6))*/</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ev(ans1,simp)</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1313491755</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-a Potenzrechenregeln Ia – Exponenten addieren (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Fangen wir damit an, die Exponenten zu addieren, wenn die Basis gleich ist und multipliziert wird.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^a*c^b,"\\(c^{\\,a}\\cdot c^{\\,b}\\)"],
+[a2,x^a*x^b,"\\(x^{\\,a}\\cdot x^{\\,b}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1724483596</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-a Potenzrechenregeln Ia – Exponenten addieren (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Fangen wir damit an, die Exponenten zu addieren, wenn die Basis gleich ist und multipliziert wird.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^a*c^b,"\\(c^{\\,a}\\cdot c^{\\,b}\\)"],
+[a2,x^a*x^b,"\\(x^{\\,a}\\cdot x^{\\,b}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>337440314</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-b Potenzrechenregeln Ib – Exponenten subtrahieren (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Das funktioniert auch in die andere Richtung.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^a/c^b,"\\(\\frac{c^{\\,a}}{c^{\\,b}}\\)"],
+[a2,x^a/x^b,"\\(\\frac{x^{\\,a}}{x^{\\,b}}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>29351489</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-b Potenzrechenregeln Ib – Exponenten subtrahieren (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Das funktioniert auch in die andere Richtung.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^a/c^b,"\\(\\frac{c^{\\,a}}{c^{\\,b}}\\)"],
+[a2,x^a/x^b,"\\(\\frac{x^{\\,a}}{x^{\\,b}}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1996084793</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-c Potenzrechenregeln Ic - Wurzel als Potenz darstellen (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Stellen Sie den Ausdruck in der Form \(c^{\frac{1}{n}}\) dar.<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Mithilfe von Potenzen der Form \(c^{\frac{1}{n}}\) lässt sich die n-te Wurzel von \(c\), also \(\;\sqrt[n]{c}\;\), darstellen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(1/6),"\\(\\sqrt[6]{c}\\)"],
+[a2,c^(1/5),"\\(\\sqrt[5]{c}\\)"],
+[a3,c^(1/4),"\\(\\sqrt[4]{c}\\)"],
+[a4,c^(1/3),"\\(\\sqrt[3]{c}\\)"],
+[a5,c^(1/7),"\\(\\sqrt[7]{c}\\)"],
+[a6,c^(1/8),"\\(\\sqrt[8]{c}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Sie können noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1074873352</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-c Potenzrechenregeln Ic - Wurzel als Potenz darstellen (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Stellen Sie den Ausdruck in der Form \(c^{\frac{1}{n}}\) dar.<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Mithilfe von Potenzen der Form \(c^{\frac{1}{n}}\) lässt sich die n-te Wurzel von \(c\), also \(\;\sqrt[n]{c}\;\), darstellen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(1/6),"\\(\\sqrt[6]{c}\\)"],
+[a2,c^(1/5),"\\(\\sqrt[5]{c}\\)"],
+[a3,c^(1/4),"\\(\\sqrt[4]{c}\\)"],
+[a4,c^(1/3),"\\(\\sqrt[3]{c}\\)"],
+[a5,c^(1/7),"\\(\\sqrt[7]{c}\\)"],
+[a6,c^(1/8),"\\(\\sqrt[8]{c}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Sie können noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>460473552</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-c Potenzrechenregeln Ic - Wurzel als Potenz darstellen (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Stellen Sie den Ausdruck in der Form \(c^{\frac{1}{n}}\) dar.<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Mithilfe von Potenzen der Form \(c^{\frac{1}{n}}\) lässt sich die n-te Wurzel von \(c\), also \(\;\sqrt[n]{c}\;\), darstellen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(1/6),"\\(\\sqrt[6]{c}\\)"],
+[a2,c^(1/5),"\\(\\sqrt[5]{c}\\)"],
+[a3,c^(1/4),"\\(\\sqrt[4]{c}\\)"],
+[a4,c^(1/3),"\\(\\sqrt[3]{c}\\)"],
+[a5,c^(1/7),"\\(\\sqrt[7]{c}\\)"],
+[a6,c^(1/8),"\\(\\sqrt[8]{c}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Sie können noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>771365681</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-c Potenzrechenregeln Ic - Wurzel als Potenz darstellen (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Stellen Sie den Ausdruck in der Form \(c^{\frac{1}{n}}\) dar.<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Mithilfe von Potenzen der Form \(c^{\frac{1}{n}}\) lässt sich die n-te Wurzel von \(c\), also \(\;\sqrt[n]{c}\;\), darstellen.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(1/6),"\\(\\sqrt[6]{c}\\)"],
+[a2,c^(1/5),"\\(\\sqrt[5]{c}\\)"],
+[a3,c^(1/4),"\\(\\sqrt[4]{c}\\)"],
+[a4,c^(1/3),"\\(\\sqrt[3]{c}\\)"],
+[a5,c^(1/7),"\\(\\sqrt[7]{c}\\)"],
+[a6,c^(1/8),"\\(\\sqrt[8]{c}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Sie können noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1250006169</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-d Potenzrechenregeln Id – Exponenten multiplizieren (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Wird ein Ausdruck, der eine Potenz enthält, potenziert, lassen sich die Exponenten miteinander multiplizieren.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(a*b),"\\((c^a)^b\\)",c^a*b],
+[a2,x^(a*b),"\\((x^a)^b\\)",x^a*b]
+];
+RUL_a:rand(RUL_A);
+wa:RUL_a[4];
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast die Klammer falsch gesetzt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1495340815</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-d Potenzrechenregeln Id – Exponenten multiplizieren (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>
+ <div>Vereinfachen Sie soweit wie möglich:<br></div>
+</div>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p></p>
+<p class="hint">Wird ein Ausdruck, der eine Potenz enthält, potenziert, lassen sich die Exponenten miteinander multiplizieren.<br></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(a*b),"\\((c^a)^b\\)",c^a*b],
+[a2,x^(a*b),"\\((x^a)^b\\)",x^a*b]
+];
+RUL_a:rand(RUL_A);
+wa:RUL_a[4];
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>wa</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du hast die Klammer falsch gesetzt.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1196787611</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-e Potenzrechenregeln Ie - Potenzrechenregeln anwenden (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>Nutzen Sie die Potenzrechenregeln, um folgenden Ausdruck zu vereinfachen.<br></div>
+<p>
+</p>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p>
+<div class="bubble in-modal no-arrow">
+ <div>Hier zur Erinnerung die wichtigsten Potenzrechenregeln. Für \(x, y \neq 0\) und \(n, m \in \mathbb{Z}\) gilt:</div>
+<div>
+ <div>
+ <div>
+ <ul>
+ <li>\(x^{n+m} = x^n\,x^m\;\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \(2^5 = 2^{2+3} = 2^2 \cdot 2^3 = 4 \cdot 8 = 32\)</span></div></li></ul><ul>
+ <li>
+ <div>
+ <div>\(\left( x^n \right)^m = x^{n\,m}\;\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \(\left( 2^2 \right)^3 = 2^6 = 64\)</span></div></div>
+ </div>
+ </li>
+ <li>
+ <div>
+ <div>
+ <div>
+ <div>\((x\,y)^n = x^n\,y^n\;\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \(6^2 = (2 \cdot 3)^2 = 2^2 \cdot 3^2 = 4 \cdot 9 = 36\)</span></div></div>
+ </div>
+ </div>
+ </div>
+ </li>
+ <li>\(\frac{1}{x^n} = x^{-n}\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \( \frac{1}{x^2} \cdot x^2 = x^{-2} \cdot x^2 = x^{-2+2} = x^0 = 1\)</span><br></div></li>
+ <li>\(\sqrt[n]{x} = x^{\frac{1}{n}}\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \( \sqrt[3]{x} \cdot x^3 = x^{\frac{1}{3}} \cdot x^3 = x^{\frac{1}{3}+3} = x^1 = x\)</span></div></li>
+ </ul>
+ </div>
+ </div>
+</div>
+<p></p>
+<div>
+ <div>
+ <div>
+ <ul></ul>
+ </div>
+ </div>
+</div>
+</div></p>
+<p class="hint">Um diese Aufgabe zu lösen, kannst du mehrere der gerade erläuterten Regeln kombinieren. </p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(13/6),"\\(\\sqrt[6]{c} \\cdot c^2\\)"],
+[a2,x^10,"\\(\\frac{x^5}{x^{-5}}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Richtig, aber du kannst noch weiter vereinfachen.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>1602709371</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t5_rul Potenzrechenregeln</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t5-01-e Potenzrechenregeln Ie - Potenzrechenregeln anwenden (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>
+
+
+<p></p>
+<div>Nutzen Sie die Potenzrechenregeln, um folgenden Ausdruck zu vereinfachen.<br></div>
+<p>
+</p>
+<p></p>
+<p>{@RUL_a[3]@}\(\,=\,\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>
+<p><br></p>
+<div class="bubble in-modal no-arrow">
+ <div>Hier zur Erinnerung die wichtigsten Potenzrechenregeln. Für \(x, y \neq 0\) und \(n, m \in \mathbb{Z}\) gilt:</div>
+<div>
+ <div>
+ <div>
+ <ul>
+ <li>\(x^{n+m} = x^n\,x^m\;\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \(2^5 = 2^{2+3} = 2^2 \cdot 2^3 = 4 \cdot 8 = 32\)</span></div></li></ul><ul>
+ <li>
+ <div>
+ <div>\(\left( x^n \right)^m = x^{n\,m}\;\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \(\left( 2^2 \right)^3 = 2^6 = 64\)</span></div></div>
+ </div>
+ </li>
+ <li>
+ <div>
+ <div>
+ <div>
+ <div>\((x\,y)^n = x^n\,y^n\;\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \(6^2 = (2 \cdot 3)^2 = 2^2 \cdot 3^2 = 4 \cdot 9 = 36\)</span></div></div>
+ </div>
+ </div>
+ </div>
+ </li>
+ <li>\(\frac{1}{x^n} = x^{-n}\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \( \frac{1}{x^2} \cdot x^2 = x^{-2} \cdot x^2 = x^{-2+2} = x^0 = 1\)</span><br></div></li>
+ <li>\(\sqrt[n]{x} = x^{\frac{1}{n}}\)<br><div style="text-align: center;"><span class="" style="font-size: x-small;">Beispiel: \( \sqrt[3]{x} \cdot x^3 = x^{\frac{1}{3}} \cdot x^3 = x^{\frac{1}{3}+3} = x^1 = x\)</span></div></li>
+ </ul>
+ </div>
+ </div>
+</div>
+<p></p>
+<div>
+ <div>
+ <div>
+ <ul></ul>
+ </div>
+ </div>
+</div>
+</div></p>
+<p class="hint">Um diese Aufgabe zu lösen, kannst du mehrere der gerade erläuterten Regeln kombinieren. </p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>RUL_A:[
+[a1,c^(13/6),"\\(\\sqrt[6]{c} \\cdot c^2\\)"],
+[a2,x^10,"\\(\\frac{x^5}{x^{-5}}\\)"]
+];
+RUL_a:rand(RUL_A);
+</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>{@RUL_a[1]@}</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1.0000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-0-T </trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<script>
+ ALQuiz.incrementSolved();
+</script>
+<p dir="ltr" style="text-align: left;"><br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-0-F </falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>RUL_a[2]</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>+</truescoremode>
+ <truescore>0.1000000</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Richtig, aber du kannst noch weiter vereinfachen.</p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0.0000000</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt><input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>RUL_a[2]</tans>
+ <boxsize>20</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>1</requirelowestterms>
+ <checkanswertype>1</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input><deployedseed>547016054</deployedseed></question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-a Ganzzahlige Summanden ableiten (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Leite jeden Summanden einzeln ab.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i,i,10),4); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; exercise:nums[1]*myvar^powers[1]+nums[2]*myvar^powers[2]+nums[3]*myvar+nums[4]; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>351097132</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-a Ganzzahlige Summanden ableiten (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Leite jeden Summanden einzeln ab.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i,i,10),4); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; exercise:nums[1]*myvar^powers[1]+nums[2]*myvar^powers[2]+nums[3]*myvar+nums[4]; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1047509677</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-a Ganzzahlige Summanden ableiten (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Leite jeden Summanden einzeln ab.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i,i,10),4); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; exercise:nums[1]*myvar^powers[1]+nums[2]*myvar^powers[2]+nums[3]*myvar+nums[4]; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>442872926</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-a Ganzzahlige Summanden ableiten (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Leite jeden Summanden einzeln ab.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:rand_selection(makelist(i,i,10),4); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; exercise:nums[1]*myvar^powers[1]+nums[2]*myvar^powers[2]+nums[3]*myvar+nums[4]; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>286970886</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-b Gebrochenrationale Summanden ableiten (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@fractions[1]@} \cdot {@myvar@}^{@powers[1]@}+{@fractions[2]@} \cdot {@myvar@}^{@powers[2]@}+{@fractions[3]@} \cdot {@myvar@}+{@myint@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Leite jeden Summanden einzeln ab.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myint:rand_with_step(1,10,1); numerators:rand_selection(makelist(i+2,i,6),3); denominators:makelist(rand_with_step(numerators[i]+1,numerators[i]+5,1),i,3); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; fractions:makelist(numerators[i]/denominators[i],i,3); exercise:fractions[1]*myvar^powers[1]+fractions[2]*myvar^powers[2]+fractions[3]*myvar+myint; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>857840145</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-b Gebrochenrationale Summanden ableiten (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@fractions[1]@} \cdot {@myvar@}^{@powers[1]@}+{@fractions[2]@} \cdot {@myvar@}^{@powers[2]@}+{@fractions[3]@} \cdot {@myvar@}+{@myint@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Leite jeden Summanden einzeln ab.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myint:rand_with_step(1,10,1); numerators:rand_selection(makelist(i+2,i,6),3); denominators:makelist(rand_with_step(numerators[i]+1,numerators[i]+5,1),i,3); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; fractions:makelist(numerators[i]/denominators[i],i,3); exercise:fractions[1]*myvar^powers[1]+fractions[2]*myvar^powers[2]+fractions[3]*myvar+myint; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1543126498</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-b Gebrochenrationale Summanden ableiten (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@fractions[1]@} \cdot {@myvar@}^{@powers[1]@}+{@fractions[2]@} \cdot {@myvar@}^{@powers[2]@}+{@fractions[3]@} \cdot {@myvar@}+{@myint@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Leite jeden Summanden einzeln ab.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myint:rand_with_step(1,10,1); numerators:rand_selection(makelist(i+2,i,6),3); denominators:makelist(rand_with_step(numerators[i]+1,numerators[i]+5,1),i,3); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; fractions:makelist(numerators[i]/denominators[i],i,3); exercise:fractions[1]*myvar^powers[1]+fractions[2]*myvar^powers[2]+fractions[3]*myvar+myint; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1871228756</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-b Gebrochenrationale Summanden ableiten (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@fractions[1]@} \cdot {@myvar@}^{@powers[1]@}+{@fractions[2]@} \cdot {@myvar@}^{@powers[2]@}+{@fractions[3]@} \cdot {@myvar@}+{@myint@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint">Tipp: Leite jeden Summanden einzeln ab.</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myint:rand_with_step(1,10,1); numerators:rand_selection(makelist(i+2,i,6),3); denominators:makelist(rand_with_step(numerators[i]+1,numerators[i]+5,1),i,3); myvar:rand([a,b,c,x,y,z]); powers:[rand_with_step(3,4,1), 2]; fractions:makelist(numerators[i]/denominators[i],i,3); exercise:fractions[1]*myvar^powers[1]+fractions[2]*myvar^powers[2]+fractions[3]*myvar+myint; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>318121367</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-c Produkte ableiten I (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:rand_selection(makelist(i+1,i,4),2); myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,4),2); exercise:(myvar^powers[1]+nums[1])*(myvar^powers[2]-nums[2]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1213180404</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-c Produkte ableiten I (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:rand_selection(makelist(i+1,i,4),2); myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,4),2); exercise:(myvar^powers[1]+nums[1])*(myvar^powers[2]-nums[2]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1876101711</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-c Produkte ableiten I (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:rand_selection(makelist(i+1,i,4),2); myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,4),2); exercise:(myvar^powers[1]+nums[1])*(myvar^powers[2]-nums[2]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1520468669</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-c Produkte ableiten I (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:rand_selection(makelist(i+1,i,4),2); myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,4),2); exercise:(myvar^powers[1]+nums[1])*(myvar^powers[2]-nums[2]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1233734487</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-d Produkte ableiten II (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>num:rand_with_step(1,5,2); denom:rand_with_step(num+2, num+5,2); fraction:num/denom; nums:rand_selection(append(makelist(i-7,i,6),makelist(i,i,6)),4); myvar:rand([a,b,c,x,y,z]); power:rand([3,4]); exercise:(fraction*myvar+nums[1])*(nums[2]*myvar^power+nums[3]*myvar+nums[4]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>290055394</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-d Produkte ableiten II (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>num:rand_with_step(1,5,2); denom:rand_with_step(num+2, num+5,2); fraction:num/denom; nums:rand_selection(append(makelist(i-7,i,6),makelist(i,i,6)),4); myvar:rand([a,b,c,x,y,z]); power:rand([3,4]); exercise:(fraction*myvar+nums[1])*(nums[2]*myvar^power+nums[3]*myvar+nums[4]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1877259825</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-d Produkte ableiten II (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>num:rand_with_step(1,5,2); denom:rand_with_step(num+2, num+5,2); fraction:num/denom; nums:rand_selection(append(makelist(i-7,i,6),makelist(i,i,6)),4); myvar:rand([a,b,c,x,y,z]); power:rand([3,4]); exercise:(fraction*myvar+nums[1])*(nums[2]*myvar^power+nums[3]*myvar+nums[4]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1027269811</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-d Produkte ableiten II (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde das Produkt und die Faktoren.</p><p>Die Produktregel lautet:</p><p>\(f(x) = u \cdot v \)</p><p>\(f'(x) = u' \cdot v + u \cdot v'\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>num:rand_with_step(1,5,2); denom:rand_with_step(num+2, num+5,2); fraction:num/denom; nums:rand_selection(append(makelist(i-7,i,6),makelist(i,i,6)),4); myvar:rand([a,b,c,x,y,z]); power:rand([3,4]); exercise:(fraction*myvar+nums[1])*(nums[2]*myvar^power+nums[3]*myvar+nums[4]); ta1:diff(exercise,myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1906880472</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-e Division ableiten I (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:[rand_with_step(3,4,1), 2]; nums:rand_selection(makelist(i,i,12),5); myvar:rand([a,b,c,x,y,z]); exercise:(myvar^powers[1]+nums[1]*myvar^powers[2]+myvar)/(nums[2]*myvar^2+nums[3]*myvar+nums[4]); ta1:diff(exercise, myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1439694172</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-e Division ableiten I (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:[rand_with_step(3,4,1), 2]; nums:rand_selection(makelist(i,i,12),5); myvar:rand([a,b,c,x,y,z]); exercise:(myvar^powers[1]+nums[1]*myvar^powers[2]+myvar)/(nums[2]*myvar^2+nums[3]*myvar+nums[4]); ta1:diff(exercise, myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1028579078</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-e Division ableiten I (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:[rand_with_step(3,4,1), 2]; nums:rand_selection(makelist(i,i,12),5); myvar:rand([a,b,c,x,y,z]); exercise:(myvar^powers[1]+nums[1]*myvar^powers[2]+myvar)/(nums[2]*myvar^2+nums[3]*myvar+nums[4]); ta1:diff(exercise, myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1454088108</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-e Division ableiten I (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>powers:[rand_with_step(3,4,1), 2]; nums:rand_selection(makelist(i,i,12),5); myvar:rand([a,b,c,x,y,z]); exercise:(myvar^powers[1]+nums[1]*myvar^powers[2]+myvar)/(nums[2]*myvar^2+nums[3]*myvar+nums[4]); ta1:diff(exercise, myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1063999325</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-f Division ableiten II (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:[rand([3,5,7,11]), rand_with_step(2,5,1)]; myvar:rand([a,b,c,x,y,z]); terms:[sqrt(nums[1])*myvar-nums[2], nums[1]*myvar^2-nums[2]]; terms:random_permutation(terms); exercise:terms[1]/terms[2]; ta1:diff(exercise, myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>525681144</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-f Division ableiten II (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:[rand([3,5,7,11]), rand_with_step(2,5,1)]; myvar:rand([a,b,c,x,y,z]); terms:[sqrt(nums[1])*myvar-nums[2], nums[1]*myvar^2-nums[2]]; terms:random_permutation(terms); exercise:terms[1]/terms[2]; ta1:diff(exercise, myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1447367624</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-f Division ableiten II (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:[rand([3,5,7,11]), rand_with_step(2,5,1)]; myvar:rand([a,b,c,x,y,z]); terms:[sqrt(nums[1])*myvar-nums[2], nums[1]*myvar^2-nums[2]]; terms:random_permutation(terms); exercise:terms[1]/terms[2]; ta1:diff(exercise, myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>435810786</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-f Division ableiten II (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Finde die Division.</p><p>Die Quotientenregel lautet:</p><p>\(f(x) = \frac{u}{v}\)</p><p>\(f'(x) = \frac{u' \cdot v - u \cdot v'}{v^2}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>nums:[rand([3,5,7,11]), rand_with_step(2,5,1)]; myvar:rand([a,b,c,x,y,z]); terms:[sqrt(nums[1])*myvar-nums[2], nums[1]*myvar^2-nums[2]]; terms:random_permutation(terms); exercise:terms[1]/terms[2]; ta1:diff(exercise, myvar); ta1alt:expand(ta1);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>0</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-1-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>=</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>1</falsenextnode><falseanswernote>prt1-1-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>1</name><answertest>EqualComAss</answertest><sans>ans1</sans><tans>ta1alt</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>2</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node><node><name>2</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>0.1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-3-T</trueanswernote><truefeedback format="html"><text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-3-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1421496847</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-g Kettenregel I (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root@}]{{@myvar@}^2-{@num@}}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); root:rand([3,5]); num:rand_with_step(3,9,1); exercise:(myvar^2-num)^(1/root); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1079586531</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-g Kettenregel I (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root@}]{{@myvar@}^2-{@num@}}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); root:rand([3,5]); num:rand_with_step(3,9,1); exercise:(myvar^2-num)^(1/root); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1754291070</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-g Kettenregel I (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root@}]{{@myvar@}^2-{@num@}}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); root:rand([3,5]); num:rand_with_step(3,9,1); exercise:(myvar^2-num)^(1/root); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1751932072</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-g Kettenregel I (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root@}]{{@myvar@}^2-{@num@}}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); root:rand([3,5]); num:rand_with_step(3,9,1); exercise:(myvar^2-num)^(1/root); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt>
+ <name>prt1</name>
+ <value>1.0000000</value>
+ <autosimplify>1</autosimplify>
+ <feedbackstyle>1</feedbackstyle>
+ <feedbackvariables>
+ <text/>
+ </feedbackvariables>
+ <node>
+ <name>0</name>
+ <answertest>EqualComAss</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-1-T</trueanswernote>
+ <truefeedback format="html">
+ <text/>
+ </truefeedback>
+ <falsescoremode>=</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>1</falsenextnode>
+ <falseanswernote>prt1-1-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ <node>
+ <name>1</name>
+ <answertest>AlgEquiv</answertest>
+ <sans>ans1</sans>
+ <tans>ta1</tans>
+ <testoptions/>
+ <quiet>0</quiet>
+ <truescoremode>=</truescoremode>
+ <truescore>0.1</truescore>
+ <truepenalty/>
+ <truenextnode>-1</truenextnode>
+ <trueanswernote>prt1-2-T</trueanswernote>
+ <truefeedback format="html">
+ <text><![CDATA[<p dir="ltr" style="text-align: left;">Du kannst noch weiter vereinfachen.<br></p>]]></text>
+ </truefeedback>
+ <falsescoremode>-</falsescoremode>
+ <falsescore>0</falsescore>
+ <falsepenalty/>
+ <falsenextnode>-1</falsenextnode>
+ <falseanswernote>prt1-2-F</falseanswernote>
+ <falsefeedback format="html">
+ <text/>
+ </falsefeedback>
+ </node>
+ </prt>
+ <deployedseed>1089076165</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-h Kettenregel II (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,5),3); power:rand_with_step(3,7,2); signs:makelist(rand([-1,1]),2); exercise:(nums[1]*myvar^2+signs[1]*nums[2]*myvar+signs[2]*nums[3])^power; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1676415387</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-h Kettenregel II (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,5),3); power:rand_with_step(3,7,2); signs:makelist(rand([-1,1]),2); exercise:(nums[1]*myvar^2+signs[1]*nums[2]*myvar+signs[2]*nums[3])^power; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>146672542</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-h Kettenregel II (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,5),3); power:rand_with_step(3,7,2); signs:makelist(rand([-1,1]),2); exercise:(nums[1]*myvar^2+signs[1]*nums[2]*myvar+signs[2]*nums[3])^power; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1726255949</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-h Kettenregel II (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p class="hint"><p>Tipp: Wann braucht man die Kettenregel?</p><p>Die Kettenregel lautet:</p><p>\(f(x) = u(v(x))\)</p><p>\(f'(x) = u'(v) \cdot v'\)</p><p>Beispiel</p><p>\(f(x) = \sqrt{x^3+1} = (x^3+1)^{\frac{1}{2}}\)</p><p>\(f'(x) = \frac{1}{2} \cdot (x^3+1)^{-\frac{1}{2}} \cdot 3\,x^2\)</p><p>\(= \frac{3\,x^2}{2 \cdot (x^3+1)^{\frac{1}{2}}} = \frac{3\,x^2}{2\,\sqrt{x^3+1}}\)</p></p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,5),3); power:rand_with_step(3,7,2); signs:makelist(rand([-1,1]),2); exercise:(nums[1]*myvar^2+signs[1]*nums[2]*myvar+signs[2]*nums[3])^power; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1628089061</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-i Gemischtes I (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,5),2); nums:rand_selection(makelist(i+1,i,58),2); exercise:(myvar^powers[1]+nums[1])^powers[2]*nums[2]*myvar; ta1:diff(exercise, myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>603470063</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-i Gemischtes I (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,5),2); nums:rand_selection(makelist(i+1,i,58),2); exercise:(myvar^powers[1]+nums[1])^powers[2]*nums[2]*myvar; ta1:diff(exercise, myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1387533043</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-i Gemischtes I (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,5),2); nums:rand_selection(makelist(i+1,i,58),2); exercise:(myvar^powers[1]+nums[1])^powers[2]*nums[2]*myvar; ta1:diff(exercise, myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>820026169</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-i Gemischtes I (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,5),2); nums:rand_selection(makelist(i+1,i,58),2); exercise:(myvar^powers[1]+nums[1])^powers[2]*nums[2]*myvar; ta1:diff(exercise, myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1884036955</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-j Gemischtes II (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,3),3); nums:rand_selection(makelist(i,i,5),2); exercise:(myvar^powers[1]-nums[1])^powers[2]*(myvar+nums[2])^powers[3]; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>949540891</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-j Gemischtes II (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,3),3); nums:rand_selection(makelist(i,i,5),2); exercise:(myvar^powers[1]-nums[1])^powers[2]*(myvar+nums[2])^powers[3]; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>2032277992</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-j Gemischtes II (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,3),3); nums:rand_selection(makelist(i,i,5),2); exercise:(myvar^powers[1]-nums[1])^powers[2]*(myvar+nums[2])^powers[3]; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>504654950</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-j Gemischtes II (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); powers:rand_selection(makelist(i+1,i,3),3); nums:rand_selection(makelist(i,i,5),2); exercise:(myvar^powers[1]-nums[1])^powers[2]*(myvar+nums[2])^powers[3]; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>906697601</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-k Gemischtes III (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); terms:[rand_with_step(1,4,1)+myvar, myvar]; terms:random_permutation(terms); power:rand_with_step(3,7,1); exercise:(terms[1]/terms[2])^power; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1060600269</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-k Gemischtes III (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); terms:[rand_with_step(1,4,1)+myvar, myvar]; terms:random_permutation(terms); power:rand_with_step(3,7,1); exercise:(terms[1]/terms[2])^power; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1317786455</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-k Gemischtes III (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); terms:[rand_with_step(1,4,1)+myvar, myvar]; terms:random_permutation(terms); power:rand_with_step(3,7,1); exercise:(terms[1]/terms[2])^power; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>2016195942</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-k Gemischtes III (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); terms:[rand_with_step(1,4,1)+myvar, myvar]; terms:random_permutation(terms); power:rand_with_step(3,7,1); exercise:(terms[1]/terms[2])^power; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>79640143</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-l Gemischtes IV (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),2); power:rand_with_step(2,6,1); exercise:nums[1]*sqrt(nums[2]*myvar+myvar^power); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>63010318</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-l Gemischtes IV (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),2); power:rand_with_step(2,6,1); exercise:nums[1]*sqrt(nums[2]*myvar+myvar^power); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>2022252790</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-l Gemischtes IV (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),2); power:rand_with_step(2,6,1); exercise:nums[1]*sqrt(nums[2]*myvar+myvar^power); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>2032269463</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-l Gemischtes IV (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),2); power:rand_with_step(2,6,1); exercise:nums[1]*sqrt(nums[2]*myvar+myvar^power); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1301956355</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-m Gemischtes V (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),4); power:rand_with_step(2,5,1); terms:[(nums[1]*myvar+nums[2]), (nums[3]*myvar^power-nums[4])]; terms:random_permutation(terms); exercise:(terms[1]*terms[2])/myvar; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1627444094</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-m Gemischtes V (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),4); power:rand_with_step(2,5,1); terms:[(nums[1]*myvar+nums[2]), (nums[3]*myvar^power-nums[4])]; terms:random_permutation(terms); exercise:(terms[1]*terms[2])/myvar; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>570947981</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-m Gemischtes V (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),4); power:rand_with_step(2,5,1); terms:[(nums[1]*myvar+nums[2]), (nums[3]*myvar^power-nums[4])]; terms:random_permutation(terms); exercise:(terms[1]*terms[2])/myvar; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1123631251</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-m Gemischtes V (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})={@exercise@}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); nums:rand_selection(makelist(i+1,i,8),4); power:rand_with_step(2,5,1); terms:[(nums[1]*myvar+nums[2]), (nums[3]*myvar^power-nums[4])]; terms:random_permutation(terms); exercise:(terms[1]*terms[2])/myvar; ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})={@exercise@}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>566895213</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-n Gemischtes VI (Auto-Generation Variant 1)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); root_power:rand_with_step(3,6,1); power:rand_with_prohib(2,5,[root_power]); nums:rand_selection(makelist(i+2,i,6),2);exercise:(nums[1]*myvar-nums[2])^(power/root_power); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>466316231</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-n Gemischtes VI (Auto-Generation Variant 2)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); root_power:rand_with_step(3,6,1); power:rand_with_prohib(2,5,[root_power]); nums:rand_selection(makelist(i+2,i,6),2);exercise:(nums[1]*myvar-nums[2])^(power/root_power); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>73259082</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-n Gemischtes VI (Auto-Generation Variant 3)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); root_power:rand_with_step(3,6,1); power:rand_with_prohib(2,5,[root_power]); nums:rand_selection(makelist(i+2,i,6),2);exercise:(nums[1]*myvar-nums[2])^(power/root_power); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>253364053</deployedseed> </question>
+
+<question type="category"><category><text>$course$/top/Question Pool Einstiegsakademie/rpg/t7_der Ableitungen</text><info><text/></info></category><idnumber/></question><question type="stack">
+ <name>
+ <text>t7-01-n Gemischtes VI (Auto-Generation Variant 4)</text>
+ </name>
+ <questiontext format="html">
+ <text><![CDATA[<script>window.location.href = document.querySelector("[id*=quiznavbutton]").href; document.addEventListener("DOMContentLoaded", function() { document.querySelectorAll(".back_instruction").forEach(function(elem) { elem.style.display = "block"; }); });</script>
+<p class="back_instruction" style="display:none;">Um zurück zum Spiel zu gelangen, klicken Sie bitte in der Quiz-Navigation auf das erste Element.</p>
+<p>Bestimme die Ableitung von \(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;\).</p>
+<p>\(f’({@myvar@})=\)[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>]]></text>
+ </questiontext>
+ <generalfeedback format="html">
+ <text/>
+ </generalfeedback>
+ <defaultgrade>1.0000000</defaultgrade>
+ <penalty>0.1000000</penalty>
+ <hidden>0</hidden>
+ <idnumber/>
+ <stackversion>
+ <text>2023010400</text>
+ </stackversion>
+ <questionvariables>
+ <text>myvar:rand([a,b,c,x,y,z]); root_power:rand_with_step(3,6,1); power:rand_with_prohib(2,5,[root_power]); nums:rand_selection(makelist(i+2,i,6),2);exercise:(nums[1]*myvar-nums[2])^(power/root_power); ta1:diff(exercise,myvar);</text>
+ </questionvariables>
+ <specificfeedback format="html">
+ <text/>
+ </specificfeedback>
+ <questionnote>
+ <text>\(f({@myvar@})=\sqrt[{@root_power@}]{({@nums[1]@}\,{@myvar@}-{@nums[2]@})^{@power@}}\;f’(x)={@ta1@}\)</text>
+ </questionnote>
+ <questionsimplify>1</questionsimplify>
+ <assumepositive>0</assumepositive>
+ <assumereal>0</assumereal>
+ <prtcorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Richtige Antwort, gut gemacht!]]></text>
+ </prtcorrect>
+ <prtpartiallycorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Die Antwort ist teilweise korrekt.]]></text>
+ </prtpartiallycorrect>
+ <prtincorrect format="html">
+ <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Falsche Antwort.]]></text>
+ </prtincorrect>
+ <multiplicationsign>dot</multiplicationsign>
+ <sqrtsign>1</sqrtsign>
+ <complexno>i</complexno>
+ <inversetrig>cos-1</inversetrig>
+ <logicsymbol>lang</logicsymbol>
+ <matrixparens>[</matrixparens>
+ <variantsselectionseed/>
+ <input>
+ <name>ans1</name>
+ <type>algebraic</type>
+ <tans>ta1</tans>
+ <boxsize>15</boxsize>
+ <strictsyntax>1</strictsyntax>
+ <insertstars>5</insertstars>
+ <syntaxhint/>
+ <syntaxattribute>0</syntaxattribute>
+ <forbidwords/>
+ <allowwords/>
+ <forbidfloat>1</forbidfloat>
+ <requirelowestterms>0</requirelowestterms>
+ <checkanswertype>0</checkanswertype>
+ <mustverify>1</mustverify>
+ <showvalidation>3</showvalidation>
+ <options/>
+ </input>
+ <prt><name>prt1</name><value>1.0000000</value><autosimplify>1</autosimplify><feedbackstyle>1</feedbackstyle><feedbackvariables><text/></feedbackvariables><node><name>1</name><answertest>AlgEquiv</answertest><sans>ans1</sans><tans>ta1</tans><testoptions/><quiet>0</quiet><truescoremode>=</truescoremode><truescore>1</truescore><truepenalty/><truenextnode>-1</truenextnode><trueanswernote>prt1-2-T</trueanswernote><truefeedback format="html"><text/></truefeedback><falsescoremode>-</falsescoremode><falsescore>0</falsescore><falsepenalty/><falsenextnode>-1</falsenextnode><falseanswernote>prt1-2-F</falseanswernote><falsefeedback format="html"><text/></falsefeedback></node></prt><deployedseed>1197047345</deployedseed> </question>
+
+</quiz>
diff --git a/script/alquiz-fantasy-bg-ver3.js b/script/alquiz-fantasy-bg-ver3.js
new file mode 100644
index 0000000000000000000000000000000000000000..05478ab1e73bdeb73e2c327399b6218ccb4005d9
--- /dev/null
+++ b/script/alquiz-fantasy-bg-ver3.js
@@ -0,0 +1,4821 @@
+console.log("here starts alquiz fantasy ver 3");
+
+class GamifiedQuiz {
+ constructor(quizObject) {
+ this.currentQuestionId;
+ this.currentPage;
+ this.Parser = new DOMParser();
+ this.QuestionGroups = {};
+ this.solvedVariants = [];
+ //this.QuestionGroupsById = {};
+ if (quizObject != undefined) {
+ if (quizObject.groups != undefined) {
+ for (let questionGroupId in quizObject.groups) {
+ this.QuestionGroups[questionGroupId] = new QuestionGroup(questionGroupId, quizObject.groups[questionGroupId]);
+ }
+ }
+ let pageCount = 0;
+ if (quizObject.questions != undefined) {
+ for (let questionId in quizObject.questions) {
+ let groupToAddId;
+ if (this.QuestionGroups[quizObject.questions[questionId].group] != undefined) {
+ groupToAddId = quizObject.questions[questionId].group;
+ }
+ else {
+ //try to identify group by token, elsewise add to group "unsorted"
+ if (questionId.indexOf("_") != -1) {
+ let expectedGroupNameMatch = questionId.match(/^(.*)_/);
+ if (expectedGroupNameMatch[1] != undefined && expectedGroupNameMatch[1] != "") {
+ if (this.QuestionGroups[expectedGroupNameMatch[1]] != undefined) {
+ groupToAddId = expectedGroupNameMatch[1];
+ }
+ }
+ }
+ if (groupToAddId == undefined) {
+ if (this.QuestionGroups.unsorted == undefined) {
+ this.QuestionGroups.unsorted = new QuestionGroup("unsorted", "Unsorted Questions");
+ }
+ groupToAddId = "unsorted";
+ }
+ this.QuestionGroups[groupToAddId].addQuestion(new Question(questionId, quizObject.questions[questionId].name));
+ }
+ let ElementToAdd;
+ if (quizObject.questions[questionId].type == "instruction") {
+ ElementToAdd = new Instruction(questionId, quizObject.questions[questionId].name, pageCount, quizObject.questions[questionId].onsuccess, quizObject.questions[questionId].onfailure, quizObject.questions[questionId].BubbleInfo, quizObject.questions[questionId].onpage);
+ }
+ else {
+ ElementToAdd = new Question(questionId, quizObject.questions[questionId].name, pageCount, quizObject.questions[questionId].needs, quizObject.questions[questionId].BubbleInfo, quizObject.questions[questionId].onsuccess, quizObject.questions[questionId].onfailure, quizObject.questions[questionId].askBeforeSkip, quizObject.questions[questionId].onpage, quizObject.questions[questionId].variants, quizObject.questions[questionId].color, quizObject.questions[questionId].filter);
+ }
+ this.QuestionGroups[groupToAddId].addQuestion(ElementToAdd);
+ pageCount = pageCount + 1 + (ElementToAdd.variants > 1 ? ElementToAdd.variants-1 : 0) + (ElementToAdd.questionsOnPage > 1 ? ElementToAdd.questionsOnPage : 0);
+ }
+ }
+ }
+
+ //auto assign onsuccess and onfailure for undefined
+ let groupNames = Object.keys(this.QuestionGroups);
+ let grouplength = groupNames.length;
+ for (let i = 0; i < grouplength; i++) {
+ let questionNames = Object.keys(this.QuestionGroups[groupNames[i]].Questions);
+ let questionlength = questionNames.length;
+ for (let j = 0; j < questionlength; j++) {
+ if (!this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onsuccess || !this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onfailure) {
+ //console.log("something for "+questionNames[j]+" is undefined");
+ //probably next question or next group
+ if (j < questionlength - 1) {
+ //next question
+ if(this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onsuccess == undefined) {
+ this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onsuccess = questionNames[j + 1];
+ }
+ if(this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onfailure == undefined) {
+ this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onfailure = questionNames[j + 1];
+ }
+ } else if (i < grouplength - 1) {
+ //console.log(questionNames[j] + " leads to next group onsuccess ");
+ //first question of next group
+ if(this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onsuccess == undefined) {
+ this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onsuccess = Object.keys(this.QuestionGroups[groupNames[i + 1]].Questions)[0];
+ }
+ if(this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onfailure == undefined) {
+ this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onfailure = Object.keys(this.QuestionGroups[groupNames[i + 1]].Questions)[0];
+ }
+ } else {
+ //console.log("no other group");
+ if(this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onsuccess == undefined) {
+ this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onsuccess = "_finish";
+ }
+ if(this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onfailure == undefined) {
+ this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onfailure = "_finish";
+ }
+ }
+ }
+
+ /*if (!this.QuestionGroups[groupNames[i]].Questions[Object.keys(this.QuestionGroups[groupNames[i]].Questions)[j]].onfailure) {
+ //You may want to lead users to the first question of next group, assuming, that they are not able to solve the next (harder) question unless they are not able to solve the current (easier) question.
+ if (i < grouplength - 1) {
+ //console.log(Object.keys(this.QuestionGroups[groupNames[i]].Questions)[j] + " leads to next group onfailure ");
+ this.QuestionGroups[groupNames[i]].Questions[Object.keys(this.QuestionGroups[groupNames[i]].Questions)[j]].onfailure = Object.keys(this.QuestionGroups[groupNames[i + 1]].Questions)[0];
+ } else {
+ //console.log("no other group");
+ this.QuestionGroups[groupNames[i]].Questions[Object.keys(this.QuestionGroups[groupNames[i]].Questions)[j]].onfailure = "_finish";
+ }
+ }*/
+ };
+ }
+
+ //check for storage data
+ let solvedQuestionsAsString = sessionStorage.getItem("solved");
+ if (solvedQuestionsAsString != undefined) {
+ let solvedQuestions;
+ try {
+ solvedQuestions = JSON.parse(solvedQuestionsAsString);
+ } catch (error) {
+ console.log("Error in parsing solved questions from json. Reset solved questions to [].")
+ let solved = [];
+ sessionStorage.setItem("solved", JSON.stringify(solved));
+ }
+ if (solvedQuestions != undefined) {
+ solvedQuestions.forEach(solvedQuestion => {
+ let Question = this.getQuestion(solvedQuestion);
+ if(!Question) {
+ console.log("-- WARNING -- Quiz structure may have changed. A question id stored in session storage was not found in quiz object.");
+ }
+ else {
+ Question.solved = Question.needs;
+ }
+ });
+ }
+ }
+ else {
+ let solved = [];
+ sessionStorage.setItem("solved", JSON.stringify(solved));
+ }
+
+ let solvedVariantsAsString = sessionStorage.getItem("solvedVariants");
+ if (solvedVariantsAsString != undefined) {
+ let solvedVariants;
+ try {
+ solvedVariants = JSON.parse(solvedVariantsAsString);
+ } catch (error) {
+ console.log("Error in parsing solved Variants from json. Reset solved Variants to [].")
