Course Management

Accessing a course as a teacher shows the course in management (edit) mode.

Course Page Layout

The course page consists of a list of items. There are six types of items:

Blocks: Groupings of items (Inline Text, Linked Text, Assessments)
Inline Text Items: Text that displays on the course page
Linked Text Items: A summary displays on the course page. A link is provided that can display text, an uploaded file, or a weblink
Forum Items: Basic disussion forum
Assessments: Tests or Practice questions
Calendar: The course calendar, if you want to embed it on your course page

Blocks have a colored header. If a block is displayed collapsed, click the block name or the "Expand" button to view the block's contents. If the block is displayed as a folder (has a folder icon next to it), click the block name to view the block items.

Text items are preceded with an information ! icon, forums are preceded with a F icon, and assessments are preceded with a ? icon. The icons will be grey when the item is not available, and (depending upon install settings) may change color as a deadline approaches. The color is green at two weeks, yellow at one week, and red on due date.

The item order can be rearranged by using the number selector to the left of the item. Items can also be moved into or out of blocks using this selector.

Adding Items

Add an item by selecting the item type from the "Add Item" pulldown. Using the "Add Item" pulldown inside a block will add the item to that block.

Blocks

For Blocks, you will asked to provide:

Title: The title of the block
Available after: The first date for the item to display to students
Available until: The last date for the item to display to students
When available: Whether you want to display the block Expanded, Collapsed, or as a folder when available
When not available: Whether you want to hide the block from students when not available, or show collapsed or as folder (depending on available setting). Use the show collapsed/folder option if the block contains items that students still need to be able to access.
Colors: Allows you to specify colors other than the defaults for blocks

Inline Text Items

For Inline Text items, you will asked to provide:

Title: The title of the item
Hide title: If you want to hide the title and icon, and just display the text
Text: The actual text (displays on course page)
Files: You can attach one or more files to an inline text item. For each file, provide a description of the file. A list of the descriptions, with links to the files, will display at the bottom of your text item.
Available after: The first date for the item to display to students
Available until: The last date for the item to display to students

Linked Text Items

For Linked Text items, you will asked to provide:

Title: The title of the item
Summary: A description of the link (displays on course page)
Text: Enter one of the following:
- Type text in box provided. The text will display when link is clicked
- Enter a weblink (like http://www.google.com). The link will take students to this weblink
- Attach a file. The link will open the file. Note: Do not change the text on subsequent modifications
Available after: The first date for the item to display to students
Available until: The last date for the item to display to students

Forum Items

For Forum items, you will asked to provide:

Name: The name of the forum
Description: A description of the forum (displays on course page)
Available after: The first date for the item to display to students
Available until: The last date for the item to display to students
Group linked: If you have a group assessment, you can link the forum to the groups of that assessment. If you do this, students viewing the forum will only see posts from their group members and instructors. Be aware that posts to group linked forums often won't trigger the red "New Posts" flag on the home page.
Allow anonymous posts: Whether you want to allow students to post anonymously
Allow students to modify posts: Whether you want students to be able to modify their posts
Email notify: Whether you want to receive an email whenever a new post is made on the forum
Default display: Whether you want threads to display Expanded, Collapsed, or in Condensed format by default. Users can change the display once they view the thread
Students can reply by: Optionally set date restrictions for students replying to posts. Can be overridden in individual threads.
Students can create new threads by: Optionally set date restrictions for students creating new threads
Count in gradebook: Whether you want the forum to count in the gradebook for points. You will be able to assign points for individual posts made.
Gradebook category: Category for the gradebook, if assigning points to the forum.

When you as a teacher start a new thread, you are given the option to have it be:

A regular post
Always display at the top of the list
Displayed at top and locked (no replies can be made)
Displayed at top and replies are hidden from students

You can use the middle two options to, for example, post discussion instructions. You can use the last option to post a question in class, and have students respond without seeing other students' replies.

When viewing the forum thread list as an instructor, there is a "List Posts by Name" link which will list all posts in the forum, grouped by student name. New threads are colored in black, replies in green

Assessments

Warning: Making changes to an assessment after students have already taken it can seriously mess up those students' assessment results. It is NOT safe to change: Default points per problem or Default penalty.

Assessment Settings

You need to set the assessment settings when you add an assessment. You can change these settings by clicking the "Modify Settings" link next to the assessment in the course page.

Name: The name of the assessment
Summary: A description of the summary (shows on course page)
Intro/Instructions: Displays at the top of the test (see below for details on making question-specific instructions)
Available after: The first date for the item to be available to students
Available until: The last date for the item to be available to students. Students must complete the assessment by this date - they will be kicked out if they are in the middle of an assessment when this time is reached.
Available for review: If the checkbox is clicked, the assessment will convert to review mode after the due date until this date. Review mode defaults to Skip Around display, unlimited attempts, answers shown always. Scores are not saved in Review mode.
Count: Whether the assessment score should be counted in the gradebook, not counted in the grade total, or counted as extra credit.
Copy Options From: If you have other assessments in your course already, you can select to copy the assessment settings from another assessment.
Password: If specified, requires student to enter this password to access the assessment. Leave blank to require no password.
Time Limit: The time limit, in minutes, for the test (0 for none). If the student exceeds the time limit, their test will be recorded, and you can decide whether or not to accept it in the gradebook detail. Partial minutes are possible using decimal values. If you check the "Kick student out at timelimit" box, then the assessment will automatically finalize at the timelimit, and submission attempts after the timelimit will be rejected.
Display method:
- Full test at once: All questions are displayed on one page
- One question at a time: One question is shown at a time. Students must complete the questions in the order presented
- Full test, submit one at time: Full test is displayed, but student submits answer to one question at a time. Student can skip between questions.
- Skip around: Students are provided with a navigation bar and can jump between questions and complete them in any order
- Embedded: Similar to "Full test, submit one at time", but all questions are always active, and any one can be submitted at any time. Questions can be embedded into the Intro/Instructions using [QUESTION #] tags.
Default points per problem: How many points each problem should be worth by default. This can be changed for individual problems.
Default attempts per problem: How many attempts a student should have at each problem by default. This can be changed for individual problems. Enter 0 for unlimited attempts
Reattempts different versions: Reattempting a problem will regenerate the question with new numbers. By default, reattempts of problems receive the same version of the problem. This option does not make sense to use with Homework mode.
Default penalty per missed attempt: What percentage of points possible a student should lose for an incorrect attempt. This can be changed for individual problems. You can select a penalty for each missed attempt, to start after a certain number of missed attempts, or specify a penalty for the last possible attempt only.
Feedback method: What detail the students should see
- No scores shown: No scores, including the total, are shown to the student. If reattempts are allowed, the student is forced to retake all questions (even ones they got right the first time). With this mode, access to grade detail in the gradebook controlled by the Show Answers setting.
- Final score: Only final (total) score is shown at the end. If reattempts are allowed, the student is forced to retake all questions (even ones they got right the first time). With this mode, access to grade detail in the gradebook controlled by the Show Answers setting.
- Show score on each at end: At the end of the test, the student is shown their score on each question. If reattempts are allowed, they are then allowed to go back and reattempt problems.
- Show as submitted: As each question is submitted, the score is shown, and students are offered a chance to reattempt the problem (if allowed). This method does not apply to the "Full test at once" display method.
- Practice Test: Same as above, and the test can be regenerated (re-randomized) whenever the student wants. Students are given an opportunity to try similar problems to the one presented after completing each question (when not in Full test at once mode). Scores are cleared each time the test is regenerated, and scores are not shown by default in the gradebook. Answers can be shown after some number of attempts.
- Homework: Like "Show as submitted", but students are given an opportunity to attempt a similar question if they miss a question. Doing so resets attempts for that question (reseting attempt penalty as well). Also, show answers (see below) can be set to show answers during the homework after a number of attempts. This is best used in conjunction with the attempt penalty.
Show Answers: When (if ever) students should be able to see answers.
- Practice Tests and Homework: For practice tests and homework, you can set this to never, after 0,1,3,4,or 5 attempts are made, or after last attempt. There is also an after last attempt option that will allow students to jump directly to the answer.
- Other Tests: For other tests, you can set this to never, after the assessment due date, after the last last attempt (in Skip Around and Full test submitted one at time modes only), or immediately. Answers will be available in the gradebook review of a test. Note: Do not use the "Immediately" option if you are allowing multiple attempts per problem. Doing so would allow a student to complete the test, view the answers, then reenter the test (since more attempts are allowed) and put in the correct answers. Also be aware that if an assessment is set to allow review mode, that answers will be available to students in review mode.
Show hints when available: Whether or not to show hints if the question has them defined
Allow use of LatePasses: If you have granted LatePasses to students, this will allow use of them on this assessment
Make hard to print: Makes the assessment harder to print, for in-class tests
Shuffle item order: Randomizes the order in which questions are presented
Gradebook Category: If you have created gradebook categories, you can assign the assessment to one of those categories.
Count: Whether to count the assessment in the gradebook
Allow tutors to edit: Whether tutors should be able to change students' scores on this assessment
Minimum Score for Credit: A minimum score which must be acheived to receive credit for the assessment. Set to 0 to accept all scores. If set and score is not met, gradebook will display "NC" (No Credit).
Show based on another assessment: Use this to hide this assessment until a specific score is acheived on another assessment. Provide a point value and select an assessment to use this feature. Set the assessment to "Don't Use" to not use this feature
All questions same random seed: Usually not needed. This is only need for a set of questions designed to work together using the same random values
All students receive same version of questions: All students receive the same first version of questions. If in practice test or homework mode, when students request a similar problem, different students will receive different versions of the questions.
Penalty for questions done while in exception/LatePass: A percent penalty to take on all questions submitted after the original assignment due date while under a due date exception.
Is group assessment?: Allows students to specify group members for the assignment. All group members will receive the same score for the assignment
Show question categories?: If you plan to categorize questions and would like the categories displayed while the student is taking the test, you can select that option here
LTI access secret: An access code to place this assessment in a BasicLTI-compliant consumer. More info