+ let solvedVariants = [];
+ sessionStorage.setItem("solvedVariants", JSON.stringify(solvedVariants));
+ }
+ if (solvedVariants != undefined) {
+ this.solvedVariants = solvedVariants;
+ for(let j in this.QuestionGroups) {
+ for(let i in this.QuestionGroups[j].Questions) {
+ for(let k=0;k<this.QuestionGroups[j].Questions[i].variants;k++) {
+ if(solvedVariants.indexOf(this.QuestionGroups[j].Questions[i].page+k) != -1) {
+ this.QuestionGroups[j].Questions[i].solvedVariants.push(k);
+ }
+ }
+ }
+ }
+ }
+ }
+ else {
+ let solvedVariants = [];
+ sessionStorage.setItem("solvedVariants", JSON.stringify(solvedVariants));
+ }
+
+ }
+
+ setCurrentQuestionId(questionId) {
+ this.currentQuestionId = questionId;
+ this.markQuestionAsCurrent(this.currentQuestionId);
+ }
+
+ markQuestionAsCurrent(questionId) {
+ if(questionId != undefined) {
+ questionId = this.currentQuestionId;
+ }
+ let currentQuestion = this.getQuestion(questionId);
+ if(!currentQuestion) {
+ return;
+ }
+
+ let currentMarkedNavButtons = document.querySelectorAll(".qnbutton.thispage");
+ currentMarkedNavButtons.forEach(function(currentMarkedNavButton) {
+ currentMarkedNavButton.classList.remove("thispage");
+ });
+
+ let currentQuestionButtons = document.querySelectorAll('.qnbutton[data-quiz-page="'+currentQuestion.page+'"]');
+ currentQuestionButtons.forEach(function(currentQuestionButton) {
+ currentQuestionButton.classList.add("thispage");
+ });
+ }
+
+ markQuestionAsSolved(questionId) {
+ if(questionId != undefined) {
+ questionId = this.currentQuestionId;
+ }
+ let currentQuestion = this.getQuestion(questionId);
+ let solvedNowQuestionButtons = document.querySelectorAll('.qnbutton[data-quiz-page="'+currentQuestion.page+'"]');
+ solvedNowQuestionButtons.forEach(function(solvedNowQuestionButton) {
+ solvedNowQuestionButton.classList.add("correct");
+ });
+ }
+
+ getQuestion(id) {
+ if (id == undefined) {
+ id = this.currentQuestionId;
+ }
+ for (let i in this.QuestionGroups) {
+ if (this.QuestionGroups[i].Questions[id] != undefined) {
+ return this.QuestionGroups[i].Questions[id];
+ }
+ }
+ return false;
+ }
+
+ updateNavigation() {
+ let navPanel = document.querySelector(".qn_buttons");
+ if (!navPanel) {
+ return false;
+ }
+ let buttons = document.querySelectorAll("[id*=quiznavbutton]");
+ if (buttons.length == undefined || buttons.length < 1) {
+ return false;
+ }
+
+ let solvedQuestionsAsString = sessionStorage.getItem("solved");
+ let solvedQuestionsAsArray = [];
+ if(solvedQuestionsAsString != undefined) {
+ solvedQuestionsAsArray = JSON.parse(solvedQuestionsAsString);
+ }
+
+ let partiallyCorrectQuestionsAsString = sessionStorage.getItem("partially");
+ let partiallyCorrectQuestionsAsArray = [];
+ if(partiallyCorrectQuestionsAsString != undefined) {
+ partiallyCorrectQuestionsAsArray = JSON.parse(partiallyCorrectQuestionsAsString);
+ }
+
+ let falseQuestionsAsString = sessionStorage.getItem("false");
+ let falseQuestionsAsArray = [];
+ if(falseQuestionsAsString != undefined) {
+ falseQuestionsAsArray = JSON.parse(falseQuestionsAsString);
+ }
+
+ //group
+ //let groupHeadingNodes = [];
+ for(let m in this.QuestionGroups) {
+ //this.QuestionGroups.forEach(QuestionGroup => {
+
+ let j = 0;
+ let k = 1;
+ let questionAmount = Object.keys(this.QuestionGroups[m].Questions).length;
+
+ let wrapper = document.createElement("span");
+ wrapper.classList.add("section-wrapper");
+ wrapper.dataset.isFor = this.QuestionGroups[m].id;
+ //groupHeadingNodes.push(heading);
+
+ let heading = document.createElement("h2");
+ heading.innerHTML = this.QuestionGroups[m].description;
+ heading.style.clear = "left";
+ wrapper.appendChild(heading);
+
+ let drawerCloser;
+ for(let i in this.QuestionGroups[m].Questions) {
+ //console.log("quiznavbutton"+(this.QuestionGroups[m].Questions[i].page+1));
+ let questionCard = document.getElementById("quiznavbutton"+(this.QuestionGroups[m].Questions[i].page+1));
+ if(questionCard == undefined) {
+ console.log("bad question id "+"quiznavbutton"+(this.QuestionGroups[m].Questions[i].page+1));
+ continue;
+ }
+ let drawerParent = questionCard.closest(".drawer");
+ let drawerCloser;
+ if(drawerParent != undefined) {
+ if(drawerCloser == undefined) {
+ drawerCloser = drawerParent.querySelector("[data-action=\"closedrawer\"]");
+ }
+ }
+ //if still undefined, we are probably in a different theme
+ if(drawerCloser == undefined) {
+ inOtherTheme = true;
+ }
+ let object = this;
+ questionCard.dataset.questionId = this.QuestionGroups[m].Questions[i].id;
+ let clickFunction;
+ if(this.QuestionGroups[m].Questions[i].id != "start") {
+ clickFunction = function(event) {
+ event.preventDefault();
+ event.stopPropagation();
+
+ if(videoAnimation == true) { return; }
+
+ if(!inOtherTheme) {
+ //handle block drawer
+ let modal = document.querySelector(".modal-backdrop.show");
+ if(modal != undefined) {
+ drawerCloser.click();
+ }
+ }
+ if(object.currentQuestionId != this.dataset.questionId) {
+ object.teleportDialog(object, this.dataset.questionId);
+ };
+ return false;
+ };
+ }
+ else {
+ clickFunction = function(event) {
+ event.preventDefault();
+ event.stopPropagation();
+
+ if(videoAnimation == true) { return; }
+
+ if(!inOtherTheme) {
+ //handle block drawer
+ let modal = document.querySelector(".modal-backdrop.show");
+ if(modal != undefined) {
+ drawerCloser.click();
+ }
+ }
+ if(object.currentQuestionId != this.dataset.questionId) {
+ object.goBackToCity();
+ }
+ return false;
+ };
+ }
+ questionCard.addEventListener("click", clickFunction);
+
+ questionCard.querySelectorAll(".accesshide").forEach(slotMarker => {
+ if(slotMarker != undefined && slotMarker.nextSibling != undefined) {
+ if(!(this.QuestionGroups[m].Questions[i] instanceof Question) && this.QuestionGroups[m].Questions[i] instanceof Instruction) {
+ //assume first question to be instructions
+ slotMarker.nextSibling.data = "i";
+ }
+ else if(j < questionAmount-1) {
+ slotMarker.nextSibling.data = k;
+ k++;
+ }
+ else {
+ slotMarker.nextSibling.data = "";
+ let endbossImg = document.createElement("img");
+ if(this.QuestionGroups[m].Questions[i].id == "start") {
+ endbossImg.src = "https://marvin.hs-bochum.de/~mneugebauer/fantasy/house-solid.svg";
+ }
+ else {
+ endbossImg.src = "https://marvin.hs-bochum.de/~mneugebauer/skull.svg";
+ }
+ endbossImg.style.height = "20px";
+ slotMarker.parentNode.insertBefore(endbossImg, slotMarker.nextSibling);
+ }
+ }
+ });
+ if(!questionCard) {
+ console.log("bad question card id for question "+this.QuestionGroups[m].Questions[i].id);
+ }
+ else {
+
+ if(solvedQuestionsAsArray.indexOf(this.QuestionGroups[m].Questions[i].id) != -1) {
+ console.log(this.QuestionGroups[m].Questions[i].id + " has already been solved");
+ questionCard.classList.add("correct");
+ }
+ else if(partiallyCorrectQuestionsAsArray.indexOf(this.QuestionGroups[m].Questions[i].id) != -1) {
+ console.log(this.QuestionGroups[m].Questions[i].id + " has already been solved");
+ questionCard.classList.add("partiallycorrect");
+ }
+ else if(falseQuestionsAsArray.indexOf(this.QuestionGroups[m].Questions[i].id) != -1) {
+ console.log(this.QuestionGroups[m].Questions[i].id + " has already been solved");
+ questionCard.classList.add("incorrect");
+ }
+ wrapper.appendChild(questionCard);
+ }
+
+
+ /*if(this.QuestionGroups[m].Questions[i].questionsOnPage > 1) {
+ for(let l=this.QuestionGroups[m].Questions[i].questionsOnPage;l>0;l--) {
+ let questionCardToHide = document.getElementById("quiznavbutton"+(this.QuestionGroups[m].Questions[i].page+l+1));
+ if(questionCardToHide != undefined) {
+ questionCardToHide.style.display = "none";
+ }
+ }
+ }*/
+ if(this.QuestionGroups[m].Questions[i].variants > 1) {
+ if(this.QuestionGroups[m].Questions[i].questionsOnPage > 1) {
+ //... how to handle variants of questions with many questions on one page?
+ }
+ else {
+ //let numVariants = this.QuestionGroups[m].Questions[i].variants;
+ for(let l=1;l<this.QuestionGroups[m].Questions[i].variants;l++) {
+ let questionCardToHide = document.getElementById("quiznavbutton"+(this.QuestionGroups[m].Questions[i].page+l+1));
+ if(questionCardToHide != undefined) {
+ questionCardToHide.style.display = "none";
+ }
+ }
+ }
+ //correct enumeration
+ //k = k-this.QuestionGroups[m].Questions[i].variants+1;
+ }
+ else {
+ if(this.QuestionGroups[m].Questions[i].questionsOnPage > 1) {
+ this.hideMultipleQuestionCards(m, i);
+ }
+ }
+
+ j++;
+ };
+
+ navPanel.appendChild(wrapper);
+ }
+
+ /*
+ //put a flag instead of a skull, a number or an "i" in the very last question card
+ document.querySelectorAll(".qn_buttons span[data-is-for]:last-child a:last-child img").forEach(function (lastQuestionCard) {
+ lastQuestionCard.src = "https://marvin.hs-bochum.de/~mneugebauer/flag.svg";
+ });
+ */
+ //add a last goal flag button
+ let object = this;
+ let questionCardClone = document.getElementById("quiznavbutton1").cloneNode(true);
+ questionCardClone.id = "test";//"quiznavbutton_finish";
+ questionCardClone.classList.remove("thispage");
+ questionCardClone.classList.remove("correct");
+ questionCardClone.classList.remove("incorrect");
+ questionCardClone.classList.remove("partiallycorrect");
+ questionCardClone.removeAttribute("data-quiz-page");
+ questionCardClone.querySelector("img").src = "https://marvin.hs-bochum.de/~mneugebauer/flag.svg";
+ questionCardClone.addEventListener("click", function(event) {
+ console.log("clicked last question card");
+ event.preventDefault();
+ event.stopPropagation();
+ if(videoAnimation == true) { return; }
+
+ //handle block drawer
+ let drawerParent = this.closest(".drawer");
+ let drawerCloser;
+ if(drawerParent != undefined) {
+ drawerCloser = drawerParent.querySelector("[data-action=\"closedrawer\"]");
+ }
+ //if(drawerCloser != undefined) {
+ let modal = document.querySelector(".modal-backdrop.show");
+ if(modal != undefined && drawerCloser != undefined) {
+ drawerCloser.click();
+ }
+ if(object.currentQuestionId != this.dataset.questionId) {
+ object.teleportDialog(object, this.dataset.questionId);
+ };
+ //}
+
+ if(!object.finished) {
+ object.processNotification("Dies ist das Ziel. Du kannst dich nicht hier her teleportieren, sondern musst zunächst die Gegner besiegen.", true);
+ }
+ else {
+ object.goToNextScene(object, true, -1, true);
+ }
+
+ return false;
+ });
+ document.querySelector(".section-wrapper:last-of-type").appendChild(questionCardClone);
+
+ //show group navigation on instruction and update speech bubble navigation
+ let currentQuestion = this.getQuestion();
+ if (!(currentQuestion instanceof Question) && currentQuestion instanceof Instruction) {
+
+ let CurrentGroup;
+ for (let i in this.QuestionGroups) {
+ if (this.QuestionGroups[i].Questions[this.currentQuestionId] != undefined) {
+ CurrentGroup = this.QuestionGroups[i];
+ break;
+ }
+ };
+
+ let groupNavigation = document.querySelector(".group-navigation");
+ if (groupNavigation != undefined) {
+ //find current group
+
+ if (CurrentGroup != undefined) {
+
+ //show group navigation
+ let cards = document.querySelectorAll("[data-is-for=" + CurrentGroup.id + "] a")
+ let cardAmount = cards.length;
+ let keys = Object.keys(CurrentGroup.Questions);
+ for (let i = cardAmount - 1; i >= 0; i--) {
+ let cardClone = cards[i].cloneNode(true);
+ let stepWrapper = document.createElement("div");
+ stepWrapper.classList.add("wrap_nav_group");
+ let stepHeadingAnchor = document.createElement("a");
+ stepHeadingAnchor.href = cardClone.href;
+ let stepHeading = document.createElement("h2");
+ stepHeading.innerHTML = CurrentGroup.Questions[keys[i]].description;
+
+ stepHeadingAnchor.appendChild(stepHeading);
+ stepWrapper.appendChild(cardClone);
+ stepWrapper.appendChild(stepHeadingAnchor);
+ groupNavigation.appendChild(stepWrapper);
+ };
+
+ let groupNavCss = document.createElement("style"); groupNavCss.type = "text/css"; groupNavCss.innerHTML = ".path-mod-quiz .group-navigation .qnbutton { text-decoration: none; font-size: 14px; line-height: 20px; font-weight: 400; background-color: #fff; background-image: none; height: 40px; width: 30px; border-radius: 3px; border: 0; overflow: visible; margin: 0 6px 6px 0;} .path-mod-quiz .group-navigation .qnbutton { background: none; background-color: rgba(0, 0, 0, 0); background-color: #eee; border: 0; border-radius: 4px; color: #000000 !important; font-size: 14px; font-weight: 700; height: 45px; line-height: 25px !important; margin: 0 5px 5px 0; width: 35px;} .group-navigation .qnbutton .thispageholder { border: 1px solid #999; border-radius: 4px; z-index: 1;}.group-navigation .qnbutton .thispageholder { border: 1px solid; border-radius: 3px; z-index: 1;}.group-navigation .qnbutton .trafficlight, group-navigation .qnbutton .thispageholder { display: block; position: absolute; top: 0; bottom: 0; left: 0; right: 0;} .path-mod-quiz .group-navigation .qnbutton.notyetanswered .trafficlight, .path-mod-quiz .group-navigation .qnbutton.invalidanswer .trafficlight { background-color: #fff;}.path-mod-quiz .group-navigation .qnbutton.notyetanswered .trafficlight, .path-mod-quiz .group-navigation .qnbutton.invalidanswer .trafficlight { background-color: #fff;}.path-mod-quiz .group-navigation .qnbutton .trafficlight { border: 0; background: #fff none center / 10px no-repeat scroll; height: 20px; margin-top: 20px; border-radius: 0 0 3px 3px;} .path-mod-quiz .group-navigation .qnbutton .trafficlight { background: #fff none center 4px / 10px no-repeat scroll; background-color: rgb(255, 255, 255); border: 0; border-radius: 0 0 4px 4px; height: 20px; margin-top: 25px;} .path-mod-quiz .group-navigation .qnbutton.correct .trafficlight { background-color: #8bc34a; background-image: url(/theme/image.php/adaptable/theme/1660635117/mod/quiz/checkmark); } .path-mod-quiz .group-navigation .qnbutton.notanswered .trafficlight, .path-mod-quiz .group-navigation .qnbutton.incorrect .trafficlight { background-color: #f44336; } .path-mod-quiz .group-navigation .qnbutton.partiallycorrect .trafficlight { background-color: #ff9800; background-image: url(/theme/image.php/adaptable/theme/1660635117/mod/quiz/whitecircle); } .path-mod-quiz .group-navigation .qnbutton.thispage .thispageholder { border: 3px solid #1f536b; } .wrap_nav_group { clear:left; }";
+ document.getElementsByTagName("head")[0].appendChild(groupNavCss);
+ }
+ }
+
+ let endbossLink = document.querySelector(".endboss-link");
+ if (endbossLink != undefined) {
+ endbossLink.href = this.getPageURL(currentQuestion.onsuccess).url;
+ }
+
+ if (CurrentGroup != undefined) {
+ let questionKeys = Object.keys(CurrentGroup.Questions);
+ let nextWorldLink = document.querySelector(".link-next-world");
+ let nextWorldURL = this.getPageURL(CurrentGroup.Questions[questionKeys[questionKeys.length - 1]].onsuccess).url;
+
+ if (nextWorldLink != undefined) {
+ nextWorldLink.href = nextWorldURL;
+ }
+
+ let endbossDefeat = CurrentGroup.Questions[questionKeys[questionKeys.length - 1]].isSolved();
+ let endbossStatePhrase = document.querySelector(".endboss-state");
+ if (endbossStatePhrase != undefined) {
+ if (endbossDefeat == true) {
+ endbossStatePhrase.innerHTML = "bereits";
+ }
+ /*else {
+ endbossStatePhrase.innerHTML = "noch nicht";
+ }*/
+ }
+
+ let nextQuestionLink = document.querySelector(".link-next-question");
+ if (nextQuestionLink != undefined) {
+ if (endbossDefeat == true) {
+ nextQuestionLink.innerHTML = "der nächsten Welt";
+ nextQuestionLink.href = nextWorldURL;
+ //overwrite default next question
+ document.querySelector(".btn-next-question").href = nextWorldURL;
+ }
+ else {
+ let i;
+ let page;
+ for (i in CurrentGroup.Questions) {
+ if (!CurrentGroup.Questions[i].isSolved() && CurrentGroup.Questions[i] instanceof Question) {
+ page = CurrentGroup.Questions[i].page;
+ break;
+ }
+ }
+ //console.log(page);
+ nextQuestionLink.setAttribute("onclick", 'tutorialFocusElement(document.querySelector(\'.wrap_nav_group [data-quiz-page="' + page + '"]\'));');
+ document.querySelector(".btn-next-question").href = this.getPageURL(i).url;
+ }
+ }
+
+ let currentLevelPhrase = document.querySelector(".current-level");
+ if (currentLevelPhrase != undefined) {
+ let amount = 0;
+ let solved = 0;
+ for (let i in CurrentGroup.Questions) {
+ if (CurrentGroup.Questions[i] instanceof Question) {
+ amount++;
+ if (CurrentGroup.Questions[i].isSolved()) {
+ solved++;
+ }
+ }
+ }
+ if (endbossDefeat == true) {
+ currentLevelPhrase.innerHTML = amount + " von " + amount;
+ }
+ else {
+ currentLevelPhrase.innerHTML = solved + " von " + amount;
+ }
+ }
+ }
+
+ sessionStorage.setItem("camefrom", currentQuestion.id);
+ }
+
+ }
+ getNextQuestionId(questionId) {
+ if (questionId == undefined) {
+ questionId = this.currentQuestionId;
+ }
+ let returnValue = false;
+
+ let groupKeys = Object.keys(this.QuestionGroups);
+ let length = groupKeys.length;
+ console.log("get next question id");
+ for (let i = 0; i < length; i++) {
+ //console.log(this.QuestionGroups[groupKeys[i]].description);
+ if (this.QuestionGroups[groupKeys[i]].Questions[questionId] != undefined) {
+ let nextStep = this.QuestionGroups[groupKeys[i]].Questions[questionId].isSolved() ? this.QuestionGroups[groupKeys[i]].Questions[questionId].onsuccess : this.QuestionGroups[groupKeys[i]].Questions[questionId].onfailure;
+ switch (nextStep) {
+ case "_finish":
+ return -1;
+ default:
+ return nextStep;
+ break;
+ }
+ }
+ }
+ console.log("question id not found");
+ return false;
+ }
+
+ getNextUnsolvedQuestionId(questionId) {
+ if (questionId == undefined) {
+ questionId = this.currentQuestionId;
+ }
+ do {
+ questionId = this.getNextQuestionId(questionId);
+ if(questionId == -1) {
+ //special handling for very last question
+ return questionId;
+ }
+ } while (this.getQuestion(questionId).isSolved());
+
+ return questionId;
+ }
+
+ getPageURL(questionId) {
+ if (questionId == undefined) {
+ questionId = this.currentQuestionId;
+ }
+ let currQuestion = this.getQuestion(questionId);
+ let firstQuestionNavElement = document.querySelector("#quiznavbutton1");
+ if (!firstQuestionNavElement) {
+ return false;
+ }
+ let plainUrl = "";
+ if (!firstQuestionNavElement.href || firstQuestionNavElement.href == "#") {
+ plainUrl = window.location.href;
+ } else {
+ plainUrl = firstQuestionNavElement.href;
+ }
+
+ //let sanitizedUrl = plainUrl.replace(/(.*?)(?:#|&page=\d*#*|&scrollpos=\d*#*)/, "\1");
+ let sanitizedUrl = plainUrl;
+ let relPos = plainUrl.indexOf("&scrollpos");
+ if (relPos == -1) {
+ relPos = plainUrl.indexOf("&page");
+ if (relPos == -1) {
+ relPos = plainUrl.indexOf("#");
+ }
+ }
+
+ if (relPos > -1) {
+ sanitizedUrl = plainUrl.slice(0, relPos);
+ }
+
+ let pageToReturn = currQuestion.page;
+ //pick a random variant if existent
+ let numVariants = currQuestion.variants;
+ if(numVariants > 1) {
+ if(numVariants > currQuestion.solvedVariants.length) {
+ let unsolvedVariants = [];
+ for(let i=0;i<numVariants;i++) {
+ if(currQuestion.solvedVariants.indexOf(i) == -1) {
+ unsolvedVariants.push(i);
+ }
+ }
+ console.log("unsolved variants: ", unsolvedVariants);
+ let randomPage = pageToReturn+unsolvedVariants[Math.floor(Math.random()*unsolvedVariants.length)];
+ /*let randomPage = pageToReturn;
+ let match = window.location.href.match(/page=(\d*)/);
+ if(match != undefined && match[1] != undefined) {
+ let currentPage = match[1];
+ do {
+ randomPage = pageToReturn+Math.floor(Math.random()*numVariants);
+ } while(randomPage == currentPage);
+ }
+ else {
+ randomPage = pageToReturn+Math.floor(Math.random()*numVariants);
+ }*/
+ pageToReturn = randomPage;
+ }
+ else {
+ console.log("all variants solved, give random");
+ //If all variants are already solved, pick any of them.
+ let randomPage = pageToReturn;
+ let currentPage = this.currentPage;
+ do {
+ randomPage = pageToReturn+Math.floor(Math.random()*numVariants);
+ } while(randomPage == currentPage);
+ pageToReturn = randomPage;
+ }
+ }
+ return {page:pageToReturn, url:sanitizedUrl + "&page=" + pageToReturn};
+ }
+
+ getNextPageInfo(questionId, forceURL, skipSolved) {
+ if (questionId == undefined) {
+ questionId = this.currentQuestionId;
+ }
+ let Question = this.getQuestion(questionId);
+
+ if (forceURL == undefined) {
+ forceURL = false;
+ }
+
+ let nextPageUrl = "";
+ let nextPageLinkText = "";
+ let nextQuestionId = skipSolved ? this.getNextUnsolvedQuestionId() : this.getNextQuestionId();
+ let nextPageURLInfo = this.getPageURL(nextQuestionId);
+ let possibleNextPageUrl = nextPageURLInfo.url;
+ let possibleNextPageNumber = nextPageURLInfo.page;
+
+ if (nextQuestionId == -1) {
+ //finish
+ let finishAttemptElement = document.querySelector(".endtestlink.aalink");
+ if (!finishAttemptElement || !finishAttemptElement.href) {
+ possibleNextPageUrl = "summary.php";
+ } else {
+ possibleNextPageUrl = finishAttemptElement.href;
+ }
+ nextPageLinkText = "Finish";
+ }
+ else {
+ nextPageLinkText = "Next question";
+ }
+
+ //actually means a real skip, no right or wrong
+ if (Question.askBeforeSkip == true && !forceURL && !Question.isSolved() && document.querySelector(".stackprtfeedback") == undefined) {
+ //ask before skip
+ nextPageUrl = "javascript:showAskBeforeSkipModal();";
+ document.querySelector(".skip-yes").href = possibleNextPageUrl;
+ }
+ else {
+ nextPageUrl = possibleNextPageUrl;
+ }
+ return {
+ url: nextPageUrl,
+ linkText: nextPageLinkText,
+ id: nextQuestionId,
+ page: possibleNextPageNumber
+ };
+ }
+}
+
+class FantasyQuiz extends GamifiedQuiz {
+ constructor(quizObject) {
+ super(quizObject);
+ this.GameElements = {};
+ this.monstersCamp;
+ this.targetedEnemy;
+ this.validationElement;
+ this.speechBubbleElement;
+ this.notificationBubbleContainer;
+ this.notificationBubbleElement;
+ this.updateValidationTimerId;
+ this.validationLastState;
+ this.spiral;
+ this.fader;
+ this.enterSpellContainer;
+ this.inputElement;
+ this.formulaContainer;
+ this.fairyPlaceHolderAtEnemy;
+ this.background;
+ this.questionBubbleElement;
+ this.fairyFollowSignPost;
+ this.nextSceneSignPost;
+ this.followPrompt;
+ this.manaBadge;
+ this.manaScoreTimer;
+ this.fairyBadge;
+ this.fairyScoreTimer;
+ this.Score = { fairies:0, mana:20 }
+ let scoreFromStorage = sessionStorage.getItem("score");
+ if(scoreFromStorage != undefined) {
+ let scoreObject = JSON.parse(scoreFromStorage);
+ if(scoreObject != undefined) {
+ this.Score.fairies = scoreObject.fairies;
+ this.Score.mana = scoreObject.mana;
+ }
+ }
+ this.fairyHome;
+ this.fairyModal;
+ this.settingsModal;
+ this.creditsModal;
+ this.freedFairyBoxes = [];
+ this.saveStateInput;
+ this.preInputField;
+ this.postInputField;
+ this.finished = false;
+ this.contentContainer;
+ this.introState = 0;
+ }
+
+ init() {
+ console.log("init");
+ /* CSS-Hacks */
+ let style = document.createElement("style");
+ style.type = "text/css";
+ //.que .outcome background-color is #fcefdc;
+ let generalGameCSS = ":root { --background-height:500px; --transformAnimationStart:2s; --speedX:5s; --speedY:10s;} .bubble { /* layout*/ position: absolute; /*max-width: 30em;*/ max-height:500px; /* looks*/ background-color: #fcefdc; padding: 1.125em 1.5em; font-size: 1.25em; border-radius: 1rem; box-shadow: 0 0.125rem 0.5rem rgba(0, 0, 0, .3), 0 0.0625rem 0.125rem rgba(0, 0, 0, .2); /*transition*/ transition:max-height 1s, padding-top 1s, padding-bottom 1s; overflow:visible; z-index:1; } .bubble .bubble-content { /*an additional div to ensure scrollability by simultaneously keep the speech-bubble-arrow visible, which indeed is an overflow*/ overflow-y:scroll; max-height:450px; max-width:100vw; } .bubble.fairy-help { /* not necessary when scene will scroll with exceeding text z-index:50;*/overflow:hidden; width:100%; } .bubble.fairy-help.closed { overflow:hidden; } .bubble.fairy-help.show-overflow { overflow:visible; } .bubble:not(.no-arrow):not(.spell-in-progress)::before { /* layout*/ content: ''; position: absolute; width: 0; height: 0; top: 100%; left: 1.5em; /* offset should move with padding of parent*/ border: .75rem solid transparent; border-bottom: none; /* looks*/ border-top-color: #fcefdc; filter: drop-shadow(0 0.0625rem 0.0625rem rgba(0, 0, 0, .1)); } /*.bubble.middle-arrow {max-width:unset; }*/ .bubble.middle-arrow::before { left:50% !important; } .bubble.closed { max-height:0px; padding-top:0px; padding-bottom:0px; } .bubble.middle-up-arrow::before { left:50% !important; top: unset !important; bottom:100%; /* offset should move with padding of parent*/ border: .75rem solid transparent; border-top: none !important; /* looks*/ border-bottom: .75rem solid #fcefdc !important; filter: none !important; } .bubble.closed { max-height:0px; padding-top:0px; padding-bottom:0px; } .bubble.spell-in-progress { background-color:rgba(255,255,255,0.9); border:1px solid black; border-radius:10%; overflow:hidden; } .exclamation { width:20px; visibility:hidden; text-align:center; opacity:1; color:red; font-weight:bold; transform:rotate(-10deg); font-size:1.2em; } .enter-spell-container.error .exclamation, .exclamation.active { visibility:visible; } .exclamation.temporarily-hidden { opacity:0; } .spiral { width:30px; height:auto; position:absolute; opacity:1; transition:left 1s, bottom 1s, opacity 1s; visibility:hidden; /*filters the black svg to light yellow*/ filter:invert(97%) sepia(61%) saturate(443%) hue-rotate(12deg) brightness(108%) contrast(108%); z-index:1; } .exclamation.reverse { transform:rotate(10deg); }.spiral img { width:100%; height:100%; } .spiral.active { visibility:visible; left:90% !important; opacity:0; } @keyframes fairyMovement { 0% { transform:translate(var(--xoffset), var(--yoffset)); } 100% { transform:translate(0,0); }} .notifying { animation:fairyMovement ease 3s forwards; } .returning { animation:fairyMovement ease 3s forwards; } .fader { z-index:0; position:absolute; width:100%; /*height:var(--background-height);*/ height:100%; background-color:#000000; opacity:0; transition:opacity,1s;} .fader.fade-out { display:block; opacity:1; z-index:10; } .fader.fade-in { display:block; opacity:0; z-index:2; } .content.city .sign-post-container { position:absolute; } .content.city .sign-post-container.point-left { left:5%; } .content.city .sign-post-container.point-right { right:5%; } .sign-post-container { width:100px; height:auto; bottom: 20%; z-index:1; } .sign-post-container.point-left { /*align-self:flex-start;*/ } .sign-post-container.point-right { /* align-self:flex-end; */ } .sign-post-container .sign-post { width:100%; object-fit:contain; } .sign-post-container.point-left .sign-post { transform:scaleX(-1);} .content:not(.city) .sign-post-container { display:none; }/*hide some elements in city*/ .city input.algebraic, .intro input.algebraic { display:none !important; } .city .spell, .intro .spell, .clearing .spell { display:none; } .content:not(.city):not(.intro) .sign-post-container.standalone-arrow { display:flex; } .city .enemy-container { display:none; } .formula-container { position:absolute; top:50%; left:50%; overflow:visible; background-color:rgba(255,255,255,0.5); border-radius:10%; transform:translate(-50%,-50%); padding:5px; transition:background-color,1s; z-index:1; } .enemy-container:hover .formula-container, .enemy-container.targeted .formula-container { background-color:rgba(255,255,255,0.9);} .moveable-bg { height:var(--background-height); z-index:0; width:100%; background-size:auto 100%; transform:translateY(-100%); position:relative; background-image:url(https://marvin.hs-bochum.de/~mneugebauer/fantasy/bg-forest1.png); background-repeat:no-repeat; } .content.city~* .moveable-bg { background-image:url(https://marvin.hs-bochum.de/~mneugebauer/fantasy/bg-elven_land4.png); } .content.clearing~* .moveable-bg { background-image:url(https://marvin.hs-bochum.de/~mneugebauer/fantasy/bg-forest4.png); } .city .standalone-arrow, .intro .standalone-arrow { display:none; } .clearing .standalone-arrow.point-right { display:none !important; } .player-container { z-index:2; /* transition for player is defined individually transition:left 3s linear; */} .content.intro:not(.city) .player-container { display:none; } .enemy-container { z-index:1; } .monsters-camp.solved .enemy-container .img-wrapper { filter:grayscale(1); } .content { min-height:/*calc(var(--background-height)*2)*/var(--background-height); max-width:calc(var(--background-height)*1.778); } .air { min-height:100px; } .helper-container { z-index:1; } .enter-spell-container { z-index:1; position:relative; } .battleground { position:relative; } .ground { display:flex; flex-direction:row; width:100%; justify-content:space-between; align-items:center; flex-wrap:wrap; padding-top:1em; } .enemy-container.invisible { display:none; } .targeted { background: linear-gradient(to right, black 4px, transparent 4px) 0 0, linear-gradient(to right, black 4px, transparent 4px) 0 100%, linear-gradient(to left, black 4px, transparent 4px) 100% 0, linear-gradient(to left, black 4px, transparent 4px) 100% 100%, linear-gradient(to bottom, black 4px, transparent 4px) 0 0, linear-gradient(to bottom, black 4px, transparent 4px) 100% 0, linear-gradient(to top, black 4px, transparent 4px) 0 100%, linear-gradient(to top, black 4px, transparent 4px) 100% 100%; background-repeat:no-repeat; background-size: 50px 50px; border-radius:5%; } .monsters-camp { position: relative; float: right; display: flex; flex-direction: row; max-width: 90%; flex-wrap: wrap; justify-content: flex-end; z-index:1; } .monster-analysis-fairy-animation-placeholder { width: 50px; height: 50px; position: absolute; /*border: 4px solid red;*/ z-index: 1; left: 0; top:0; } .monster-analysis-fairy-animation-placeholder.animate { animation:monster-camp-analysis 2s linear 0s 1 normal, switch-foreground-background 5s linear 0s 1 normal; animation-fill-mode:forwards; } @keyframes monster-camp-analysis { 0% { left:0%; top:0%; } 50% { left:100%; top:50%; }/*25% { left:100%; top:25%; } 50% { left:0%; top:50%; } 75% { left:100%; top:75%; }*/ 100% { left:0%; top:100%; } } @keyframes switch-foreground-background { 0% { z-index:1; } 100% { z-index:3; }} .fairy-place-holder-at-enemy { width: 50px; height: 50px; z-index: 2; position: absolute; left: 50%; top: 10%; transform: translate(-50%,-50%); } .monsters-camp .freed { visibility:hidden; z-index:2; align-self:center; top:50%; left:50%; transform:translate(-50%,-50%); } .content.intro .fairy-place-holder-at-enemy { top:50%; } .monsters-camp.transform { z-index:1; animation:transformToZero 3s ease-in 0s 1 normal forwards; } @keyframes transformToZero { 0% { transform:scale(1,1); } 50% { transform:scale(0.5,0.5) } 100% { transform:sacle(1,1); } } .monsters-camp.transform .enemy-container img { animation:monsterBlur 1.5s linear 0s 1 normal forwards; } @keyframes monsterBlur { 0% { filter:blur(0px) saturate(0) brightness(100%); opacity:1; } 16% { filter:blur(1px) saturate(16) brightness(116%); } 33% { filter:blur(3px) saturate(33) brightness(133%); } 50% { filter:blur(0px) saturate(50) brightness(150%); } 76% { filter:blur(3px) saturate(76) brightness(176%); } 83% { filter:blur(6px) saturate(83) brightness(183%); } 100% { filter:blur(10px) saturate(100) brightness(200%); opacity:0; } } .monsters-camp.transform .formula-container, .monsters-camp.appeared .formula-container { opacity:0; } .monsters-camp.appeared .enemy-container { visibility:hidden; } .monsters-camp.appeared .freed { visibility:visible; } .monsters-camp.transform .freed { visibility:visible; animation:fairyAppear 3s ease-in 0s 1 normal forwards; } @keyframes fairyAppear { 0% { opacity:0; } 50% { opacity:1; } 100% { opacity:1; } } .monsters-camp.solved .freed { visibility:hidden; } .monsters-camp.appear .enemy-container { visibility:hidden; } .monsters-camp.appear { animation:transformToFull 4s ease-in 0s 1 normal forwards; } @keyframes transformToFull { 0% { transform:scale(0,0); } 100% { transform:scale(1,1); } } .monsters-camp.appear .formula-container { opacity:0; } .monsters-camp.appear .freed { display:block; } .help-notification-container { position:relative; width:100%; top:-50px; } .freed.leave-scene { transform-origin: 0px 50px;animation:fairy-leave-scene 3s ease-in 0s 1 normal forwards; } .leave-scene.reverse { animation-name:fairy-leave-scene-reverse; } @keyframes fairy-leave-scene-reverse { 0% { transform:rotate(0deg); margin-left:0vw; } 50% { transform:rotate(180deg); margin-left:0vw; } 100% { transform:rotate(180deg); left:110%; margin-left:-55vw; } } @keyframes fairy-leave-scene { 0% { transform:rotate(0deg); margin-left:0vw; } 50% { transform:rotate(-180deg); margin-left:0vw; } 100% { transform:rotate(-180deg); left:110%; margin-left:55vw; } } .content.city .fairy-home { left:50% !important; } .enemy-container { cursor:pointer; } .monsters-camp.transform .enemy-container { cursor:default; } .sign-post-container { cursor:pointer; } .bubble.spell-in-progress { cursor:pointer; } .fairy-img { cursor:pointer; } .enter-spell-container.error .exclamation, .exclamation.active { cursor:pointer; } .fairy-follow-sign-post { display:flex !important; position:absolute; transition:transform 1s ease 0s; transform:scaleY(0); right:0; } .fairy-follow-sign-post.active { transform:scaleY(1); } .fairy-follow-sign-post .fairy-representation { width:40px; position:absolute; opacity:0.9; } .sign-post-container.disabled { /*cursor:not-allowed;*/cursor:pointer; }.sign-post-container.disabled img { filter:grayscale(1); } .que { overflow:hidden; } /*.que.scene-end { overflow:hidden; }*/ .enter-spell-container.error input { border:2px solid red; } .error-info { display:none; color:white; background-color:red; border-radius:50%; height:1.2em; width:1.2em; text-align:center; margin-left:5px; font-weight:bold; font-style:italic; font-family: 'Brush Script MT', cursive; }.enter-spell-container.error .error-info { display:inline-block; } .enter-spell-container .exclamation { display:inline-block; } .fairy-place-holder { transform:translateX(-8px); z-index:2; left:50%; position:absolute; } .player-container.teleport { animation:teleport 3s linear 0s 1 normal forwards; } @keyframes teleport { 0% { filter:blur(0px) drop-shadow(1px 0px 0 #99ccff) drop-shadow(0px 1px 0 #99ccff) drop-shadow(-1px -0px 0 #99ccff) drop-shadow(-0px -1px 0 #99ccff); opacity:1; } 75% { filter:blur(0px) drop-shadow(4px 0px 0 #99ccff) drop-shadow(0px 4px 0 #99ccff) drop-shadow(-4px -0px 0 #99ccff) drop-shadow(-0px -4px 0 #99ccff); opacity:1; }75% { filter:blur(3px) drop-shadow(4px 0px 0 #99ccff) drop-shadow(0px 4px 0 #99ccff) drop-shadow(-4px -0px 0 #99ccff) drop-shadow(-0px -4px 0 #99ccff); opacity:1; } 100% { filter:blur(10px) drop-shadow(8px 0px 0 #99ccff) drop-shadow(0px 8px 0 #99ccff) drop-shadow(-8px -0px 0 #99ccff) drop-shadow(-0px -8px 0 #99ccff); opacity:0; } } .player-container.appear { opacity:0; animation:teleport 2s linear 1s 1 reverse forwards; } .moveable-bg-container { position:relative; width:100%; height:0; overflow:visible; } .new-question-container { display:none; } .fairy-home { position:absolute; z-index:2; } .fairy-img.leave-scene { animation:fairy-leave-scene-right 3s ease-in 0s 1 normal forwards; transform:translate(var(--xoffset), var(--yoffset)); } @keyframes fairy-leave-scene-right { 0% { left:0; } 90% { left:1000px; } 100% { left:2000px; } } .fairy-img.leave-scene.to-top { animation-name:fairy-leave-scene-top; } @keyframes fairy-leave-scene-top { 0% { top:0; } 10% { top:50px; } 90% { top:-1000px; } 100% { top:-2000px; } } .fairy-img.leave-scene.to-left { animation-name:fairy-leave-scene-left; transform-origin: 5px 5px; animation-timing-function:linear; } @keyframes fairy-leave-scene-left { 0% { left:0; transform:rotate(0deg); } 50% { left:0; transform:rotate(360deg);} 90% { left:-1000px; transform:rotate(360deg); } 100% { left:-2000px; transform:rotate(360deg); } } .fairy-home.alerting { animation:fairy-alert 3s 0s infinite; } @keyframes fairy-alert { 0% { transform:translateY(0px); } 10% { transform:translateY(-20px); } 20% { transform:translateY(0px); } 30% { transform:translateY(-20px); } 40% { transform:translateY(0px); } 50% { transform:translateY(-20px); } 60% { transform:translateY(0px); } 100% { transform:translateY(0px); }} .content:not(.city).intro~* .moveable-bg { box-shadow:inset 0px 0px 50px 50px rgba(0,0,0,0.9); } .intro .formula-container { display:none; } .enemy-container.fairy-to-monster .fairy-place-holder-at-enemy { animation:fairyAppear 2s ease-in 2s 1 reverse forwards; animation-delay:var(--transformAnimationStart); } .enemy-container.fairy-to-monster .img-wrapper img { animation:monsterBlur 1.5s linear 2s 1 reverse forwards; animation-delay:var(--transformAnimationStart); } .moveable-bg-container.fantasy-modal { z-index:20; display:none; } .moveable-bg-container.fantasy-modal .moveable-bg { padding:10%; background-color:rgba(0,0,0,0.75); background-image:none; overflow:scroll; height:var(--background-height); } .simple-fairy-representation { display:inline-block; width:40px;height:40px; } .fantasy-modal.active { display:block; } .moving-linear { animation-timing-function:linear; } .moving-quick { animation-duration:1s; } .close-modal-button { cursor:pointer; position:absolute; top:50px; right:50px; color:white; font-weight:bold; font-size:2em; } .close-modal-button:hover { color:#e2001a; } .menu-option { position:relative; display:block; width:200px; text-align:center; margin: 10px auto !important; color:#000000; } .menu-option:hover { background-color:#fcefdc; }/*.menu-option::after, .menu-option::before { box-sizing:content-box; }*/ .credits-modal { color:#ffffff; } /*.idle-freed-fairy-box { position:absolute; height:40px; width:40px; z-index:2; } .idle-freed-fairy-box.x { animation: up-down 2s linear infinite alternate; } @keyframes up-down { 0% { top:0%; } 100% { top:100%; } } .idle-freed-fairy-box .y { animation: left-right 4s linear infinite alternate; } @keyframes left-right { 0% { left:0%; } 100% { left:100%; } }*/ .idle-freed-fairy-box { position:absolute; height:40px; width:40px; z-index:2; opacity:0.5; animation: left-right var(--speedX) linear infinite alternate, up-down var(--speedY) linear infinite alternate; visibility:hidden; } .idle-freed-fairy-box.active { visibility:visible; } @keyframes up-down { 0% { top:0%; } 100% { top:94%; } } @keyframes left-right { 0% { left:0%; } 100% { left:94%; } } .fairy-stop-sign-container { flex: 70%; display: flex; justify-content: center; align-items: center; } .input-surrounding-math { color:#ffffff; display:inline-block; } .clearing .enter-spell-container { display:none; } .clearing .monsters-camp { display:none; } .outcome { display:none; } .matrixtable .selected-entry { font-weight:bold; background: linear-gradient(to right, black 1px, transparent 1px) 0 0, linear-gradient(to right, black 1px, transparent 1px) 0 100%, linear-gradient(to left, black 1px, transparent 1px) 100% 0, linear-gradient(to left, black 1px, transparent 1px) 100% 100%, linear-gradient(to bottom, black 1px, transparent 1px) 0 0, linear-gradient(to bottom, black 1px, transparent 1px) 100% 0, linear-gradient(to top, black 1px, transparent 1px) 0 100%, linear-gradient(to top, black 1px, transparent 1px) 100% 100%; background-repeat:no-repeat; background-size: 4px 10px; border-radius:10%; } .matrixtable td:not(:empty) { min-width:1em; cursor:pointer; text-align:center; } .content.finished .badge.square .badge__label { font-size:100px; } .credits-modal a { font-weight:bold; color:#ffffff; } .hint { display:none; } .hint.show-hint { display:block; }";
+
+ let pulsingPointsCSS = '@keyframes introduceBadge { 0% { opacity: 0; } 100% { opacity: 1; } } @keyframes pulseBadge { 0% { transform: scale(1); } 50% { transform: scale(1.05); } 100% { transform: scale(1); } } @keyframes pulseBadge2 { 0% { transform: scale(1); } 50% { transform: scale(1.1); } 100% { transform: scale(1); } } .badge { animation: introduceBadge 1s linear 0s 1 both; background: rgba(0, 113, 246, 0.7); border-radius: 50%; height: 68px; perspective: 600px; position: relative; width: 68px; z-index:1; } .badge:before, .badge:after { animation: pulseBadge 3s cubic-bezier(0.86, 0, 0.07, 1) 0s infinite both; border: 2px dashed #99ccff; border-radius: inherit; bottom: -8px; content: ""; left: -8px; opacity: 0.6; position: absolute; right: -8px; top: -8px; } .badge:after { animation-name: pulseBadge2; bottom: -16px; left: -16px; opacity: 0.4; right: -16px; top: -16px; } @keyframes introduceLabel { 0% { opacity: 0; transform: translate(-50%, -50%) scale(0.4) rotateY(-1800deg); } 100% { opacity: 1; transform: translate(-50%, -50%) scale(1) rotateY(20deg); } } @keyframes rotateLabel { 0% { transform: translate(-50%, -50%) rotateY(20deg); } 50% { transform: translate(-50%, -50%) rotateY(-20deg); } 100% { transform: translate(-50%, -50%) rotateY(20deg); } } .badge__label { /*animation: introduceLabel 2s cubic-bezier(0.19, 1, 0.22, 1) 1s 1 both, rotateLabel 5s linear 3s infinite;*/ color: #99ccff; font: 900 50px/1 -apple-system, BlinkMacSystemFont; left: 50%; position: absolute; text-align: center; text-shadow: 0px 4px 8px rgba(0, 113, 246, 0.2); top: 50%; transform: translate(-50%, -50%); } .badge.rotate .badge__label { animation:rotateLabel 5s linear 0s infinite; } .badge.appear .badge__label { animation: introduceLabel 2s cubic-bezier(0.19, 1, 0.22, 1) 0s 1 both, rotateLabel 4s linear 2s infinite; } .badge.square { border-radius:0%; } .badges-container { display:flex; justify-content: center; align-items: center; z-index:1; flex-grow:2; gap:3em; } .content.intro .badge { display:none; } .badge { cursor:pointer; }';
+
+ let addCSS = generalGameCSS + " " + pulsingPointsCSS;
+ style.innerHTML = addCSS;
+
+ document.getElementsByTagName('head')[0].appendChild(style);
+
+ //assume safe place in the very beginning
+ document.querySelector(".que .content").classList.add("city");
+
+ //center fixed width game environment
+ try {
+ console.log("center now");
+ let questionForm = document.getElementById("responseform");
+
+ questionForm.style.display = "flex";
+ questionForm.style.justifyContent = "center";
+ //questionForm.style.alignContent = "stretch";
+ questionForm.firstChild.style.flexBasis = "calc(var(--background-height)*1.778)";
+ }
+ catch (error) {
+ console.log("game environment could not be centered:");
+ console.log(error);
+ }
+
+
+ let questionContainer = document.querySelector(".formulation.clearfix");
+ /*let formula = document.querySelector(".formulation.clearfix p");
+ formula.classList.add("chosen_formula");
+ formula.style.position = "absolute";
+ formula.style.top = "50%";
+ formula.style.left = "50%";
+ formula.style.backgroundColor = "rgba(255,255,255,0.9)";
+ formula.style.borderRadius = "10%";
+ formula.style.transform = "translate(-50%, -50%)";
+ formula.style.padding = "5px";*/
+
+ let object = this;
+
+
+ let input = document.querySelector(".formulation.clearfix textarea, .formulation.clearfix input[type=text]");
+ input.addEventListener("keypress", function(event) {
+ if(event.key == "Enter") {
+ object.speechBubbleElement.click();
+ }
+ });
+ input.removeAttribute("readonly");
+ this.inputElement = input;
+
+ //hide the save state input
+ let saveStateInput = questionContainer.querySelector("input.maxima-string");
+ if(saveStateInput == undefined) {
+ console.log("state can't be saved due to missing save state input field");
+ }
+ else {
+ saveStateInput.style.display = "none";
+ let savedStateAsString = saveStateInput.value;
+ if(savedStateAsString != "" && savedStateAsString != undefined) {
+ let loadedSaveState;
+ try {
+ loadedSaveState = JSON.parse(savedStateAsString);
+
+ let saveStateConvertAsString = localStorage.getItem("saveStateConvert");
+ let saveStateConvert;
+ if(saveStateConvert != undefined) {
+ try {
+ saveStateConvert = JSON.parse(saveStateConvertAsString);
+ }
+ catch(error) {
+ console.log("Error in parsing converted save state");
+ }
+ }
+ console.log("check for conversion condition here");
+ if(loadedSaveState != undefined) {
+ //What's newer? Current process: Overwrite session storage with saved state.