Qustion-specific instructions (deprecated)

Note: The following approach is deprecated, and no longer recommended. Using the [+Text] button on the Add/Remove Questions page instead to insert text between questions.

In the Intro/Instructions box, you can make question-specific instructions by putting a tag of the form [Q #] or [Q #-#] before the text specific to that question or range of questions. Here is an example:

This is the general info

[Q 1]

This text will display before question 1

[Q 3-4]

This text will display before questions 3 and 4. Since there was no tag for question 2, it will display directly after question 1, with no associated intro text. Likewise, if there was a question 5, it would display directly after question 4 with no associated intro text.

Adding Questions to an Assessment

You can add existing questions to an assessment by clicking the "Select Library" button to choose libraries to search, then the "Search" button to list potential questions. Leave the "Search" entry blank to list all questions in the libraries selected. The checkboxes can be used to search in all libraries (not just the selected ones), list only questions you own, or exclude questions you've already added to your assessment.

From this list you can:

Use the checkboxes to select questions, then click the "Add (using defaults)" button to add the questions. Adding this way will use the assessment default settings for points, attempts allowed, and penalty per attempt. You can change these later by clicking the "Change Settings" link.
Use the checkboxes to select questions, then click the "Add" button to add the questions. Adding this way will allow you to override the default settings for points, attempts allowed, and penalty per attempt if you wish, and add a question multiple times.
Choose "Add" from the Action dropdown. This will allow you to change the default question settings
Choose "Use as template for New Question" from the Action dropdown. This will create a new question based upon the existing question. This allows you to avoid rewriting a question from scratch if a similar question exists
Click "Preview" to preview the question

Alternatively, you can click the "Select from Assessments" button to choose questions from existing assessments. In this mode, select the assessments you wish to pull questions from and click "Use these assessments". Then select the questions you wish to use.