+ if(saveStateConvert != undefined && (loadedSaveState.saveState == undefined ||saveStateConvert.solvedVariants.length >= loadedSaveState.solvedVariants.length)) {
+ console.log("loaded converted solved variants array");
+ loadedSaveState = saveStateConvert;
+ }
+ else {
+ console.log("conditition for converting not met");
+ }
+ this.loadFromSaveState(loadedSaveState);
+ }
+ }
+ catch(error) {
+ console.log("Save state could not be loaded, possibly due to JSON parse error");
+ console.log(error);
+ }
+ }
+ else {
+ //Try conversion.
+ console.log("try conversion 2");
+ let saveStateConvertAsString = localStorage.getItem("saveStateConvert");
+ let saveStateConvert;
+ if(saveStateConvertAsString != undefined) {
+ try {
+ saveStateConvert = JSON.parse(saveStateConvertAsString);
+ console.log("loaded converted save state");
+ this.loadFromSaveState(saveStateConvert);
+ }
+ catch(error) {
+ console.log("Error in parsing converted save state");
+ console.log(error)
+ }
+ }
+ }
+ }
+ this.saveStateInput = saveStateInput;
+
+ let validation = document.querySelector(".formulation.clearfix .stackinputfeedback");
+ validation.style.display = "none";
+
+ this.validationElement = validation;
+
+ let speechBubble = document.createElement("div");
+ speechBubble.classList.add("bubble");
+ speechBubble.classList.add("spell");
+ speechBubble.classList.add("spell-in-progress");
+
+ speechBubble.onclick = function () {
+ if (this.classList.contains("spell-in-progress")) {
+
+ this.classList.remove("spell-in-progress")
+ //animate player
+ //submit answer via ajax
+ //process response
+ //old version: fetch form from current page let form = document.getElementById("responseform");
+ //new version: fetch from from current question saved in question query
+ if (nextQuestionQuery == undefined) {
+ return;
+ }
+ let form = nextQuestionQuery;
+ if (form == undefined) {
+ //error handling
+ console.log("no form to submit");
+ return false;
+ }
+ let formData = new FormData(form);
+ let submitButtonData = document.querySelector("input.submit, button.submit");
+ if (submitButtonData == undefined) {
+ //error handling
+ //...
+ console.log("no submit button found");
+ return false;
+ }
+ //let formDataAnswer = structuredClone(formData);
+ let formDataAnswer = new FormData(form);
+ formDataAnswer.append(submitButtonData.name, submitButtonData.value);
+
+
+ //Get expected form, fill entered value and give dummy-values (or already correct) for all others.
+ let expectedInputs = battleGround.querySelectorAll("input[type=text], textarea");
+ if(expectedInputs.length > 1) {
+ if(object.targetedEnemy == undefined) {
+ object.targetEnemy();
+ }
+ /*let targetedInputName = "";
+ if(object.targetedEnemy.container.dataset.matrixinput != undefined) {
+ targetedInputName = object.targetedEnemy.container.dataset.matrixinput;
+ }
+ else {
+ targetedInputName =
+ }*/
+ expectedInputs.forEach(function(expectedInput) {
+ if(object.targetedEnemy.container.dataset.refer == expectedInput.name) {
+ formDataAnswer.set(expectedInput.name, object.inputElement.value);
+ }
+ else {
+ //insert already correct answer or compute dummy value
+ if(expectedInput.dataset.correctAnswer != undefined) {
+ formDataAnswer.set(expectedInput.name, expectedInput.dataset.correctAnswer);
+ }
+ else {
+ //if numeric
+ formDataAnswer.set(expectedInput.name, "429876543210");
+ //add other cases
+ //...
+ }
+ }
+ });
+ }
+ else {
+ if(object.targetedEnemy == undefined) {
+ let firstEnemyContainer = document.querySelector(".enemy-container:not(.invisible)");
+ for(let i=0;i<object.GameElements.enemies.length;i++) {
+ if(object.GameElements.enemies[i].container == firstEnemyContainer) {
+ object.targetedEnemy = object.GameElements.enemies[i];
+ }
+ }
+ }
+ //fill input of the current text input into form data
+ let nameOfTextInput = expectedInputs[0].name;
+ formDataAnswer.set(nameOfTextInput, object.inputElement.value);
+ }
+
+ fetch(form.action, { method: "POST", body: formDataAnswer })
+ .then(response => {
+ return response.text();
+ })
+ .then(text => {
+ let fetchedPage = object.Parser.parseFromString(text, "text/html");
+ let formFetchedPage = fetchedPage.getElementById("responseform");
+ //form has to be updated to pass sequence check (to prevent out of sequence error, Moodle Error code: submissionoutofsequencefriendlymessage)
+ //nextQuestionQuery = formFetchedPage;
+
+ let repeatButton = fetchedPage.querySelector(".mod_quiz-redo_question_button");
+ console.log(repeatButton);
+ if (repeatButton == undefined) {
+ let stackinputerrorSpan = fetchedPage.querySelector(".stackinputerror");
+ if(stackinputerrorSpan != undefined) {
+ //Probably an input was submitted despite of an syntax error.
+ nextQuestionQuery.querySelectorAll("[name$=sequencecheck]").forEach(function(sequenceCheckFieldToRaise) {
+ sequenceCheckFieldToRaise.value = parseInt(sequenceCheckFieldToRaise.value)+1;
+ });
+ throw new Error("Stack input error 1");
+ }
+ //If there is no repeat button, we are probably on a validation page (e. g. "Please answer all parts of the question" or "Please check whether what you entered was intepreted as expected"), which happens for unknown reasons. Submit again to get feedback page.
+ let submitButton = fetchedPage.querySelector("input.submit, button.submit");
+ if(submitButton == undefined) {
+ throw new Error("Error in promise chain: (1) For some reason, question could neither be repeated nor input could be resubmitted. Probably sequence check error (Moodle error code submissionoutofsequencefriendlymessage).");
+ }
+ let matchSubmit = [
+ "",
+ submitButton.name,
+ submitButton.value
+ ];
+
+ let formDataSubmitValidation = new FormData(formFetchedPage);
+
+ formDataSubmitValidation.append(matchSubmit[1], matchSubmit[2]);
+
+ return fetch(formFetchedPage.action, { method: "POST", body: formDataSubmitValidation }).then(response => { return response.text(); }).then(text => { return object.Parser.parseFromString(text, "text/html"); });
+ }
+ else {
+ return fetchedPage;
+ }
+ })
+ .then(fetchedPage => {
+ let saveInfo;
+ //console.log(text);
+ let toAppendToMessage;
+ //let fetchedPage = Parser.parseFromString(text, "text/html");
+ let formFetchedPage = fetchedPage.getElementById("responseform");
+ //form has to be updated to pass sequence check (to prevent out of sequence error, Moodle Error code: submissionoutofsequencefriendlymessage)
+ //nextQuestionQuery = formFetchedPage;
+
+ //if response is not positive, immediately repeat question
+ //get information about repeat button from response
+ //we look for input.mod_quiz-redo_question_button
+ //let matchRedo = text.match(/input.*?name="(.*?)".*?value="(.*?)".*?class=".*?mod_quiz-redo_question_button.*?/);
+ let repeatButton = fetchedPage.querySelector(".mod_quiz-redo_question_button");
+
+ //Check again for missing repeat button. It is especially missing, when there is a validation error (e. g. "Please answer all parts of the question").
+ let validationErrorSpan = fetchedPage.querySelector(".validationerror");
+ console.log(validationErrorSpan);
+ if(validationErrorSpan != undefined) {
+ //Raise sequence check to pass sequence check and prevent sequence check error (Moodle error code submissionoutofsequencefriendlymessage).
+ nextQuestionQuery.querySelectorAll("[name$=sequencecheck]").forEach(function(sequenceCheckFieldToRaise) {
+ sequenceCheckFieldToRaise.value = parseInt(sequenceCheckFieldToRaise.value)+2;
+ });
+ throw new Error("Validation error. Probably \"Please answer all parts of the question.\"");
+ }
+ else {
+ //If we had an error, sequencecheck-field has to be reset to stay in the correct sequence.
+ nextQuestionQuery.querySelectorAll("[name$=sequencecheck]").forEach(function(sequenceCheckFieldToReset) {
+ sequenceCheckFieldToReset.value = 1;
+ });
+ }
+
+ let matchRedo = [
+ "",
+ repeatButton.name,
+ repeatButton.value
+ ];
+ console.log("match redo");
+ console.log(matchRedo);
+ //For feedback, we look for .stackprtfeedback (each of them).
+ //let matchFeedback = text.match(/class=".*?stackprtfeedback.*?".*?><div class="(.*?)">([\d\D]*?)<div class="outcome clearfix/);
+ //console.log(matchFeedback);
+
+
+ //console.log(formFetchedPage);
+
+ let message = "";
+ let lastStroke = false;
+
+ let possibleVictoryTexts = [
+ "Du hast es geschafft! Weiter so!",
+ "Super! Das war richtig!",
+ "Wunderbar! Du hast es geschafft!"
+ ];
+
+ if(expectedInputs.length > 1) {
+ let allAnswered = false;
+ console.log("process feedback to multiple questions");
+ //expect feedback in the same order as the input fields appeared
+ //let specificFeedbackFieldEvaluations = fetchedPage.querySelectorAll(".stackprtfeedback .correct, .stackprtfeedback .incorrect, ...");
+ let specificFeedbackFields = fetchedPage.querySelectorAll(".stackprtfeedback");
+ //console.log("Looking for specific feedback field number "+object.targetedEnemy.container.dataset.count);
+ if(specificFeedbackFields[object.targetedEnemy.container.dataset.count] == undefined) {
+ //emergency routine
+ //...
+ throw new Error("no adequate feedback found (error variant 1)");
+ }
+
+ //Evaluate feedback for targeted enemy.
+ let specificFeedbackFieldEvaluation = specificFeedbackFields[object.targetedEnemy.container.dataset.count].querySelector(".correct, .incorrect, .partiallycorrect");
+ if(specificFeedbackFieldEvaluation == undefined) {
+ //emergency routine
+ //...
+ throw new Error("no adequate feedback evaluation found (error variant 2)");
+ }
+
+ //Previously, check for special handling on matrix input.
+ console.log("START ANALYSIS");
+ //Find out more in case of matrix input
+ if(object.targetedEnemy.container.dataset.matrixinput != undefined) {
+ /*
+ querySelector won't work, because style of wrong parts is not yet appended.
+ Analyse the real part...
+ '<span class="nolink"><span class="nolink"><span class="MathJax_Preview"><a href="https://moodle.hs-bochum.de/filter/tex/displaytex.php?texexp=%20%5Cleft%28%5Cbegin%7Barray%7D%7Bccc%7D%20%7B%5Ccolor%7Bred%7D%7B%5Cunderline%7B1%7D%7D%7D%20%26%20%7B%5Ccolor%7Bred%7D%7B%5Cunderline%7B429876543210%7D%7D%7D%20%26%20%7B%5Ccolor%7Bred%7D%7B%5Cunderline%7B429876543210%7D%7D%7D%20%5C%5C%20%7B%5Ccolor%7Bred%7D%7B%5Cunderline%7B429876543210%7D%7D%7D%20%26%20%7B%5Ccolor%7Bred%7D%7B%5Cunderline%7B429876543210%7D%7D%7D%20%26%20%7B%5Ccolor%7Bred%7D%7B%5Cunderline%7B429876543210%7D%7D%7D%20%5C%5C%20%7B%5Ccolor%7Bred%7D%7B%5Cunderline%7B429876543210%7D%7D%7D%20%26%20%7B%5Ccolor%7Bred%7D%7B%5Cunderline%7B429876543210%7D%7D%7D%20%26%20%7B%5Ccolor%7Bred%7D%7B%5Cunderline%7B429876543210%7D%7D%7D%20%5Cend%7Barray%7D%5Cright%29" id="action_link648326912307e122" class="" title="TeX"><img class="texrender" title=" \\left(\\begin{array}{ccc} {\\color{red}{\\underline{1}}} & {\\color{red}{\\underline{429876543210}}} & {\\color{red}{\\underline{429876543210}}} \\\\ {\\color{red}{\\underline{429876543210}}} & {\\color{red}{\\underline{429876543210}}} & {\\color{red}{\\underline{429876543210}}} \\\\ {\\color{red}{\\underline{429876543210}}} & {\\color{red}{\\underline{429876543210}}} & {\\color{red}{\\underline{429876543210}}} \\end{array}\\right)" alt=" \\left(\\begin{array}{ccc} {\\color{red}{\\underline{1}}} & {\\color{red}{\\underline{429876543210}}} & {\\color{red}{\\underline{429876543210}}} \\\\ {\\color{red}{\\underline{429876543210}}} & {\\color{red}{\\underline{429876543210}}} & {\\color{red}{\\underline{429876543210}}} \\\\ {\\color{red}{\\underline{429876543210}}} & {\\color{red}{\\underline{429876543210}}} & {\\color{red}{\\underline{429876543210}}} \\end{array}\\right)" src="https://moodle.hs-bochum.de/filter/tex/pix.php/09631cdc594f40a1d92784f0a9e9250f.png"></a></span><script type="math/tex"> \\left(\\begin{array}{ccc} {\\color{red}{\\underline{1}}} & {\\color{red}{\\underline{429876543210}}} & {\\color{red}{\\underline{429876543210}}} \\\\ {\\color{red}{\\underline{429876543210}}} & {\\color{red}{\\underline{429876543210}}} & {\\color{red}{\\underline{429876543210}}} \\\\ {\\color{red}{\\underline{429876543210}}} & {\\color{red}{\\underline{429876543210}}} & {\\color{red}{\\underline{429876543210}}} \\end{array}\\right)</script></span></span>'*/
+ /*
+ let wrongParts = specificFeedbackFields[object.targetedEnemy.container.dataset.count].querySelectorAll(".mn[style*='red']");
+ console.log(specificFeedbackFields);
+ console.log(specificFeedbackFields[object.targetedEnemy.container.dataset.count]);
+ console.log(wrongParts);
+ console.log("WRONG PARTS: "+wrongParts.length);*/
+
+ let amountOfWrongParts = 0;
+ let matchedWrong = [];
+ let latexScript = specificFeedbackFields[object.targetedEnemy.container.dataset.count].querySelector("script");
+ if(latexScript != undefined && latexScript.innerHTML != "" && latexScript.innerHTML != undefined) {
+ //Have \underline be the criteria for wrong. Could be \color (red) also.
+ matchedWrong = latexScript.innerHTML.match(/underline/g);
+ console.log(latexScript.innerHTML);
+ console.log(matchedWrong);
+ }
+ if(matchedWrong == null) {
+ console.log("probably already solved whole matrix");
+ matchedWrong = [];
+ }
+ amountOfWrongParts = matchedWrong.length;
+ if(amountOfWrongParts < object.targetedEnemy.container.dataset.matrixelementstosolve) {
+ console.log("probably correct");
+ let relevantInputField = document.querySelector("[name='"+object.targetedEnemy.container.dataset.refer+"']");
+ relevantInputField.parentNode.querySelector(".input-replacer").innerHTML = object.inputElement.value;//Better: Deep copy of parsed latex math.
+ relevantInputField.dataset.correctAnswer = object.inputElement.value;
+ object.targetedEnemy.container.dataset.matrixelementstosolve = parseInt(object.targetedEnemy.container.dataset.matrixelementstosolve)-1;
+ message = "Gut, weiter so!";
+ if(object.targetedEnemy.container.dataset.matrixelementstosolve == 0) {
+ //Obviously, the following will not fire, because the question is already registered as solved.
+ console.log("Will this fire?");
+ message = "Gut gemacht!";
+ }
+ //Target next matrix element, if existent.
+ let matrixTableParent = relevantInputField.closest(".matrixtable");
+ if(matrixTableParent != undefined) {
+ let allInputFields = matrixTableParent.querySelectorAll("input");
+ let currentIndex = -1;
+ for(let i=0;i<allInputFields.length;i++) {
+ if(allInputFields[i].isEqualNode(relevantInputField)) {
+ currentIndex = i;
+ break;
+ }
+ }
+ let selected = false;
+ if(currentIndex != -1) {
+ for(let i = currentIndex+1;i<allInputFields.length;i++) {
+ if(allInputFields[i].dataset.correctAnswer == undefined) {
+ //select this one
+ console.log("select "+allInputFields[i].name);
+ selected = true;
+ let relevantTd = allInputFields[i].closest("td");
+ if(relevantTd != undefined) {
+ matrixTdSelect(null, relevantTd);
+ }
+ break;
+ }
+ }
+ //If not selected one in the first loop, loop again from the beginning.
+ if(!selected) {
+ for(let i = 0;i<currentIndex;i++) {
+ if(allInputFields[i].dataset.correctAnswer == undefined) {
+ //select this one
+ console.log("select "+allInputFields[i].name+" in second turn");
+ selected = true;
+ let relevantTd = allInputFields[i].closest("td");
+ if(relevantTd != undefined) {
+ matrixTdSelect(null, relevantTd);
+ }
+ break;
+ }
+ }
+ }
+ }
+ }
+ }
+ else {
+ console.log("probably false");
+ message = specificFeedbackFieldEvaluation.innerHTML;
+ if(message == "" || message == undefined) {
+ message = "Leider falsch!";
+ }
+ }
+ console.log("Wrong parts of matrix: "+amountOfWrongParts);
+ /*}
+ else {
+ console.log("Could not find Latex Script. Probably solved matrix. (Or error?)");
+
+ }*/
+ }
+ else {
+ //console.log("is not matrix input");
+ }
+ console.log("END ANALYSIS");
+
+
+ if(specificFeedbackFieldEvaluation.classList.contains("correct")) {
+ //well done
+ lastStroke = true;
+ message = possibleVictoryTexts[Math.floor(Math.random() * possibleVictoryTexts.length)];
+ object.targetedEnemy.container.querySelector("input, textarea").dataset.correctAnswer = object.enterSpellContainer.querySelector("input").value;
+ //check wether all enemies are defeated now
+
+ //In case of matrix input, the last correct entered matrix element is not yet recognized. Check here.
+ if(object.targetedEnemy.container.dataset.matrixinput != undefined) {
+
+ }
+
+ allAnswered = true;
+ expectedInputs.forEach(function(expectedInput){
+ if(allAnswered == false) {
+ return;
+ }
+ if(expectedInput.dataset.correctAnswer == undefined) {
+ allAnswered = false;
+ }
+ });
+ if(allAnswered) {
+ console.log("all questions are answered correctly now.");
+ console.log("victory");
+ object.incrementSolved();
+
+ let continueContainer = document.createElement("span");
+ continueContainer.innerHTML = " ";
+ let continueLink = document.createElement("a");
+ continueLink.innerHTML = "Tiefer in den Wald";
+ continueLink.href = "javascript:;";
+ continueLink.onclick = function () {
+ object.goToNextScene(object, true);
+ };
+ continueContainer.appendChild(continueLink);
+ toAppendToMessage = continueContainer;
+
+ object.markQuestionAsSolved();
+
+ setTimeout(function() { object.animateTransformation(); }, 2000);
+ //Score raise happens delayed, so saving the state has to be equipped with delay, too.
+ //setTimeout(function() { object.saveState(); }, 5000);
+ saveInfo = "Solved all enemies."
+ }
+ else {
+ saveInfo = "Solved one (of many)."
+ }
+ }
+ //Matrix input is already handled above.
+ else if(object.targetedEnemy.container.dataset.matrixinput == undefined) {
+ if(object.targetedEnemy.container.dataset.matrixinput == undefined && (specificFeedbackFieldEvaluation.classList.contains("partiallycorrect") || specificFeedbackFieldEvaluation.classList.contains("incorrect"))) {
+ message = specificFeedbackFieldEvaluation.innerHTML;
+ saveInfo = "Partially or incorrect (one of many) or matrix input.";
+
+ }
+ else {
+ //emergency routine
+ //...
+ message = specificFeedbackFieldEvaluation.innerHTML;
+ console.log("feedback evaluation found, but unsure wether correct, incorrect or partially correct");
+ saveInfo = "Neither correct, incorrect nor partiallycorrect.";
+ }
+ }
+ this.classList.add("spell-in-progress");
+
+ //in any case (except everything is solved?), reload the question
+ //if(!allAnswered) {
+ let formDataRetry = new FormData(formFetchedPage);
+ formDataRetry.append(matchRedo[1], matchRedo[2]);
+ fetch(formFetchedPage.action, { method: "POST", body: formDataRetry });
+ //}
+ }
+ else {
+ let generalFeedbackNode = fetchedPage.querySelector(".stackprtfeedback .partiallycorrect, .stackprtfeedback .incorrect, .stackprtfeedback .correct");
+ let feedbackContentNode = fetchedPage.querySelector(".stackprtfeedback");
+ let matchFeedback = [
+ "",
+ generalFeedbackNode.classList.item(0),
+ feedbackContentNode.innerHTML
+ ];
+
+ if (matchFeedback[1] == "partiallycorrect" || matchFeedback[1] == "incorrect") {
+ message = matchFeedback[2];
+ this.classList.add("spell-in-progress");
+
+ //get ready for redo
+ let formDataRetry = new FormData(formFetchedPage);
+ formDataRetry.append(matchRedo[1], matchRedo[2]);
+
+ //return fetch(formFetchedPage.action, {method:"POST", body:formDataRetry});
+ fetch(formFetchedPage.action, { method: "POST", body: formDataRetry });
+ saveInfo = "Partially or incorrect (one enemy).";
+ }
+ else {
+ //correct or undefined
+ console.log("victory");
+ object.incrementSolved();
+
+ message = possibleVictoryTexts[Math.floor(Math.random() * possibleVictoryTexts.length)];
+ let continueContainer = document.createElement("span");
+ continueContainer.innerHTML = " ";
+ let continueLink = document.createElement("a");
+ continueLink.innerHTML = "Tiefer in den Wald";
+ continueLink.href = "javascript:;";
+ continueLink.onclick = function () {
+ object.goToNextScene(object, true);
+ };
+ continueContainer.appendChild(continueLink);
+ toAppendToMessage = continueContainer;
+ lastStroke = true;
+
+ object.markQuestionAsSolved();
+
+ setTimeout(function() { object.animateTransformation(); }, 2000);
+
+ let formDataRetry = new FormData(formFetchedPage);
+ formDataRetry.append(matchRedo[1], matchRedo[2]);
+ fetch(formFetchedPage.action, { method: "POST", body: formDataRetry });
+ saveInfo = "Solved (one enemy)."
+ }
+
+
+
+ }
+ object.animateAttack(lastStroke);
+ //show feedback
+ setTimeout(function () { object.processNotification(message, true, undefined, undefined, toAppendToMessage); }, 1000);
+ setTimeout(function() { object.saveState(saveInfo); }, 5000);
+ })
+ .catch(error => {
+ this.classList.add("spell-in-progress");
+ object.saveState("Error"+error);
+ console.log(error);
+ })
+ /*
+ .then(response => {
+ return response.text();
+ })
+ .then(text => {
+ //update current form?
+ //let fetchedPage = Parser.parseFromString(text, "text/html");
+ //let formFetchedPage = fetchedPage.getElementById("responseform");
+ console.log(text);
+
+ //let formDataSubmitValidation = new FormData(formFetchedPage);
+ //console.log(formDataSubmitNextTry);
+ //console.log(formData);
+
+ //For some unknown reason, fetchedPage is a validation page, so given input has to be sent again.
+
+ /*for(let pair of formDataSubmitNextTry.entries()) {
+ console.log("changed "+form.elements[pair[0]].value+" in "+pair[0]);
+ form.elements[pair[0]].value = pair[1];
+ console.log("to "+pair[1]);
+ console.log("-------");
+ }
+
+ formDataSubmitNextTry.append("q684007:17_ans1_val","y=2");
+ formDataSubmitNextTry.append("q684007:17_ans1","y=2");
+
+ //test submit
+ //return fetch(formFetchedPage.action, {method:"POST", body:formDataSubmitNextTry});
+
+ console.log(formFetchedPage.querySelector("input[type=submit].submit"));
+ console.log(document.querySelector("input[type=submit].submit"))
+ console.log("chain succeeded");
+ })
+ //.then(response => { return response.text();})*/
+ ;
+ }
+ else {
+ //bumping speech-bubble just for fun?
+ }
+ };
+ //speechBubble.style.display = "inline";
+ this.speechBubbleElement = speechBubble;
+
+ let questionFormulationBubble = document.createElement("p");
+ questionFormulationBubble.classList.add("bubble", "no-arrow", "closed", "question-bubble", "fairy-help");
+ questionFormulationBubble.style.position = "relative";
+ questionFormulationBubble.addEventListener("transitionend", function () {
+ if (!this.classList.contains("closed")) {
+ this.classList.add("show-overflow");
+ }
+ });
+
+ let questionFormulationContent = document.createElement("div");
+ questionFormulationContent.classList.add("bubble-content");
+ questionFormulationBubble.appendChild(questionFormulationContent);
+
+ this.questionBubbleElement = questionFormulationBubble;
+ this.questionBubbleContentElement = questionFormulationContent;
+
+ //create and implement fantasy elements
+ let enterSpellContainer = document.createElement("div");
+ enterSpellContainer.classList.add("enter-spell-container");
+ //let enterSpellText = document.createElement("p");
+ //let helpContainer = document.createElement("div");
+
+ let errorInfo = document.createElement("div");
+ errorInfo.classList.add("exclamation");
+ errorInfo.innerHTML = "!";
+
+ errorInfo.onclick = function() { if(this.closest(".enter-spell-container").classList.contains("error")) { object.showNotificationSpeechBubble(); }};
+
+ let helpNotificationContainer = document.createElement("div");
+ helpNotificationContainer.classList.add("help-notification-container");
+ let helpNotification = document.createElement("p");
+ helpNotification.classList.add("bubble", "no-arrow", "closed", "fairy-help", "middle-up-arrow");
+ //helpNotification.style.maxHeight = "0px";
+ helpNotification.style.position = "absolute";
+ //helpNotification.style.overflow = "hidden";
+ helpNotification.addEventListener("transitionend", function () {
+ if (!this.classList.contains("closed")) {
+ this.classList.add("show-overflow");
+ }
+ });
+
+ let helpNotificationContent = document.createElement("div");
+ helpNotificationContent.classList.add("bubble-content");
+ helpNotification.appendChild(helpNotificationContent);
+
+
+ let fairyPlaceHolderBottom = document.createElement("p");
+ fairyPlaceHolderBottom.style.width = "0px";
+ fairyPlaceHolderBottom.style.height = "0px";
+ fairyPlaceHolderBottom.style.top = "-40px";
+ fairyPlaceHolderBottom.style.position = "relative";
+ fairyPlaceHolderBottom.style.zIndex = 1;
+ fairyPlaceHolderBottom.classList.add("fairy-place-holder");
+ //fairyPlaceHolderBottom.style.marginLeft = "50%";
+
+ helpNotificationContainer.appendChild(fairyPlaceHolderBottom);
+ helpNotificationContainer.appendChild(helpNotification);
+ this.notificationBubbleElement = helpNotification;
+ this.notificationBubbleContainer = helpNotificationContainer;
+
+ let fairyPlaceHolder = document.createElement("p");
+ fairyPlaceHolder.style.width = "0px";
+ fairyPlaceHolder.style.height = "0px";
+ fairyPlaceHolder.style.position = "relative";
+ fairyPlaceHolder.style.zIndex = 1;
+ fairyPlaceHolder.classList.add("fairy-place-holder");
+ //fairyPlaceHolder.style.marginLeft = "50%";
+ //fairyPlaceHolder.style.right = "60%";
+
+ let preInputField = document.createElement("div");
+ preInputField.classList.add("input-surrounding-math");
+ this.preInputField = preInputField;
+
+ let postInputField = document.createElement("div");
+ postInputField.classList.add("input-surrounding-math");
+ this.postInputField = postInputField;
+
+ //enterSpellText.innerHTML = "Enter your spell here:";
+ //enterSpellContainer.appendChild(enterSpellText);
+ //enterSpellContainer.appendChild(questionFormulationBubble);
+ enterSpellContainer.appendChild(preInputField);
+ enterSpellContainer.appendChild(input);
+ enterSpellContainer.appendChild(errorInfo);
+ enterSpellContainer.appendChild(postInputField);
+ //is appended below -- enterSpellContainer.appendChild(helpNotification);
+ //is append to air instead -- enterSpellContainer.appendChild(fairyPlaceHolder);
+
+ this.enterSpellContainer = enterSpellContainer;
+
+ /*
+ Background specific: Remove "Enter your spell here" (happens above), add background, remove unnecessary elements, add "air".
+ */
+ document.querySelectorAll(".info").forEach(function (infoNode) {
+ infoNode.remove();
+ });
+ document.querySelectorAll(".que .content").forEach(contentNode => {
+ contentNode.style.margin = "0";
+ //contentNode.style.height = "500px";
+ //contentNode.style.background = "url(https://marvin.hs-bochum.de/~mneugebauer/fantasy/bg-forest1.png)";
+ //contentNode.style.background = "url(https://marvin.hs-bochum.de/~mneugebauer/fantasy/bg-elven_land4.png)";
+ contentNode.style.backgroundSize = "auto 100%";
+
+ let air = document.createElement("div");
+ air.classList.add("air");
+ //air.style.height = "100px";
+ contentNode.insertBefore(air, contentNode.firstChild);
+
+ air.appendChild(this.questionBubbleElement);
+ air.appendChild(fairyPlaceHolder);
+ //this.notificationBubbleElement.style.display = "none";
+
+ let fader = document.createElement("div");
+ fader.classList.add("fader");
+ //document.getElementById("responseform").appendChild(fader);
+ contentNode.insertBefore(fader, contentNode.firstChild);
+
+ console.log("add event listener");
+
+ this.fader = fader;
+
+ });
+ document.querySelectorAll(".que .content .formulation").forEach(function (formulationNode) {
+ console.log("setting border to none");
+ console.log(formulationNode.style.border);
+ formulationNode.style.setProperty("border", "none", "important");
+ console.log(formulationNode.style.border);
+ });
+
+ document.querySelectorAll("input[value=Check]").forEach(function (checkButton) {
+ checkButton.style.display = "none";
+ });
+
+
+ /*
+
+ */
+
+
+ let Player = new Elf();
+ Player.setSize(Player.Sprites.idle.spriteWidth / 5);
+ Player.container.style.left = "40%";
+ Player.container.style.bottom = "0px";
+ Player.container.classList.add("player-container");
+
+ //Define multiple enemies. Each enemy has a Placeholder for the fairy, several events on click and mouse over / mouse out, a formula container.
+ let monstersCamp = document.createElement("div");
+ let fairyPlaceHolderMonsterAnalysisAnimation = document.createElement("div");
+ fairyPlaceHolderMonsterAnalysisAnimation.classList.add("monster-analysis-fairy-animation-placeholder")
+ monstersCamp.appendChild(fairyPlaceHolderMonsterAnalysisAnimation);
+ monstersCamp.classList.add("monsters-camp");
+
+ //let Enemy = new Golem(1);
+ let Enemy1 = new Troll(1);
+ Enemy1.setSize(Enemy1.Sprites.idle.spriteWidth / 3);
+ /*Enemy1.container.style.right = "0px";
+ Enemy1.container.style.bottom = "0px";*/
+ //Other than any other game elements, enemies are automatically positioned with regard to responsiveness.
+ Enemy1.container.style.position = "relative";
+ Enemy1.container.classList.add("enemy-container", "invisible");
+
+ let Enemy2 = new IceGolem(1);
+ Enemy2.setSize(Enemy2.Sprites.idle.spriteWidth / 5);
+ /*Enemy2.container.style.right = "200px";
+ Enemy2.container.style.bottom = "0px";*/
+ Enemy2.container.style.position = "relative";
+ Enemy2.container.classList.add("enemy-container", "invisible");
+
+ let Enemy3 = new ForestGolem(1);
+ Enemy3.setSize(Enemy2.Sprites.idle.spriteWidth / 5);
+ Enemy3.container.style.position = "relative";
+ Enemy3.container.classList.add("enemy-container", "invisible");
+
+
+ let Enemy4 = new ForestGolem(1);
+ Enemy4.setSize(Enemy4.Sprites.idle.spriteWidth / 5);
+ Enemy4.container.style.position = "relative";
+ Enemy4.container.classList.add("enemy-container", "invisible");
+
+ let Enemy5 = new IceGolem(1);
+ Enemy5.setSize(Enemy5.Sprites.idle.spriteWidth / 5);
+ /*Enemy2.container.style.right = "200px";
+ Enemy2.container.style.bottom = "0px";*/
+ Enemy5.container.style.position = "relative";
+ Enemy5.container.classList.add("enemy-container", "invisible");
+
+ let Enemy6 = new Troll(1);
+ Enemy6.setSize(Enemy6.Sprites.idle.spriteWidth / 3);
+ /*Enemy2.container.style.right = "200px";
+ Enemy2.container.style.bottom = "0px";*/
+ Enemy6.container.style.position = "relative";
+ Enemy6.container.classList.add("enemy-container", "invisible");
+
+
+
+ //let trolls be added in the end
+ let Enemies = [Enemy4, Enemy2, Enemy3, Enemy5, Enemy6, Enemy1];
+
+ Enemies.forEach(function(Enemy) {
+ Enemy.container.addEventListener("click", function(event) {
+ //event.stopPropagation();
+ //target enemy
+ Enemies.forEach(function(EnemyToUntarget) {
+ EnemyToUntarget.container.classList.remove("targeted");
+ });
+ Enemy.container.classList.add("targeted");
+
+ //Add information before and after the input field
+ object.targetedEnemy = Enemy;
+ object.updateInputSurroundingMath(object);
+ });
+
+ Enemy.container.onmouseover = function () {
+ if(videoAnimation == true) { return; }
+ object.GameElements.helper.sendTo(Enemy.fairyPlaceHolder);
+ };
+
+ Enemy.container.onmouseout = function () {
+ if(videoAnimation == true) { return; }
+ object.GameElements.helper.sendBack();
+ };
+
+ monstersCamp.appendChild(Enemy.container);
+ });
+ this.monstersCamp = monstersCamp;
+
+
+
+
+ /*let formulaContainer = document.createElement("div");
+ formulaContainer.classList.add("formula-container");
+ Enemy.container.appendChild(formulaContainer);
+ this.formulaContainer = formulaContainer;*/
+
+ let fairyHome = document.createElement("div");
+ fairyHome.classList.add("fairy-home");
+ let Helper = new Fairy();
+ Helper.setSize(Helper.Sprites.idle.spriteWidth / 3);
+ fairyHome.style.left = Player.container.style.left;
+ fairyHome.style.bottom = (Player.Sprites.idle.spriteHeight / 5 + 10) + "px";
+ //Helper.container.style.left = Player.container.style.left;
+ //Helper.container.style.bottom = (Player.Sprites.idle.spriteHeight / 5 + 10) + "px";
+ //add place for exclamations
+ Helper.node.classList.add("fairy-img");
+ Helper.node.style.height = "40px";
+ Helper.node.style.position = "absolute";
+ //Helper.container.style.height = Helper.Sprites.idle.spriteHeight / 3 * 2 + "px";
+ fairyHome.style.height = Helper.Sprites.idle.spriteHeight / 3 * 2 + "px";
+ let exclamation = document.createElement("div");
+ exclamation.style.height = Helper.Sprites.idle.spriteHeight / 3;
+ exclamation.innerHTML = "!";
+ exclamation.classList.add("exclamation");
+ exclamation.onclick = function() { if(this.classList.contains("active")) { object.showNotificationSpeechBubble(); }};
+ Helper.container.style.overflow = "visible";
+ Helper.container.insertBefore(exclamation, Helper.node);
+ Helper.container.classList.add("helper-container");
+ Helper.container.onclick = function () { if(object.introState == 1) { object.introState = 2; } object.showNotificationSpeechBubble(); };
+ fairyHome.appendChild(exclamation);
+ fairyHome.appendChild(Helper.container);
+ this.fairyHome = fairyHome;
+
+ let Freed = new Fairy("https://marvin.hs-bochum.de/~mneugebauer/fantasy/fairy-black.svg");
+ Freed.setSize(Freed.Sprites.idle.spriteWidth / 3);
+ Freed.node.style.height = "40px";
+ Freed.node.style.position = "absolute";
+ Freed.container.style.overflow = "visible";
+ Freed.container.classList.add("freed");
+ this.GameElements.freed = Freed;
+ monstersCamp.insertBefore(Freed.container, monstersCamp.firstChild);
+
+ let followPrompt = document.createElement("span");
+ followPrompt.innerHTML = " ";
+ let followLink = document.createElement("a");
+ followLink.innerHTML = "Folgen";
+ followLink.href = "javascript:;";
+ followLink.onclick = function() { object.goToNextScene(object, false); };
+ followPrompt.appendChild(followLink);
+ this.followPrompt = followPrompt;
+
+ this.GameElements.player = Player;
+ //this.GameElements.enemy = Enemy;
+ //this.GameElements.enemy2 = Enemy2;
+ this.GameElements.enemies = Enemies;
+ this.GameElements.helper = Helper;
+
+ let battleGround = document.createElement("div");
+ battleGround.classList.add("battleground");
+ battleGround.style.height = "194px";
+ //battleGround.style.height = Enemy.Sprites.idle.spriteHeight/3+"px";
+ //battleGround.appendChild(validation);
+
+ let signPostImgHref = "https://marvin.hs-bochum.de/~mneugebauer/fantasy/sign-post.png";
+ let signPostRightContainer = document.createElement("div");
+ signPostRightContainer.classList.add("sign-post-container", "point-left");
+ let signPostRight = document.createElement("img");
+ signPostRight.classList.add("sign-post");
+ signPostRight.src = signPostImgHref;
+ let fairyPlaceHolderAtSignpost = document.createElement("div");
+ fairyPlaceHolderAtSignpost.classList.add("fairy-place-holder");
+ signPostRightContainer.appendChild(fairyPlaceHolderAtSignpost);
+ signPostRightContainer.appendChild(signPostRight);
+ //already declared above? let object = this;
+
+ let signPostLeftContainer = signPostRightContainer.cloneNode(true);
+ signPostRightContainer.classList.remove("point-left");
+ signPostRightContainer.classList.add("point-right");
+
+
+ let signPostContainers = [signPostLeftContainer, signPostRightContainer];
+
+ signPostContainers.forEach(function (signPostContainer) {
+ signPostContainer.onmouseover = function() {
+ if(videoAnimation) { return; }
+ console.log("mouse in");
+ object.GameElements.helper.sendTo(this.querySelector(".fairy-place-holder"));
+ };
+
+ signPostContainer.onmouseout = function () {
+ if(videoAnimation) { return; }
+ console.log("mouse out");
+ object.GameElements.helper.sendBack();
+ };
+
+ signPostContainer.onclick = function() { /*object.goToNextScene.bind(null, object, true);*/ if(videoAnimation == true) { if(object.contentContainer.classList.contains("intro")) { object.GameElements.helper.node.click(); } return; } object.goToNextScene(object, true, undefined, false); };
+ /*signPostContainer.onclick = function() {
+ //let object = this;
+ waitingForNextQuestion = true;
+ nextQuestionQuery = undefined;
+ //fetch next question and reset scene to next question
+ let nextQuestionLink = object.getNextPageInfo(undefined, true).url;
+ if(nextQuestionLink == undefined) {
+ console.log("no next question found");
+ return;
+ }
+ object.fader.addEventListener("transitionend", buildNewScene.bind(null, object), {once:true});
+ object.sceneEnd();
+ fetch(nextQuestionLink).then(function(response) {
+ console.log("fetched next question");
+ //console.log(response);
+ return response.text();
+ })
+ .then(function(responseText) {
+ //extract exercise from response
+ let fetchedDoc = object.Parser.parseFromString(responseText, "text/html");
+ let questionDiv = fetchedDoc.querySelector("#responseform");
+ nextQuestionQuery = questionDiv;
+ console.log(questionDiv);
+
+ let newQuestionContainer = document.querySelector(".new-question-container");
+ if(newQuestionContainer == undefined) {
+ newQuestionContainer = document.createElement("div");
+ newQuestionContainer.classList.add("new-question-container");
+ document.querySelector("div[role=main]").appendChild(newQuestionContainer);
+ }
+ while(newQuestionContainer.firstChild) {
+ newQuestionContainer.removeChild(newQuestionContainer.firstChild);
+ }
+ newQuestionContainer.appendChild(questionDiv);
+ MathJax.Hub.Typeset();
+
+
+ })
+ .catch(function(error) {
+ console.log("error in promise chain fetching next question");
+ console.log(error);
+ });
+ }*/
+ });
+
+
+ //sign post info
+ let signPostInfoHref = "https://marvin.hs-bochum.de/~mneugebauer/fantasy/wooden-sign-posts-info.png";
+ let signPostInfoContainer = document.createElement("div");
+ signPostInfoContainer.classList.add("sign-post-container", "point-left");
+ let signPostInfo = document.createElement("img");
+ signPostInfo.classList.add("sign-post");
+ signPostInfo.src = signPostInfoHref;
+ signPostInfoContainer.appendChild(signPostInfo);
+
+ signPostInfoContainer.onclick = object.showSettings.bind(null, object);
+
+ let signPostStandaloneArrowImgHref = "https://marvin.hs-bochum.de/~mneugebauer/fantasy/wooden-sign-post-standalone-right.png";
+ let signPostStandaloneArrowRightContainer = document.createElement("div");
+ signPostStandaloneArrowRightContainer.classList.add("sign-post-container", "point-left", "standalone-arrow");
+ let signPostStandaloneArrowRight = document.createElement("img");
+ signPostStandaloneArrowRight.classList.add("sign-post");
+ signPostStandaloneArrowRight.src = signPostStandaloneArrowImgHref;
+ signPostStandaloneArrowRightContainer.appendChild(signPostStandaloneArrowRight);
+ //already declared above? let object = this;
+
+ let signPostStandaloneArrowLeftContainer = signPostStandaloneArrowRightContainer.cloneNode(true);
+ signPostStandaloneArrowRightContainer.classList.remove("point-left");
+ signPostStandaloneArrowRightContainer.classList.add("point-right");
+ let signPostStandAloneArrowRightContainerFollowFairy = signPostStandaloneArrowRightContainer.cloneNode(true);
+ signPostStandaloneArrowRightContainer.classList.add("disabled");
+
+ this.nextSceneSignPost = signPostStandaloneArrowRightContainer;
+
+ let signPostStandaloneArrowContainers = [signPostStandaloneArrowLeftContainer, signPostStandaloneArrowRightContainer];
+ /*signPostStandaloneArrowContainers.forEach(function(signPostStandaloneArrowContainer) {
+ signPostStandaloneArrowContainer.onclick = function() {
+ console.log("clicked sign post standalone arrow");
+ };
+ });*/
+ signPostStandaloneArrowLeftContainer.onclick = function () {
+ if(videoAnimation == true) { return; }
+ object.goBackToCity();
+ };
+
+ signPostStandaloneArrowRightContainer.onclick = function() {
+ if(videoAnimation == true) { return; }
+ let currQuestion = object.getQuestion();
+ if(currQuestion.isSolved() || currQuestion.id == "start") {
+ object.goToNextScene();
+ }
+ else {
+ //let neededMana = 5;
+ object.teleportDialog(object, undefined/*, neededMana*/);
+ }
+ };
+ //manipulate next question button to not really send the player to the next question page, but initiate game environment to load next question
+ document.getElementById("mod_quiz-next-nav").onclick = function(event) {
+ event.preventDefault();
+ event.stopPropagation();
+
+ signPostStandaloneArrowRightContainer.click();
+ };
+
+ signPostStandAloneArrowRightContainerFollowFairy.classList.add("fairy-follow-sign-post");
+ /*let signPostImg = signPostStandAloneArrowRightContainerFollowFairy.querySelector("img");
+ if(signPostImg != undefined) {
+ //signPostImg.src = "https://marvin.hs-bochum.de/~mneugebauer/fantasy/wooden-sign-posts-cropped-bnw.png";
+ signPostImg.src = "https://marvin.hs-bochum.de/~mneugebauer/fantasy/wooden-sign-post-standalone-right.png";
+ //signPostImg.style.filter = "invert(37%) sepia(88%) saturate(1564%) hue-rotate(166deg) brightness(102%) contrast(103%)";
+ }
+ else {
+ console.log("unable to change color of fairy follow signpost");
+ }*/
+ signPostStandAloneArrowRightContainerFollowFairy.onclick = function() {
+ object.goToNextScene(object, false);
+ };
+
+
+
+ let fairyStopSignContainer = document.createElement("div");
+ fairyStopSignContainer.classList.add("fairy-stop-sign-container");
+
+ let test = document.createElement("img");
+ test.src = "https://marvin.hs-bochum.de/~mneugebauer/fantasy/wooden-sign-post-stop.png";
+ test.classList.add("sign-post");
+
+ let fairyRepresentation = document.createElement("img");
+ fairyRepresentation.classList.add("fairy-representation");
+ fairyRepresentation.src = "https://marvin.hs-bochum.de/~mneugebauer/fantasy/fairy-black-paused.svg";
+
+ fairyStopSignContainer.appendChild(test);
+ fairyStopSignContainer.appendChild(fairyRepresentation);
+
+ signPostStandAloneArrowRightContainerFollowFairy.appendChild(fairyStopSignContainer);
+
+ this.fairyFollowSignPost = signPostStandAloneArrowRightContainerFollowFairy;
+ enterSpellContainer.appendChild(signPostStandAloneArrowRightContainerFollowFairy);
+
+ //Background, that stays in its position when the speech bubble does not extend a given height, but will move down with all other elements, when height is exceeded.
+ let moveableBgContainer = document.createElement("div");
+ moveableBgContainer.classList.add("moveable-bg-container");
+ let moveableBg = document.createElement("div");
+ moveableBg.classList.add("moveable-bg");
+ moveableBgContainer.appendChild(moveableBg);
+ this.background = moveableBgContainer;
+ //let moveableBg = document.createElement("img");
+ //moveableBgContainer.appendChild(moveableBg);
+
+ let ground = document.createElement("div");
+ ground.classList.add("ground");
+ signPostStandaloneArrowContainers.forEach(function (signPostStandaloneArrowContainer) {
+ ground.appendChild(signPostStandaloneArrowContainer);
+ });
+ //console.log(formula);
+
+ let badgesContainer = document.createElement("div");
+ badgesContainer.classList.add("badges-container");
+ let badgeFairies = document.createElement("div");
+ badgeFairies.classList.add("badge");
+ let badgeFairiesLabel = document.createElement("div");
+ badgeFairiesLabel.innerHTML = this.Score.fairies;
+ badgeFairiesLabel.classList.add("badge__label");
+ badgeFairies.appendChild(badgeFairiesLabel);
+
+ badgeFairies.onclick = function() {
+ object.fairyModal.classList.add("active");
+ };
+
+ let badgeMana = badgeFairies.cloneNode(true);
+ badgeMana.classList.add("square");
+ badgeMana.querySelector(".badge__label").innerHTML = this.Score.mana;
+
+ badgeMana.onclick = function() {
+ if(videoAnimation == true) {
+ return;
+ }
+ let mapLink = object.getPointToMapLink(object, "einen Ort im Wald");
+ let textPassageContainer = document.createElement("span");
+
+ let textPassagePre = document.createElement("span"); textPassagePre.innerHTML = "Wähle ";
+ let textPassagePost = document.createElement("span"); textPassagePost.innerHTML = " , zu dem du dich teleportieren möchtest.";
+
+ textPassageContainer.appendChild(textPassagePre);
+ textPassageContainer.appendChild(mapLink);
+ textPassageContainer.appendChild(textPassagePost);
+ object.processNotification("", true, undefined, undefined, textPassageContainer);
+ };
+
+ badgesContainer.appendChild(badgeFairies);
+ badgesContainer.appendChild(badgeMana);
+
+ this.manaBadge = badgeMana;
+ this.fairyBadge = badgeFairies;
+
+ let fairyModalContainer = document.createElement("div");
+ fairyModalContainer.classList.add("moveable-bg-container");
+ fairyModalContainer.classList.add("fantasy-modal");
+ fairyModalContainer.onclick = function() {
+ this.classList.remove("active");
+ };
+
+ let defaultbox = document.createElement("img");
+ defaultbox.src = "https://marvin.hs-bochum.de/~mneugebauer/fantasy/fairy-black.svg";
+ defaultbox.classList.add("idle-freed-fairy-box");
+
+ //find out question with largest amount of variants
+ let variantsMax = 0;
+ for(let j in this.QuestionGroups) {
+ for(let i in this.QuestionGroups[j].Questions) {
+ if(this.QuestionGroups[j].Questions[i].variants > variantsMax) {
+ variantsMax = this.QuestionGroups[j].Questions[i].variants;
+ }
+ }
+ }
+ for(let i=0;i<variantsMax;i++) {
+ let freedFairyBox = defaultbox.cloneNode(true);
+ //set animation time between 5 and 10 in 0.5 steps
+ freedFairyBox.style.setProperty("--speedX", (5+(Math.floor(Math.random()*10)/2))+"s");
+ freedFairyBox.style.setProperty("--speedY", (5+(Math.floor(Math.random()*10)/2))+"s");
+ this.background.querySelector(".moveable-bg").appendChild(freedFairyBox);
+ this.freedFairyBoxes.push(freedFairyBox);
+ }
+
+ let modal = document.createElement("div");
+ modal.classList.add("moveable-bg");
+ fairyModalContainer.appendChild(modal);
+
+ let settingsModalContainer = fairyModalContainer.cloneNode(true);
+
+ let closeButtonSettings = document.createElement("span");
+ closeButtonSettings.classList.add("close-modal-button");
+ closeButtonSettings.innerHTML = "×";
+ let settingsModalContent = settingsModalContainer.querySelector(".moveable-bg");
+ settingsModalContent.appendChild(closeButtonSettings);
+
+ let creditsModalContainer = settingsModalContainer.cloneNode(true);
+
+ let funcIntro = function() {
+ object.settingsModal.classList.remove("active");
+ object.fader.addEventListener("transitionend", function() {
+ object.animateIntro();
+ object.fadeSceneIn();
+ }, {once:true});
+ object.fadeSceneOut();
+ };
+
+ let funcCredits = function() {
+ this.closest(".fantasy-modal").classList.remove("active");
+ object.creditsModal.classList.add("active");
+ };
+
+ let funcClose = function() {
+ this.closest(".fantasy-modal").classList.remove("active");
+ };
+
+ closeButtonSettings.onclick = funcClose;
+
+ let options = [
+ {text:"Intro", func:funcIntro},
+ {text:"Credits", func:funcCredits},
+ {text:"Zurück", func:funcClose}
+ ];
+
+ options.forEach(function(option) {
+ let optionContainer = object.createSettingsOptionsContainer(option.text, option.func);
+
+ settingsModalContent.appendChild(optionContainer);
+ });
+
+
+ creditsModalContainer.querySelector(".close-modal-button").onclick = funcClose;
+
+ let creditsModalContent = creditsModalContainer.querySelector(".moveable-bg");
+ let creditsSection = document.createElement("div");
+ creditsSection.innerHTML = "All graphics are from free sources.<br />Sorcerer Elve, Trolls, Golems, Backgrounds: <a href=\"https://craftpix.net/\" target=\"_blank\">Craftpix team</a> on <a href=\"https://craftpix.net/\" target=\"_blank\">craftpix.net</a>.<br />Wooden sign posts: <a href=\"https://www.freepik.com/author/pch-vector\" target=\"_blank\">pch.vector</a> on <a href=\"https://www.freepik.com/\" target=\"_blank\">freepik.com</a><br />Special ♥ to <a href=\"https://codepen.io/sosuke/\" target=\"_blank\">Barrett Sonntag</a> and <a href=\"https://codepen.io/simonwuyts/\" target=\"_blank\">Simon Wuyts</a> for their code snippets on <a href=\"https://codepen.io/\" target=\"_blank\">codepen.io</a>.<br />Special ☕ to the teams from <a href=\"https://www.hochschule-bochum.de/en/\" target=\"_blank\">University of applied sciences (UAS) Bochum</a> and <a href=\"https://www.en.w-hs.de/\" target=\"_blank\">Westphalian UAS</a>.<br /><br />Published under MIT Licence by Malte Neugebauer from UAS Bochum.<br />Find the code for your Learning Management System here: <a href=\"https://bit.ly/3HRpyu0\" target=\"_blank\">Project repository</a>.<br /><br />In whatever way you reproduce this product, please preserve these lines.";
+ let creditsBackButton = this.createSettingsOptionsContainer("Zurück", function() { this.closest(".fantasy-modal").classList.remove("active"); object.settingsModal.classList.add("active"); });
+
+ creditsModalContent.appendChild(creditsSection);
+ creditsModalContent.appendChild(creditsBackButton);
+
+
+ fairyModalContainer.classList.add("fairy-modal");
+ creditsModalContainer.classList.add("credits-modal");
+ settingsModalContainer.classList.add("settings-modal");
+
+ //Loop through questions and visualize solved and unsolved variants in fairy modal.
+ let simpleFairyRepresentation = document.createElement("img");
+ simpleFairyRepresentation.src = "https://marvin.hs-bochum.de/~mneugebauer/fantasy/fairy-black-paused.svg";
+ simpleFairyRepresentation.classList.add("simple-fairy-representation");
+
+ for(let j in this.QuestionGroups) {
+ for(let i in this.QuestionGroups[j].Questions) {
+ if(this.QuestionGroups[j].Questions[i].id == "start") {
+ continue;
+ }
+ let l = 0;
+ //let solvedVariantsAmount = this.QuestionGroups[j].Questions[i].solvedVariants.length;
+ for(let k=0;k<this.QuestionGroups[j].Questions[i].variants;k++) {
+ let representation = simpleFairyRepresentation.cloneNode(true);
+ representation.dataset.represents = this.QuestionGroups[j].Questions[i].page+k;
+ modal.appendChild(representation);
+ if(this.QuestionGroups[j].Questions[i].solvedVariants.indexOf(k) > -1) {
+ representation.style.filter = this.QuestionGroups[j].Questions[i].filter;
+ }
+ else {
+ representation.style.filter = "invert(100%) sepia(1%) saturate(7496%) hue-rotate(88deg) brightness(106%) contrast(101%)";
+ }
+ l++;
+ }
+ }
+ }
+
+ modal.appendChild(this.createSettingsOptionsContainer("Zurück"));
+
+ this.fairyModal = fairyModalContainer;
+ this.settingsModal = settingsModalContainer;
+ this.creditsModal = creditsModalContainer;
+
+ //-------------------APPEND EVERYTHING-------------------
+ ground.insertBefore(badgesContainer, signPostStandaloneArrowRightContainer);
+ //ground.insertBefore(badgeFairies, signPostStandaloneArrowRightContainer);
+ //ground.insertBefore(badgeMana, signPostStandaloneArrowRightContainer);
+
+ battleGround.appendChild(Player.container);
+ //battleGround.appendChild(validation);
+ /*Enemies.forEach(function(Enemy) {
+ battleGround.appendChild(Enemy.container);
+ });*/
+ battleGround.appendChild(monstersCamp);
+ battleGround.appendChild(speechBubble);
+ //battleGround.appendChild(Helper.container);
+ battleGround.appendChild(fairyHome);
+
+ //battleGround.appendChild(signPostLeftContainer);
+ battleGround.appendChild(signPostRightContainer);
+ battleGround.appendChild(signPostInfoContainer);
+
+ questionContainer.appendChild(enterSpellContainer);
+ questionContainer.appendChild(battleGround);
+
+ //battleGround.parentNode.appendChild(helpNotificationContainer);
+
+ if (battleGround.nextSibling != undefined) {
+ battleGround.parentNode.insertBefore(ground, battleGround.nextSibling);
+ }
+ else {
+ battleGround.parentNode.appendChild(ground);
+ }
+
+ let contentContainer = document.querySelector(".que .content");
+ this.contentContainer = contentContainer;
+
+ if (contentContainer.nextSibling != undefined) {
+ contentContainer.parentNode.insertBefore(moveableBgContainer, contentContainer.nextSibling);
+ //contentContainer.parentNode.insertBefore(helpNotificationContainer, contentContainer.nextSibling);
+ }
+ else {
+ contentContainer.parentNode.appendChild(moveableBgContainer);
+ //contentContainer.parentNode.appendChild(helpNotificationContainer);
+ }
+ contentContainer.parentNode.insertAdjacentElement("afterend", helpNotificationContainer);
+
+ this.background.parentNode.insertBefore(fairyModalContainer, this.background);
+ this.background.parentNode.insertBefore(settingsModalContainer, this.background);
+ this.background.parentNode.insertBefore(creditsModalContainer, this.background);
+ //--------------------------------APPEND END-----------------------------
+
+ //After loading, if last question is solved, give full access to all exercises.
+ let questionGroupsKeys = Object.keys(this.QuestionGroups);
+ let LastQuestionGroup = this.QuestionGroups[questionGroupsKeys[questionGroupsKeys.length-1]];
+ let LastQuestionsKeys = Object.keys(LastQuestionGroup.Questions);
+ let VeryLastQuestion = LastQuestionGroup.Questions[LastQuestionsKeys[LastQuestionsKeys.length-1]];
+ console.log(VeryLastQuestion);
+ if(VeryLastQuestion.isSolved() == true) {
+ console.log("solved everything");
+ this.finished = true;
+ this.contentContainer.classList.add("finished");
+ this.manaBadge.querySelector(".badge__label").innerHTML = "∞";
+ this.manaBadge.classList.add("appear");
+ }
+
+
+ this.updateValidationTimerId = setInterval(this.updateValidation, 1500, this);
+
+ //preload spiral
+ let img = new Image();
+ img.src = "https://marvin.hs-bochum.de/~mneugebauer/fantasy/oily-spiral-svgrepo-com.svg";
+
+ let spiralContainer = document.createElement("div");
+ spiralContainer.classList.add("spiral");
+ spiralContainer.style.left = this.GameElements.player.container.style.width;
+ spiralContainer.style.bottom = "calc(" + this.GameElements.player.container.style.height + "/2)";
+ spiralContainer.addEventListener("transitionend", function () {
+ this.classList.remove("active");
+ });
+
+ let spiral = document.createElement("img");
+ spiral.src = "https://marvin.hs-bochum.de/~mneugebauer/fantasy/oily-spiral-svgrepo-com.svg";
+
+ spiralContainer.appendChild(spiral);
+ battleGround.appendChild(spiralContainer);
+
+ //console.log("calc("+this.GameElements.player.container.style.height+"/2)");
+
+ this.spiral = spiralContainer;
+
+ this.updateNavigation();
+
+ if(this.solvedVariants.length == 0) {
+ this.animateIntro();
+ }
+ else {
+ this.resetFairyBubbleToDefault();
+ }
+ }
+
+ showSettings(object) {
+ console.log("show settings");
+ if(object == undefined) {
+ object = this;
+ }
+ object.settingsModal.classList.add("active");
+ };
+
+ createSettingsOptionsContainer(innerHTML, func) {
+ let optionContainer = document.createElement("p");
+ optionContainer.classList.add("menu-option");
+ optionContainer.classList.add("bubble");
+ optionContainer.classList.add("spell-in-progress");
+ optionContainer.innerHTML = innerHTML;
+ if(func != undefined) {
+ optionContainer.onclick = func;
+ }
+ return optionContainer;
+ }
+
+ loadFromSaveState(SaveStateObject) {
+ this.Score = SaveStateObject.score;
+ sessionStorage.setItem("solved", JSON.stringify(SaveStateObject.solved));
+ for(let i in this.QuestionGroups) {
+ for(let j in this.QuestionGroups[i].Questions) {
+ if(SaveStateObject.solved.indexOf(this.QuestionGroups[i].Questions[j].id) != -1) {
+ this.QuestionGroups[i].Questions[j].solved = this.QuestionGroups[i].Questions[j].needs;
+ }
+ }
+ }
+ this.solvedVariants = SaveStateObject.solvedVariants;
+ sessionStorage.setItem("solvedVariants", JSON.stringify(SaveStateObject.solvedVariants));
+ }
+
+ updateInputSurroundingMath(object, Enemy) {
+ if(object == undefined) {
+ object = this;
+ }
+
+ while(object.preInputField.firstChild) {
+ object.preInputField.removeChild(object.preInputField.firstChild);
+ }
+ while(object.postInputField.firstChild) {
+ object.postInputField.removeChild(object.postInputField.firstChild);
+ }
+
+ if(Enemy == undefined) {
+ Enemy = this.targetedEnemy;
+ }
+ if(Enemy == undefined) {
+ console.log("no enemy targeted to update input surrounding math");
+ return;
+ }
+ let questionMarkNode = Enemy.container.querySelector(".input-replacer");
+ Enemy.container.querySelectorAll(".formula-container .nolink").forEach(function(mathInFormulaContainer) {
+ let clone = mathInFormulaContainer.cloneNode(true);
+ if(mathInFormulaContainer.compareDocumentPosition(questionMarkNode) == Node.DOCUMENT_POSITION_PRECEDING) {
+ //If question mark comes before the math, put math in the end.
+ object.postInputField.appendChild(clone);
+ }
+ else {
+ //In any toher case: Put it in the beginning.
+ object.preInputField.appendChild(clone);
+ }
+ });
+ /*
+ window.addEventListener("keydown", function(event) {
+ if(event.defaulPrevented) {
+ return;
+ }
+
+ switch(event.key) {
+ case "Enter":
+ console.log("enter pressed");
+ break;
+ case "Tab":
+ console.log("tab pressed");
+ break;
+ default:
+ return;
+ }
+ event.preventDefault();
+ }, true);*/
+ }
+
+ changeScore(target, amount) {
+ if(target == undefined) {
+ target = this.fairyBadge;
+ }
+ if(amount == undefined) {
+ amount = 1;
+ }
+ let currentScore;
+ if(target == this.fairyBadge) {
+ currentScore = this.Score.fairies;
+ this.Score.fairies += amount;
+ }
+ else if(target == this.manaBadge) {
+ currentScore = this.Score.mana;
+ this.Score.mana += amount;
+ }
+ else {
+ return;
+ }
+
+ clearInterval(target.dataset.intervaldId);
+ target.querySelector(".badge__label").innerHTML = currentScore;
+
+ let object = this;
+ let points = amount;
+ let badgeLabel = target.querySelector(".badge__label");
+ let from = parseInt(badgeLabel.innerHTML, 10);
+ if(amount > 0) {
+ badgeLabel.innerHTML = "+"+points;
+ target.classList.add("appear");
+ setTimeout(function() {
+ target.classList.remove("appear");
+ badgeLabel.innerHTML = from;
+ object.animatePointRaise(target, from+points);
+ //badgeLabel.innerHTML = parseInt(badgeLabel.innerHTML, 10)+points;
+ }, 4000);
+ }
+ if(amount < 0) {
+ this.animatePointLoose(target, from+points);
+ }
+ }
+ animatePointRaise(target, points) {
+ if(points == undefined) {
+ points = 10;
+ }
+ let intervalId;
+ let object = this;
+ target.dataset.intervaldId = setInterval(function() { object.pointRaise(target, points, intervalId); }, 250);
+ }
+
+ pointRaise(target, limit, intervalId) {
+ let badgeLabel = target.querySelector(".badge__label");
+ let currentPoints = parseInt(badgeLabel.innerHTML, 10);
+ if(currentPoints >= limit) {
+ clearInterval(target.dataset.intervaldId);
+ return;
+ }
+ badgeLabel.innerHTML = currentPoints+1;
+ }
+
+ animatePointLoose(target, points) {
+ if(points == undefined) {
+ points = 10;
+ }
+ let intervalId;
+ let object = this;
+ intervalId = setInterval(function() { object.pointLoose(target, points, intervalId); }, 250);
+ }
+
+ pointLoose(target, limit, intervalId) {
+ let badgeLabel = target.querySelector(".badge__label");
+ let currentPoints = parseInt(badgeLabel.innerHTML, 10);
+ if(currentPoints <= limit || currentPoints <= 0) {
+ clearInterval(intervalId);
+ return;
+ }
+ badgeLabel.innerHTML = currentPoints-1;
+ }
+
+ goToNextScene(object, proceed, questionId, animateTeleport) {
+ /*
+ proceed: boolean. Defines whether to go to next question (true) or to give another variant of the current question (false).
+ */
+ if (object == undefined) {
+ object = this;
+ }
+ if(proceed == undefined) {
+ proceed = true;
+ }
+ if(animateTeleport == undefined) {
+ if(questionId == undefined) {
+ animateTeleport = false;
+ }
+ else {
+ animateTeleport = true;
+ }
+ }
+ waitingForNextQuestion = true;
+ nextQuestionQuery = undefined;
+
+ object.untargetEnemy();
+
+ let nextQuestionLink;
+ if(questionId == undefined) {
+ //fetch next unsolved question and reset scene to next question
+ if(proceed == true) {
+ let nextPageInfo = object.getNextPageInfo(undefined, true, true);
+ console.log(nextPageInfo);
+ if (nextPageInfo == undefined) {
+ console.log("no next question found");
+ return;
+ }
+
+ nextQuestionLink = nextPageInfo.url;
+ object.setCurrentQuestionId(nextPageInfo.id)
+ object.currentPage = nextPageInfo.page;
+ }
+ else {
+ let nextPageURLInfo = object.getPageURL();
+ nextQuestionLink = nextPageURLInfo.url;
+ object.currentPage = nextPageURLInfo.page;
+ //currentQuestionId stays the same
+ }
+ }
+ else {
+ let nextPageURLInfo = object.getPageURL(questionId);
+ nextQuestionLink = nextPageURLInfo.url;
+ object.setCurrentQuestionId(questionId);
+ object.currentPage = nextPageURLInfo.page;
+ }
+
+ console.log(nextQuestionLink);
+ object.sceneEnd(animateTeleport);
+
+ if(object.currentQuestionId == -1) {
+ //FINISH!
+ console.log("build victory scene");
+ object.fader.addEventListener("transitionend", object.buildVictoryScene.bind(null, object), { once: true });
+ return null;
+ }
+ else {
+ object.fader.addEventListener("transitionend", buildNewScene.bind(null, object), { once: true });
+ }
+ fetch(nextQuestionLink).then(function (response) {
+ console.log("fetched next question");
+ //console.log(response);
+ return response.text();
+ })
+ .then(function (responseText) {
+ if(responseText != null) {
+ //extract exercise from response
+ let fetchedDoc = object.Parser.parseFromString(responseText, "text/html");
+ let questionDiv = fetchedDoc.querySelector("#responseform");
+ questionDiv.id = "responseform_clone";
+ nextQuestionQuery = questionDiv;
+ console.log(questionDiv);
+
+ let newQuestionContainer = document.querySelector(".new-question-container");
+ if (newQuestionContainer == undefined) {
+ newQuestionContainer = document.createElement("div");
+ newQuestionContainer.classList.add("new-question-container");
+ document.querySelector("div[role=main]").appendChild(newQuestionContainer);
+ }
+ while (newQuestionContainer.firstChild) {
+ newQuestionContainer.removeChild(newQuestionContainer.firstChild);
+ }
+ newQuestionContainer.appendChild(questionDiv);
+
+ //MathJax.Hub.Typeset();
+
+ //Probably, scene did not fade out yet. If so, wait for scene to be built up handled by transition event listeners. Only if not, build scene here.
+ if(object.fader.classList.contains("fade-out")) {
+ buildNewScene(object);
+ }
+
+ //save state to save timestamp of starting new question and to ensure that user always starts at start element by having the start element always fetched last.
+ //object.saveState("start "+object.currentQuestionId);
+ }
+ })
+ .catch(function (error) {
+ console.log("error in promise chain fetching next question");
+ console.log(error);
+ });
+ }
+
+ getDistanceFromLastSolved(questionId, includeCurrent) {
+ if(includeCurrent == undefined) {
+ includeCurrent = true;
+ }
+ let found = false;
+ let dist = 0;
+ let groupKeys = Object.keys(this.QuestionGroups);
+ let numQuestionGroups = groupKeys.length;
+ for(let j=numQuestionGroups-1;j>=0;j--) {
+ let questionKeys = Object.keys(this.QuestionGroups[groupKeys[j]].Questions);
+ let numQuestions = questionKeys.length;
+ for(let i=numQuestions-1;i>=0;i--) {
+ if(found == true) {
+ dist+=1;
+ if(this.QuestionGroups[groupKeys[j]].Questions[questionKeys[i]].isSolved() || this.QuestionGroups[groupKeys[j]].Questions[questionKeys[i]].id == "start" || (includeCurrent == true && this.QuestionGroups[groupKeys[j]].Questions[questionKeys[i]].id == this.currentQuestionId)) {
+ return dist;
+ }
+ }
+ else {
+ if(this.QuestionGroups[groupKeys[j]].Questions[questionKeys[i]].id == questionId) {
+ found = true;
+ }
+ }
+ }
+ }
+ return false;
+ }
+
+ teleportDialog(object, questionId, neededMana) {
+ if(object == undefined) {
+ object = this;
+ }
+ let nextEnemyPhrase = "";
+ let manaPhrase = "";
+ if(neededMana == undefined) {
+ if(questionId != undefined) {
+ neededMana = 10*this.getDistanceFromLastSolved(questionId)-10;
+ }
+ else {
+ neededMana = 10;
+ }
+ }
+ if(!object.finished) {
+ manaPhrase = " für "+neededMana+" Energiepunkte ";
+ }
+ if(questionId == undefined) {
+ nextEnemyPhrase = " zum nächsten Gegner ";
+ }
+ else {
+ nextEnemyPhrase = " hierher ";
+ }
+ let confirmLink = document.createElement("a");
+ confirmLink.classList.add(".confirm-link");
+ confirmLink.href = "javascript:;";
+ confirmLink.innerHTML = "Ja";
+ confirmLink.onclick = function() {
+ if(neededMana == 0 || object.finished == true) {
+ object.goToNextScene(object, true, questionId);
+ }
+ else if(object.Score.mana >= neededMana) {
+ object.changeScore(object.manaBadge, -neededMana);
+ object.goToNextScene(object, true, questionId, true);
+ }
+ else {
+ object.processNotification("Du hast nicht genug Energiepunkt, um "+nextEnemyPhrase+" zu springen. Besiege zunächst andere Gegner.", true);
+ }
+ };
+ object.processNotification("Willst du"+manaPhrase+nextEnemyPhrase+"springen? ", true, object.notificationBubbleElement, object.GameElements.helper, confirmLink);
+ }
+
+ resetValidation(object) {
+ if (object == undefined) {
+ object = this;
+ }
+ object.inputElement.value = "";
+ object.inputElement.dispatchEvent(new Event("input"));
+ return true;
+ }
+
+ updateValidation(object) {
+ if (object == undefined) {
+ object = this;
+ }
+
+ let workingValidationElement = object.validationElement.cloneNode(true);
+ workingValidationElement.id = workingValidationElement.id + "_clone";
+ workingValidationElement.style.display = "";
+ workingValidationElement.style.background = "none";
+ workingValidationElement.style.border = "none";
+
+ //has changed?
+ if (!object.validationLastState) {
+ //probably an update is needed
+ }
+ else {
+ let presentationElementClone = workingValidationElement.querySelector("[role=presentation]");
+ if (presentationElementClone == undefined) {
+ //console.log("nothing to display or error");
+ if (workingValidationElement.classList.contains("error")) {
+ //console.log("error");
+ //same error as last time?
+ let stackinputerrorElementLast = object.validationLastState.querySelector(".stackinputerror");
+ //console.log(stackinputerrorElementLast);
+ let stackinputerrorElementCurrent = workingValidationElement.querySelector(".stackinputerror");
+ //console.log(stackinputerrorElementCurrent);
+ /*if(stackinputerrorElementLast != undefined && stackinputerrorElementCurrent != undefined) {
+ console.log(stackinputerrorElementLast.isEqualNode(stackinputerrorElementCurrent));
+ }*/
+ if (stackinputerrorElementLast != undefined && stackinputerrorElementCurrent != undefined && stackinputerrorElementLast.isEqualNode(stackinputerrorElementCurrent)) {
+ //nothing changed
+ console.log("nothing to change (same error)");
+ return false;
+ }
+ //else continue below
+ }
+ else if(workingValidationElement.classList.contains("empty")) {
+ //console.log("nothing to parse");
+ if(object.validationLastState.classList.contains("empty")) {
+ console.log("nothing to change (same nothing)");
+ return false;
+ }
+ }
+ else {
+ console.log("nothing to change");
+ return false;
+ }
+ }
+ else {
+ let presentationElementLast = object.validationLastState.querySelector("[role=presentation]");
+ if (presentationElementClone.isEqualNode(presentationElementLast)) {
+ //console.log("no update neccessary")
+ return false;
+ }
+ }
+ }
+
+
+ //check state
+ if (workingValidationElement.classList.contains("error")) {
+ console.log("error");
+ //error routine
+ object.fairyHome.querySelector(".exclamation").classList.add("active");
+ object.enterSpellContainer.classList.add("error");
+ object.speechBubbleElement.style.color = "#999999";
+
+ //guess error type
+ let errType;
+ let errorTextElement = workingValidationElement.querySelector(".stackinputerror");
+ if (!errorTextElement) {
+ errType = "unknown_error";
+ }
+ else {
+ let errorText = errorTextElement.innerHTML;
+ //console.log(errorText);
+ if (errorText.indexOf("missing * characters") != -1) {
+ errType = "multiplication_dot_missing";
+ }
+ else if (errorText.indexOf("invalid final character") != -1) {
+ errType = "invalid_final_char";
+ }
+ else if (errorText.indexOf("listing the values") != -1) {
+ errType = "invalid_value_listing";
+ }
+ else {
+ errType = "unknown_error"
+ }
+ }
+ console.log(errType);
+ object.processError(errType);
+ //return false;
+ }
+ else if (workingValidationElement.classList.contains("loading")) {
+ console.log("wait a moment and try again in some seconds");
+ }
+ else {
+ //if a previously detected error
+ object.GameElements.helper.container.parentNode.querySelector(".exclamation").classList.remove("active");
+ object.enterSpellContainer.classList.remove("error");
+ //Where is our fairy? If user is currently notified by speech bubble due to error, send back!
+ let helperNode = document.querySelector(".fairy-place-holder img");
+ if (helperNode != undefined) {
+ hideNotificationSpeechBubble();
+ }
+
+ object.speechBubbleElement.style.color = "";
+
+ //clean speeach bubble and insert into speech bubble
+ while (object.speechBubbleElement.lastChild) {
+ object.speechBubbleElement.removeChild(object.speechBubbleElement.lastChild);
+ }
+ object.speechBubbleElement.appendChild(workingValidationElement);
+ }
+ //console.log("reached end of updateVali");
+
+ object.validationLastState = workingValidationElement;
+
+ return true;
+ }
+
+ killUpdateValidationTimer() {
+ clearTimeout(this.updateValidationTimerId);
+ }
+
+ processError(errType) {
+ if (errType == undefined) {
+ errType = "unknown_error";
+ }
+ let texts = {
+ multiplication_dot_missing: [
+ "Mind to cast your spell with stars * for multiplications!",
+ "Mind the *!",
+ "Don't forget to use stars * for your multiplications!"
+ ],
+ invalid_final_char: [
+ "This spell can't be casted, because it is not allowed to end like this.",
+ "Your spell ends invalid.",
+ "No, like this the spell can't be casted because of the final character."
+ ],
+ invalid_value_listing: [
+ "Two give more than one solution, cast your spell like this: y = ? or y = ?"
+ ],
+ unknown_error: [
+ "Something is wrong with your spell, try again!",
+ "This spell can't be casted. Maybe you misspelled something?",
+ "This won't work and I don't know why. Please try again!"
+ ]
+ };
+ let possibleTexts = texts[errType];
+ let text = "";
+ if (possibleTexts == undefined) {
+ possibleTexts = texts.unknown_error;
+ }
+ text = possibleTexts[Math.floor(Math.random() * possibleTexts.length)];
+ //this.notificationBubbleElement.innerHTML = text;
+ this.processNotification(text, false);
+ console.log(text);
+ }
+
+ processNotification(message, autoShowSpeechBubble, target, fairyToSend, elementToAppend, scrollInView) {
+ if (message == undefined) {
+ console.log("no message to process");
+ return false;
+ }
+ if (autoShowSpeechBubble == undefined) {
+ autoShowSpeechBubble = false;
+ }
+ if(target == undefined) {
+ target = this.notificationBubbleElement;
+ }
+
+ if(fairyToSend == undefined) {
+ fairyToSend = this.GameElements.helper;
+ }
+
+ if(scrollInView == undefined) {
+ if(target == this.notificationBubbleElement) {
+ //console.log("scroll in view is set to true by default");
+ scrollInView = true;
+ }
+ else {
+ scrollInView = false;
+ }
+ }
+
+ //If speech bubble is already opened, close it first, then rerun function to process message.
+ let object = this;
+ if(!target.classList.contains("closed")) {
+ target.addEventListener("transitionend", function() {
+ object.processNotification(message, autoShowSpeechBubble, target, fairyToSend, elementToAppend, scrollInView);
+ }, {once:true});
+ target.classList.add("closed");
+ target.classList.remove("show-overflow");
+ return;
+ }
+ target.querySelector(".bubble-content").innerHTML = message;
+
+ if(elementToAppend != undefined) {
+ target.querySelector(".bubble-content").appendChild(elementToAppend);
+ }
+
+ if (autoShowSpeechBubble) {
+ this.showNotificationSpeechBubble(target, fairyToSend, scrollInView);
+ }
+
+ //Special handling in case of math formulas in the helper bubble
+ if(target == this.notificationBubbleElement/* && message.indexOf("<script type=\"math/tex") != -1*/) {
+ try {
+ MathJax.Hub.Typeset(target)
+ }
+ catch(error) {
+ console.log("error using MathJax");
+ console.log(error);
+ }
+ }
+ }
+
+ showNotificationSpeechBubble(target, fairyToSend, scrollInView) {
+ console.log("show speech bubble");
+ if(target == undefined) {
+ target = this.notificationBubbleElement;
+ }
+ if(fairyToSend == undefined) {
+ fairyToSend = this.GameElements.helper;
+ }
+
+ if(scrollInView == undefined) {
+ if(target == this.notificationBubbleElement) {
+ //console.log("scroll in view is set to true by default");
+ scrollInView = true;
+ }
+ else {
+ scrollInView = false;
+ }
+ }
+
+ //console.log("auto show speech bubble");
+ //let helpSpeechBubble = document.querySelector(".fairy-help");
+ let helpSpeechBubble = target;
+
+ helpSpeechBubble.classList.remove("closed", "no-arrow");
+ if(target == this.notificationBubbleElement) {
+ helpSpeechBubble.classList.add("middle-up-arrow");
+ }
+ else {
+ helpSpeechBubble.classList.add("middle-arrow");
+ }
+ //helpSpeechBubble.style.maxHeight = "500px";
+
+ let fairyPlaceHolder = target.parentNode.querySelector(".fairy-place-holder");
+ /*let helperNode = document.querySelector(".helper-container img");
+
+ //compute distance between container and (future) node
+ let rectHelperNode = helperNode.getBoundingClientRect();
+ let rectContainer = fairyPlaceHolder.getBoundingClientRect();
+ let xoffset = rectHelperNode.x-rectContainer.x;
+ let yoffset = rectHelperNode.y-rectContainer.y;
+ helperNode.style.setProperty("--xoffset",xoffset+"px");
+ helperNode.style.setProperty("--yoffset",yoffset+"px");
+
+ helperNode.classList.add("notifying");
+ helperNode.classList.remove("returning");
+ fairyPlaceHolder.style.maxHeight = "40px";
+ fairyPlaceHolder.appendChild(helperNode);
+
+ let exclamationContainer = document.querySelector(".exclamation");
+ //exclamationContainer.classList.remove("active");
+ exclamationContainer.classList.add("temporarily-hidden");*/
+ if(fairyPlaceHolder != undefined && fairyToSend != undefined) {
+ fairyToSend.sendTo(fairyPlaceHolder);
+ fairyPlaceHolder.style.maxHeight = "40px";
+ document.addEventListener("click", hideNotificationSpeechBubble);
+ }
+ if(scrollInView == true) {
+ target.querySelector(".bubble-content").scrollIntoView({behavior:"smooth", block:"center"});
+ }
+ }
+
+ //following function is declared below as global function
+ hideNotificationSpeechBubble(event) {
+ hideNotificationSpeechBubble(event);
+ }
+
+ animateAttack(finalStroke) {
+ if (finalStroke == undefined) {
+ finalStroke = false;
+ }
+ //animate spiral in the middle of attack animation
+ this.GameElements.player.setState("attack", "once");
+ this.spiral.style.transitionDelay = (this.GameElements.player.Sprites.attack.frameAmount / 2 * this.GameElements.player.Sprites.attack.animationInterval) + "ms";
+ //console.log(this.spiral.style.transitionDelay);
+ this.spiral.classList.add("active");
+
+ if(this.targetedEnemy == undefined) {
+ //Assume an unsolved enemy to be dying now.
+ //object.targetEnemy();
+ console.log("no enemy to be hit targeted");
+ return;
+ }
+ if (!finalStroke) {
+ setTimeout(function (object) { object.targetedEnemy.setState("hurt", "once"); }, 750, this);
+ }
+ else {
+ console.log(this.targetedEnemy.container, " shall die now");
+ setTimeout(function (object) { object.targetedEnemy.setState("die", "toend", undefined, object.untargetEnemy.bind(null, object)); }, 750, this);
+ }
+ }
+
+ fadeSceneIn() {
+ this.fader.classList.remove("fade-out");
+ this.fader.addEventListener("transitionend", removeFaderAfterFadingIn);
+ this.fader.classList.add("fade-in");
+ }
+
+ fadeSceneOut() {
+ this.fader.classList.remove("fade-in");
+ this.fader.removeEventListener("transitionend", removeFaderAfterFadingIn);
+ this.fader.classList.add("fade-out");
+ }
+
+ fadeScene() {
+ if (this.fader.classList.contains("fade-in") || (!this.fader.classList.contains("fade-in") && !this.fader.classList.contains("fade-out"))) {
+ this.fadeSceneOut();
+ return true;
+ }
+ this.fadeSceneIn();
+ return true;
+ }
+
+ sceneEnd(teleport) {
+ let object = this;
+ if(teleport == undefined) {
+ teleport = false;
+ }
+ videoAnimation = true;
+ if(!teleport) {
+ if (this.GameElements.player != undefined) {
+ this.GameElements.player.setState("run");
+ this.GameElements.player.container.style.transition = "left 3s linear";
+ this.GameElements.player.container.style.left = "110%";
+ //this.GameElements.player.container.style.zIndex = "1";
+
+
+ }
+
+
+ if(this.GameElements.helper != undefined) {
+ //on transitioning or animation, compute distance to target und offset to ensure fluent animation
+
+ if(this.GameElements.helper.isCurrentlyMoving() == true) {
+ //Send home to calc offset, but immediately stop normal fairy movement animation by adding the new one.
+ this.GameElements.helper.sendBack();
+ }
+ this.GameElements.helper.node.classList.add("leave-scene", "to-right");
+ }
+ }
+ else {
+ console.log("teleport animation");
+ if (this.GameElements.player != undefined) {
+ this.GameElements.player.setState("attack", "once");
+ //this.GameElements.player.container.style.transition = "left 3s linear";
+ //this.GameElements.player.container.style.left = "110%";
+ //this.GameElements.player.container.style.zIndex = "1";
+
+ this.GameElements.player.container.classList.add("teleport");
+
+ this.GameElements.player.container.addEventListener("animationend", function () {
+ console.log("player arrived");
+ object.fadeSceneOut();
+ }, { once: true });
+ console.log("added event listener \"player arrived\".")