Once added to the assessment you can:

Reorder Questions: Using the number selectors next to each question will allow you to rearrange the order of the questions. This is only useful if you are not shuffling the question order
Group Questions: Use the checkboxes to select questions, then press the "Group" button to group questions. Then you can specify how many questions from the group you want the system to randomly assign to students, and whether to make that selection with or without replacement.
Change Settings: Override the default settings for points, attempts allowed, and penalty per attempt, if desired. When done for one question using the "Change Settings" option in the Action dropdown there are more settings you can edit than when using the checkboxes and the "Change Settings" button.
Edit Code: In the Action Dropdown. Change the question code or wording, if it is your question
View Code: In the Action Dropdown. View the question code, if it is not your question
Edit Personal Copy: In the Action Dropdown, if it is not your question. Creates a copy of the question, and will trade out the original question for your personal copy.
Template: In the Action Dropdown. Create a new question based on this one. The original will not be removed from the assessment.
Remove from assessment: From the Action dropdown, or use the checkboxes and press the "Remove" button. Removes the question(s) from the assessment. This does not delete the question itself.

Icons used in question listing

Has a video help (if is shown, the video has captions)
Has help resource
Has a written solution
Has "show work" enabled
Has a rubric associated

Adding an Introduction to a Question

In addition to the assignment Introduction, each question can have an individual introduction. A common example is to display a video and then a related question as part of a video assignment.

To add a question introduction, click on + Text below the last question. An editable text box will appear where you can write instuctions or drag in a video link. After you edit your text, click the Save All icon in the editor toolbar. You can expand/collapse each question intro by clicking the Expand and Edit or Collapse icons in the lower right of the question intro. Once you modify a question intro, you'll need to save it to collapse it.

When you click Save All, all changes you have made in any other question intros will also be saved. If you leave a question intro with unsaved changes, the Save All button will be highlighted.

A question intro can be displayed for multiple consecutive questions (except on Embedded assignments). In the Show for selector, select the number of questions that question intro should be used for.

Embedded assignments can include page titles. Check the New Page checkbox to add a page title. Then add your title in the editor and save it.

Below the last questions is an Expand All button which will expand all the question intros. Click on any one to edit it.

After the Assessment has been Taken

If students have taken the assessment, you will not be allowed to make as many changes to the assessment, as it will mess up existing student attempts. If you need to change the assessment a lot, you can clear all student attempts. Otherwise you can change individual question settings (be careful!) or edit the question if it's yours. If there is a problem with the question, you modify it, and want to give students another chance on that question, you can clear all attempts on a single question by clicking the "Clear Attempts" link here

Adding New Questions

Click the "Add New Question" to write a new question from scratch, then add it to the assessment. See the help section on Writing Questions for help on writing new questions

Categorizing Questions

After adding questions to an assessment, click the "Categorize Questions" button to categorize the questions in the assessment. Categorization allows you and students to see a score breakdown by question category.

In the question categorization page, you will see each question listed, followed by a category pull-down. By default, the list contains the names of all libraries containing the question. If you'd like to define a category not in the lists, type in the new category name in the box provided and click the "Add Category" button. The new category name will now appear in the pull-down lists next to each question, and can be selected to assign the question to that category. When you are done, click the "Record" button.

Making Print Copies

After adding questions to an assessment, click the "Create Print Version" to layout your assessment for printing.

On the first page, you will be asked what you would like to include in the test header. You will also be asked to enter your print margins setup. These can be found by choosing "Page Setup" from the "File" menu in your browser. In the Page Setup you may also wish to remove the default header and footer materials included in printouts by your browser.

On the next page, you will see alternating blue and green rectangles indicating the size of pages. Use the resizing buttons next to each question to increase or decrease the space after each question until the questions fall nicely onto the pages. You can use Print Preview in your browser to verify that the print layout looks correct. After you have completed the print layout, you will be given the chance to specify additional print options. Longer questions, such as those with graphs, may appear cut off in the print layout page. Be sure to resize those questions to show the entire question.