+ }
+
+ if(this.GameElements.helper != undefined) {
+ if(this.GameElements.helper.isCurrentlyMoving() == true) {
+ //Send home to calc offset, but immediately stop normal fairy movement animation by adding the new one.
+ this.GameElements.helper.sendBack();
+ }
+ this.GameElements.helper.node.classList.add("leave-scene", "to-top");
+ }
+ }
+
+ this.GameElements.player.container.addEventListener("transitionend", function () {
+ console.log("player arrived");
+ object.fadeSceneOut();
+ }, { once: true });
+ console.log("added event listener \"player arrived\".")
+
+ if (this.speechBubbleElement != undefined) {
+ this.speechBubbleElement.classList.add("spell-in-progress");
+ this.speechBubbleElement.classList.add("closed");
+ }
+
+ this.GameElements.enemies.forEach(function(Enemy) {
+ if (Enemy != undefined) {
+ Enemy.container.style.zIndex = "1";
+ }
+ });
+
+ //As long as overflow-x and overflow-y don't work properly together, we have to time the overflow property of the environment properly to have the environment clip the player's character but does not clip the bottom speech bubble.
+ /*if(!this.notificationBubbleElement.classList.contains("closed")) {
+ this.notificationBubbleElement.addEventListener("transitionend", function() {
+ document.querySelector(".que").classList.add("scene-end");
+ }, {once:true});
+ }
+ else {
+ document.querySelector(".que").classList.add("scene-end");
+ }*/
+
+ this.questionBubbleElement.classList.add("closed", "no-arrow");
+ this.questionBubbleElement.classList.remove("middle-arrow");
+ this.questionBubbleElement.classList.remove("show-overflow");
+
+ this.notificationBubbleElement.classList.add("closed", "no-arrow");
+ this.notificationBubbleElement.classList.remove("middle-arrow");
+ this.notificationBubbleElement.classList.remove("show-overflow");
+
+ if(this.GameElements.freed != undefined) {
+ this.GameElements.freed.node.classList.add("leave-scene");
+ }
+
+ this.fairyFollowSignPost.classList.remove("active");
+ }
+
+ pseudoEverythingBackToStart() {
+ videoAnimation = false;
+ this.GameElements.player.setState("idle");
+ this.GameElements.player.container.style.transition = "none";
+ this.GameElements.player.container.style.left = "0px";
+
+ this.GameElements.player.container.classList.remove("teleport");
+
+ //this.GameElements.helper.node.style.left = "0px";
+ this.fairyHome.style.left = "0px";
+ this.GameElements.helper.node.classList.remove("notifying");
+ this.GameElements.helper.node.classList.remove("returning");
+ this.GameElements.helper.node.classList.remove("leave-scene");
+ this.GameElements.helper.node.classList.remove("to-right");
+ this.GameElements.helper.node.classList.remove("to-top");
+ this.GameElements.helper.node.classList.remove("to-left");
+ this.GameElements.helper.node.classList.remove("moving-linear");
+ this.GameElements.helper.node.classList.remove("moving-quick");
+ this.GameElements.helper.container.appendChild(this.GameElements.helper.node);
+
+ this.GameElements.enemies.forEach(function(Enemy) {
+ Enemy.setState("idle");
+ Enemy.container.style.zIndex = 1;
+ });
+
+ this.monstersCamp.classList.remove("transform", "appeared");
+
+ this.inputElement.value = "";
+
+ this.speechBubbleElement.classList.add("spell-in-progress");
+ this.speechBubbleElement.innerHTML = "";
+ this.speechBubbleElement.classList.remove("closed");
+
+ this.GameElements.freed.node.classList.remove("leave-scene");
+ this.GameElements.freed.node.classList.remove("reverse");
+ this.GameElements.freed.container.appendChild(this.GameElements.freed.node);
+ this.GameElements.freed.node.style.filter = this.getQuestion().filter;
+
+ this.resetValidation();
+
+ let currentVisibleEnemies = this.monstersCamp.querySelectorAll(".enemy-container:not(.invisible)");
+ let prePhrase;
+ if(currentVisibleEnemies == undefined || currentVisibleEnemies.length == 1) {
+ prePhrase = "F";
+ }
+ else {
+ prePhrase = "Wähle deinen Gegner (klick) und f"
+ }
+ this.notificationBubbleContainer.querySelector(".bubble-content").innerHTML = prePhrase+"ühre deinen Zauber aus (Enter oder klick auf die Formel), um die Fee zurückzuverwandeln.";
+
+ //document.querySelector(".que").classList.remove("scene-end");
+
+ //reset free bouncing fairies
+ this.freedFairyBoxes.forEach(function(freedFairyBox) {
+ freedFairyBox.classList.remove("active");
+ });
+ let currQuestion = this.getQuestion();
+ if(!!currQuestion) {
+ //Especially for the finish part (question id is -1) there is no question.
+ if(currQuestion.id != "start") {
+ for(let i=0;i<currQuestion.solvedVariants.length;i++) {
+ this.freedFairyBoxes[i].classList.add("active");
+ this.freedFairyBoxes[i].style.filter = currQuestion.filter;
+ }
+ }
+ if(currQuestion.isSolved() == false) {
+ this.nextSceneSignPost.classList.add("disabled");
+ }
+ }
+ else {
+ this.nextSceneSignPost.classList.remove("disabled");
+ }
+ this.monstersCamp.classList.remove("solved");
+ }
+
+ pseudoEndAndReset() {
+ let object = this;
+ this.GameElements.player.container.addEventListener("transitionend", function () {
+ console.log("player arrived");
+ object.fader.addEventListener("transitionend", function () {
+ console.log("faded out");
+ object.pseudoEverythingBackToStart();
+ //object.
+ object.fadeSceneIn();
+ }, { once: true });
+ object.fadeSceneOut();
+
+ }, { once: true });
+ this.pseudoSceneEnd();
+ }
+
+ animateIntro() {
+ videoAnimation = true;
+ let object = this;
+ let exclamation = document.querySelector(".fairy-home .exclamation");
+ exclamation.innerHTML = "!!!";
+
+ object.contentContainer.classList.add("intro");
+ this.introState = 1;
+
+ this.contentContainer.parentNode.addEventListener("click", proceedIntroOnClick);
+
+ object.GameElements.helper.node.style.setProperty("--yoffset", "0px");
+ object.GameElements.helper.node.style.setProperty("--xoffset", "500px");
+ object.GameElements.helper.node.classList.add("notifying");
+ object.GameElements.helper.container.appendChild(object.GameElements.helper.node);
+
+ /*object.GameElements.helper.node.addEventListener("animationend", function() {
+ exclamation.classList.add("active");
+ exclamation.classList.add("reverse");
+ object.fairyHome.classList.add("alerting");
+ object.fairyHome.addEventListener("click", function() { object.fairyHome.classList.remove("alerting"); }, {once:true});
+ }, {once:true});*/
+
+ object.GameElements.helper.node.addEventListener("animationend", object.animateFairyAlert, {once:true});
+ object.GameElements.helper.node.addEventListener("click", function() { this.removeEventListener("animationend", object.animateFairyAlert); }, {once:true});
+
+ let actionSpace = document.createElement("span");
+
+ let confirmLink = document.createElement("a");
+ confirmLink.innerHTML = "Ok";
+ confirmLink.href = "javascript:;";
+
+ let orSpace = document.createElement("span");
+ orSpace.innerHTML = " oder ";
+ let skipLink = document.createElement("a");
+ skipLink.innerHTML = "überspringen";
+ skipLink.href = "javascript:;";
+ skipLink.onclick = function() {
+ object.introCleanUp();
+ object.processNotification("Klicke auf den Wegweiser (rechts), um loszulegen. Verwandle die Monster zurück in Feen, indem du die Rätsel löst und komme dem Geheimnis auf die Spur, indem du das Ziel erreichst.", true);
+ };
+
+ actionSpace.appendChild(confirmLink);
+ actionSpace.appendChild(orSpace);
+ actionSpace.appendChild(skipLink);
+
+ let colors = ["invert(75%) sepia(32%) saturate(1024%) hue-rotate(352deg) brightness(102%) contrast(97%)", "invert(31%) sepia(93%) saturate(4185%) hue-rotate(7deg) brightness(105%) contrast(110%)", "invert(94%) sepia(80%) saturate(1438%) hue-rotate(304deg) brightness(109%) contrast(101%)", "invert(88%) sepia(22%) saturate(727%) hue-rotate(38deg) brightness(103%) contrast(107%)", "invert(96%) sepia(97%) saturate(787%) hue-rotate(29deg) brightness(100%) contrast(108%)", "invert(67%) sepia(72%) saturate(618%) hue-rotate(43deg) brightness(110%) contrast(103%)", "invert(79%) sepia(18%) saturate(3453%) hue-rotate(45deg) brightness(97%) contrast(91%)", "invert(54%) sepia(21%) saturate(1222%) hue-rotate(49deg) brightness(99%) contrast(83%)", "invert(76%) sepia(34%) saturate(6604%) hue-rotate(231deg) brightness(102%) contrast(98%)", "invert(37%) sepia(85%) saturate(3762%) hue-rotate(272deg) brightness(104%) contrast(97%)", "invert(26%) sepia(92%) saturate(2035%) hue-rotate(275deg) brightness(86%) contrast(153%)"];
+ confirmLink.onclick = function() {
+ object.introState = 3;
+ object.fader.addEventListener("transitionend", function() {
+ object.contentContainer.classList.remove("city");
+ let i=0;
+ /*object.contentContainer.querySelectorAll(".enemy-container").forEach(function(enemyContainer) {
+ enemyContainer.classList.remove("invisible");
+ enemyContainer.classList.add("fairy-to-monster");
+ enemyContainer.style.setProperty("--transformAnimationStart", 1+i*0.5+"s");
+ enemyContainer.querySelector("img").style.opacity = "0";
+ let defaultFairy = document.createElement("img");
+ defaultFairy.src = "https://marvin.hs-bochum.de/~mneugebauer/fantasy/fairy-black.svg";
+ defaultFairy.style.filter = colors[Math.floor(Math.random()*colors.length)];
+ enemyContainer.querySelector(".fairy-place-holder-at-enemy").appendChild(defaultFairy);
+
+ i++;
+ });*/
+ object.GameElements.enemies.forEach(function(Enemy) {
+ if(Enemy instanceof IceGolem || Enemy instanceof ForestGolem) {
+ Enemy.container.classList.remove("invisible");
+ Enemy.container.classList.add("fairy-to-monster");
+ Enemy.container.style.setProperty("--transformAnimationStart", 1+i*0.5+"s");
+ Enemy.container.querySelector("img").style.opacity = "0";
+ let defaultFairy = document.createElement("img");
+ defaultFairy.src = "https://marvin.hs-bochum.de/~mneugebauer/fantasy/fairy-black.svg";
+ defaultFairy.style.filter = colors[Math.floor(Math.random()*colors.length)];
+ Enemy.container.querySelector(".fairy-place-holder-at-enemy").appendChild(defaultFairy);
+
+ i++;
+ }
+ });
+
+ /*let confirmLink2 = document.createElement("a");
+ confirmLink2.innerHTML = "Ok";
+ confirmLink2.href = "javascript:;";*/
+
+ confirmLink.onclick = function() {
+ object.introState = 4;
+ object.fadeScene();
+ object.fader.addEventListener("transitionend", function() {
+ //back to city
+ object.fairyHome.querySelector(".exclamation").classList.remove("active");
+ object.GameElements.helper.sendTo(object.GameElements.helper.container);
+
+ object.fader.addEventListener("transitionend", function() {
+ //object.GameElements.helper.sendTo(object.GameElements.fairyBadge);
+ object.contentContainer.classList.add("city");
+
+ object.fairyBadge.style.display = "block";
+
+ object.processNotification("Hier siehst du, wie viele Feen du bereits gerettet hast. ", true, undefined, undefined, confirmLink);
+ confirmLink.onclick = function() {
+ object.introState = 5;
+ confirmLink.onclick = function() {
+ object.introState = 0;
+ let goalLink = object.getPointToMapLink(object, "Ziel (klick)", document.querySelector("span.section-wrapper:last-child .qnbutton:last-child"), document.querySelector(".sign-post-container.point-right:not(.fairy-follow-sign-post) .fairy-place-holder")); /*document.createElement("a");
+ goalLink.innerHTML = "Ziel (klick)";
+
+ goalLink.href = "javascript:;";
+ goalLink.onclick = function() {
+ let navDrawer = document.querySelector(".qnbutton").closest(".drawer");
+ if(!navDrawer) {
+ return;
+ }
+ if(!navDrawer.classList.contains("show")) {
+ if(document.querySelector('.qnbutton').closest('.drawer.show') == undefined) {
+ document.querySelector('[data-target='+navDrawer.id+']:not([data-action="closedrawer"])').click();
+ }
+ }
+
+ //toggle some switches to ensure fairy movement to last element is visible
+ navDrawer.style.zIndex = "1050";
+ let navDrawerContent = navDrawer.querySelector(".drawercontent");
+ navDrawerContent.style.overflowY = "visible";
+
+ object.GameElements.helper.sendTo(document.querySelector("span.section-wrapper:last-child .qnbutton:last-child"));
+
+ let comeBackAfterGoalTourAnimation = function(event) {
+ if(event.target != undefined && (event.target.closest(".fairy-img") != undefined || event.target.closest(".bubble") != undefined)) {
+ return;
+ }
+
+ if(event.target.closest(".drawer") != undefined) {
+ //close drawer if player clicked into it
+ navDrawer.querySelector(".drawertoggle").click();
+ }
+
+ navDrawer.style.zIndex = "";
+ navDrawerContent.style.overflowY = "";
+
+ //object.GameElements.helper.sendBack();
+ object.GameElements.helper.sendTo(document.querySelector(".sign-post-container.point-right:not(.fairy-follow-sign-post) .fairy-place-holder"));
+
+ /*navDrawer.querySelector(".drawertoggle").removeEventListener("click", comeBackAfterGoalTourAnimation);
+
+ document.querySelector(".modal-backdrop").removeEventListener("click", comeBackAfterGoalTourAnimation);
+
+ document.removeEventListener("click", comeBackAfterGoalTourAnimation);
+ };
+
+ document.addEventListener("click", comeBackAfterGoalTourAnimation);
+
+ /*navDrawer.querySelector(".drawertoggle").addEventListener("click", comeBackAfterGoalTourAnimation);
+ document.querySelector(".modal-backdrop").addEventListener("click", comeBackAfterGoalTourAnimation);
+
+
+ };*/
+
+ let textPassageContainer = document.createElement("span");
+
+ let textPassagePre = document.createElement("span"); textPassagePre.innerHTML = "Erreiche das ";
+ let textPassagePost = document.createElement("span"); textPassagePost.innerHTML = " bevor es zu spät ist und der Wald in völlige Dunkelheit verfällt. Rette auf dem Weg so viele Feen wie möglich. Folge mir nun nach rechts in den Wald, indem du auf den Wegweiser klickst.";
+
+ //textPassageContainer.innerHTML = textPassagePre;
+ textPassageContainer.appendChild(textPassagePre);
+ textPassageContainer.appendChild(goalLink);
+ textPassageContainer.appendChild(textPassagePost);
+ //textPassageContainer.innerHTML += textPassagePost;
+ /*confirmLink.onclick = function() {
+
+ };*/
+ object.processNotification("", true, undefined, undefined, textPassageContainer);
+ videoAnimation = false;
+
+ document.addEventListener("click", object.introCleanUp.bind(object), {once:true});
+ };
+ object.processNotification("Und hier wie viele Energiepunkte du hast. Mit Energiepunkten kannst du dich an Orte im Wald teleportieren. Jeder besiegte Gegner gibt dir Energiepunkte. Wenn du alle Feen einer Farbe rettest, bekommst du Extra-Energiepunkte. ", true, undefined, undefined, confirmLink);
+ object.manaBadge.style.display = "block";
+
+
+ };
+ }, {once:true});
+ object.fadeScene();
+ }, {once:true});
+
+ };
+
+ object.processNotification("Etwas hat alle meine Freunde in Monster verwandelt. Nur du kannst sie zurückverwandeln. und dem Geheimnis auf die Spur kommen. ", true, undefined, undefined, confirmLink);
+
+ object.fadeScene();
+ }, {once:true});
+ object.fadeScene();
+ };
+ this.processNotification("Hey, es ist etwas Schreckliches passiert. Bitte hör mir zu. ", false, undefined, undefined, actionSpace, false);
+
+ }
+
+ animateFairyAlert() {
+ let object = this;
+ let exclamation = document.querySelector(".fairy-home .exclamation");
+ let fairyHome = document.querySelector(".fairy-home");
+ fairyHome.classList.add("alerting");
+ exclamation.classList.add("active");
+ exclamation.classList.add("reverse");
+ fairyHome.addEventListener("click", function() { this.classList.remove("alerting"); }, {once:true});
+ }
+
+ introCleanUp() {
+ let object = this;
+ videoAnimation = false;
+ object.contentContainer.classList.remove("intro");
+
+ let exclamation = document.querySelector(".fairy-home .exclamation");
+ exclamation.innerHTML = "!";
+ exclamation.classList.remove("reverse");
+ exclamation.classList.remove("active");
+
+ object.fairyHome.classList.remove("alerting");
+ object.introState = 0;
+ object.contentContainer.parentNode.removeEventListener("click", proceedIntroOnClick);
+
+ object.contentContainer.querySelectorAll(".enemy-container").forEach(function(enemyContainer) {
+ enemyContainer.classList.add("invisible");
+ enemyContainer.classList.remove("fairy-to-monster");
+ enemyContainer.style.removeProperty("--transformAnimationStart");
+ enemyContainer.querySelector("img").style.opacity = "";
+ let fairyPlaceholderAtEnemy = enemyContainer.querySelector(".fairy-place-holder-at-enemy");
+ if(fairyPlaceholderAtEnemy != undefined) {
+ while(fairyPlaceholderAtEnemy.firstChild != undefined) {
+ fairyPlaceholderAtEnemy.removeChild(fairyPlaceholderAtEnemy.firstChild);
+ }
+ }
+ });
+ }
+
+ getPointToMapLink(object, innerHTML, targetQuestionNode, targetAfterNode) {
+ if(object == undefined) {
+ object = this;
+ }
+ let link = document.createElement("a");
+ if(innerHTML == undefined) {
+ innerHTML = "Karte";
+ }
+ link.innerHTML = innerHTML;
+
+ if(targetQuestionNode == undefined) {
+ targetQuestionNode = document.querySelector(".section-wrapper .qnbutton");
+ }
+
+ if(targetAfterNode == undefined) {
+ targetAfterNode = object.fairyHome;
+ }
+
+ link.href = "javascript:;";
+ link.onclick = function() {
+ let navDrawer = document.querySelector(".qnbutton").closest(".drawer");
+ if(!navDrawer) {
+ return;
+ }
+ if(!navDrawer.classList.contains("show")) {
+ if(document.querySelector('.qnbutton').closest('.drawer.show') == undefined) {
+ document.querySelector('[data-target='+navDrawer.id+']:not([data-action="closedrawer"])').click();
+ }
+ }
+
+ //toggle some switches to ensure fairy movement to last element is visible
+ navDrawer.style.zIndex = "1050";
+ let navDrawerContent = navDrawer.querySelector(".drawercontent");
+ navDrawerContent.style.overflowY = "visible";
+
+ object.GameElements.helper.sendTo(targetQuestionNode);
+
+ let comeBackAfterGoalTourAnimation = function(event) {
+ if(event.target != undefined && (event.target.closest(".fairy-img") != undefined || event.target.closest(".bubble") != undefined)) {
+ return;
+ }
+
+ if(event.target.closest(".drawer") != undefined) {
+ //close drawer if player clicked into it
+ navDrawer.querySelector(".drawertoggle").click();
+ }
+
+ navDrawer.style.zIndex = "";
+ navDrawerContent.style.overflowY = "";
+ object.GameElements.helper.sendTo(targetAfterNode);
+ document.removeEventListener("click", comeBackAfterGoalTourAnimation);
+ };
+
+ document.addEventListener("click", comeBackAfterGoalTourAnimation);
+ };
+
+ return link;
+ }
+
+ goBackToCity() {
+ let object = this;
+ console.log("go back to city");
+ videoAnimation = true;
+ this.GameElements.player.container.style.transition = "left 2.5s linear";
+ this.GameElements.player.setOrientation(1);
+ this.GameElements.player.setState("run");
+ this.GameElements.player.container.style.left = "-20%";
+
+ this.GameElements.player.container.addEventListener("transitionend", this.cityReturnAnimation.bind(null, this), { once: true });
+
+ if(this.GameElements.helper.isCurrentlyMoving() == true) {
+ //Send home to calc offset, but immediately stop normal fairy movement animation by adding the new one.
+ this.GameElements.helper.sendBack();
+ this.GameElements.helper.node.classList.add("moving-linear", "moving-quick");
+ this.GameElements.helper.node.addEventListener("animationend", function() { object.GameElements.helper.node.classList.add("leave-scene", "to-left"); }, {once:true});
+ }
+ else {
+ this.GameElements.helper.node.classList.add("leave-scene", "to-left");
+ }
+
+ /*if(!this.notificationBubbleElement.classList.contains("closed")) {
+ this.notificationBubbleElement.addEventListener("transitionend", function() {
+ document.querySelector(".que").classList.add("scene-end");
+ }, {once:true});
+ }
+ else {
+ document.querySelector(".que").classList.add("scene-end");
+ }*/
+
+ this.questionBubbleElement.classList.add("closed", "no-arrow");
+ this.questionBubbleElement.classList.remove("middle-arrow");
+ this.questionBubbleElement.classList.remove("show-overflow");
+
+ this.notificationBubbleElement.classList.add("closed", "no-arrow");
+ this.notificationBubbleElement.classList.remove("middle-arrow");
+ this.notificationBubbleElement.classList.remove("show-overflow");
+
+
+ this.GameElements.freed.node.classList.add("leave-scene", "reverse");
+ this.fairyFollowSignPost.classList.remove("active");
+
+ this.untargetEnemy();
+ }
+
+ cityReturnAnimation(object) {
+ //Screen is black and player comes from origin point (probably right) to the middle.
+ if (object == undefined) {
+ object = this;
+ }
+ object.GameElements.player.container.style.transition = "none";
+ let orientation = object.GameElements.player.getOrientation();
+ if (orientation == 1) {
+ //Player comes from the right
+ object.GameElements.player.container.style.left = "120%";
+ }
+ else {
+ //Player comes from the left
+ object.GameElements.player.container.style.left = "-20%";
+ }
+ object.fadeSceneOut();
+ object.fader.addEventListener("transitionend", function () {
+ object.fadeSceneIn();
+
+ object.GameElements.helper.node.classList.remove("notifying");
+ object.GameElements.helper.node.classList.remove("returning");
+ object.GameElements.helper.node.classList.remove("leave-scene");
+ object.GameElements.helper.node.classList.remove("to-right");
+ object.GameElements.helper.node.classList.remove("to-top");
+ object.GameElements.helper.node.classList.remove("to-left");
+ object.GameElements.helper.node.classList.remove("moving-linear");
+ object.GameElements.helper.node.classList.remove("moving-quick");
+
+ object.GameElements.helper.node.style.setProperty("--yoffset", "0px");
+ object.GameElements.helper.node.style.setProperty("--xoffset", "500px");
+ object.GameElements.helper.node.classList.add("notifying");
+ object.GameElements.helper.container.appendChild(object.GameElements.helper.node);
+
+ //object.GameElements.helper.node.style.left = "120%";
+ //object.GameElements.helper.sendBack();
+
+ //object.GameElements.helper.container.appendChild(object.GameElements.helper.node);
+
+ object.freedFairyBoxes.forEach(function(freedFairyBox) {
+ freedFairyBox.classList.remove("active");
+ });
+
+ let contentElement = document.querySelector(".que .content")
+ contentElement.classList.add("city");
+ contentElement.classList.remove("clearing");
+ object.GameElements.player.container.style.transition = "left 2.5s linear";
+ object.GameElements.player.container.style.left = "50%";
+ /*object.GameElements.player.container.addEventListener("transitionend", function() {
+ document.querySelector(".que").classList.remove("scene-end");
+ }, {once:true});*/
+ object.GameElements.player.container.addEventListener("transitionend", function () { object.GameElements.player.setOrientation(0); object.GameElements.player.setState("idle"); videoAnimation = false; }, { once: true });
+ object.setCurrentQuestionId("start");
+ object.currentPage = 0;
+
+ object.resetFairyBubbleToDefault();
+ }, { once: true });
+ }
+
+ resetFairyBubbleToDefault() {
+ let object = this;
+ let optionTeleportPhrase;
+ let navDrawer = document.querySelector(".qnbutton").closest(".drawer");
+ if(navDrawer == undefined || navDrawer.classList.contains("show")) {
+ optionTeleportPhrase = "zu einem beliebigen Punkt im Wald teleportieren (links)";
+ }
+ else {
+ let clickOpenDrawerFunction = "if(document.querySelector('.qnbutton').closest('.drawer.show') == undefined) { document.querySelector('[data-target=\\'"+navDrawer.id+"\\']:not([data-action=\\'closedrawer\\'])').click(); }";
+ optionTeleportPhrase = "<a href=\"javascript:;\" onclick=\""+clickOpenDrawerFunction+"\">zu einem beliebigen Punkt im Wald teleportieren</a>";
+ }
+ object.notificationBubbleContainer.querySelector(".bubble-content").innerHTML = "Von hier aus kannst du <a href=\"javascript:void(0);\" onclick=\"ALQuiz.goToNextScene();\">zum nächsten Gegner gehen</a> oder dich "+optionTeleportPhrase+".";
+ }
+
+ buildVictoryScene(object) {
+ if(object == undefined) {
+ object = this;
+ }
+ object.pseudoEverythingBackToStart();
+ object.fadeSceneIn();
+ object.fader.addEventListener("transitionend", function() {
+ object.processNotification("Du bist am Ziel angekommen. Der Wald ist gerettet! Jetzt kannst du dich frei im Wald teleportieren, ohne Energiepunkte investieren zu müssen. Aber noch nicht alle Feen sind gerettet. Springe zu den Gegnern (auch zu den bereits besiegten) und lass dir von den Feen den Weg zu ihren Freunden zeigen!", true);
+ //Alle Feen, die du rettest, erscheinen hier auf der Lichtung, um dir zu danken.
+ }, {once:true});
+ if(!object.finished) {
+ object.finished = true;
+ object.manaBadge.querySelector(".badge__label").innerHTML = "∞";
+ object.contentContainer.classList.add("finished");
+ object.manaBadge.classList.add("appear");
+ }
+ object.contentContainer.classList.add("clearing");
+ object.contentContainer.classList.remove("city");
+ }
+
+ incrementSolved(id) {
+ if (id == undefined) {
+ id = this.currentQuestionId;
+ }
+ let currQuestion = this.getQuestion(id);
+ currQuestion.solved++;
+ currQuestion.currentlySolved++;
+
+ if (currQuestion.isSolved()) {
+
+ if(currQuestion.solvedVariants.indexOf(this.currentPage-currQuestion.page) == -1) {
+ currQuestion.solvedVariants.push(this.currentPage-currQuestion.page);
+ }
+ if(this.solvedVariants.indexOf(this.currentPage) == -1) {
+ this.solvedVariants.push(this.currentPage);
+ }
+
+ let solvedQuestionsAsString = sessionStorage.getItem("solved");
+ if (solvedQuestionsAsString != undefined) {
+ let solvedQuestions = JSON.parse(solvedQuestionsAsString);
+ if (solvedQuestions != undefined) {
+ if (solvedQuestions.indexOf(id) == -1) {
+ solvedQuestions.push(id);
+ sessionStorage.setItem("solved", JSON.stringify(solvedQuestions));
+ }
+ }
+ }
+
+ /*let solvedVariantsAsString = sessionStorage.getItem("solvedVariants");
+ if (solvedVariantsAsString != undefined) {
+ let solvedVariants = JSON.parse(solvedVariantsAsString);
+ if (solvedVariants != undefined) {
+ if (solvedVariants.indexOf(this.currentPage) == -1) {
+ solvedVariants.push(this.currentPage);*/
+ sessionStorage.setItem("solvedVariants", JSON.stringify(this.solvedVariants));
+ /*}
+ }
+ }*/
+
+ //update saved fairies overview
+ let fairyRepresentation = this.fairyModal.querySelector("[data-represents='"+this.currentPage+"']");
+ if(fairyRepresentation != undefined) {
+ fairyRepresentation.style.filter = currQuestion.filter;
+ }
+ }
+
+ }
+
+ animateMonsterAnalysis(completelySolved, hintNodes) {
+ /*
+ * completelySolved: Boolean, that defines how to animate. If all variants are already solved, the animation differs.
+ */
+ if(completelySolved == undefined) {
+ completelySolved = false;
+ }
+
+ videoAnimation = true;
+ let object = this;
+ let monsterAnalysisAnimationFrame = document.querySelector(".monster-analysis-fairy-animation-placeholder");
+ let helperNode = object.GameElements.helper.node;
+ helperNode.classList.add("moving-linear");
+ helperNode.classList.add("moving-quick");
+ /*let rectHelperNode = helperNode.getBoundingClientRect();
+ let rectContainer = monsterAnalysisAnimationFrame.getBoundingClientRect();
+ //console.log(rectContainer);
+ let xoffset = rectHelperNode.x - rectContainer.x;
+ let yoffset = rectHelperNode.y - rectContainer.y;
+ monsterAnalysisAnimationFrame.style.setProperty("--x2offset", xoffset + "px");
+ monsterAnalysisAnimationFrame.style.setProperty("--y2offset", yoffset + "px");
+
+ helperNode.classList.remove("notifying");
+ monsterAnalysisAnimationFrame.classList.remove("animate");
+ monsterAnalysisAnimationFrame.classList.add("animate");
+ monsterAnalysisAnimationFrame.appendChild(helperNode);*/
+ helperNode.addEventListener("animationend", function(event) {
+ event.stopPropagation();
+ monsterAnalysisAnimationFrame.classList.add("animate");
+ monsterAnalysisAnimationFrame.addEventListener("animationend", function() {
+ console.log("animation ends now");
+ object.GameElements.helper.node.addEventListener("animationend", function() {
+ helperNode.style.setProperty("--xoffset", "0px");
+ helperNode.style.setProperty("--yoffset", "0px");
+ helperNode.classList.remove("moving-linear", "moving-quick");
+ if(completelySolved == false) {
+ videoAnimation = false;
+ let preText = "";
+ //if no single variant is solved, give an explanation
+ if(object.solvedVariants == undefined || object.solvedVariants.length == 0) {
+ preText = "Nutze das Textfeld, um deinen Zauber zu formulieren und klicke auf die Formel, um ihn auszufüren. Oder benutze die Enter-Taste.";
+ //object.processNotification("Nutze das Textfeld, um deinen Zauber zu formulieren und klicke auf die Formel, um ihn auszufüren. Oder benutze die Enter-Taste.", true);
+ /*object.GameElements.helper.node.addEventListener("animationend", function() {
+ videoAnimation = false;
+ }, {once:true});*/
+ }
+ else if(document.querySelectorAll(".monsters-camp .enemy-container:not(.invisible)").length > 1) {
+ //Multiple monsters information if not yet killded any in the first world.
+ let multipleMonstersVariants = [];
+ for(let i=5;i<17;i++) {
+ multipleMonstersVariants.push(i);
+ }
+ if(!object.solvedVariants.some(r => multipleMonstersVariants.indexOf(r) >= 0)) {
+ //object.processNotification("Ziele auf das Monster, das du verwandeln möchtest, indem du es anklickst.", true);
+ preText = "Ziele auf das Monster, das du verwandeln möchtest, indem du es anklickst.";
+ /*object.GameElements.helper.node.addEventListener("animationend", function() {
+ videoAnimation = false;
+ }, {once:true});*/
+ }
+ }
+ if(preText != "" || hintNodes != undefined) {
+ let hintNodesDiv = document.createElement("div");
+ hintNodes.forEach(function(hintNode) {
+ hintNode.classList.add("show-hint");
+ hintNodesDiv.append(hintNode);
+ });
+
+ object.processNotification(preText, true, undefined, undefined, hintNodesDiv);
+ object.GameElements.helper.node.addEventListener("animationend", function() {
+ videoAnimation = false;
+ }, {once:true});
+ }
+ }
+ else {
+ object.processNotification("Du hast hier bereits alle Feen gerettet. Du kannst hier weiter üben, bekommst aber weniger Punkte.", true);
+ object.GameElements.helper.node.addEventListener("animationend", function() {
+ videoAnimation = false;
+ }, {once:true});
+ }
+ }, {once:true});
+ object.showNotificationSpeechBubble(object.questionBubbleElement);
+ monsterAnalysisAnimationFrame.classList.remove("animate");
+ }, {once:true}); }, {once:true});
+ object.GameElements.helper.sendTo(monsterAnalysisAnimationFrame);
+ /*this.GameElements.helper.node.addEventListener("animationend", function() { monsterAnalysisAnimationFrame.classList.add("animate"); }, {once:true});*/
+ //monsterAnalysisAnimationFrame.addEventListener("animationend", function() { object.GameElements.helper.sendBack(); }, {once:true});
+ //this.GameElements.helper.sendTo(monsterAnalysisAnimationFrame);
+ }
+
+ animateTransformation() {
+ let object = this;
+ let currQuestion = object.getQuestion();
+ let completelySolved = (currQuestion.solvedVariants.length == currQuestion.variants);
+ let completelySolvedBefore = object.monstersCamp.classList.contains("solved");
+ this.monstersCamp.addEventListener("animationend", function(event) {
+ object.monstersCamp.classList.add("appeared");
+ object.monstersCamp.classList.remove("transform");
+ if(!completelySolvedBefore) {
+ object.changeScore(object.fairyBadge, 1);
+ }
+ /*setTimeout(function() { object.monstersCamp.addEventListener("animationend", function(e) {
+ console.log("send freed fairy to say thanks");
+
+ //setTimeout(function() { object.GameElements.freed.sendTo(object.questionBubbleElement.parentNode.querySelector(".fairy-place-holder")); }, 3000);
+
+ object.processNotification("Danke, dass du mich gerettet hast! Bitte, bevor du tiefer in den Wald gehst, verwandle auch meine Freunde zurück! Folgen", true, object.questionBubbleElement, object.GameElements.freed);
+ }, {once:true}); }, 50);*/
+ setTimeout(function() {
+ let message = "";
+ let toAppendToMessage = undefined;
+ if(completelySolvedBefore) {
+ if(!object.finished) {
+ object.changeScore(object.manaBadge, 5);
+ }
+ }
+ else {
+ if(completelySolved == true) {
+ message = "Danke, du hast alle meine Freunde der gleichen Farbe gerettet! Gehe tiefer in den Wald und rette noch alle anderen!";
+ if(!object.finished) {
+ object.changeScore(object.manaBadge, 30);
+ }
+ }
+ else {
+ message = "Danke, dass du mich gerettet hast! Bitte, bevor du tiefer in den Wald gehst, verwandle auch meine Freunde zurück! ("+currQuestion.solvedVariants.length+" von "+currQuestion.variants+")";
+ object.fairyFollowSignPost.classList.add("active");
+ toAppendToMessage = object.followPrompt;
+ if(!object.finished) {
+ object.changeScore(object.manaBadge, 10);
+ }
+ }
+ object.processNotification(message, true, object.questionBubbleElement, object.GameElements.freed, toAppendToMessage);
+ }
+ object.nextSceneSignPost.classList.remove("disabled");
+ //object.saveState(); -- Saving should work independent of animation. But it still has to take the time offset of raised score in account. It's moved to promise chain and equipped with delay.
+ //object.questionBubbleElement.appendChild(object.followPrompt);
+ }, 500);
+
+ //object.monstersCamp.classList.remove("transform");
+ }, {once:true});
+ this.monstersCamp.classList.add("transform");
+ }
+
+ animateThanks() {
+
+ }
+
+ targetEnemy(object) {
+ if(object == undefined) {
+ object = this;
+ }
+ for(let i=0;i<object.GameElements.enemies.length;i++) {
+ let inputFieldOfEnemyToTarget = object.GameElements.enemies[i].container.querySelector("input, textarea");
+ if(inputFieldOfEnemyToTarget != undefined && inputFieldOfEnemyToTarget.dataset.correctAnswer == undefined) {
+ object.targetedEnemy = object.GameElements.enemies[i];
+ break;
+ }
+ }
+ //if still undefined: error
+ if(object.targetedEnemy == undefined) {
+ throw new Error("No enemy could be targeted, because all seem to be solved already.")
+ }
+ }
+
+ untargetEnemy(object) {
+ if(object == undefined) {
+ object = this;
+ }
+
+ //clear pre and post input fields
+ while(object.preInputField.firstChild) {
+ object.preInputField.removeChild(object.preInputField.firstChild);
+ }
+ while(object.postInputField.firstChild) {
+ object.postInputField.removeChild(object.postInputField.firstChild);
+ }
+
+ if(object.targetedEnemy == undefined) {
+ return;
+ }
+ object.targetedEnemy.container.classList.remove("targeted");
+ object.targetedEnemy = undefined;
+
+ }
+
+ saveState(info) {
+ //ino: string, info is added to the default save state JSON as additional member.
+ let object = this;
+ if(this.saveStateInput == undefined) {
+ console.log("Tried to save, but failed due to undefined saveStateInput member.")
+ return;
+ }
+ //get current form
+ let firstForm = document.querySelector("#responseform");
+ console.log(firstForm);
+
+ //Instead of immediately reload a question, regarding safe state, a redo is done before new input, to ensure the old save state is still presented on re-attempting the quiz.
+ let repeatButton = firstForm.querySelector(".mod_quiz-redo_question_button");
+ let prePromiseChain = async function(input) {
+ return input;
+ };
+ if(repeatButton == undefined && (this.saveStateInput.value == "" || this.saveStateInput.value == undefined)) {
+ //initial save - do nothing, no conflict with already saved state expected.
+ }
+ else {
+ //Page not yet reloaded (which leads to no present opportunity to repeat) or repeat button is there, but has to be refetched (because name of redo button input changes over re-attempting). Fetch current state of start page and return to save promise chain.
+ prePromiseChain = async function(input) {
+ let urlOfStartPage = object.getPageURL("start").url;
+ return fetch(urlOfStartPage).then(function(response) {
+ return response.text();
+ })
+ .then(text => {
+ let fetchedPage = object.Parser.parseFromString(text, "text/html");
+ let formFetchedPage = fetchedPage.getElementById("responseform");
+
+ let redoButton = formFetchedPage.querySelector(".mod_quiz-redo_question_button");
+ if(redoButton == undefined) {
+ throw new Error("Redo Button not found, despite fetching page.")
+ }
+ let redoFormData = new FormData(formFetchedPage);
+ redoFormData.append(redoButton.name, redoButton.value);
+
+ return fetch(formFetchedPage.action, { method: "POST", body: redoFormData }).then(response => {
+ if(response.status == 200) {
+ console.log("everything seems to be fine with save");
+ }
+ else {
+ throw new Error("something seems to went wrong with save");
+ }
+ return response.text();
+ }).catch(error => {
+ console.log("error in promise chain trying to reload question to save new state");
+ console.log(error);
+ });
+ })
+ .catch(error => {
+ console.log("error in fetching redo button");
+ console.log(error);
+ });
+ };
+ }
+ //The following would be nice in case of the redo-button is there but the page hasn't reloaded yet: Reload question normally before saving. But unfortunately, we have to fetch the start page again to get the right name of input.mod_quiz-redo_question_button (redoslot1, redoslot2, ...).
+ /*prePromiseChain = async function(input) {
+ //Reset sequencecheck
+ firstForm.querySelectorAll("input[name$=sequencecheck]:not(.bubble input)").forEach(function(sequenceCheckFieldToReset) {
+ sequenceCheckFieldToReset.value = 1;
+ });
+ let redoFormData = new FormData(firstForm);
+
+ redoFormData.append(repeatButton.name, repeatButton.value);
+
+ return fetch(firstForm.action, { method: "POST", body: redoFormData }).then(response => {
+ if(response.status == 200) {
+ console.log("everything seems to be fine with save question reload.");
+ }
+ else {
+ throw new Error("something seems to went wrong with save question reload.");
+ }
+ return response.text();
+ }).catch(error => {
+ console.log("error in promise chain trying to reload question to save new state (page already reloaded after initial start)");
+ console.log(error);
+ });
+ };*/
+
+ let solved = [];
+ let solvedJSONString = sessionStorage.getItem("solved");
+ if(solvedJSONString != undefined) {
+ solved = JSON.parse(solvedJSONString);
+ if(solved == undefined) {
+ solved = [];
+ }
+ }
+ let currentState = new SaveState(Date.now(), solved, this.solvedVariants, this.Score);
+ if(info != undefined) {
+ currentState.info = info;
+ }
+ object.saveStateInput.value = currentState.asString();
+ console.log("save state:");
+ console.log(this.saveStateInput.value);
+
+ //Reset sequencecheck
+ /*firstForm.querySelectorAll("input[name$=sequencecheck]:not(.bubble input)").forEach(function(sequenceCheckFieldToReset) {
+ sequenceCheckFieldToReset.value = 1;
+ });*/
+
+ let formDataSave = new FormData(firstForm);
+ let algebraicInput = firstForm.querySelector("input.algebraic:not(.formula-container input)");
+ if(algebraicInput == undefined) {
+ throw new Error("Save not possible because algebraic input element not found");
+ }
+ formDataSave.delete(algebraicInput.name);
+ formDataSave.append(algebraicInput.name, "x=42");
+
+ prePromiseChain(undefined).then(function(responsetext) {
+ let submitButton;
+ if(responsetext != undefined) {
+ let fetchedPage = object.Parser.parseFromString(responsetext, "text/html");
+ let formFetchedPage = fetchedPage.getElementById("responseform");
+ submitButton = formFetchedPage.querySelector("input:not(.bubble input)[type='submit'][name$='submit'],button:not(.bubble button)[type='submit'][name$='submit']");
+
+ let sequenceCheck = fetchedPage.querySelector("input[name$=sequencecheck]:not(.bubble input)");
+ console.log("save sequence check value: "+sequenceCheck.value);
+
+ formDataSave.set(sequenceCheck.name, sequenceCheck.value);
+ }
+ else {
+ submitButton = firstForm.querySelector("input:not(.bubble input)[type='submit'][name$='submit'],button:not(.bubble button)[type='submit'][name$='submit']");
+ }
+ if(submitButton == undefined) {
+ throw new Error("save couldn't be performed due to missing submit button");
+ }
+ //Append submit
+ formDataSave.append(submitButton.name, submitButton.value);
+
+
+
+ fetch(firstForm.action, { method: "POST", body: formDataSave })
+ .then(response => {
+ return response.text();
+ })
+ .then(text => {
+ let fetchedPage = object.Parser.parseFromString(text, "text/html");
+ let formFetchedPage = fetchedPage.getElementById("responseform");
+
+ let repeatButton = fetchedPage.querySelector(".mod_quiz-redo_question_button");
+ console.log(repeatButton);
+ if (repeatButton == undefined) {
+ let stackinputerrorSpan = fetchedPage.querySelector(".stackinputerror");
+ if(stackinputerrorSpan != undefined) {
+ //Probably an input was submitted despite of an syntax error.
+ /*nextQuestionQuery.querySelectorAll("[name$=sequencecheck]").forEach(function(sequenceCheckFieldToRaise) {
+ sequenceCheckFieldToRaise.value = parseInt(sequenceCheckFieldToRaise.value)+2;
+ });*/
+ throw new Error("Stack input error 2");
+ }
+ //If there is no repeat button, we are probably on a validation page (e. g. "Please answer all parts of the question" or "Please check whether what you entered was intepreted as expected"), which happens for unknown reasons. Submit again to get feedback page.
+ let submitButton = fetchedPage.querySelector("input.submit, button.submit");
+ if(submitButton == undefined) {
+ throw new Error("Error in promise chain: (2) For some reason, question could neither be repeated nor input could be resubmitted. Probably sequence check error (Moodle error code submissionoutofsequencefriendlymessage).");
+ }
+ let matchSubmit = [
+ "",
+ submitButton.name,
+ submitButton.value
+ ];
+
+ //set sequencecheck to 1 to prevent "submissionoutofsequencefriendlymessage".
+
+
+ let formDataSubmitValidation = new FormData(formFetchedPage);
+
+ formDataSubmitValidation.append(matchSubmit[1], matchSubmit[2]);
+
+ return fetch(formFetchedPage.action, { method: "POST", body: formDataSubmitValidation }).then(response => {
+ //Reset sequencecheck
+ /*firstForm.querySelectorAll("input[name$=sequencecheck]:not(.bubble input)").forEach(function(sequenceCheckFieldToReset) {
+ sequenceCheckFieldToReset.value = 1;
+ });*/
+ return response.text();
+ }).then(text => { return object.Parser.parseFromString(text, "text/html"); });
+ }
+ else {
+ return fetchedPage;
+ }
+ })
+ .catch(function(error) {
+ console.log("Error during saving.")
+ console.log(error);
+ });
+ });
+ }
+
+ rearrangeMath() {
+ if (MathJax != undefined) {
+ //Interestingly, the input replacer ("?") in the enemies bar seems to irritate MathJax, concluding to line breaks in between formulas. Setting display to "none" prevents it.
+ let temp = document.createElement("div");
+ document.querySelectorAll(".input-replacer").forEach(function(inputReplacer) {
+ inputReplacer.innerHTML = "";
+ //temp.appendChild(inputReplacer);
+ });
+ //setTimeout(MathJax.Hub.Typeset(), 2500);
+ MathJax.Hub.Typeset()
+ setTimeout(
+ function() {
+ document.querySelectorAll(".input-replacer").forEach(function(inputReplacer) {
+ inputReplacer.innerHTML = "?";
+ });
+ }
+ ,
+ 1000
+ );
+ }
+ else {
+ console.log("no mathjax object found");
+ }
+ }
+}
+
+class MatrixObject {
+ constructor(id, node) {
+ this.id = id;
+ this.node = node;
+ if(node == undefined) {
+ this.node = document.getElementById(id)
+ }
+ }
+
+ selectElement(name) {
+ this.node.querySelectorAll("input").forEach(function(inputElement) {
+ let inputReplacerNode = inputElement.parentNode.querySelector(".input-replacer");
+ inputReplacerNode.classList.remove("selected");
+ });
+ let elementNode = this.node.querySelector("name='"+name+"'");
+ if(elementNode == undefined) {
+ return;
+ }
+ elementNode.classList.add("selected");
+ }
+}
+
+class SaveState {
+ constructor(timestamp, solved, solvedVariants, score) {
+ this.timestamp = timestamp;
+ this.solved = solved;
+ this.solvedVariants = solvedVariants;
+ this.score = score;
+ }
+
+ asString() {
+ return JSON.stringify(this);
+ }
+}
+
+class QuestionGroup {
+ constructor(id, description, Questions, nextGroup) {
+ this.id = id;
+ this.description = description;
+ this.Questions = {};
+ if (!!Questions) {
+ Questions.forEach(Question => {
+ this.Questions[Question.id] = Question;
+ });
+ }
+ }
+
+ addQuestion(QuestionObject) {
+ this.Questions[QuestionObject.id] = QuestionObject;
+ }
+}
+
+class Instruction {
+ constructor(id, description, page, onsuccess, onfailure, BubbleInfo, questionsOnPage) {
+ this.id = id;
+ this.page = page;
+ /* success means: challenge accepted and go to endboss*/
+ this.onsuccess = onsuccess;
+ /*failure means: give me the first easy question*/
+ this.onfailure = onfailure;
+ this.description = description;
+ this.BubbleInfo = BubbleInfo;
+
+ this.questionsOnPage = questionsOnPage == undefined ? 1 : questionsOnPage;
+ }
+
+ isSolved() {
+ return false;
+ }
+
+ isCurrentlySolved() {
+ return false;
+ }
+}
+
+class Question extends Instruction {
+ constructor(id, description, page, needs, BubbleInfo, onsuccess, onfailure, askBeforeSkip, questionsOnPage, variants, color, filter) {
+ super(id, description, page, onsuccess, onfailure, BubbleInfo, questionsOnPage);
+ this.needs = needs == undefined ? 1 : needs;
+ this.solved = 0;
+ /*solved means: solved at least once in this attempt, currentlySolved means: solved actually now in the current scope of js variables*/
+ this.currentlySolved = 0;
+ this.askBeforeSkip = askBeforeSkip == undefined ? false : askBeforeSkip;
+
+ this.variants = variants == undefined ? 1 : variants;
+ this.solvedVariants = [];
+
+ this.color = color;
+ this.filter = filter;
+ }
+
+ isSolved(onlyOnCurrentlySolved) {
+ if (onlyOnCurrentlySolved == undefined) {
+ onlyOnCurrentlySolved = false;
+ }
+ let solvedAtAskedTime = (!onlyOnCurrentlySolved ? this.solved : this.currentlySolved);
+ if (solvedAtAskedTime >= this.needs) {
+ return true;
+ }
+ return false;
+ }
+
+ ifCurrentlySolved() {
+ if (this.currentlySolved >= this.needs) {
+ return true;
+ }
+ return false;
+ }
+}
+
+class GameSprite {
+ constructor(src, spriteWidth, spriteHeight, xEndOfSpritesheet, animationInterval, frameAmount, height) {
+ this.src = src;
+ this.spriteWidth = spriteWidth;
+ this.spriteHeight = spriteHeight
+ this.height = height == undefined ? spriteHeight : height;
+ this.xEndOfSpritesheet = xEndOfSpritesheet;
+
+ this.frameAmount = frameAmount;
+
+ this.curPos;
+ this.curFrame = 0;
+ //animationInterval is interval in milliseconds
+ this.animationInterval = animationInterval;
+
+ this.timerId;
+
+ //Preload image, especially for short animations (e. g. attack) to be shown promptly.
+ let img = new Image();
+ img.src = src;
+ let invisibleContainer = document.createElement("div");
+ invisibleContainer.style.display = "none";
+ invisibleContainer.appendChild(img);
+ document.body.appendChild(invisibleContainer);
+ }
+
+ getSrc() {
+ return this.src;
+ }
+
+}
+
+class GameElement {
+ constructor(SpritesObject, orientation, state) {
+ this.Sprites = SpritesObject;
+ this.state = state == undefined ? "idle" : state;
+ this.orientation = orientation;
+ this.node;
+ this.container;
+ this.createDOMNode();
+ this.startAnimation();
+ }
+
+ createDOMNode() {
+ let container = document.createElement("div");
+ container.style.width = this.Sprites[this.state].spriteWidth + "px";
+ container.style.height = this.Sprites[this.state].spriteHeight + "px";
+ container.style.overflow = "hidden";
+ container.style.position = "absolute";
+ let node = document.createElement("img");
+ node.style.width = "auto";
+ node.style.height = "100%";
+ //node.style.transform = "translateX(0px)";
+ if (!!this.orientation) {
+ node.style.transform = "scaleX(-1);"
+ }
+ node.src = this.Sprites[this.state].src;
+
+ container.appendChild(node);
+
+ this.node = node;
+ this.container = container;
+
+ return container;
+ }
+
+ startAnimation(repeat, backto, callback) {
+ //console.log("start animation "+this.state);
+ if (repeat == undefined) {
+ repeat = "infinite";
+ }
+ //assume node.src is already set
+ this.Sprites[this.state].timerId = setInterval(this.nextAnimation, this.Sprites[this.state].animationInterval, this, repeat, backto, callback);
+ }
+
+ nextAnimation(object, repeat, backto, callback) {
+ if (object == undefined) {
+ object = this;
+ }
+ if (repeat == undefined) {
+ repeat = "infinite";
+ }
+ if (backto == undefined) {
+ backto = "idle";
+ }
+ if (object.Sprites[object.state].curFrame < object.Sprites[object.state].frameAmount - 1) {
+ object.Sprites[object.state].curFrame++;
+ }
+ else {
+ object.Sprites[object.state].curFrame = 0;
+ if (repeat == "once") {
+ object.setState(backto);
+ }
+ else if (repeat == "toend") {
+ object.stopAnimation();
+ object.Sprites[object.state].curFrame = object.Sprites[object.state].frameAmount - 1;
+ if(callback != undefined) {
+ callback();
+ }
+ }
+ }
+ let sign = "";
+ let frameNum = object.Sprites[object.state].curFrame;
+ if (!!object.orientation) {
+ object.node.style.transform = "scaleX(-1) ";
+ frameNum = object.Sprites[object.state].frameAmount - frameNum - 1;
+ }
+ else {
+ object.node.style.transform = "";
+ sign = "-"
+ }
+ object.node.style.transform += "translateX(" + sign + (frameNum / object.Sprites[object.state].frameAmount) * 100 + "%)";
+
+ }
+
+ setState(state, repeat, backto, callback) {
+ if (state == undefined) {
+ state = "idle";
+ }
+ if (repeat == undefined) {
+ repeat = "infinite";
+ }
+ if (backto == undefined) {
+ backto = this.state;
+ }
+ if (this.Sprites[state] == undefined) {
+ console.log("undefined state");
+ return false;
+ }
+
+ this.stopAnimation();
+
+ this.state = state;
+ this.node.src = this.Sprites[this.state].src;
+ this.startAnimation(repeat, backto, callback);
+ }
+
+ stopAnimation() {
+ clearInterval(this.Sprites[this.state].timerId);
+ this.Sprites[this.state].timerId = null;
+ this.Sprites[this.state].curFrame = 0;
+ }
+
+ setSize(width, height) {
+ /*
+ * Set width and/or height in pixels. Auto adjust pixel-size for undefined value.
+ */
+ if (width == undefined && height == undefined) {
+ console.log("no size given to set")
+ return;
+ }
+ if (height == undefined) {
+ height = this.Sprites[this.state].spriteHeight / (this.Sprites[this.state].spriteWidth / width);
+ }
+ else if (width == undefined) {
+ width = this.Sprites[this.state].spriteWidth / (this.Sprites[this.state].spriteHeight / height);
+ }
+ this.container.style.width = width + "px";
+ this.container.style.height = height + "px";
+ }
+
+ setOrientation(orientation, object) {
+ if (object == undefined) {
+ object = this;
+ }
+ object.orientation = orientation;
+ }
+
+ getOrientation() {
+ return this.orientation;
+ }
+}
+
+class GameElementWithFormula extends GameElement {
+ constructor(SpritesObject, orientation, state) {
+ super(SpritesObject, orientation, state);
+
+ this.formulaContainer = document.createElement("div");
+ this.formulaContainer.classList.add("formula-container");
+ this.container.appendChild(this.formulaContainer);
+
+ let imgWrapper = document.createElement("div");
+ imgWrapper.style.width = "100%";
+ imgWrapper.style.height = "100%";
+ imgWrapper.style.overflow = "hidden";
+ imgWrapper.classList.add("img-wrapper");
+
+ this.container.style.overflow = "visible";
+ imgWrapper.appendChild(this.node);
+
+ this.container.appendChild(imgWrapper);
+
+ let fairyPlaceHolderAtEnemy = document.createElement("div");
+ /*fairyPlaceHolderAtEnemy.style.width = "50px";
+ fairyPlaceHolderAtEnemy.style.height = "50px";
+ //fairyPlaceHolderAtEnemy.style.right = this.container.style.right;
+ //fairyPlaceHolderAtEnemy.style.bottom = this.container.style.bottom;
+ //fairyPlaceHolderAtEnemy.style.transform = "translate(calc(-" + this.container.style.width + "/2),calc(-" + this.container.style.height + "/2))";
+ //fairyPlaceHolderAtEnemy.style.position = "absolute";
+ fairyPlaceHolderAtEnemy.style.zIndex = 1;*/
+ fairyPlaceHolderAtEnemy.classList.add("fairy-place-holder-at-enemy");
+ this.fairyPlaceHolder = fairyPlaceHolderAtEnemy;
+ this.container.appendChild(fairyPlaceHolderAtEnemy);
+ }
+
+ clearFormulas() {
+ if(this.formulaContainer == undefined) {
+ return;
+ }
+ while (this.formulaContainer.firstChild != undefined) {
+ this.formulaContainer.removeChild(this.formulaContainer.firstChild);
+ }
+ }
+}
+
+class Elf extends GameElement {
+ constructor(orientation) {
+ super(
+ {
+ idle: new GameSprite("https://marvin.hs-bochum.de/~mneugebauer/fantasy/Elf_03__IDLE_spritesheet.png", 450, 580, 4500, 75, 10),
+ attack: new GameSprite("https://marvin.hs-bochum.de/~mneugebauer/fantasy/Elf_03__ATTACK_spritesheet.png", 450, 580, 4500, 75, 10),
+ run: new GameSprite("https://marvin.hs-bochum.de/~mneugebauer/fantasy/Elf_03__RUN_spritesheet.png", 465, 580, 4650, 75, 10)
+ },
+ orientation)
+ }
+}
+
+class Troll extends GameElementWithFormula {
+ constructor(orientation) {
+ super(
+ {
+ idle: new GameSprite("https://marvin.hs-bochum.de/~mneugebauer/fantasy/Troll_01_1_IDLE_spritesheet.png", 750, 580, 7500, 90, 10),
+ hurt: new GameSprite("https://marvin.hs-bochum.de/~mneugebauer/fantasy/Troll_01_1_HURT_spritesheet.png", 770, 580, 7700, 90, 10),
+ die: new GameSprite("https://marvin.hs-bochum.de/~mneugebauer/fantasy/Troll_01_1_DIE_spritesheet.png", 1010, 580, 10100, 90, 10),
+ walk: new GameSprite("https://marvin.hs-bochum.de/~mneugebauer/fantasy/Troll_01_1_WALK_spritesheet.png", 775, 580, 7750, 90, 10),
+ attack: new GameSprite("https://marvin.hs-bochum.de/~mneugebauer/fantasy/Troll_01_1_ATTACK_spritesheet.png", 900, 830, 9000, 90, 10)
+ },
+ orientation
+ )
+ }
+}
+
+class IceGolem extends GameElementWithFormula {
+ constructor(orientation) {
+ super(
+ {
+ idle: new GameSprite("https://marvin.hs-bochum.de/~mneugebauer/fantasy/Golem_01_1_IDLE_spritesheet.png", 700, 750, 12600, 50, 18),
+ hurt:new GameSprite("https://marvin.hs-bochum.de/~mneugebauer/fantasy/Golem_01_1_HURT_spritesheet.png", 700, 750, 8400, 50, 12),
+ die:new GameSprite("https://marvin.hs-bochum.de/~mneugebauer/fantasy/Golem_01_1_DIE_spritesheet.png", 700, 750, 10500, 50, 15)/*,
+ walk:new GameSprite("https://marvin.hs-bochum.de/~mneugebauer/fantasy/Golem_01_1_WALK_spritesheet.png", 775, 580, 7750, 90, 10),
+ attack:new GameSprite("https://marvin.hs-bochum.de/~mneugebauer/fantasy/Golem_01_1_ATTACK_spritesheet.png", 900, 830, 9000, 90, 10)*/
+ },
+ orientation
+ )
+ }
+}
+
+class ForestGolem extends GameElementWithFormula {
+ constructor(orientation) {
+ super(
+ {
+ idle: new GameSprite("https://marvin.hs-bochum.de/~mneugebauer/fantasy/Golem_02_1_IDLE_spritesheet.png", 700, 750, 12600, 40, 18),
+ hurt:new GameSprite("https://marvin.hs-bochum.de/~mneugebauer/fantasy/Golem_02_1_HURT_spritesheet.png", 700, 750, 8400, 40, 12),
+ die:new GameSprite("https://marvin.hs-bochum.de/~mneugebauer/fantasy/Golem_02_1_DIE_spritesheet.png", 700, 750, 10500, 40, 15)/*,
+ walk:new GameSprite("https://marvin.hs-bochum.de/~mneugebauer/fantasy/Golem_01_1_WALK_spritesheet.png", 775, 580, 7750, 90, 10),
+ attack:new GameSprite("https://marvin.hs-bochum.de/~mneugebauer/fantasy/Golem_01_1_ATTACK_spritesheet.png", 900, 830, 9000, 90, 10)*/
+ },
+ orientation
+ )
+ }
+}
+
+class Fairy extends GameElement {
+ constructor(imgsrc) {
+ if(imgsrc == undefined) {
+ imgsrc = "https://marvin.hs-bochum.de/~mneugebauer/fantasy/fairy.svg";
+ }
+ super({ idle: new GameSprite(imgsrc, 60, 60, 60) })
+ }
+
+ sendTo(targetNode) {
+ //let homeNode = document.querySelector(".helper-container");
+ let homeNode = this.container;
+ if (targetNode == undefined) {
+ targetNode = homeNode;
+ }
+
+
+ //probably the speech bubble arrows have to be removed
+ /*if(targetNode.classList.contains(".fairy-place-holder")) {
+
+ }*/
+ let speechBubbleElements = document.querySelectorAll(".bubble");
+ speechBubbleElements.forEach(function(bubble) {
+ let relatedFairyPlaceHolder = bubble.parentNode.querySelector(".fairy-place-holder");
+ if(relatedFairyPlaceHolder != undefined) {
+ bubble.classList.remove("show-overflow");
+ }
+ });
+ /*speechBubbleElementsWFairy.forEach(function(speechBubbleElementWFairy) {
+ let relatedBubble = speechBubbleElementWFairy.closest(".bubble");
+ relatedBubble.classList.add("no-arrow");
+ });*/
+
+ //console.log(targetNode);
+ let helperNode = this.node;
+ let fairyPlaceHolder = targetNode;
+ let helpSpeechBubble = document.querySelector(".fairy-help");
+
+ let rectHelperNode = helperNode.getBoundingClientRect();
+ let rectContainer = fairyPlaceHolder.getBoundingClientRect();
+ //console.log(rectContainer);
+ let xoffset = rectHelperNode.x - rectContainer.x;
+ let yoffset = rectHelperNode.y - rectContainer.y;
+ helperNode.style.setProperty("--xoffset", Math.floor(xoffset) + "px");
+ helperNode.style.setProperty("--yoffset", Math.floor(yoffset) + "px");
+
+ //console.log(xoffset, yoffset);
+
+ helperNode.classList.add("notifying");
+ helperNode.classList.remove("returning");
+ //fairyPlaceHolder.style.maxHeight = "40px";
+ fairyPlaceHolder.appendChild(helperNode);
+ /*helperContainer.style.left = "50%";
+ helperContainer.style.bottom = "";
+ helperContainer.style.position = "relative";*/
+
+ //let exclamationContainer = document.querySelector(".helper-container .exclamation");
+ let exclamationContainer = document.querySelector(".fairy-home .exclamation");
+ //exclamationContainer.classList.remove("active");
+ if(targetNode == homeNode) {
+ exclamationContainer.classList.remove("temporarily-hidden");
+ }
+ else {
+ exclamationContainer.classList.add("temporarily-hidden");
+ }
+ }
+
+ sendBack() {
+ //leaving target node empty will send fairy back to player
+ this.sendTo();
+ }
+
+ isCurrentlyMoving() {
+ let targetRect = this.node.parentNode.getBoundingClientRect();
+ let currentRect = this.node.getBoundingClientRect();
+ let diffX = targetRect.x-currentRect.x;
+ let diffY = targetRect.y-currentRect.y;
+
+ return (diffX != 0 && diffY != 0);
+ }
+}
+
+function __(htmlId) {
+ let toFind = document.getElementById(htmlId);
+ if (!toFind) {
+ console.log(htmlId + " not found with __");
+ }
+ return toFind;
+}
+
+function ___(htmlSelector) {
+ let toFind = document.querySelector(htmlSelector);
+ if (!toFind) {
+ console.log(htmlSelector + " not found with ___");
+ }
+ return toFind;
+}
+
+function ____(htmlSelector) {
+ let toFind = document.querySelectorAll(htmlSelector);
+ if (!toFind) {
+ console.log(htmlSelector + " not found with ____");
+ }
+ return toFind;
+}
+
+function hideNotificationSpeechBubble(event) {
+ console.log("try to return fairy");
+ if(this.introState > 0) {
+ return;
+ }
+ if (event == undefined || (event.target.closest(".enter-spell-container") == undefined && event.target != document.querySelector(".fairy-img") && event.target.closest(".bubble") == undefined && event.target.closest(".fairy-home") == undefined && event.target.closest(".sign-post-container") == undefined && event.target != document.querySelector(".confirm-link") && event.target.closest(".badge") == undefined)) {
+ console.log("return fairy");
+ //helperContainer.style.position = "absolute";
+ //helperContainer.style.left = playerContainer.style.left;
+ //helperContainer.style.bottom = playerContainer.style.height;
+
+ let helperContainer = document.querySelector(".helper-container");
+ let helperNode = document.querySelector(".fairy-img");
+ let fairyPlaceHolder = document.querySelector(".fairy-place-holder");
+ let helpSpeechBubble = document.querySelector(".fairy-help:not(.question-bubble)");
+ let exclamationContainer = document.querySelector(".exclamation");
+
+ if (helperNode == undefined) {
+ console.log("no fairy here to return");
+ showExclamationMarkAfterReturnAnimation();
+ }
+ else {
+ //compute distance between container and (future) node
+ let rectHelperNode = helperNode.getBoundingClientRect();
+ let rectContainer = helperContainer.getBoundingClientRect();
+ let xoffset = rectHelperNode.x - rectContainer.x;
+ let yoffset = rectHelperNode.y - rectContainer.y;
+ helperNode.style.setProperty("--xoffset", Math.floor(xoffset) + "px");
+ helperNode.style.setProperty("--yoffset", Math.floor(yoffset) + "px");
+ console.log(xoffset, yoffset);
+ //this.GameElements.helper.sendBack();
+ helperNode.classList.remove("notifying");
+ helperNode.classList.add("returning");
+ helperContainer.appendChild(helperNode);
+ helperNode.addEventListener("animationend", showExclamationMarkAfterReturnAnimation);
+ }
+ helpSpeechBubble.classList.add("closed", "no-arrow");
+ helpSpeechBubble.classList.remove("middle-arrow");
+ helpSpeechBubble.classList.remove("show-overflow");
+
+ fairyPlaceHolder.style.maxHeight = "0px";
+
+ document.removeEventListener("click", hideNotificationSpeechBubble);
+ }
+}
+
+function showExclamationMarkAfterReturnAnimation() {
+ let exclamationContainer = document.querySelector(".fairy-home .exclamation");
+ exclamationContainer.classList.remove("temporarily-hidden");
+ document.querySelector(".fairy-img").removeEventListener("animationend", showExclamationMarkAfterReturnAnimation);
+}
+
+function removeFaderAfterFadingIn() {
+ this.classList.remove("fade-in");
+}
+
+function proceedIntroOnClick(event) {
+ console.log("Try to proceed intro on click");
+ if(ALQuiz == undefined) {
+ return;
+ }
+ if(event.target.closest(".bubble.fairy-help") == undefined && event.target.closest(".fairy-img") == undefined && event.target.closest(".badges-container") == undefined && event.target.closest(".sign-post-container.point-left") == undefined) {
+ let toClick;
+ event.preventDefault();
+ event.stopPropagation();
+ switch(ALQuiz.introState) {
+ case 0:
+ //do nothing
+ break;
+ case 1:
+ toClick = document.querySelector(".fairy-img");
+ break;
+ default:
+ toClick = document.querySelector(".bubble.fairy-help a");
+ break;
+ }
+ if(toClick != undefined) {
+ toClick.click();
+ }
+ }
+ else {
+ console.log("we are in else routine");
+ }
+}
+
+function matrixTdSelect(event, node) {
+ if(node == undefined) {
+ node = this;
+ }
+ if(node == undefined) {
+ console.log("undefined node in matrixTdSelect");
+ return;
+ }
+ let matrixTableNode = node.closest(".matrixtable");
+ if(matrixTableNode == undefined) {
+ return;
+ }
+ matrixTableNode.querySelectorAll("input").forEach(function(inputElement) {
+ let closestTd = inputElement.closest("td");
+ closestTd.classList.remove("selected-entry");
+ });
+ node.classList.add("selected-entry");
+ let selectedInputName = node.querySelector("input").name;
+ node.closest(".enemy-container").dataset.refer = selectedInputName;
+ console.log("REFER: "+node.closest(".enemy-container").dataset.refer);
+}
+
+function buildNewScene(object) {
+ //console.log(this);
+ //doesn't work properly., so a check function is needed document.querySelector(".fader").removeEventListener("transitionend", buildNewScene.bind(null, object));
+ console.log("faded out");
+
+ //let currQuestion = object.getQuestion();
+
+ //rest speechbubble element
+ //this.speechBubbleElement.classList.remove("no-arrow");
+
+ /*if(object.fader.classList.contains("fade-out")) {
+ //okay, reload is desired
+ console.log("reload is desired");
+ }*/
+
+ if (nextQuestionQuery == undefined) {
+ //do nothing, wait for the promise to resolve
+ console.log("do nothing, wait for the promise to resolve");
+ //show loading animation
+ //...
+ }
+ else {
+ console.log("next question is already there");
+ waitingForNextQuestion = false;
+
+ //arrange enemies etc.
+
+ //identify input fields
+ let matriceTableNames = [];
+ let matriceTableInfoObjects = {};
+ let matriceTables = nextQuestionQuery.querySelectorAll(".que .formulation .matrixtable");
+ matriceTables.forEach(function(matriceTable) {
+ let matriceTableInfoObject = {};
+ matriceTableInfoObject.table = matriceTable;
+ matriceTableInfoObject.tablewbrackets = matriceTable.closest(".matrixroundbrackets");
+ matriceTableInfoObject.appended = false;
+ //Find out shape and prepare table.
+ matriceTableInfoObjects[matriceTable.id] = matriceTableInfoObject;
+ });
+ console.log(matriceTableNames);
+
+ //check amount of enemies
+ let inputs = nextQuestionQuery.querySelectorAll(".que .formulation input:not([type=hidden]):not([type=submit])");
+
+ //remove all formula elements from all enemies
+ /*while (object.formulaContainer.firstChild != undefined) {
+ object.formulaContainer.removeChild(object.formulaContainer.firstChild);
+ }*/
+
+ /*document.querySelectorAll(".formula-container").forEach(formulaContainer => {
+ while (formulaContainer.firstChild != undefined) {
+ formulaContainer.removeChild(formulaContainer.firstChild);
+ }
+ });*/
+ object.GameElements.enemies.forEach(function(Enemy) {
+ Enemy.clearFormulas();
+ });
+
+ let allEnemies = document.querySelectorAll(".enemy-container");
+ allEnemies.forEach(enemyContainer => {
+ enemyContainer.classList.add("invisible")
+ enemyContainer.removeAttribute("data-refer");
+ enemyContainer.removeAttribute("data-count");
+ enemyContainer.removeAttribute("data-matrixinput")
+ enemyContainer.removeAttribute("data-matrixelementstosolve");
+ });
+
+ //For each input field, pick a random enemy and attach paragraph to it
+ let i = 0;
+ inputs.forEach(inputField => {
+ let matriceId = undefined;
+ let target = undefined;
+ let potentialMatriceTableContainer = inputField.closest(".matrixtable");
+ if(potentialMatriceTableContainer != undefined) {
+ //Special handling for matrice inputs.
+ //Append formula container to be targeted here.
+ matriceId = potentialMatriceTableContainer.id;
+ if(matriceId != undefined && matriceTableInfoObjects[matriceId] != undefined) {
+ if(matriceTableInfoObjects[matriceId].appended == true) {
+ //Append matrice to enemy.
+ target = matriceTableInfoObjects[matriceId].table.closest(".enemy-container");
+ //target = chosenEnemy;
+ target.dataset.matrixelementstosolve = parseInt(target.dataset.matrixelementstosolve)+1;
+ }
+ }
+ }
+
+ console.log(inputField);
+ if(target == undefined) {
+ let allInactiveEnemies = document.querySelectorAll(".enemy-container.invisible");
+ let randomEnemy = allInactiveEnemies[Math.floor(Math.random()*allInactiveEnemies.length)];
+
+ if(randomEnemy == undefined) {
+ //console.log(allInactiveEnemies);
+ console.log("unable to choose enemy");
+ return false;
+ }
+ randomEnemy.classList.remove("invisible");
+ console.log("invisible class is removed here for enemy");
+ target = randomEnemy;
+ }
+
+ let relevantParagraph = undefined;
+ if(matriceId == undefined) {
+ relevantParagraph = inputField.closest("p");
+ }
+ else {
+ if(matriceTableInfoObjects[matriceId].appended == false) {
+ relevantParagraph = matriceTableInfoObjects[matriceId].tablewbrackets == undefined ? matriceTableInfoObjects[matriceId].table : matriceTableInfoObjects[matriceId].tablewbrackets;
+ matriceTableInfoObjects[matriceId].appended = true;
+ matriceTableInfoObjects[matriceId].object = new MatrixObject(matriceId)
+ target.dataset.matrixinput = true;
+ target.dataset.count = i;
+ i++;
+ target.dataset.matrixelementstosolve = 1;
+ //Replace the whole matrices div with question mark.
+ //...
+ }
+ }
+ //Remove or replace with question mark
+ let questionMark = document.createElement("span");
+ questionMark.classList.add("input-replacer");
+ questionMark.innerHTML = "";
+ inputField.parentNode.insertBefore(questionMark, inputField);
+ inputField.style.display = "none";
+ console.log("relevantParagraph2: ");
+ console.log(relevantParagraph);
+ if (relevantParagraph != undefined) {
+ /*relevantParagraph.childNodes.forEach(function (inParagraph) {
+ randomEnemy.querySelector(".formula-container").appendChild(inParagraph);
+ });*/
+ target.querySelector(".formula-container").appendChild(relevantParagraph);
+ }
+ else {
+ console.log("no formula found");
+ }
+
+ if(matriceId != undefined) {
+ //Add extra field to append it.
+ }
+
+ //First enemy is the auto-targeted one. Fill input surrounding divs with math.
+ if(i == 0) {
+ let FirstEnemyObject;
+ for(let j in object.GameElements.enemies) {
+ if(object.GameElements.enemies[j].container == target) {
+ FirstEnemyObject = object.GameElements.enemies[j];
+ break;
+ }
+ }
+ if(FirstEnemyObject == undefined) {
+ console.log("error in finding default enemy");
+ }
+ else {
+ object.targetedEnemy = FirstEnemyObject;
+ object.updateInputSurroundingMath(object);
+ }
+ }
+
+ target.dataset.refer = inputField.name;
+ if(matriceId == undefined) {
+ target.dataset.count = i;
+ i++;
+ }
+ else {
+ let relevantTd = inputField.closest("td");
+ relevantTd.addEventListener("click", matrixTdSelect);/*function() {
+ let matrixTableNode = this.closest("matrixtable");
+ if(matrixTableNode == undefined) {
+ return;
+ }
+ matrixTableNode.querySelectorAll("input").forEach(function(inputElement) {
+ let closestTd = inputElement.closest("td");
+ closestTd.classList.remove("selected-entry");
+ });
+ this.classList.add("selected-entry");
+ let selectedInputName = this.querySelector("input").name;
+ this.closest(".enemy-container").dataset.refer = selectedInputName;
+ console.log("REFER: "+this.closest(".enemy-container").dataset.refer);
+ };*/
+ }
+ });
+ //just to go for sure: remove invisible-class again (in some rare moments, enemies stayed invisible for unknown reasons)
+ document.querySelectorAll(".enemy-container[data-refer]").forEach(function(enemyContainer) {
+ enemyContainer.classList.remove("invisible");
+ });
+
+ //Parse question text into speech bubble.
+ let questionContent = nextQuestionQuery.querySelector(".formulation");
+ if (questionContent == undefined) {
+ console.log("no question content in query found");
+ return;
+ }
+ questionContent.querySelectorAll("input, .im-controls, .stackinputfeedback").forEach(function (nodeToRemove) {
+ //nodeToRemove.parentNode.removeChild(nodeToRemove);
+ nodeToRemove.style.display = "none";
+ });
+
+ let hintNodes = [];
+ questionContent.querySelectorAll(".hint").forEach(function (hintNode) {
+ //nodeToRemove.parentNode.removeChild(nodeToRemove);
+ hintNodes.push(hintNode);
+ });
+ //console.log(questionContent.innerHTML, questionContent);
+ object.processNotification(questionContent.innerHTML, false, object.questionBubbleElement);
+
+ //and add new on his representation
+ //old version: all possible
+ /*let formulas = nextQuestionQuery.querySelectorAll(".nolink");
+ formulas.forEach(function(formula) {
+ let plainDiv = document.createElement("div");
+ plainDiv.appendChild(formula);
+ object.formulaContainer.appendChild(plainDiv);
+ });*/
+
+ //new version: only one
+ //try to find relevant quantity
+ /*let inputField = nextQuestionQuery.querySelector("input.algebraic, textarea");
+ //console.log(inputField);
+ //expect input field to be embedded in a paragraph
+ let relevantParagraph = inputField.closest("p");
+ //console.log(relevantParagraph);
+ //Remove or replace with question mark
+ let questionMark = document.createElement("span");
+ questionMark.innerHTML = "?";
+ inputField.parentNode.insertBefore(questionMark, inputField);
+ inputField.style.display = "none";
+ if (relevantParagraph != undefined) {
+ relevantParagraph.childNodes.forEach(function (inParagraph) {
+ object.formulaContainer.appendChild(inParagraph);
+ });
+ }
+ else {
+ console.log("no formula found");
+ }*/
+
+ object.rearrangeMath()
+
+ /*formula.classList.add("chosen_formula");
+ formula.style.position = "absolute";
+ formula.style.top = "50%";
+ formula.style.left = "50%";
+ formula.style.backgroundColor = "rgba(255,255,255,0.9)";
+ formula.style.borderRadius = "10%";
+ formula.style.transform = "translate(-50%, -50%)";
+ formula.style.padding = "5px";
+ console.log(formula);*/
+
+ //this.notificationBubbleElement.style.display = "block";
+
+ //battleGround.appendChild(validation);
+ //battleGround.appendChild(Enemy.container);
+ //battleGround.appendChild(object.speechBubbleElement);
+
+ //questionContainer.appendChild(object.enterSpellContainer);
+ //object.updateValidationTimerId = setInterval(object.updateValidation, 1500, object);
+
+ //object.GameElements.enemy.container.appendChild(formula);
+
+ /*document.querySelectorAll(".sign-post-container").forEach(function(signPostContainer) {
+ signPostContainer.style.display="none";
+ });*/
+
+ //Is safe place? If yes: Adjust overall object display (block/none) with .city CSS class.
+ let contentElement = document.querySelector(".que .content");
+ contentElement.classList.remove("city");
+ contentElement.classList.remove("clearing");
+
+ //Handle completely solved questions differently.
+
+ let currQuestion = object.getQuestion();
+ if(!!currQuestion) {
+ object.fairyFollowSignPost.querySelector(".fairy-representation").style.filter = currQuestion.filter;
+ }
+ let completelySolved = (currQuestion.variants == currQuestion.solvedVariants.length);
+
+ object.pseudoEverythingBackToStart();
+ object.fader.addEventListener("transitionend", function() {
+ object.GameElements.helper.node.classList.add("notifying");
+ object.animateMonsterAnalysis(completelySolved, hintNodes);
+ }, {once:true});
+ object.fadeSceneIn();
+
+ if(completelySolved == true) {
+ object.monstersCamp.classList.add("solved");
+ }
+ }
+}
+
+//////////////////////////////MAIN ROUTINE/////////////////////////////////////////
+//nextQuestionQuery: Global var that contains information about the next question. It helps to check, whether the promise, that fetches the next question, is already resolved. If it is undefined, the next question wasn't yet fetched. If it contains a question, the next scene can be filled with the contained information.
+var nextQuestionQuery;
+
+var testVar;
+
+//videoAnimation: Global var, boolean, if true, interactions are blocked, so that a currently running animation can't be interrupted and gains the total attention of the user.
+var videoAnimation;
+
+//waitingForNextQuestion: Global var, boolean, that tells, whether the new scene can already be parsed, when the fader transition ended, because we are not waiting, or if we should keep the screen black and wait for the promise to be resolved.
+var waitingForNextQuestion;
+
+//inOtherTheme: Global var, boolean. If not in BO theme, classic is assumed. Some things have to be handled differently.
+var inOtherTheme;
+
+//IDEA (is currently handled in FantasyQuiz::init()): initialLoad: Global var, boolean, is true on new page load and set to false after all initial processes are done, especially loading save state from first question.
+//var initialLoad = true;
+
+//solved: Array, that consists of the solved exercises-
+/*let solvedQuestionsAsString = sessionStorage.getItem("solved");
+if (solvedQuestionsAsString != undefined) {
+ let solvedQuestions = JSON.parse(solvedQuestionsAsString);
+ if (solvedQuestions != undefined) {
+ solvedQuestions.forEach(function (solvedQuestion) {
+ let Question = ALQuiz.getQuestion(solvedQuestion);
+ Question.solved = Question.needs;
+ });
+ }
+} else {
+ let solved = [];
+ sessionStorage.setItem("solved", JSON.stringify(solved));
+}*/
+
+/*let ALQuiz = new FantasyQuiz();
+let Parser = new DOMParser();
+let quizObject = ALQuiz;
+
+//let navBlock = __("mod_quiz_navblock");
+
+
+//Current version includes questions from first element.
+document.addEventListener("DOMContentLoaded", function() {
+ let linkToLastQuizItem = ___("#mod_quiz_navblock a:last-child");
+ if(linkToLastQuizItem != undefined && linkToLastQuizItem.href != undefined) {
+ //console.log(linkToLastQuizItem.href)
+ }
+ else {
+ //throw clean error
+ return;
+ }
+ fetch(linkToLastQuizItem.href).then(function(response) {
+ return response.text();
+ })
+ .then(function(htmlText) {
+
+ let regexresult = htmlText.match(/class=".*?qtext.*?">([\d\D]*?)<\/div>/);
+ if(!regexresult) {
+ //throw clean error
+ return false;
+ }
+ let firstBrace = regexresult[0].indexOf('{');
+ let lastBrace = regexresult[0].lastIndexOf('}');
+
+ let jsonString = regexresult[0].slice(firstBrace, lastBrace+1);
+
+ let quizObject = JSON.parse(jsonString);
+ ALQuiz = new FantasyQuiz(quizObject);
+
+ //console.log(JSON.parse(jsonString));
+ //If everything went fine up to here, the last element of the quiz contained the configuration and is to be hidden.
+ linkToLastQuizItem.style.display = "none";
+
+ ALQuiz.updateNavigation();
+
+ //implement fantasy
+ ALQuiz.init();
+
+ return true;
+ });
+});*/
+//setTimeout(function() { }, 500);
\ No newline at end of file
diff --git a/script/alquiz-qpool-instant-tutoring.js b/script/alquiz-qpool-instant-tutoring.js
new file mode 100644
index 0000000000000000000000000000000000000000..e61578cd64175b680078494df8d75ad2110930d1
--- /dev/null
+++ b/script/alquiz-qpool-instant-tutoring.js
@@ -0,0 +1,2103 @@
+/*
+MIT License
+
+Copyright (c) 2022 Malte Neugebauer, Hochschule Bochum
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+*/
+
+
+///START AL QUIZ SCRIPT///
+class QuestionGroup {
+ constructor(id, description, Questions, nextGroup) {
+ this.id = id;
+ this.description = description;
+ this.Questions = {};
+ if (!!Questions) {
+ Questions.forEach(Question => {
+ this.Questions[Question.id] = Question;
+ });
+ }
+ }
+
+ addQuestion(QuestionObject) {
+ this.Questions[QuestionObject.id] = QuestionObject;
+ }
+}
+
+class BubbleInfo {
+ constructor(stateStringAssociation) {
+ /*this.success = success;
+ this.validation = validation;
+ this.failure = failure;
+ this.redo = redo;
+ this.camebackaftersuccess = camebackaftersuccess;
+ this.error = error;*/
+ for(let i in stateStringAssociation) {
+ this[i] = stateStringAssociation[i];
+ }
+ }
+
+ getText(state) {
+ if (this[state] != undefined) {
+ return this[state];
+ }
+ return undefined;
+ }
+}
+
+class Instruction {
+ constructor(id, description, page, onsuccess, onfailure, BubbleInfoObject, questionsOnPage) {
+ this.id = id;
+ /* success means: challenge accepted and go to endboss*/
+ this.onsuccess = onsuccess;
+ /*failure means: give me the first easy question*/
+ this.onfailure = onfailure;
+ this.description = description;
+ this.page = page;
+ this.BubbleInfo = BubbleInfoObject;
+ if(this.BubbleInfo == undefined) {
+ this.BubbleInfo = new BubbleInfo({});
+ }
+
+ this.questionsOnPage = questionsOnPage == undefined ? 1 : questionsOnPage;
+ }
+
+ isSolved() {
+ return false;
+ }
+
+ isCurrentlySolved() {
+ return false;
+ }
+}
+
+class Question extends Instruction {
+ constructor(id, description, page, needs, BubbleInfo, onsuccess, onfailure, askBeforeSkip, questionsOnPage, autoTriggerFeedbackCondition, variants) {
+ super(id, description, page, onsuccess, onfailure, BubbleInfo, questionsOnPage);
+ this.needs = needs;
+ this.solved = 0;
+ /*solved means: solved at least once in this attempt, currentlySolved means: solved actually now in the current scope of js variables*/
+ this.currentlySolved = 0;
+ this.askBeforeSkip = askBeforeSkip == undefined ? true : askBeforeSkip;
+ if(!!autoTriggerFeedbackCondition) {
+ try {
+ this.autoTriggerFeedbackCondition = Function(autoTriggerFeedbackCondition);
+ }
+ catch(error) {
+ this.autoTriggerFeedbackCondition = false;
+ console.log("error during converting an auto trigger feedback condition function string into a function");
+ console.log(error);
+ }
+ }
+ //elsewise, this.autoTriggerFeedbackCondition remains undefined
+ this.variants = variants == undefined ? 1 : variants;
+ }
+
+ isSolved(onlyOnCurrentlySolved) {
+ if(onlyOnCurrentlySolved == undefined) {
+ onlyOnCurrentlySolved = false;
+ }
+ let solvedAtAskedTime = (!onlyOnCurrentlySolved ? this.solved : this.currentlySolved);
+ if (solvedAtAskedTime >= this.needs) {
+ return true;
+ }
+ return false;
+ }
+
+ ifCurrentlySolved() {
+ if (this.currentlySolved >= this.needs) {
+ return true;
+ }
+ return false;
+ }
+}
+
+class Quiz {
+ constructor(quizObject/*QuestionGroups*/, currentQuestionId, enableAskBeforeSkip) {
+ this.QuestionGroups = {};
+ this.currentQuestionId;
+ this.askBeforeSkipEnabled = enableAskBeforeSkip == undefined ? false : enableAskBeforeSkip;
+ //console.log(quizObject);
+ if(quizObject != undefined) {
+ if(quizObject.groups != undefined) {
+ for(let questionGroupId in quizObject.groups) {
+ this.QuestionGroups[questionGroupId] = new QuestionGroup(questionGroupId, quizObject.groups[questionGroupId]);
+ console.log("added "+questionGroupId);
+ }
+ console.log(this.QuestionGroups);
+ this.currentQuestionId = currentQuestionId;
+ if(currentQuestionId == undefined) {
+ //If currentQuestionId is undefined, take first question in JSON-object.