On the next page, select how many versions of the test you would like to generate, and whether you'd like to generate answer keys. After hitting continue, you print version of the test will be displayed. Choose Print in your browser to print your tests.

Quick View

Quick view is a condensed view of the course page. You can use it to quickly look over your entire course. It is more useful for major editing

It allows easy drag-and-drop reordering of course items. Changes will not be recorded until the "Record Changes" button is pressed.

You can also quickly rename items by clicking on their titles and changing the text. Again, changes will not be recorded until the "Record Changes" button is pressed.

When done in quick view, click the "Return to regular view" link to get back to the regular course page

Calendar

The calendar can be accessed from the course navigation bars, or by embedding the calendar on your course page. The calendar autopopulates with assessment item due dates, and discussion forum post-by and reply-by dates. Text items have options to place them on the calendar. The calendar displays with the current date on the top line; you can jump later in the future or look in the past using the "< <" and "> >" links above the calendar.

You can add additional items to the Calendar using the "Manage Events" link on the calendar. All items to be placed on the calendar need a date, a description, and a single letter or symbol tag that will show on the calendar

Question Set Management

Manage Question Set

Clicking the "Manage Question Set" link will allow you to search through the Question Set, modify questions, add questions, remove question, transfer ownership, or add a set of questions to a question library. Only administrators or question owners have the rights to remove a question. Be aware that if you remove a question that is currently being used in an assessment (as shown in the "Times Used" column), it will mess up that assessment.

The options available in the question set manager are:

Modify: Change the source code of the question and make library assignments. You will only see this option for questions you own or when the owner has given permission for anyone to modify the question.
View: View the source code of the question and make library assignements. You will only see this option for question you do not own.
Template: Create a new question, using the code of an existing question as a starting point. When you template a question, the original question is not changed.
Delete: Delete the question completely from the questionset and all libraries. You will only see this option for questions you own or when the owner has given permission for anyone to modify the question. You can delete many questions at once by selecting questions with the checkboxes, then clicking the Delete button near the top of the page.
Transfer: Transfer ownership of the question to another user. You will only see this option for questions you own. You can transfer many questions at once by selecting questions with the checkboxes, then clicking the Transfer button near the top of the page.
Library Assignment: The Library Assignment button near the top of the page can be used with the checkboxes to add or change your library assignments for the selected questions. This will not affect other people's assignments

Note that the assignment of questions into libraries can be done by anyone, but only the person who made the assignment is able to remove the question from the assigned library

Library Management

Manage Libraries

Use the library manager to remove, rename, change rights, change parent, or transfer ownership of question libraries. Be aware that if a library is deleted, the questions in that library will become unassigned; they are not deleted.

Libraries have a tree structure, where each library has a parent library. When you add or modify a library, you can change it's parent library. If you change a library's parent, all children library move with a library. You can only specify an empty library or existing parent library as a parent.

Libraries have use rights. Options are:

Private: Only the owner or an administrator can list questions in these libraries
Closed to group, private to others: Anyone in group can list and use questions, , but only the owner or an admin can add questions to the library. Hidden to anyone outside the group.
Open to group, private to others: Anyone in group can list and use questions and add to the library. Hidden to anyone outside the group.
Closed to all: Everyone can list and use questions, but only the owner or an admin can add questions to the library
Open to group, close to others: Anyone in group can list and use questions and add to the library. Outside the group, users can only list and use questions; they cannot add questions to the library
Open to all: Everyone can list and use questions and add to the library

With library rights, child rights take precedence over parent rights. For example, if an open library is a child to a private library, the parent will not be hidden from other users. However a private library as child to a private parent will be hidden from other users.

Depending upon the system configuration, non-admins may be limited to creating libraries that are private to others outside their group. If this is the case, a non-admin will need to contact an admin to create a library that is closed or open to all.

Library assignments are done in question management. Library assignments can be done by any user, but only the person who made the assignment can remove that assignment.

Export Libraries

Use the "Export Libraries" feature to export an entire library or tree of libraries for backup or sharing. Use the tree to select libraries to export. Note that if a parent library is selected, it's children libraries are automatically included in the export, and heirarchy will be maintained. If libraries from different trees are selected, the topmost libraries in each branch selected will be exported at the same level.

Import Libraries

Use the "Import Libraries" feature to import an entire library or tree of libraries. Note this feature may be restricted to admin users only. After selecting a file, the tree of libraries in the import file will be shown, and you can deselect libraries you do not want to import. Note that if a parent library is not selected, NONE of the children libraries will be added, regardless of whether they're checked or not.

You will be asked if you want to update existing questions/libraries, or add as new. If a library or question (identified by a unique id) in the import already exists on your system, this will tell the importer whether to update the existing libraries/questions, or import the libraries/questions as a new copy (a new unique id is assigned). If you have modified questions previously imported, you may want to add as new. Note that only the original importer can update questions they imported.

Imported libraries and questions will have ownership assigned to the importer. Select the userights you want to apply to all imported questions and libraries. You can select a parent in the library tree for all (top level) imported libraries

If you load a file that does not have a library tree embedded in the file, you will be told to use the Import Question Set feature instead. Even if a file has a library tree, you can use the Import Question Set feature to import specific questions from the file.

List Students

Use the "List Students" link to list the students in your class. On this page you can import (register and enroll) students from a file, enroll a student (already registered) with a known username. This is the easiest way to add a guest user to your class. Note that the "Last Login" date shows the last time the student logged into IMathAS, not necessarily the last time they accessed your course.

The List Students page also gives you access to student email addresses, as well as a link to send out a mass email or message to all students

Exceptions

Click the "Make Exception" link to change the Start or End date of an assessment for a single student. If you need to make exceptions for multiple students at once, or want to make exceptions for multiple assessments at once, use the "Make Exception" button in connection with the checkboxes in the Gradebook.

Resetting Passwords / Changing Info

Use the "Chg Info" link to reset a student's password, update their email address, username or full name, or change their section or code. You can also lock the student out of the course on this page. Doing so will display a message to the student that they need to see their instructor to regain access to the course. On this page you can also set a time limit multiplier for students needing extra time on timed assessments. Setting the multiplier to 1.5 would give the student 1.5 times the usual timelimit for all assessments.

Unenrolling

Use the "Unenroll" link to unenroll a student from the class, or the "Unenroll All" button to unenroll all students. This can be useful to clear out a classroom at the end of a term. Unenrolling all students will also delete all regular posts from the course's forums.

Import Students from File

Use the Import Students from File feature to register and enroll a set of students automatically from a CSV (commas separated values) file. You can generate a CSV file using any spreadsheet program.

The form will guide you through specifying which columns of the CSV file contain First name, Last name, email address, and desired username. Once setting these options, the first five rows of the file will be displayed so you can verify that the import settings are correct. The students will be both registered and enrolled in the current class upon submission.

Assigning Section and/or Code Numbers

Click the "Assign section and/or code numbers" link to assign section or code numbers to students. These only serve for identification purposes, the the gradebook will be sorted first by section, then by name. Section can be alphanumeric; code number must be numeric, up to 4 digits.

Manage LatePasses

Click the "Manage LatePasses" link to give students LatePasses. Students can redeed a LatePass for an extension on an online assessment without your intervention, provided you have clicked the "Allow use of latepasses" option in that assessment.

On this page you can also define the number of hours extension a LatePass will grant

Manage Tutors

Click the "Manage Tutors" link to manage tutors for your class. Tutors can have an instructor account or student account. Tutors will be able to view students' scores and online assessments. If given permission, tutors can edit or enter online or offline scores.