+ this.currentQuestionId = Object.keys(quizObject.questions)[0];
+ }
+ }
+ let pageCount = 0;
+ if(quizObject.questions != undefined) {
+ for(let questionId in quizObject.questions) {
+ let groupToAddId;
+ if(this.QuestionGroups[quizObject.questions[questionId].group] != undefined) {
+ groupToAddId = quizObject.questions[questionId].group;
+ }
+ else {
+ //try to identify group by token, elsewise add to group "unsorted"
+ if(questionId.indexOf("_") != -1) {
+ let expectedGroupNameMatch = questionId.match(/^(.*)_/);
+ if(expectedGroupNameMatch[1] != undefined && expectedGroupNameMatch[1] != "") {
+ if(this.QuestionGroups[expectedGroupNameMatch[1]] != undefined) {
+ groupToAddId = expectedGroupNameMatch[1];
+ }
+ }
+ }
+ if(groupToAddId == undefined) {
+ if(this.QuestionGroups.unsorted == undefined) {
+ this.QuestionGroups.unsorted = new QuestionGroup("unsorted", "Unsorted Questions");
+ }
+ groupToAddId = "unsorted";
+ }
+ //Note: Clarify: Why are the parameters of this function differing from the parameters below?
+ this.QuestionGroups[groupToAddId].addQuestion(new Question(questionId,quizObject.questions[questionId].name));
+ }
+
+ let BubbleInfoObject;
+ if(quizObject.questions[questionId].BubbleInfo != undefined) {
+ BubbleInfoObject = new BubbleInfo(quizObject.questions[questionId].BubbleInfo);
+ }
+ let needs = 1;
+ if(quizObject.questions[questionId].needs != undefined) {
+ needs = quizObject.questions[questionId].needs;
+ }
+
+ let ElementToAdd;
+ if(quizObject.questions[questionId].type == "instruction") {
+ ElementToAdd = new Instruction(questionId,quizObject.questions[questionId].name,pageCount, quizObject.questions[questionId].onsuccess, quizObject.questions[questionId].onfailure, BubbleInfoObject, quizObject.questions[questionId].onpage);
+ }
+ else {
+ ElementToAdd = new Question(questionId,quizObject.questions[questionId].name,pageCount, needs, BubbleInfoObject, quizObject.questions[questionId].onsuccess, quizObject.questions[questionId].onfailure, quizObject.questions[questionId].askBeforeSkip, quizObject.questions[questionId].onpage, quizObject.questions[questionId].autoTriggerFeedbackCondition, quizObject.questions[questionId].variants);
+ if(!!quizObject.questions[questionId].autoTriggerFeedbackCondition) {
+ console.log("found "+quizObject.questions[questionId].autoTriggerFeedbackCondition);
+ console.log("interpreted as");
+ console.log(ElementToAdd.autoTriggerFeedbackCondition);
+ }
+ }
+ this.QuestionGroups[groupToAddId].addQuestion(ElementToAdd);
+ pageCount = pageCount + 1 + (ElementToAdd.variants > 1 ? ElementToAdd.variants-1 : 0) + (ElementToAdd.questionsOnPage > 1 ? ElementToAdd.questionsOnPage : 0);
+ }
+ }
+ }
+
+ //auto assign onsuccess and onfailure for undefined
+ let groupNames = Object.keys(this.QuestionGroups);
+ let grouplength = groupNames.length;
+ for (let i = 0; i < grouplength; i++) {
+ //If desried to lead the learners always to the next exercise independent of success or failure, use the following lines.
+ let questionNames = Object.keys(this.QuestionGroups[groupNames[i]].Questions);
+ let questionlength = questionNames.length;
+ for (let j = 0; j < questionlength; j++) {
+ if (!this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onsuccess || !this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onfailure) {
+ //console.log("something for "+questionNames[j]+" is undefined");
+ //probably next question or next group
+ if (j < questionlength - 1) {
+ //next question
+ if(this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onsuccess == undefined) {
+ this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onsuccess = questionNames[j + 1];
+ }
+ if(this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onfailure == undefined) {
+ this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onfailure = questionNames[j + 1];
+ }
+ } else if (i < grouplength - 1) {
+ //console.log(questionNames[j] + " leads to next group onsuccess ");
+ //first question of next group
+ if(this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onsuccess == undefined) {
+ this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onsuccess = Object.keys(this.QuestionGroups[groupNames[i + 1]].Questions)[0];
+ }
+ if(this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onfailure == undefined) {
+ this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onfailure = Object.keys(this.QuestionGroups[groupNames[i + 1]].Questions)[0];
+ }
+ } else {
+ //console.log("no other group");
+ if(this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onsuccess == undefined) {
+ this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onsuccess = "_finish";
+ }
+ if(this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onfailure == undefined) {
+ this.QuestionGroups[groupNames[i]].Questions[questionNames[j]].onfailure = "_finish";
+ }
+ }
+ }
+ };
+
+ //If desired to let the learners continue in the same world on success and send to the next world on failure, uncomment the following lines.
+ /*
+ let questionlength = Object.keys(this.QuestionGroups[groupNames[i]].Questions).length;
+ for (let j = 0; j < questionlength; j++) {
+ if (!this.QuestionGroups[groupNames[i]].Questions[Object.keys(this.QuestionGroups[groupNames[i]].Questions)[j]].onsuccess) {
+ //probably next question or next group
+ if (j < questionlength - 1) {
+ //next question
+ this.QuestionGroups[groupNames[i]].Questions[Object.keys(this.QuestionGroups[groupNames[i]].Questions)[j]].onsuccess = Object.keys(this.QuestionGroups[groupNames[i]].Questions)[j + 1];
+ } else if (i < grouplength - 1) {
+ //console.log(Object.keys(this.QuestionGroups[groupNames[i]].Questions)[j] + " leads to next group onsuccess ");
+ //first question of next group
+ this.QuestionGroups[groupNames[i]].Questions[Object.keys(this.QuestionGroups[groupNames[i]].Questions)[j]].onsuccess = Object.keys(this.QuestionGroups[groupNames[i + 1]].Questions)[0];
+ } eonfailure
+ }
+
+ if (!this.QuestionGroups[groupNames[i]].Questions[Object.keys(this.QuestionGroups[groupNames[i]].Questions)[j]].onfailure) {
+ //You may want to lead users to the first question of next group, assuming, that they are not able to solve the next (harder) question unless they are not able to solve the current (easier) question.
+ if (i < grouplength - 1) {
+ //console.log(Object.keys(this.QuestionGroups[groupNames[i]].Questions)[j] + " leads to next group onfailure ");
+ this.QuestionGroups[groupNames[i]].Questions[Object.keys(this.QuestionGroups[groupNames[i]].Questions)[j]].onfailure = Object.keys(this.QuestionGroups[groupNames[i + 1]].Questions)[0];
+ } else {
+ //console.log("no other group");
+ this.QuestionGroups[groupNames[i]].Questions[Object.keys(this.QuestionGroups[groupNames[i]].Questions)[j]].onfailure = "_finish";
+ }
+ }
+ };
+ */
+ }
+ }
+
+ getQuestions() {
+ let objects = [];
+ this.QuestionGroups.forEach(QuestionGroup => {
+ for (let k in QuestionGroup.Questions) {
+ objects.push(QuestionGroup.Questions[k]);
+ }
+ });
+ return objects;
+ }
+
+ getQuestion(id) {
+ if (id == undefined) {
+ id = this.currentQuestionId;
+ }
+ for (let i in this.QuestionGroups) {
+ if (this.QuestionGroups[i].Questions[id] != undefined) {
+ return this.QuestionGroups[i].Questions[id];
+ }
+ }
+ return false;
+ }
+
+ getNextQuestionId(questionId) {
+ if (questionId == undefined) {
+ questionId = this.currentQuestionId;
+ }
+ //let returnValue = false;
+ for (let i in this.QuestionGroups) {
+ if(this.QuestionGroups[i].Questions[questionId] != undefined) {
+ let nextStep = this.QuestionGroups[i].Questions[questionId].isSolved() ? this.QuestionGroups[i].Questions[questionId].onsuccess : this.QuestionGroups[i].Questions[questionId].onfailure;
+ switch (nextStep) {
+ case "_finish":
+ return -1;
+ break;
+ default:
+ return nextStep;
+ break;
+ }
+ }
+ }
+ console.log("question id not found");
+ return false;
+ }
+
+ getPageURL(questionId) {
+ if (questionId == undefined) {
+ questionId = this.currentQuestionId;
+ }
+
+ let firstQuestionNavElement = document.querySelector("#quiznavbutton1");
+ if (!firstQuestionNavElement) {
+ return false;
+ }
+ let plainUrl = "";
+ if (!firstQuestionNavElement.href || firstQuestionNavElement.href == "#") {
+ plainUrl = window.location.href;
+ } else {
+ plainUrl = firstQuestionNavElement.href;
+ }
+
+ //let sanitizedUrl = plainUrl.replace(/(.*?)(?:#|&page=\d*#*|&scrollpos=\d*#*)/, "\1");
+ let sanitizedUrl = plainUrl;
+ let relPos = plainUrl.indexOf("&scrollpos");
+ if (relPos == -1) {
+ relPos = plainUrl.indexOf("&page");
+ if (relPos == -1) {
+ relPos = plainUrl.indexOf("#");
+ }
+ }
+
+ if (relPos > -1) {
+ //sanitizedUrl = plainUrl.substr(0, relPos);
+ sanitizedUrl = plainUrl.slice(0, relPos);
+ }
+
+ let pageToReturn = this.getRandomPageOfQuestion(questionId);
+ /*let pageToReturn = this.getQuestion(questionId).page;
+ //pick a random variant if existent
+ let numVariants = this.getQuestion(questionId).variants;
+ if(this.getQuestion(questionId).variants > 1) {
+ let randomPage = pageToReturn;
+ let match = window.location.href.match(/page=(\d*)/);
+ if(match != undefined && match[1] != undefined) {
+ let currentPage = match[1];
+ do {
+ randomPage = pageToReturn+Math.floor(Math.random()*numVariants);
+ } while(randomPage == currentPage);
+ }
+ else {
+ randomPage = pageToReturn+Math.floor(Math.random()*numVariants);
+ }
+ pageToReturn = randomPage;
+ }*/
+ return sanitizedUrl + "&page=" + pageToReturn;
+ }
+
+ getRandomPageOfQuestion(questionId) {
+ if (questionId == undefined) {
+ questionId = this.currentQuestionId;
+ }
+ let CurrQuestion = this.getQuestion(questionId);
+ let pageToReturn = CurrQuestion.page;
+ //pick a random variant if existent
+ let numVariants = CurrQuestion.variants;
+ if(numVariants > 1) {
+ let randomPage = pageToReturn;
+ let match = window.location.href.match(/page=(\d*)/);
+ if(match != undefined && match[1] != undefined) {
+ let currentPage = match[1];
+ do {
+ randomPage = pageToReturn+Math.floor(Math.random()*numVariants);
+ } while(randomPage == currentPage);
+ }
+ else {
+ randomPage = pageToReturn+Math.floor(Math.random()*numVariants);
+ }
+ pageToReturn = randomPage;
+ }
+ return pageToReturn;
+ }
+
+ getNextPageInfo(questionId, forceURL) {
+ if (questionId == undefined) {
+ questionId = this.currentQuestionId;
+ }
+ let Question = this.getQuestion(questionId);
+
+ if(forceURL == undefined) {
+ forceURL = false;
+ }
+
+ let nextPageUrl = "";
+ let nextPageLinkText = "";
+ let nextQuestionId = this.getNextQuestionId();
+ let possibleNextPageUrl = this.getPageURL(nextQuestionId);
+
+ if (nextQuestionId == -1) {
+ //finish
+ let finishAttemptElement = document.querySelector(".endtestlink.aalink");
+ if (!finishAttemptElement || !finishAttemptElement.href) {
+ possibleNextPageUrl = "summary.php";
+ } else {
+ possibleNextPageUrl = finishAttemptElement.href;
+ }
+ nextPageLinkText = "Übung beenden";
+ }
+ else {
+ nextPageLinkText = "Nächste Frage";
+ }
+
+ //actually means a real skip, no right or wrong
+ if(this.askBeforeSkipEnabled == true && Question.askBeforeSkip == true && !forceURL && !Question.isSolved() && document.querySelector(".stackprtfeedback") == undefined) {
+ //ask before skip
+ nextPageUrl = "javascript:showAskBeforeSkipModal();";
+ document.querySelector(".skip-yes").href = possibleNextPageUrl;
+ }
+ else {
+ nextPageUrl = possibleNextPageUrl;
+ }
+ return {
+ url: nextPageUrl,
+ linkText: nextPageLinkText
+ };
+ }
+
+ updateMoodleNavButtons() {
+ let buttonDivs = document.querySelectorAll(".submitbtns");
+ buttonDivs.forEach(buttonDiv => {
+ buttonDiv.childNodes.forEach(buttonDivChild => {
+ buttonDivChild.style.visibility = "hidden";
+ buttonDivChild.style.width = "0";
+ });
+ });
+
+ let cameFrom = localStorage.getItem("camefrom");
+ if(cameFrom == undefined) {
+ let previousPageButton = document.getElementById("mod_quiz-prev-nav");
+ if(previousPageButton != undefined) {
+ previousPageButton.value = "Zurück";
+ previousPageButton.style.visibility = "visible";
+ previousPageButton.style.width = "auto";
+ }
+ }
+ else {
+ let prevButton = document.createElement("a");
+ prevButton.classList.add("btn", "btn-primary", "btn-prev-question");
+ prevButton.href = this.getPageURL(cameFrom);
+ prevButton.innerHTML = "Zurück";
+
+ buttonDivs.forEach(buttonDiv => {
+ buttonDiv.insertBefore(prevButton, buttonDiv.firstChild);
+ });
+
+ localStorage.removeItem("camefrom");
+ }
+
+ let nextButton = document.createElement("a");
+ nextButton.classList.add("btn", "btn-primary", "btn-next-question");
+ let nextPageInfos = this.getNextPageInfo();
+ nextButton.href = nextPageInfos.url;
+ nextButton.innerHTML = nextPageInfos.linkText;
+
+ buttonDivs.forEach(buttonDiv => {
+ buttonDiv.appendChild(nextButton);
+ });
+ }
+
+ updateSpeechBubbles(id) {
+ if (id == undefined) {
+ id = this.currentQuestionId;
+ }
+ let currQuestion = this.getQuestion(id);
+ if (!currQuestion || !currQuestion.BubbleInfo) {
+ return false;
+ }
+ let bubbles = document.querySelectorAll(".bubble:not(.in-modal)");
+ if (bubbles.length != 1) {
+ console.log("bad amount of speech bubbles");
+ return false;
+ }
+ let bubble = bubbles[0];
+ let text = "";
+
+ let icon = document.querySelector(".dm-icon");
+ let iconUrls = {
+ grin:"https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg",
+ think:"https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-think.svg",
+ sad:"https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-sad.svg",
+ happy:"https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-happy.svg"
+ };
+ let imgReaction = "";
+
+ //on instruction, the revisit property of the bubble info plays a special role, so...
+ if(currQuestion instanceof Instruction && !(currQuestion instanceof Question) && currQuestion.visited == true) {
+ let revisitText = currQuestion.BubbleInfo.getText("revisit");
+ if(revisitText != "" && revisitText != undefined) {
+ text = revisitText;
+ }
+ }
+
+ //get current state of question
+ let stackFeedback = document.querySelector(".stackprtfeedback");
+ if (stackFeedback != undefined) {
+ //solved, false or partially correct
+
+ //only move feedback to the speech bubble on one feedback field
+ let stackFeedbacks = document.querySelectorAll(".stackprtfeedback");
+
+ if (currQuestion.isSolved(true) == true) {
+ imgReaction = "happy";
+ if (currQuestion.BubbleInfo.getText("success") == undefined) {
+ if (stackFeedbacks.length == 1) {
+ //move the stack feedback in the speech bubble by default and add "Nächste Frage/Übung beenden"
+ let stackFeedbackInWords = "";//stackFeedback.querySelector("div");
+ let first = true;
+ //console.log(stackFeedback.childNodes);
+ stackFeedback.childNodes.forEach(function(childNode) {
+ //console.log(childNode.innerHTML);
+ if(first == false) { stackFeedbackInWords += " "; } else { first = false; }
+ if(childNode.innerHTML != undefined && childNode.innerHTML != "" && childNode.tagName != "SCRIPT") {
+ stackFeedbackInWords += childNode.innerHTML;
+ }
+ });
+ if (stackFeedbackInWords == "" /*stackFeedbackInWords == undefined || stackFeedbackInWords.innerHTML == undefined || stackFeedbackInWords.innerHTML == ""*/) {
+ text = "Richtig!";
+ console.log("no feedback found to move");
+ }
+ let nextPageInfos = this.getNextPageInfo();
+ text = stackFeedbackInWords + "Wenn es dir mehr Sicherheit gibt, kannst du diese <a href=\"javascript:;\" onclick=\"repeatQuestion();\">Aufgabe mit anderen Zahlen wiederholen</a>. Ansonsten bist du bereit für die <a href=\"" + nextPageInfos.url + "\">" + nextPageInfos.linkText + "</a>.";
+ stackFeedback.style.display = "none";
+ }
+ else {
+ text = "Richtig!";
+ console.log("using standard speech-bubble-feedback because of undefined feedback text for solved state and too many feedback fields")
+ }
+ }
+ else {
+ text = currQuestion.BubbleInfo.getText("success");
+ }
+ }
+ else {
+ //false or partially correct
+ imgReaction = "sad";
+ if (currQuestion.BubbleInfo.getText("failure") == undefined) {
+ console.log("no fail text");
+ if (stackFeedbacks.length == 1) {
+ //move the stack feedback in the speech bubble by default and add "Erneut versuchen"
+ let stackFeedbackInWords = "";/*stackFeedback.querySelector("div");*/
+ let first = true;
+ stackFeedback.childNodes.forEach(function(childNode) {
+ //console.log(childNode.innerHTML);
+ if(first == false) { stackFeedbackInWords += " "; } else { first = false; }
+ if(childNode.innerHTML != undefined && childNode.innerHTML != "" && childNode.tagName != "SCRIPT") {
+ stackFeedbackInWords += childNode.innerHTML;
+ }
+ });
+
+ if (stackFeedbackInWords == ""/* || stackFeedbackInWords.innerHTML == undefined || stackFeedbackInWords.innerHTML == ""*/) {
+ text = "Falsch!";
+ console.log("no feedback found to move");
+ }
+
+
+ let nextPageInfos = this.getNextPageInfo();
+ text = stackFeedbackInWords + " Erneut versuchen? <a href=\"#\" onclick=\"document.querySelector('input[name*=redoslot],button[name*=redoslot]').click();\">Ja</a> <a href=\"" + nextPageInfos.url + "\">Nein (" + nextPageInfos.linkText + ")</a>"
+ stackFeedback.style.display = "none";
+ }
+ else {
+ text = "Falsch.";
+ console.log("using standard speech-bubble-feedback because of undefined feedback text for failure state and too many feedback fields")
+ }
+ }
+ else {
+ text = currQuestion.BubbleInfo.getText("failure");
+ }
+ }
+ }
+ else {
+ //verfication, syntax error or came back to main question
+ if (document.querySelector(".validationerror") != undefined) {
+ //verification state
+ text = currQuestion.BubbleInfo.getText("validation") == undefined ? "Wurde deine Eingabe richtig interpretiert? <a href=\"#\" onclick=\"document.querySelector('input[id*=q][name$=_-submit],button[id*=q][name$=_-submit]').click();\">Ja</a> <a href=\"#\" onclick=\"this.parentNode.innerHTML='Ändere deine Eingabe und klicke erneut auf "Prüfen"'\">Nein</a>" : currQuestion.BubbleInfo.getText("validation");
+ }
+ else if(/*document.querySelector(".alert")*/document.querySelector(".stackinputerror") != undefined) { //Switched from ".alert" to ".stackinputerror", because in quiz preview may a block with class ".alert" appear to inform the previewer that -- e. g. -- a test is not yet activated.
+ //syntax error
+ imgReaction = "think";
+ text = currQuestion.BubbleInfo.getText("error") == undefined ? "Oh! Offenbar gibt es einen Fehler bei der Eingabe. Bitte schau dir den Hinweis am Eingabefeld an, korrigiere und klicke erneut auf Prüfen." : currQuestion.BubbleInfo.getText("error");
+ }
+ /*else {
+ //came back to main question after the last of this group is solved
+ console.log("start routine to check for coming back");
+ let i = 0;
+ for (i in this.QuestionGroups) {
+ if (QuestionGroups[i].Questions[this.currentQuestionId] != undefined) {
+ break;
+ }
+ }
+ //console.log(this.currentQuestionId + " is in group " + i);
+ let keys = Object.keys(this.QuestionGroups[i].Questions);
+ if (keys[0] == this.currentQuestionId) {
+ //console.log(this.currentQuestionId + " is the first question of this group");
+ if (this.QuestionGroups[i].Questions[keys[keys.length - 1]] != undefined && this.QuestionGroups[i].Questions[keys[keys.length - 1]].isSolved() == true) {
+ console.log("came back after solving last question of group");
+ if (currQuestion.BubbleInfo.getText("camebackaftersuccess") == undefined) {
+ text = "Willkommen zurück zu dieser Aufgabe. Haben dir die letzten Aufgaben geholfen, diese Aufgabe zu verstehen? Versuche es doch nochmal! Gehe ansonsten weiter zur nächsten Aufgabe.";
+ } else {
+ text = currQuestion.BubbleInfo.getText("camebackaftersuccess");
+ }
+ currQuestion.onfailure = currQuestion.onsuccess;
+ //this.updateMoodleNavButtons();
+ }
+ }
+ }*/
+ //if(in verification state)
+ //text = Question.BubbleInfo.getText("verify") == undefined ? "Wurde deine Eingabe richtig interpretiert? %check% <a onclick=\"...\">Nein</a>" : Question.BubbleInfo.getText("verify");
+ //else if(in false state)
+ //else if(in syntax error state)
+ //else if(in redo state)
+ //else
+ //assume initial state
+ //text = Question.BubbleInfo.getText("initial")
+ }
+
+ //bubble.classList.remove("hidden");
+
+ if (text != "") {
+ //append special links to text, e. g. %nextlink%, %linktoquestionid_id%, %check%
+ bubble.innerHTML = text;
+ }
+ if(imgReaction != "" && icon != undefined) {
+ icon.src = iconUrls[imgReaction];
+ }
+
+ return true;
+ }
+
+ updateNavigation() {
+ let navPanel = document.querySelector(".qn_buttons");
+ if(!navPanel) {
+ return false;
+ }
+ let buttons = document.querySelectorAll("[id*=quiznavbutton]");
+ if(buttons.length == undefined || buttons.length < 1) {
+ return false;
+ }
+ //group
+ //let groupHeadingNodes = [];
+ for(let m in this.QuestionGroups) {
+ //this.QuestionGroups.forEach(QuestionGroup => {
+ let wrapper = document.createElement("span");
+ wrapper.dataset.isFor = this.QuestionGroups[m].id;
+ //groupHeadingNodes.push(heading);
+
+ let heading = document.createElement("h2");
+ heading.innerHTML = this.QuestionGroups[m].description;
+ heading.style.clear = "left";
+ wrapper.appendChild(heading);
+
+ let j = 0;
+ let k = 1;
+ let questionAmount = Object.keys(this.QuestionGroups[m].Questions).length;
+
+ let solvedQuestionsAsString = localStorage.getItem("solved");
+ let solvedQuestionsAsArray = [];
+ if(solvedQuestionsAsString != undefined) {
+ solvedQuestionsAsArray = JSON.parse(solvedQuestionsAsString);
+ }
+
+ let partiallyCorrectQuestionsAsString = localStorage.getItem("partially");
+ let partiallyCorrectQuestionsAsArray = [];
+ if(partiallyCorrectQuestionsAsString != undefined) {
+ partiallyCorrectQuestionsAsArray = JSON.parse(partiallyCorrectQuestionsAsString);
+ }
+
+ let falseQuestionsAsString = localStorage.getItem("false");
+ let falseQuestionsAsArray = [];
+ if(falseQuestionsAsString != undefined) {
+ falseQuestionsAsArray = JSON.parse(falseQuestionsAsString);
+ }
+
+ for(let i in this.QuestionGroups[m].Questions) {
+ //console.log("quiznavbutton"+(this.QuestionGroups[m].Questions[i].page+1));
+ let questionCard = document.getElementById("quiznavbutton"+(this.QuestionGroups[m].Questions[i].page+1));
+
+ questionCard.querySelectorAll(".accesshide").forEach(slotMarker => {
+ if(slotMarker != undefined && slotMarker.nextSibling != undefined) {
+ if(!(this.QuestionGroups[m].Questions[i] instanceof Question) && this.QuestionGroups[m].Questions[i] instanceof Instruction) {
+ //assume first question to be instructions
+ slotMarker.nextSibling.data = "i";
+ }
+ else if(j < questionAmount-1) {
+ slotMarker.nextSibling.data = k;
+ k++;
+ }
+ else {
+ console.log("entering algorithm for "+this.QuestionGroups[m].Questions[i].id);
+ slotMarker.nextSibling.data = "";
+ let endbossImg = document.createElement("img");
+ if(this.QuestionGroups[m].Questions[i].id == "start") {
+ console.log("setting start to house");
+ endbossImg.src = "https://marvin.hs-bochum.de/~mneugebauer/fantasy/house-solid.svg";
+ }
+ else {
+ endbossImg.src = "https://marvin.hs-bochum.de/~mneugebauer/skull.svg";
+ }
+ endbossImg.style.height = "20px";
+ slotMarker.parentNode.insertBefore(endbossImg, slotMarker.nextSibling);
+ }
+ }
+ });
+ if(!questionCard) {
+ console.log("bad question card id for question "+this.QuestionGroups[m].Questions[i].id);
+ }
+ else {
+
+ if(solvedQuestionsAsArray.indexOf(this.QuestionGroups[m].Questions[i].id) != -1) {
+ console.log(this.QuestionGroups[m].Questions[i].id + " has already been solved");
+ questionCard.classList.add("correct");
+ }
+ else if(partiallyCorrectQuestionsAsArray.indexOf(this.QuestionGroups[m].Questions[i].id) != -1) {
+ console.log(this.QuestionGroups[m].Questions[i].id + " has already been solved");
+ questionCard.classList.add("partiallycorrect");
+ }
+ else if(falseQuestionsAsArray.indexOf(this.QuestionGroups[m].Questions[i].id) != -1) {
+ console.log(this.QuestionGroups[m].Questions[i].id + " has already been solved");
+ questionCard.classList.add("incorrect");
+ }
+ wrapper.appendChild(questionCard);
+ }
+
+
+ /*if(this.QuestionGroups[m].Questions[i].questionsOnPage > 1) {
+ for(let l=this.QuestionGroups[m].Questions[i].questionsOnPage;l>0;l--) {
+ let questionCardToHide = document.getElementById("quiznavbutton"+(this.QuestionGroups[m].Questions[i].page+l+1));
+ if(questionCardToHide != undefined) {
+ questionCardToHide.style.display = "none";
+ }
+ }
+ }*/
+ if(this.QuestionGroups[m].Questions[i].variants > 1) {
+ if(this.QuestionGroups[m].Questions[i].questionsOnPage > 1) {
+ //... how to handle variants of questions with many questions on one page?
+ }
+ else {
+ //let numVariants = this.QuestionGroups[m].Questions[i].variants;
+ for(let l=1;l<this.QuestionGroups[m].Questions[i].variants;l++) {
+ let questionCardToHide = document.getElementById("quiznavbutton"+(this.QuestionGroups[m].Questions[i].page+l+1));
+ if(questionCardToHide != undefined) {
+ questionCardToHide.style.display = "none";
+ }
+ }
+ }
+ //correct enumeration
+ //k = k-this.QuestionGroups[m].Questions[i].variants+1;
+ }
+ else {
+ if(this.QuestionGroups[m].Questions[i].questionsOnPage > 1) {
+ this.hideMultipleQuestionCards(m, i);
+ }
+ }
+
+ j++;
+ };
+
+ navPanel.appendChild(wrapper);
+ }/*)*/;
+
+ //put a flag instead of a skull, a number or an "i" in the very last question card
+ document.querySelectorAll(".qn_buttons span[data-is-for]:last-child a:last-child img").forEach(function(lastQuestionCard) {
+ lastQuestionCard.src = "https://marvin.hs-bochum.de/~mneugebauer/flag.svg";
+ });
+
+ //show group navigation on instruction and update speech bubble navigation
+ let currentQuestion = this.getQuestion();
+ if(!(currentQuestion instanceof Question) && currentQuestion instanceof Instruction) {
+
+ let CurrentGroup;
+ for(let i in this.QuestionGroups) {
+ if(this.QuestionGroups[i].Questions[this.currentQuestionId] != undefined) {
+ CurrentGroup = this.QuestionGroups[i];
+ break;
+ }
+ };
+
+ let groupNavigation = document.querySelector(".group-navigation");
+ if(groupNavigation != undefined) {
+ //find current group
+
+ if(CurrentGroup != undefined) {
+
+ //show group navigation
+ let cards = document.querySelectorAll("[data-is-for="+CurrentGroup.id+"] a")
+ let cardAmount = cards.length;
+ let keys = Object.keys(CurrentGroup.Questions);
+ for(let i=cardAmount-1;i>=0;i--) {
+ let cardClone = cards[i].cloneNode(true);
+ let stepWrapper = document.createElement("div");
+ stepWrapper.classList.add("wrap_nav_group");
+ let stepHeadingAnchor = document.createElement("a");
+ stepHeadingAnchor.href = cardClone.href;
+ let stepHeading = document.createElement("h2");
+ stepHeading.innerHTML = CurrentGroup.Questions[keys[i]].description;
+
+ stepHeadingAnchor.appendChild(stepHeading);
+ stepWrapper.appendChild(cardClone);
+ stepWrapper.appendChild(stepHeadingAnchor);
+ groupNavigation.appendChild(stepWrapper);
+ };
+
+ let groupNavCss = document.createElement("style");groupNavCss.type="text/css";groupNavCss.innerHTML = ".path-mod-quiz .group-navigation .qnbutton { text-decoration: none; font-size: 14px; line-height: 20px; font-weight: 400; background-color: #fff; background-image: none; height: 40px; width: 30px; border-radius: 3px; border: 0; overflow: visible; margin: 0 6px 6px 0;} .path-mod-quiz .group-navigation .qnbutton { background: none; background-color: rgba(0, 0, 0, 0); background-color: #eee; border: 0; border-radius: 4px; color: #000000 !important; font-size: 14px; font-weight: 700; height: 45px; line-height: 25px !important; margin: 0 5px 5px 0; width: 35px;} .group-navigation .qnbutton .thispageholder { border: 1px solid #999; border-radius: 4px; z-index: 1;}.group-navigation .qnbutton .thispageholder { border: 1px solid; border-radius: 3px; z-index: 1;}.group-navigation .qnbutton .trafficlight, group-navigation .qnbutton .thispageholder { display: block; position: absolute; top: 0; bottom: 0; left: 0; right: 0;} .path-mod-quiz .group-navigation .qnbutton.notyetanswered .trafficlight, .path-mod-quiz .group-navigation .qnbutton.invalidanswer .trafficlight { background-color: #fff;}.path-mod-quiz .group-navigation .qnbutton.notyetanswered .trafficlight, .path-mod-quiz .group-navigation .qnbutton.invalidanswer .trafficlight { background-color: #fff;}.path-mod-quiz .group-navigation .qnbutton .trafficlight { border: 0; background: #fff none center / 10px no-repeat scroll; height: 20px; margin-top: 20px; border-radius: 0 0 3px 3px;} .path-mod-quiz .group-navigation .qnbutton .trafficlight { background: #fff none center 4px / 10px no-repeat scroll; background-color: rgb(255, 255, 255); border: 0; border-radius: 0 0 4px 4px; height: 20px; margin-top: 25px;} .path-mod-quiz .group-navigation .qnbutton.correct .trafficlight { background-color: #8bc34a; background-image: url(/theme/image.php/adaptable/theme/1660635117/mod/quiz/checkmark); } .path-mod-quiz .group-navigation .qnbutton.notanswered .trafficlight, .path-mod-quiz .group-navigation .qnbutton.incorrect .trafficlight { background-color: #f44336; } .path-mod-quiz .group-navigation .qnbutton.partiallycorrect .trafficlight { background-color: #ff9800; background-image: url(/theme/image.php/adaptable/theme/1660635117/mod/quiz/whitecircle); } .path-mod-quiz .group-navigation .qnbutton.thispage .thispageholder { border: 3px solid #1f536b; } .wrap_nav_group { clear:left; }";
+ document.getElementsByTagName("head")[0].appendChild(groupNavCss);
+ }
+ }
+
+ let endbossLink = document.querySelector(".endboss-link");
+ if(endbossLink != undefined) {
+ endbossLink.href = this.getPageURL(currentQuestion.onsuccess);
+ }
+
+ if(CurrentGroup != undefined) {
+ let questionKeys = Object.keys(CurrentGroup.Questions);
+ let nextWorldLink = document.querySelector(".link-next-world");
+ let nextWorldURL = this.getPageURL(CurrentGroup.Questions[questionKeys[questionKeys.length-1]].onsuccess);
+
+ if(nextWorldLink != undefined) {
+ nextWorldLink.href = nextWorldURL;
+ }
+
+ let endbossDefeat = CurrentGroup.Questions[questionKeys[questionKeys.length-1]].isSolved();
+ let endbossStatePhrase = document.querySelector(".endboss-state");
+ if(endbossStatePhrase != undefined) {
+ if(endbossDefeat == true) {
+ endbossStatePhrase.innerHTML = "bereits";
+ }
+ /*else {
+ endbossStatePhrase.innerHTML = "noch nicht";
+ }*/
+ }
+
+ let nextQuestionLink = document.querySelector(".link-next-question");
+ if(nextQuestionLink != undefined) {
+ if(endbossDefeat == true) {
+ nextQuestionLink.innerHTML = "der nächsten Welt";
+ nextQuestionLink.href = nextWorldURL;
+ //overwrite default next question
+ document.querySelector(".btn-next-question").href = nextWorldURL;
+ }
+ else {
+ let i;
+ let page;
+ for(i in CurrentGroup.Questions) {
+ if(!CurrentGroup.Questions[i].isSolved() && CurrentGroup.Questions[i] instanceof Question) {
+ page = CurrentGroup.Questions[i].page;
+ break;
+ }
+ }
+ //console.log(page);
+ nextQuestionLink.setAttribute("onclick", 'tutorialFocusElement(document.querySelector(\'.wrap_nav_group [data-quiz-page="'+page+'"]\'));');
+ document.querySelector(".btn-next-question").href = this.getPageURL(i);
+ }
+ }
+
+ let currentLevelPhrase = document.querySelector(".current-level");
+ if(currentLevelPhrase != undefined) {
+ let amount = 0;
+ let solved = 0;
+ for(let i in CurrentGroup.Questions) {
+ if(CurrentGroup.Questions[i] instanceof Question) {
+ amount++;
+ if(CurrentGroup.Questions[i].isSolved()) {
+ solved++;
+ }
+ }
+ }
+ if(endbossDefeat == true) {
+ currentLevelPhrase.innerHTML = amount+" von "+amount;
+ }
+ else {
+ currentLevelPhrase.innerHTML = solved+" von "+amount;
+ }
+ }
+ }
+
+ localStorage.setItem("camefrom", currentQuestion.id);
+ }
+
+ }
+
+
+ hideMultipleQuestionCards(m, i) {
+ if(this.QuestionGroups[m].Questions[i].questionsOnPage > 1) {
+ for(let l=this.QuestionGroups[m].Questions[i].questionsOnPage;l>0;l--) {
+ let questionCardToHide = document.getElementById("quiznavbutton"+(this.QuestionGroups[m].Questions[i].page+l+1));
+ if(questionCardToHide != undefined) {
+ questionCardToHide.style.display = "none";
+ }
+ }
+ }
+ }
+
+ setCurrentQuestionId(id) {
+ this.currentQuestionId = id;
+
+ //save question as visited, so next time on loading the script, question will carry the visited property with true
+ let visitedQuestionsAsString = localStorage.getItem("visited");
+ if (visitedQuestionsAsString != undefined) {
+ let visitedQuestions = JSON.parse(visitedQuestionsAsString);
+ if (visitedQuestions != undefined && visitedQuestions.indexOf(id) < 0) {
+ visitedQuestions.push(id);
+ localStorage.setItem("visited", JSON.stringify(visitedQuestions));
+ }
+ } else {
+ let visited = [];
+ localStorage.setItem("visited", JSON.stringify(visited));
+ }
+ this.markQuestionAsCurrent(id)
+ }
+
+ incrementSolved(id) {
+ if (id == undefined) {
+ id = this.currentQuestionId;
+ }
+ this.getQuestion(id).solved++;
+ this.getQuestion(id).currentlySolved++;
+
+ if (this.getQuestion(id).isSolved()) {
+ let solvedQuestionsAsString = localStorage.getItem("solved");
+ if (solvedQuestionsAsString != undefined) {
+ let solvedQuestions = JSON.parse(solvedQuestionsAsString);
+ if (solvedQuestions != undefined) {
+ if (solvedQuestions.indexOf(id) == -1) {
+ solvedQuestions.push(id);
+ localStorage.setItem("solved", JSON.stringify(solvedQuestions));
+ }
+ }
+ }
+ else {
+ let toSave = '["'+id+'"]';
+ localStorage.setItem("solved", toSave);
+ }
+ }
+ }
+
+ saveState(state, id) {
+ if(state != "false" && state != "partially") {
+ return;
+ }
+ if(id == undefined) {
+ id = this.currentQuestionId;
+ }
+
+ let saveStateQuestionsAsString = localStorage.getItem(state);
+ if (saveStateQuestionsAsString != undefined) {
+ let saveStateQuestions = JSON.parse(saveStateQuestionsAsString);
+ if (saveStateQuestions != undefined) {
+ if (saveStateQuestions.indexOf(id) == -1) {
+ saveStateQuestions.push(id);
+ localStorage.setItem(state, JSON.stringify(saveStateQuestions));
+ }
+ }
+ }
+ else {
+ let toSave = '["'+id+'"]';
+ localStorage.setItem(state, toSave);
+ }
+ }
+
+ markQuestionAsCurrent(questionId) {
+ if(questionId != undefined) {
+ questionId = this.currentQuestionId;
+ }
+ let currentQuestion = this.getQuestion(questionId);
+ if(!currentQuestion) {
+ return;
+ }
+
+ let currentMarkedNavButtons = document.querySelectorAll(".qnbutton.thispage");
+ currentMarkedNavButtons.forEach(function(currentMarkedNavButton) {
+ currentMarkedNavButton.classList.remove("thispage");
+ });
+
+ let currentQuestionButtons = document.querySelectorAll('.qnbutton[data-quiz-page="'+currentQuestion.page+'"]');
+ currentQuestionButtons.forEach(function(currentQuestionButton) {
+ currentQuestionButton.classList.add("thispage");
+ });
+ }
+}
+
+class InstantTutoringQuiz extends Quiz {
+
+ constructor(quizObject/*QuestionGroups*/, currentQuestionId) {
+ super(quizObject/*QuestionGroups*/, currentQuestionId);
+ console.log(quizObject);
+
+ this.validationElement;
+ this.notificationBubbleContainer;
+ this.updateValidationTimerId;
+ this.validationLastState;
+ this.exclamationContainer;
+ this.globalMessage = "";
+ this.globalElementToAppend;
+
+ }
+
+ init() {
+ let currentlyViewingQuestion = this.getQuestion() instanceof Question;
+
+ this.validationElement = document.querySelector(".formulation.clearfix .stackinputfeedback");
+
+ if(this.validationElement == undefined) {
+ console.log("ALQuiz: UpdateValidation not started, because no validation element found "+(currentlyViewingQuestion == true ? "for unknown reasons" : " because we are on an instruction element")+".");
+ }
+ else {
+ this.updateValidationTimerId = setInterval(this.updateValidation, 1500, this);
+ }
+
+ if(currentlyViewingQuestion == true) {
+ let fixedContainer = document.createElement("div");
+ fixedContainer.classList.add("chat-ui");
+
+ let dmIcon = document.createElement("img");
+ dmIcon.classList.add("dm-icon");
+ dmIcon.src = "https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg";
+ dmIcon.onclick = function() {
+ let bubble = document.querySelector(".chat-ui .bubble");
+ if(bubble.dataset.isTransitioning == true) {
+ return;
+ }
+ bubble.classList.toggle("active");
+ if(bubble.classList.contains("active") == true) {
+ bubble.classList.toggle("temporarily-removed");
+ }
+ document.querySelector(".chat-ui .red-dot").classList.remove("active");
+ }
+
+ let speechBubbleContainer = document.createElement("div");
+ speechBubbleContainer.classList.add("bubble", /*"temporarily-removed"*/"active");
+ speechBubbleContainer.addEventListener("transitionend", removeSpeechBubbleAfterTransitionEnd);
+ let speechBubbleContentElement = document.createElement("div");
+ speechBubbleContentElement.classList.add("bubble-content");
+ speechBubbleContainer.appendChild(speechBubbleContentElement);
+ this.notificationBubbleContainer = speechBubbleContainer;
+ this.notificationBubbleContentElement = speechBubbleContentElement;
+
+ speechBubbleContainer.dataset.isTransitioning = "0";
+ speechBubbleContainer.ontransitionstart = function() {
+ this.dataset.isTransitioning = "1";
+ }
+ speechBubbleContainer.ontransitionend = function() {
+ this.dataset.isTransitioning = "0";
+ }
+
+ let iconContainer = document.createElement("div");
+ //iconContainer.style.float = "right";
+ iconContainer.style.position = "relative";
+
+ let exclamationContainer = document.createElement("div");
+ exclamationContainer.classList.add("red-dot");
+ this.exclamationContainer = exclamationContainer;
+
+ fixedContainer.appendChild(speechBubbleContainer);
+ iconContainer.appendChild(dmIcon);
+ iconContainer.appendChild(exclamationContainer);
+ fixedContainer.appendChild(iconContainer);
+
+ document.querySelector(".formulation").appendChild(fixedContainer);
+
+ document.querySelector("button[id$=_-submit], input[id$=_-submit]").addEventListener("click", function(event) {
+ event.preventDefault();
+ receiveFeedback();
+ });
+ }
+ }
+
+ //overwrites parent function
+ updateSpeechBubbles(id) {
+ let currentlyViewingQuestion = this.getQuestion() instanceof Question;
+ if(currentlyViewingQuestion == false) {
+ //Don't update when viewing instruction elements.
+ return;
+ }
+ if (id == undefined) {
+ id = this.currentQuestionId;
+ }
+ let currQuestion = this.getQuestion(id);
+ if (!currQuestion || !currQuestion.BubbleInfo) {
+ return false;
+ }
+ let bubbles = document.querySelectorAll(".bubble:not(.in-modal) .bubble-content");
+ if (bubbles.length != 1) {
+ console.log("bad amount of speech bubbles");
+ return false;
+ }
+ let bubble = bubbles[0];
+ let text = "";
+
+ let icon = document.querySelector(".dm-icon");
+ let iconUrls = {
+ grin:"https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg",
+ think:"https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-think.svg",
+ sad:"https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-sad.svg",
+ happy:"https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-happy.svg"
+ };
+ let imgReaction = "";
+ let alert = false;
+
+ //initial state
+ console.log("update speech bubble to initial state");
+ text = currQuestion.BubbleInfo.getText("init") == undefined ? "Starte mit der Bearbeitung dieser Aufgabe, damit ich dir Rückmeldung geben kann." : currQuestion.BubbleInfo.getText("init");
+ alert = true;
+
+ //First of all, if there is a single hint on the page, move it into the speech bubble. It may be overwritten in the ongoing process.