Add tutors by listing their usernames in the box provided. Remove tutors by clicking the "Remove" checkboxes next to tutors and clicking Update

Once tutors are added, you can limit them to a single section of the course. If selected, tutors will only be able to see scores for students in the section they're limited to. This can be used in conjunction with the diagnostic system, since second-level selections become the student's section identifier

Gradebook

Click the "Gradebook" link to show the gradebook. The gradebook shows each student's score on each assessment and any offline grades you've entered. Click on a student's assessment score to show detail on their assessment attempt, or on a student's offline grade to change their grade. Click the Settings link in the table header if you need to change an assessment's settings. Click on an assessment's average score to view an breakdown showing the average score on each question. Click on an offline grade's average score or the Settings link in the table header to change the settings for that item or modify all students' grades at once.

By using checkboxes next to student's names, you can send messages or emails to multiple students, or make due date exceptions for multiple students at once

Gradebook Settings and Categories

Click the "Gradebook Settings" to change Gradebook settings and create or modify categories. This allows you to create a grading scheme.

Your overall settings are:

Calculate total using: Select "points earned" to use a points earned out of points possible grading scheme. Select "Category weights" to assign a percentage weight to each category in calculation of total grade.
Gradebook display: Select whether to order the gradebook by item dates (Available until dates for assessments, Show After dates for offline grades) or if you want to group items by category

The next section lets you define categories. There is always the "Default" category, but it will not display if there are no items assigned to it. To add a new category, click the "Add Category" link to add a new line to the table, then fill in the name and other info, then click "Update"

For each category, you can specify:

Name: The name of the category
Scale (optional): Scale the category total by specifying a point value or percent value to be scaled up to 100%. For example, if the category point value was 80 points, and a student earned 50 points, their category total would be 50 points (62.5%). If you specified to scale 60 points to a perfect score, then the students grade would become 80*(50/60) = 66.7 points out of 80 = 83.4%. You can also base the scale on a percent value, which is usually easier: If you specified to scale 80% to a perfect score, and a student's category total started at 70%, it would be scaled to 70*(100/80) = 87.5%. You can specify whether grades that would end up over 100% should be chopped to 100%. You can specify no scale by leaving the Scale box blank.
Drops (optional): You can specify whether to drop the lowest N scores, or keep the highest N scores from the category. Set the number to 0 to keep all scores.
Weight/Fix Category Point Total: If you are using a "Category Weights" grading scheme, enter the percent weights for each category here. If the category percents don't add to 100%, they are all scaled equally so they do add to 100%. If you are using a "Points earned" grading scheme, you can fix the point value for the category here (optional). For example, if the current category total is 50 points and a student earns 40 points, if you specified a fixed point value of 100 points, the students score would become 80 points. Leave this blank to use the actual category point total.
Remove: When you remove a category, any items currently assigned to that category will be assigned to the Default category

Offline Grades

To add an offline grade, click the "Add Offline Grade" link on the gradebook page. You can specify:

Name: The name to give the grade item
Points: The number of points possible on the item
Show to students after: The date after which to show the item to students
Gradebook Category: The gradebook category you wish to assign the item to
Count: Whether to count the score in the gradebook total, not count it, or count it as extra credit
Allow tutors to edit: Whether tutors should be able to edit scores for this item

You can then enter grades for each student. If you leave a grade blank, no grade will be recorded for that student. You can edit these settings or edit all students' grades at a later time by clicking the "Average" in the gradebook for this item. You can edit an individual student's grade by clicking on their score in the gradebook for this item. You can leave feedback for students about their grade using the boxes provided.

You can manage offline grades by clicking the "Offline Grades: Manage" link on the gradebook page. This page allows you to delete, change the availability, or change the gradebook assignment of a set of offline grade items.

Gradebook Detail

When you click on a student's score in the gradebook, you will see the specific assessment that they received and the last answer they provided, as well as their score on each question and the attempts used. You can override the scores they received on this page. You can also send a student a message about a question, quoting their version of the question in the message. At the bottom of the page is a box to leave the student feedback about the assessment.