+ let hints = document.querySelectorAll(".hint");
+ if(hints.length != 1) {
+ console.log("bad amount of hints");
+ //do nothing, text stays the same
+ }
+ else if(hints[0].innerHTML != "") {
+ text = hints[0].innerHTML;
+ hints[0].style.display = "none";
+ }
+ else {
+ console.log("Found hint, but it's empty.")
+ }
+
+ if (text != "") {
+ //append special links to text, e. g. %nextlink%, %linktoquestionid_id%, %check%
+ //...
+ bubble.innerHTML = text;
+ }
+ if(imgReaction != "" && icon != undefined) {
+ icon.src = iconUrls[imgReaction];
+ }
+ if(alert == true) {
+ this.exclamationContainer.classList.add("active");
+ }
+
+ //rerun MathJax if possible to convert text-code to formulas
+ try {
+ if(MathJax != undefined) {
+ console.log("convert tex to formulas");
+ MathJax.Hub.Typeset();
+ }
+ else {
+ /*Somehow there is a problem with Tex-Code in Speech Bubbles...
+ //try again in five second
+ setTimeout(function() {
+ console.log("set mathjax timeout");
+ if(MathJax != undefined) {
+ console.log("convert tex to formulas");
+ MathJax.Hub.Typeset();
+ MathJax.Hub.Typeset();
+ }
+ else {*/
+ console.log("MathJax not existent.");
+ /*}
+ }, 5000);
+ console.log("MathJax not existent.");*/
+ }
+ }
+ catch(Error) {
+ console.log("error in rerunning MathJax");
+ console.log(Error);
+ }
+
+ return true;
+ }
+
+ updateValidation(object) {
+ if(object == undefined) {
+ object = this;
+ }
+
+ let workingValidationElement = object.validationElement.cloneNode(true);
+ workingValidationElement.id = workingValidationElement.id+"_clone";
+ workingValidationElement.style.display = "";
+ workingValidationElement.style.background = "none";
+ workingValidationElement.style.border = "none";
+
+ //has changed?
+ if(!object.validationLastState) {
+ //probably an update is needed
+ }
+ else {
+ let presentationElementClone = workingValidationElement.querySelector("[role=presentation]");
+ if(presentationElementClone == undefined) {
+ //console.log("nothing to display or error");
+ if(workingValidationElement.classList.contains("error")) {
+ //console.log("error");
+ //same error as last time?
+ let stackinputerrorElementLast = object.validationLastState.querySelector(".stackinputerror");
+ //console.log(stackinputerrorElementLast);
+ let stackinputerrorElementCurrent = workingValidationElement.querySelector(".stackinputerror");
+ //console.log(stackinputerrorElementCurrent);
+ /*if(stackinputerrorElementLast != undefined && stackinputerrorElementCurrent != undefined) {
+ console.log(stackinputerrorElementLast.isEqualNode(stackinputerrorElementCurrent));
+ }*/
+ if(stackinputerrorElementLast != undefined && stackinputerrorElementCurrent != undefined && stackinputerrorElementLast.isEqualNode(stackinputerrorElementCurrent)) {
+ //nothing changed
+ console.log("nothing to change (same error)");
+ return false;
+ }
+ //else continue below
+ }
+ else {
+ console.log("nothing to change");
+ return false;
+ }
+ }
+ else {
+ let presentationElementLast = object.validationLastState.querySelector("[role=presentation]");
+ if(presentationElementClone.isEqualNode(presentationElementLast)) {
+ //console.log("no update neccessary")
+ return false;
+ }
+ }
+ }
+
+
+ //check state
+ if(workingValidationElement.classList.contains("error")) {
+ console.log("error");
+ //error routine
+ //object.GameElements.helper.container.querySelector(".exclamation").classList.add("active");
+ //object.speechBubbleElement.style.color = "#999999";
+
+ //guess error type
+ let errorText = "";
+ let errType;
+ //the following lines work for validation next to input[type=text]-elements
+ /*let errorTextElement = workingValidationElement.querySelector(".stackinputerror");
+ if(!errorTextElement) {
+ errType = "unknown_error";
+ }
+ else {
+ errorText = errorTextElement.innerHTML;
+ console.log(errorText);
+ if(errorText.indexOf("missing * characters") != -1) {
+ errType = "multiplication_dot_missing";
+ }
+ else if(errorText.indexOf("invalid final character") != -1) {
+ errType = "invalid_final_char";
+ }
+ else {
+ errType = "unknown_error"
+ }
+ }
+ console.log(errType);
+ object.processError(errType);*/
+
+ //the following lines work for validation next to textarea-elements
+ let nodesContainingErrorInfos = workingValidationElement/*.querySelector(".stackinputerror")*/;
+ let first = true;
+ nodesContainingErrorInfos.childNodes.forEach(function(nodeContainingErrorInfos) {
+ if(first == false) { errorText += " "; } else { first = false; }
+ if(nodeContainingErrorInfos.nodeType == 3) {
+ errorText += nodeContainingErrorInfos.nodeValue;
+ }
+ });
+
+ if(errorText == "") {
+ errType = "unknown_error";
+ }
+ //below is relevant for each branch
+ else {
+ //errorText = errorTextElement.innerHTML;
+ if(errorText.indexOf("missing * characters") != -1) {
+ errType = "multiplication_dot_missing";
+ }
+ else if(errorText.indexOf("invalid final character") != -1) {
+ errType = "invalid_final_char";
+ }
+ else if(errorText.indexOf("listing the values") != -1) {
+ errType = "invalid_value_listing";
+ }
+ else {
+ errType = "unknown_error"
+ }
+ }
+
+ object.processError(errType, false);
+ //return false;
+ }
+ else if(workingValidationElement.classList.contains("loading")) {
+ console.log("wait a moment and try again in some seconds");
+ }
+ else {
+ //hide notification speech bubble after reattempting after error
+ if(object.validationLastState != undefined && object.validationLastState.classList.contains("error")) {
+ object.hideNotificationSpeechBubble();
+ }
+
+ //Following lines are relevant for fantasy branch.
+ /*
+ object.GameElements.helper.container.querySelector(".exclamation").classList.remove("active");
+ //Where is our fairy? If user is currently notified by speech bubble due to error, send back!
+ let helperNode = document.querySelector(".fairy-place-holder img");
+ if(helperNode != undefined) {
+ hideNotificationSpeechBubble();
+ }
+
+ object.speechBubbleElement.style.color = "";
+
+ //clean speeach bubble and insert into speech bubble
+ while(object.speechBubbleElement.lastChild) {
+ object.speechBubbleElement.removeChild(object.speechBubbleElement.lastChild);
+ }
+ object.speechBubbleElement.appendChild(workingValidationElement);
+ */
+ }
+ //console.log("reached end of updateVali");
+
+ object.validationLastState = workingValidationElement;
+
+ //On autoTriggerFeedback, check if autoTriggerCondition is met.
+ let currentQuestion = object.getQuestion();
+ if(currentQuestion.autoTriggerFeedbackCondition != undefined && typeof currentQuestion.autoTriggerFeedbackCondition == "function" && currentQuestion.autoTriggerFeedbackCondition() == true) {
+ receiveFeedback();
+ }
+
+ return true;
+ }
+
+ killUpdateValidationTimer() {
+ clearTimeout(this.updateValidationTimerId);
+ }
+
+ processError(errType, autoShowSpeechBubble) {
+ if(errType == undefined) {
+ errType = "unknown_error";
+ }
+ let texts = {
+ multiplication_dot_missing:[
+ //"Mind to enter your answers with stars * for multiplications!",
+ "Denke daran, für Multiplikationen Sterne * zu nutzen.",
+ //"Mind the *!",
+ "Denk' an die *!",
+ //"Don't forget to use stars * for your multiplications!"
+ "Vergiss nicht, durch Sterne * deine Multiplilkationen anzuzeigen."
+ ],
+ invalid_final_char:[
+ //"It is not possible to end a term like this.",
+ "So darf der Term nicht enden.",
+ //"Your term ends invalid.",
+ "Mit dem letzten Zeichen in deinem Termn stimmt etwas nicht.",
+ //"No, like this the term can't be interpreted because of a wrong final character."
+ "So kann der Term nicht interpretiert werden, weil das letzte Zeichen falsch ist."
+ ],
+ invalid_value_listing:[
+ //"To give more than one solution, do it like this: y = ? or y = ?"
+ "Um mehr als eine Lösung anzugeben, gehe so vor: y = ? or y = ? ."
+ ],
+ unknown_error:[
+ //"Something is wrong with your syntax, try again!",
+ "Etwas stimmt mit der Syntax nicht. Bitte versuche es noch einmal.",
+ //"This term can't be interpreted. Maybe you misspelled something?",
+ "Dieser Term kann nicht interpretiert werden. Hast du dich vielleicht vertippt?",
+ //"This won't work and I don't know why. Please try again!"
+ "Dieser Term funktioniert nicht und ich weiß nicht warum. Bitte versuche es noch einmal."
+ ]
+
+ };
+ let possibleTexts = texts[errType];
+ let text = "";
+ if(possibleTexts == undefined) {
+ possibleTexts = texts.unknown_error;
+ }
+ text = possibleTexts[Math.floor(Math.random()*possibleTexts.length)];
+ //this.notificationBubbleContainer.innerHTML = text;
+ //this.exclamationContainer.classList.add("active");
+ this.processNotification(text, autoShowSpeechBubble);
+ }
+
+ processNotification(message, autoShowSpeechBubble, elementToAppend) {
+ console.log("processing notification");
+ if(message == undefined) {
+ console.log("no message to process");
+ return false;
+ }
+ if(autoShowSpeechBubble == undefined) {
+ autoShowSpeechBubble = false;
+ }
+
+ if(this.notificationBubbleContainer.classList.contains("active")) {
+ this.notificationBubbleContainer.classList.remove("active");
+
+ this.globalMessage = message;
+ this.globalElementToAppend = elementToAppend;
+ this.notificationBubbleContainer.addEventListener("transitionend", showSpeechBubbleAgainAfterClose, false);
+ return;
+ }
+ else {
+ this.notificationBubbleContainer.removeEventListener("transitionend", showSpeechBubbleAgainAfterClose);
+
+ this.notificationBubbleContainer.classList.add("active");
+ this.notificationBubbleContainer.classList.remove("temporarily-removed");
+ }
+
+ this.notificationBubbleContentElement.innerHTML = message;
+ this.updateQuestionLinks();
+ //rerun MathJax if possible to convert text-code to formulas
+ if(!!MathJax) {
+ console.log("convert tex to formulas");
+ MathJax.Hub.Typeset();
+ }
+ else {
+ console.log("MathJax not existent.");
+ }
+
+ if(elementToAppend != undefined) {
+ this.notificationBubbleContentElement.appendChild(elementToAppend);
+ }
+ else {
+ console.log("elementToAppend is undefined");
+ }
+ //console.log(message);
+ if(autoShowSpeechBubble) {
+ this.showNotificationSpeechBubble();
+ }
+ }
+
+ showNotificationSpeechBubble() {
+ this.notificationBubbleContainer.classList.remove("temporarily-removed");
+ this.notificationBubbleContainer.classList.add("active");
+ this.exclamationContainer.classList.remove("active");
+ }
+
+ hideNotificationSpeechBubble() {
+ this.notificationBubbleContainer.classList.remove("active");
+ this.exclamationContainer.classList.remove("active");
+ }
+
+ updateQuestionLinks() {
+ let ALQuizObject = this;
+ document.querySelectorAll("[data-question-link]").forEach(function(questionLink) {
+ let url = ALQuizObject.getPageURL(questionLink.dataset.questionLink);
+ if(!url) {
+ return;
+ }
+ questionLink.href = url;
+ });
+ }
+
+ markQuestionAsSolved(questionId) {
+ if(questionId != undefined) {
+ questionId = this.currentQuestionId;
+ }
+ let currentQuestion = this.getQuestion(questionId);
+ let solvedNowQuestionButtons = document.querySelectorAll('.qnbutton[data-quiz-page="'+currentQuestion.page+'"]');
+ solvedNowQuestionButtons.forEach(function(solvedNowQuestionButton) {
+ solvedNowQuestionButton.classList.add("correct");
+ });
+ }
+}
+
+async function createALQuizFromLastQuizElement() {
+ //Expect gamified quiz structure in last element of quiz in json-format.
+ let linkToLastQuizItem = document.querySelector("#mod_quiz_navblock a:last-child");
+ if(linkToLastQuizItem != undefined && linkToLastQuizItem.href != undefined) {
+ //console.log(linkToLastQuizItem.href)
+ }
+ else {
+ //throw clean error
+ return;
+ }
+ //console.log(linkToLastQuizItem.href);
+ return await fetch(linkToLastQuizItem.href).then(function(response) {
+ return response.text();
+ })
+ .then(function(htmlText) {
+ //console.log(htmlText);
+ let regexresult = htmlText.match(/class=".*?qtext.*?">([\d\D]*?)<\/div>/);
+ if(!regexresult) {
+ //throw clean error
+ return false;
+ }
+ let firstBrace = regexresult[0].indexOf('{');
+ let lastBrace = regexresult[0].lastIndexOf('}');
+
+ let jsonString = regexresult[0].slice(firstBrace, lastBrace+1);
+
+ //In the moodle backend, sometimes unwanted line breaks are added, probably by TinyMCE. These are removed with the following line. Line breaks inserted into the JSON texts with "\n" are not removed (this would be /\\n/).
+ //Furthermore, for yet unknown reasons Moodle adds <span class="nolink">...</span>-Tags around LaTex code. This is completely removed here.
+ jsonString = jsonString.replace(/\n/g,"").replace(/<span class="[\d\D]*?nolink.*?>(.*?)<\/span>/g, "$1");
+ //console.log(jsonString);
+
+ let quizObject = JSON.parse(jsonString);
+ //ALQuiz = new Quiz(quizObject);
+
+ //console.log(JSON.parse(jsonString));
+ //If everything went fine up to here, the last element of the quiz contained the configuration and is to be hidden.
+ linkToLastQuizItem.style.display = "none";
+
+ return quizObject;
+ });
+}
+let currentQuestionId;
+
+//Will be overwritten later, but is initialized to ensure any calls of ALQuiz in the question text will be processed.
+let ALQuiz = new Quiz();
+/*let ALQuiz = new Quiz(QuestionGroups);
+
+let solvedQuestionsAsString = localStorage.getItem("solved");
+if (solvedQuestionsAsString != undefined) {
+ let solvedQuestions = JSON.parse(solvedQuestionsAsString);
+ if (solvedQuestions != undefined) {
+ solvedQuestions.forEach(function (solvedQuestion) {
+ let Question = ALQuiz.getQuestion(solvedQuestion);
+ Question.solved = Question.needs;
+ });
+ }
+} else {
+ let solved = [];
+ localStorage.setItem("solved", JSON.stringify(solved));
+}
+
+let visitedQuestionsAsString = localStorage.getItem("visited");
+if (visitedQuestionsAsString != undefined) {
+ let visitedQuestions = JSON.parse(visitedQuestionsAsString);
+ if (visitedQuestions != undefined) {
+ visitedQuestions.forEach(function (visitedQuestion) {
+ let Question = ALQuiz.getQuestion(visitedQuestion);
+ Question.visited = true;
+ });
+ }
+} else {
+ let visited = [];
+ localStorage.setItem("visited", JSON.stringify(visited));
+}*/
+
+document.addEventListener("DOMContentLoaded", function () {
+
+ if (window.location.href.indexOf("review.php") < 0) {
+
+ createALQuizFromLastQuizElement().then(createdQuizObject => {
+
+ ALQuiz = new InstantTutoringQuiz(createdQuizObject, ALQuiz.currentQuestionId);
+
+ //add ask-before-skip modal
+ let modal = document.createElement("div");
+ modal.classList.add("dmmodal");
+ modal.addEventListener("click", function(event) {
+ if(!event.target.closest(".dmmodal-content")) {
+ this.style.display = "none";
+ }
+ });
+ let modalContent = document.createElement("div");
+ modalContent.classList.add("dmmodal-content", "formulation");
+ let closeSpan = document.createElement("span");
+ closeSpan.classList.add("dmclose");
+ closeSpan.innerHTML = "×";
+ closeSpan.onclick = function() { this.closest(".dmmodal").style.display="none"; };
+ let contentParagraph = document.createElement("p");
+ let modalBubble = document.createElement("p");
+ modalBubble.classList.add("bubble", "in-modal");
+ modalBubble.innerHTML = "Bist du sicher, dass du diese Aufgabe überspringen möchtest?";
+ if(ALQuiz != undefined && ALQuiz.getQuestion() != undefined && ALQuiz.getQuestion().BubbleInfo != undefined && ALQuiz.getQuestion().BubbleInfo.getText("beforeskip") != undefined) {
+ modalBubble.innerHTML = ALQuiz.getQuestion().BubbleInfo.getText("beforeskip");
+ }
+ modalBubble.style.marginTop = "50px";
+ let dmicon = document.createElement("img");
+ dmicon.classList.add("dm-icon");
+ dmicon.src="https://marvin.hs-bochum.de/~mneugebauer/dm-avatar-grin.svg";
+ let yesButton = document.createElement("a");
+ yesButton.classList.add("skip-yes");
+ yesButton.href = "javascript:;";
+ yesButton.innerHTML = "Ja";
+ let noButton = document.createElement("a");
+ noButton.classList.add("skip-no");
+ noButton.href = "javascript:;";
+ noButton.innerHTML = "Nein";
+ noButton.onclick = function() { this.closest(".dmmodal").style.display="none"; };
+
+ modalBubble.appendChild(yesButton);
+ modalBubble.innerHTML += " ";
+ modalBubble.appendChild(noButton);
+
+ modalContent.appendChild(closeSpan);
+ modalContent.appendChild(modalBubble);
+ modalContent.appendChild(dmicon);
+ modalContent.appendChild(contentParagraph);
+ modal.appendChild(modalContent);
+ document.body.appendChild(modal);
+
+ ALQuiz.init();
+ //in development state: interrupt button update to give the main page time to recognize the inline scripts like increment solved and set current question id
+ /*setTimeout('*/ALQuiz.updateSpeechBubbles(); ALQuiz.updateMoodleNavButtons(); ALQuiz.updateNavigation(); /*', 500)*/;
+
+ //If there are textareas, a STACK-equivalence-reasoning task is expected. In this case, we pull feedback after each new line.
+ document.querySelectorAll(".formulation textarea").forEach(function(questionTextareaField) {
+ questionTextareaField.addEventListener("input", receiveInstantFeedbackOnNewLine);
+ });
+ });
+ }
+
+
+ //add styles, e. g. speech bubble
+ let style = document.createElement("style");
+ style.type = "text/css";
+ //.que .outcome background-color is #fcefdc;
+ style.innerHTML = ".red-dot { position: absolute; top: 2%; right:0%; background:#e2001a; padding:1em; box-sizing:border-box; border-radius: 100%; display:none; } .red-dot.active { display:block; } .chat-ui { position:fixed; bottom:50px; right:50px; z-index:1; float:right; display:flex; flex-direction:column; } .bubble { /* layout*/ position: relative; max-width:15em; display:block; /* looks*/ background-color: #fcefdc; padding: 1.125em 1.5em; font-size: 1.25em; border-radius: 1rem; box-shadow:0 0.125rem 0.5rem rgba(0, 0, 0, .3), 0 0.0625rem 0.125rem rgba(0, 0, 0, .2); transition:transform 1s; transform-origin:bottom; z-index:1; max-height:60vh; } .bubble:not(.inquestion) { transform:scale(1,0); } .bubble.inquestion { max-width:unset; } .bubble.active { transform:scale(1,1); } .bubble.temporarily-removed { height:0; } .bubble:not(.no-arrow)::before { /* layout*/ content: ''; position: absolute; width: 0; top: 100%; right: 1.5em; /* offset should move with padding of parent*/ border: .75rem solid transparent; border-bottom: none; /* looks*/ border-top-color: #fcefdc; filter: drop-shadow(0 0.0625rem 0.0625rem rgba(0, 0, 0, .1)); } .bubble.inquestion:not(.no-arrow)::before { right:unset; left:1.5em; } .bubble .bubble-content { /*an additional div to ensure scrollability by simultaneously keep the speech-bubble-arrow visible, which indeed is an overflow*/ overflow:scroll; max-height:50vh; } .formulation a { text-decoration:underline; } .mathsinput { position:fixed; display:flex; width:100vw; bottom:0px; z-index:1; } .mathsinput button { flex-grow:1; } table.trigonometry_table { border:1px solid black;width:100%; } table.trigonometry_table th, td { border:1px solid black;text-align:center; } .dm-icon { float:right; border:2px solid black; border-radius:50%; width: 7.5em; box-shadow: 0 0.125rem 0.5rem rgba(0, 0, 0, .3), 0 0.0625rem 0.125rem rgba(0, 0, 0, .2); } .dm-icon.inquestion { float:none; } .user-focus { background-color: #000; width: 100%; height: 100%; position: absolute; opacity: 0.5; overflow: none; display: block; left: 0; z-index:2; } .user-focus.hide-top { top:0; } .user-focus.hide-bottom { bottom:0; } .dmmodal { display: none; /* Hidden by default */ position: fixed; /* Stay in place */ z-index: 1; /* Sit on top */ padding-top: 100px; /* Location of the box */ left: 0; top: 0; width: 100%; /* Full width */ height: 100%; /* Full height */ overflow: auto; /* Enable scroll if needed */ background-color: rgb(0,0,0); /* Fallback color */ background-color: rgba(0,0,0,0.4); /* Black w/ opacity */ } /* Modal Content */ .dmmodal-content { background-color: #fefefe; margin: auto; padding: 20px; border: 1px solid #888; width: 80%; } /* The Close Button */ .dmclose { color: #aaaaaa; float: right; font-size: 28px; font-weight: bold; } .close:hover, .close:focus { color: #000; text-decoration: none; cursor: pointer; } .mathsinput { position:fixed; display:flex; width:100vw; bottom:0px; z-index:1; } .mathsinput button { flex-grow:1; } .show-on-mobile-only { display:inline-block; } .show-on-desktop-only { display:none; } .mathsbutton { float:right; border:1px solid black; border-radius:50%; height:2em; width:2em; background-color:#aaaaaa; background-image:url(\"https://marvin.hs-bochum.de/~mneugebauer/operators-white.svg\"); background-repeat:no-repeat; background-size:90%; background-position:50%; } .mathsbutton.active { background-color:#e2001a; } @media (min-width:991px) { .mathsinput { display:none; } .show-on-mobile-only { display:none; } .show-on-desktop-only { display:inline-block; } .chat-ui { position:relative; flex-direction:row; width:100%; float:left; bottom:auto; right:auto; } /*add max-height transition to ensure other relative positioned elements move together with bubble on transition*/ .bubble:not(.inquestion) { max-height:0em; order:2; transform-origin:top; transition:transform 1s, max-height 1s; max-width:unset; } .bubble.active { max-height:20em; } .bubble .bubble-content { max-height:19em; } .bubble:not(.no-arrow):not(.inquestion)::before { left:auto; right:100%; top:1.5em; border-bottom:.75rem solid transparent; border-left: none; border-top-color:transparent; border-right-color:#fcefdc; box-shadow:none; } } .stackinputerror { display:none !important; }";
+ document.getElementsByTagName('head')[0].appendChild(style);
+
+ /*let butt = document.createElement("input");
+ butt.value = "Try another question like this";
+ butt.classList.add("btn");
+ butt.classList.add("btn-secondary");
+ butt.type = "submit";
+ butt.name = "redoslot" + ALQuiz.getQuestion().page;
+ document.getElementById("responseform").appendChild(butt);*/
+
+ //show additional maths input if neccessary
+ document.querySelectorAll("input, textarea").forEach(function(inputElement) {
+ inputElement.addEventListener("focus", function() {
+ lastFocusedInputElement = this;
+ });
+ });
+
+ let mathsInput = ["+", "-", "*", "/", "(", ")", "^", "="];
+ let mathsButtons = [];
+ mathsInput.forEach(function(mathsInputSymbol) {
+ let button = document.createElement("button");
+ button.type = "button";
+ button.innerHTML = mathsInputSymbol;
+ button.onclick = function() {
+ if (!lastFocusedInputElement) {
+ console.log("no focused element to enter maths-symbol");
+ return;
+ }
+ let caretPos = lastFocusedInputElement.selectionStart;
+ let currentContent = lastFocusedInputElement.value;
+ lastFocusedInputElement.value = currentContent.substring(0, caretPos) + mathsInputSymbol + currentContent.substring(caretPos);
+ lastFocusedInputElement.focus();
+ lastFocusedInputElement.setSelectionRange(caretPos + 1, caretPos + 1);
+ };
+ mathsButtons.push(button);
+ });
+
+ let mathsInputButtonDiv = document.createElement("div");
+ mathsInputButtonDiv.classList.add("mathsinput");
+
+ mathsButtons.forEach(function(mathsButton) {
+ mathsInputButtonDiv.appendChild(mathsButton);
+ });
+
+ document.body.appendChild(mathsInputButtonDiv);
+
+ //safari hack to show mathsinput at correct position
+ addSafariMathsInputAboveKeyboardSupport();
+
+
+ addMathsOperatorButton();
+});
+
+document.addEventListener("load", function () {
+ //ALQuiz.updateSpeechBubbles();
+});
+
+
+//INSTANT TUTORING FUNCTIONS
+let lastTextareaLength;
+let lastTextareaEndingWhitespaces;
+var Parser = new DOMParser();
+function receiveInstantFeedbackOnNewLine() {
+ let currentTextareaEndingWhitespaces = this.value.match(/.*?(\s*)$/)[1].length;
+ //console.log(this.value.charAt(this.value.length-1));
+ if(this.value.charAt(this.value.length-1) == "\n" && (lastTextareaLength < this.value.length || lastTextareaLength == undefined) && (/*cursor is at end of textare*/ this.selectionStart == this.value.length || (/*betwenn cursor and end of textarea are only whitespaces and the amount of new lines in the end raised*/ this.value.substring(this.selectionStart).match(/[^\s]/) == null && currentTextareaEndingWhitespaces > lastTextareaEndingWhitespaces))) {
+ //if(this.selectionStart == this.value.length) {
+ console.log("time to receive feedback");
+ receiveFeedback();
+ /*}
+ else {
+ //Cursor may not be at the end, but user wants feedback
+ let remainingText = this.value.substring(this.selectionStart)
+ console.log("remainingText: "+remainingText);
+ if(remainingText.match("[^\s]*") == null) {
+ //Remaining text consists only of whitespaces
+ }
+ }*/
+ }
+ lastTextareaLength = this.value.length;
+ lastTextareaEndingWhitespaces = currentTextareaEndingWhitespaces;
+}
+
+function receiveFeedback() {
+ let form = document.getElementById("responseform");
+ if(form == undefined) {
+ //error handling
+ console.log("no form to submit");
+ return false;
+ }
+ let formData = new FormData(form);
+ let submitButtonData = document.querySelector("input.submit,button.submit");
+ if(submitButtonData == undefined) {
+ //error handling
+ console.log("no submit button found");
+ return false;
+ }
+ //let formDataAnswer = structuredClone(formData);
+ let formDataAnswer = new FormData(form);
+ formDataAnswer.append(submitButtonData.name, submitButtonData.value);
+ //console.log("try to fetch 1");
+ //console.log(document.querySelector("input[name$=sequencecheck]").value);
+ //console.log(document.querySelector("input[name$=ans1_val]") == undefined ? "undefined" : document.querySelector("input[name$=ans1_val]").name);
+ fetch(form.action, {method:"POST",body:formDataAnswer})
+ .then(response => {
+ if(response.status == 404) {
+ throw new Error("test99");
+ }
+ return response.text();
+ })
+ .then(text => {
+ let fetchedPage = Parser.parseFromString(text, "text/html");
+ let formFetchedPage = fetchedPage.getElementById("responseform");
+
+ let repeatButton = fetchedPage.querySelector(".mod_quiz-redo_question_button");
+ if(repeatButton == undefined) {
+ //If there is no repeat button, we are probably on a validation page, which happens for unknown reasons. If there are no syntax errors, submit again to get feedback page. But if there are syntax errors, the form sequence check has to be corrected
+ let syntaxErrorNotification = fetchedPage.querySelector(".stackinputerror");
+ if(syntaxErrorNotification != undefined) {
+ console.log("there is a syntax error");
+ //update sequence check
+ console.log("sequence check: changed "+document.querySelector("input[name$=sequencecheck]").value+" to "+formFetchedPage.querySelector("input[name$=sequencecheck]").value);
+ document.querySelector("input[name$=sequencecheck]").value = formFetchedPage.querySelector("input[name$=sequencecheck]").value;
+ //leave promise chain here
+ throw new Error("test3");
+ }
+ let submitButton = fetchedPage.querySelector("input.submit,button.submit");
+ if(submitButton == undefined) {
+ //Maybe the user submitted an answer containing a syntax error, leading (again) to the verification page. If this is the case, there is this Moodle-information-page, informing that users entered answers out of the ordinary control sequence. In this case, the continue button resets something so we can continue.
+ throw new Error("test1");
+ }
+
+ //else
+
+ /*console.log("sequence check: changed "+document.querySelector("input[name$=sequencecheck]").value+" to "+formFetchedPage.querySelector("input[name$=sequencecheck]").value);
+ document.querySelector("input[name$=sequencecheck]").value = formFetchedPage.querySelector("input[name$=sequencecheck]").value;
+ if(document.querySelector("input[name$=ans1_val]") != undefined) {
+ console.log("element name: changed "+document.querySelector("input[name$=ans1_val]").name+" to "+formFetchedPage.querySelector("input[name$=ans1_val]").name);
+ document.querySelector("input[name$=ans1_val]").name = formFetchedPage.querySelector("input[name$=ans1_val]").name;
+ }*/
+
+ let matchSubmit = [
+ "",
+ submitButton.name,
+ submitButton.value
+ ];
+
+ let formDataSubmitValidation = new FormData(formFetchedPage);
+
+ formDataSubmitValidation.append(matchSubmit[1], matchSubmit[2]);
+
+ //console.log("try to fetch 2");
+ return fetch(formFetchedPage.action, {method:"POST", body:formDataSubmitValidation}).then(response => { return response.text(); }).then(text => { return Parser.parseFromString(text, "text/html"); });
+ }
+ else {
+ return fetchedPage;
+ }
+ })
+ .then(fetchedPage => {
+ //let fetchedPage = Parser.parseFromString(text, "text/html");
+ let toAppendToMessage;
+ let formFetchedPage = fetchedPage.getElementById("responseform");
+
+ //if response is not positive, immediately repeat question
+ //get information about repeat button from response
+ //we look for input.mod_quiz-redo_question_button
+ //let matchRedo = text.match(/input.*?name="(.*?)".*?value="(.*?)".*?class=".*?mod_quiz-redo_question_button.*?/);
+ let repeatButton = fetchedPage.querySelector(".mod_quiz-redo_question_button");
+ if(repeatButton == undefined) {
+ //Maybe the user submitted an answer containing a syntax error, leading (again) to the verification page.
+ throw new Error("test2");
+ }
+ let matchRedo = [
+ "",
+ repeatButton.name,
+ repeatButton.value
+ ];
+ //console.log(matchRedo);
+ //For feedback, we look for .stackprtfeedback (each of them).
+ //let matchFeedback = text.match(/class=".*?stackprtfeedback.*?".*?><div class="(.*?)">([\d\D]*?)<div class="outcome clearfix/);
+ //console.log(matchFeedback);
+ let generalFeedbackNode = fetchedPage.querySelector(".stackprtfeedback .partiallycorrect, .stackprtfeedback .incorrect, .stackprtfeedback .correct");
+ let feedbackContentNode = fetchedPage.querySelector(".stackprtfeedback");
+ let matchFeedback = [
+ "",
+ generalFeedbackNode.classList.item(0),
+ feedbackContentNode.innerHTML
+ ];
+
+ //console.log(formFetchedPage);
+
+ let message = "";
+ let lastStroke = false;
+
+ //if(true/*Currently, it is not possible to offer different reactions between correct and incorrect / partially correct due to out of sequence error. matchFeedback[1] == "partiallycorrect" || matchFeedback[1] == "incorrect"*/) {
+ message = matchFeedback[2];
+
+ //get ready for redo
+ let formDataRetry = new FormData(formFetchedPage);
+ formDataRetry.append(matchRedo[1], matchRedo[2]);
+
+ /*return */fetch(formFetchedPage.action, {method:"POST", body:formDataRetry});
+ //Following line: Simple but effecitve. Alternatively one could process the fetch-response and filter fetchedPage.querySelector("input[name$=sequencecheck]") and maybe also fetchedPage.querySelector("input[name$=ans1_val]") to apply these to the current document.
+ document.querySelector("input[name$=sequencecheck]").value = 1;
+
+ //}
+ //else {
+ //correct or undefined
+ /* console.log("victory");
+ let possibleTexts = [
+ "You made it! Congratulations!",
+ "Well done! You are victorious!",
+ "Wonderful! You made it!"
+ ];
+ message = possibleTexts[Math.floor(Math.random()*possibleTexts.length)];
+ lastStroke = true;
+
+ //does the following line work as expected?
+ ALQuiz.incrementSolved();*/
+
+ /* Try to prevent submission out of sequence error: This one fails
+ //fetch same page to ensure staying in the right sequence and preventing the "submission out of sequence friendly message" error to be displayed
+ console.log("refetch "+ALQuiz.getPageURL());
+ fetch(ALQuiz.getPageURL());
+ */
+ //}
+
+ if(matchFeedback[1] == "partiallycorrect" || matchFeedback[1] == "incorrect") {
+ console.log("partially or incorrect");
+ ALQuiz.saveState(matchFeedback[1] == "partiallycorrect" ? "partially" : "false");
+ }
+ else {
+ console.log("victory");
+ //important to call getPageURL to generate different variants
+ //let repeatURL = ALQuiz.getPageURL();
+ //let nextURL = ALQuiz.getPageURL(ALQuiz.getQuestion().onsuccess);
+ toAppendToMessage = document.createElement("p");
+ let repeatAnchor = document.createElement("a");
+ repeatAnchor.innerHTML = " Aufgabe mit anderen Zahlen wiederholen";
+ repeatAnchor.href = "javascript:;";
+ let nextAnchor = document.createElement("a");
+ nextAnchor.innerHTML = "nächste Aufgabe";
+ nextAnchor.href = "javascript:;";
+
+ texts = ["Wenn es dir mehr Sicherheit gibt, kannst du diese ", ". Ansonsten bist du bereit für die ", ".", "Wenn es dir mehr Sicherheit gibt, kannst du hier noch etwas experimentieren"].map(function(string) { let node = document.createElement("span"); node.innerHTML = string; return node; });
+
+ //toAppendToMessage.innerHTML = "Wenn es dir mehr Sicherheit gibt, kannst du diese ";
+ if(ALQuiz.currentQuestionId == "start") {
+ toAppendToMessage.appendChild(texts[3]);
+ }
+ else {
+ toAppendToMessage.appendChild(texts[0]);
+ toAppendToMessage.appendChild(repeatAnchor);
+ }
+ //toAppendToMessage.innerHTML += ". Ansonsten bist du bereit für die ";
+ toAppendToMessage.appendChild(texts[1]);
+ toAppendToMessage.appendChild(nextAnchor);
+ //toAppendToMessage.innerHTML += ".";
+ toAppendToMessage.appendChild(texts[2]);
+
+
+ let returnedPageRepeat = ALQuiz.getRandomPageOfQuestion();
+ repeatAnchor.addEventListener("click", function(event) {
+ event.preventDefault();
+ document.getElementById("quiznavbutton"+(returnedPageRepeat+1)).click();
+ });
+ console.log(returnedPageRepeat);
+
+
+ let returnedPageNext = ALQuiz.getRandomPageOfQuestion(ALQuiz.getQuestion().onsuccess);
+ nextAnchor.addEventListener("click", function(event) {
+ event.preventDefault();
+ document.getElementById("quiznavbutton"+(returnedPageNext+1)).click();
+ });
+ console.log(returnedPageNext);
+ //message += "Wenn es dir mehr Sicherheit gibt, kannst du diese <a href=\""+repeatURL+"\">Aufgabe wiederholen</a>. Ansonsten bist du bereit für die <a href=\"" + nextURL + "\">nächste Aufgabe</a>.";
+ console.log(toAppendToMessage);
+ //does the following line work as expected?
+ ALQuiz.incrementSolved();
+ ALQuiz.markQuestionAsSolved();
+ }
+
+
+ //object.animateAttack(lastStroke);
+ //show feedback
+ //setTimeout(function() { object.processNotification(message, true); }, 1000);
+ console.log(toAppendToMessage);
+ ALQuiz.processNotification(message, true, toAppendToMessage);
+ ALQuiz.updateQuestionLinks();
+ })
+ .catch(function(error) {
+ console.log("catched error");
+ console.log(error);
+ });
+}
+
+function removeSpeechBubbleAfterTransitionEnd() {
+ if(this.classList.contains("active") == false) {
+ this.classList.add("temporarily-removed");
+ }
+}
+
+function showSpeechBubbleAgainAfterClose() {
+ ALQuiz.processNotification(ALQuiz.globalMessage, undefined, ALQuiz.globalElementToAppend);
+ console.log("show now!");
+}
+
+//OVERALL GAMIFIED QUIZ FUNCTIONS
+function tutorialFocusElement(elem) {
+ if(!elem) {
+ console.log("element to focus not found");
+ return;
+ }
+
+ let userFocusTop = document.createElement("div");
+ userFocusTop.classList.add("user-focus", "hide-top");
+ userFocusTop.onclick = removeTutorialFocus;
+ let userFocusBottom = document.createElement("div");
+ userFocusBottom.classList.add("user-focus", "hide-bottom");
+ userFocusBottom.onclick = removeTutorialFocus;
+
+ let offset = 0;
+ let pageHeight = 0;
+ let bodyNode = null;
+ let pageElementWHS = document.getElementById("page");
+ if(!pageElementWHS) {
+ //probably not in moodle of university of applied sciences Gelsenkirchen, Germany
+ offset = window.pageYOffset;
+ pageHeight = document.documentElement.scrollHeight;
+ bodyNode = document.body;
+ }
+ else {
+ //probably in moodle of university of applied sciences Gelsenkirchen, Germany
+ //let navbar = document.querySelector("nav");
+ //offset = pageElementWHS.scrollTop - (!navbar ? 0 : navbar.getBoundingClientRect().height);
+ //pageHeight = pageElementWHS.scrollHeight;
+ //console.log("we are probably in WHS-Moodle");
+ //console.log("offset: "+offset+", pageHeight: "+pageHeight);
+ offset = -pageElementWHS.getBoundingClientRect().top+pageElementWHS.scrollTop;
+ bodyNode = pageElementWHS;
+ }
+
+ let position = elem.getBoundingClientRect(elem);
+ userFocusTop.style.height=Math.ceil(position.top+offset-20)+"px";
+
+ userFocusBottom.style.top = Math.ceil(position.bottom+offset+20)+"px";
+ userFocusBottom.style.height=Math.ceil(pageHeight-(position.bottom+offset+20))+"px";
+ //console.log(userFocusTop.style.height,userFocusBottom.style.top,userFocusBottom.style.height);
+
+ bodyNode.appendChild(userFocusTop);
+ bodyNode.appendChild(userFocusBottom);
+
+ if(supportsSmoothScrolling() == true) {
+ elem.scrollIntoView({behavior:"smooth", block:"center", inline:"center"});
+ }
+ else {
+ safariScrollTo(elem);
+ }
+}
+
+function removeTutorialFocus() {
+ document.querySelectorAll(".user-focus").forEach(function(userFocusElement) {
+ userFocusElement.parentNode.removeChild(userFocusElement);
+ });
+}
+
+function repeatQuestion() {
+ document.querySelector('.mod_quiz-redo_question_button').click();
+}
+
+function showAskBeforeSkipModal() {
+ document.querySelector(".dmmodal").style.display = "block";
+}
+
+function addMathsOperatorButton() {
+ document.querySelectorAll(".formulation.clearfix").forEach(function(questionElement) {
+ let mathsButtonDiv = document.createElement("div");
+ mathsButtonDiv.classList.add("mathsbutton");
+
+ let mathsInput = document.querySelector(".mathsinput");
+ let display = window.getComputedStyle(mathsInput).display;
+ if(display == "flex") {
+ mathsButtonDiv.classList.add("active");
+ }
+
+ mathsButtonDiv.addEventListener("click", function() {
+ //document.querySelector(".mathsinput").classList.toggle("hide");
+ //let mathsInput = document.querySelector(".mathsinput");
+ if(!mathsInput.style.display || mathsInput.style.display == "") {
+ display = window.getComputedStyle(mathsInput).display;
+ }
+ else {
+ display = mathsInput.style.display;
+ }
+
+ if(display == "none") {
+ mathsInput.style.display = "flex";
+ this.classList.add("active");
+ }
+ else {
+ mathsInput.style.display = "none";
+ this.classList.remove("active");
+ }
+ });
+ //mathsButtonDiv.appendChild(mathsButton);
+ questionElement.appendChild(mathsButtonDiv);
+ });
+}
+
+
+//SAFARI HACKS BELOW
+function addSafariMathsInputAboveKeyboardSupport() {
+ //alert("checking for safari");
+ let isSafari = /^((?!chrome|android).)*safari/i.test(navigator.userAgent);
+ if(isSafari == true) {
+
+ //alert("You are using Safari");
+
+ //sadly not working solution from stackoverflow
+ //style.innerHTML = ".testclass, .mathsinput { display:none; bottom:270px; } @media screen and (min-aspect-ratio:11/16) { .testclass, .mathsinput { display:none; } }";
+ document.querySelectorAll("input.algebraic").forEach(function(inputElement) {
+ //console.log(inputElement);
+ inputElement.onfocus = function() {
+ let mathsInput = document.querySelector(".mathsinput");
+ mathsInput.style.position = "absolute";
+ mathsInput.style.bottom = "auto";
+ let position = this.getBoundingClientRect();
+ mathsInput.style.top = Math.ceil(position.bottom+window.pageYOffset)+"px";
+ //console.log(position);
+ }
+ });
+ }
+}
+
+function supportsSmoothScrolling() {
+ let body = document.body;
+ let scrollSave = body.style.scrollBehavior;
+ body.style.scrollBehavior = 'smooth';
+ let hasSmooth = getComputedStyle(body).scrollBehavior === 'smooth';
+ body.style.scrollBehavior = scrollSave;
+ return hasSmooth;
+};
+
+//thanks to Jeff Starr from https://perishablepress.com/vanilla-javascript-scroll-anchor/
+function safariScrollTo(elem){
+
+ if(elem == undefined) {
+ return;
+ }
+ let position = elem.getBoundingClientRect();
+ let to = (position.top+window.pageYOffset)-window.screen.availHeight/2;
+ //console.log(to);
+
+ var i = parseInt(window.pageYOffset);
+ //console.log(i);
+ if ( i != to ) {
+ to = parseInt(to);
+ if (i < to) {
+ var int = setInterval(function() {
+ if (i > (to-20)) i += 1;
+ else if (i > (to-40)) i += 3;
+ else if (i > (to-80)) i += 8;
+ else if (i > (to-160)) i += 18;
+ else if (i > (to-200)) i += 24;
+ else if (i > (to-300)) i += 40;
+ else i += 60;
+ window.scroll(0, i);
+ if (i >= to) clearInterval(int);
+ }, 15);
+ }
+ else {
+ var int = setInterval(function() {
+ if (i < (to+20)) i -= 1;
+ else if (i < (to+40)) i -= 3;
+ else if (i < (to+80)) i -= 8;
+ else if (i < (to+160)) i -= 18;
+ else if (i < (to+200)) i -= 24;
+ else if (i < (to+300)) i -= 40;
+ else i -= 60;
+ window.scroll(0, i);
+ if (i <= to) clearInterval(int);
+ }, 15);
+ }
+ }
+};
+
+///END AL QUIZ SCRIPT///
\ No newline at end of file
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