If you wish to give a student another chance to take an assessment, click the "Clear Attempt" or "Clear Scores" link. Note: This will clear their current scores, answers, and attempts used. The "Clear Attempt" link will make it appear the student never started the assessment, and the student will receive a different version of the assessment when they access the assessment. The "Clear Scores" link will clear the student's scores and attempts to 0, but the student will receive the same version of the assessment when they access it.

If you categorized the questions in the assessment, you will also see a category breakdown at the bottom of the details page

Student Groups

The Student Groups page allows you to manipulate student groups associated with assessments that you have designated as group assessments. When you first access this page, you will be presented with a list of group assessments. Select the assessment you want to modify groups for

You will be presented with a list of groups (the group number is arbitrary) with the students in each group. To separate a student from the group, click the "Break from Group" link.

At the bottom of the page is a list of students not assigned to a group. If you wish to assign students to groups, click the checkboxes next to the students' names. In the "add to group: " pulldown, select the group you want to add the students to, or select "New Group", and click Add

When students are broken from the group, they retain the version of the assessment and progress the group had acheived before you broke them from the group. If a student is added to a group, any work they've already done is lost and replaced with the group's version and progress. Any changes to an assessment made by one group member affects all group members.

Messages

The message system allows you to send a message to students in the class. This is an internal message system; it is not emailed unless the student has requested email notification.

Click Send New Message to send a new message to a student. If you want to send a message to multiple students, use the "List Students" page. Select a student from the pull-down list, and type your message.

When viewing messages, you can either Reply to the message, or use the "Quote in Reply" option to quote the original message in your reply.

Copy Course Items

Course Item Copy allows you to copy items in your course or an entire course structure, or copy items from another instructor's course. Note that item structure, items, and settings are exported, but not students, assessment attempts, or forum threads.

On the first page, select a course to copy from. If you select a course that is not one of your own courses, you must enter the course Enrollment Key as verification that you have received permission to copy from the course.

On the second page, select the items you wish to import. If you export an item currently contained in a block and do not export the block, the item will be exported as an item on the main course page.

You can optionally append words to the end of the title of each item, or place the copied items into an existing block.

You can optionally also specify to copy the course settings (the items you'd set under Modify on the Admin page), or copy the gradebook scheme and gradebook categories. Copying the gradebook scheme will overwrite the existing gradebook scheme in your course. Copying the gradebook scheme will also retain any category assignments for the assessments you're copying.

Change Dates

The Change Dates page allows you to change the dates for all your course items on one page. On this page you will see a list of your course items, with inputs for start date, end date, and review date (for assessments). You can filter the list to only show one item type using the Filter selection at the top of the page, and you can change the sort order to sort by start date, end date, or name.

If you change dates on any line and click the "Send down list" button on that line, the date change will be made to all items below that item in the list. For example, if you add one day to an item and click "Send down list", one day will be added to all items lower in the list. By default the system only allows Monday-Friday dates; you can switch to a 7-day week by unchecking the "Shift by weekdays only" checkbox

Change Assessments

The Change Assessments page allows you to change assessment settings for many assessments at the same time. Begin by selecting all the assessments you want to change settings for using the checkboxes next to each assessment's name

Select which options you want to change by clicking the checkbox in the "Change?" column, then adjust the setting in the "Option" column. When you are done, click "Submit"

Import/Export Course Items (for another IMathAS system)

Course Item import/export allows you to share a course setup with other instructors, or copy a class for yourself. Note that item structure and questions are exported, but not students, assessment attempts, or forum threads.

On Export, start by selecting the items you wish to export. If you export an item currently contained in a block and do not export the block, the item will be exported as an item on the main course page. There are options on whether or not to include course and gradebook settings in the export.

On Import, first provide the import file. If there are assessment questions that do not already exist on your system, they will be added to the system. Select the library into which these questions should be imported. If a question already exists, you can select whether to update the existing question with the import question (if it is newer), or create a new copy of the question in the designated library. Select the items to import, and click "Import Items".

LTI Integration

IMathAS can be used as a LTI tool using a course-level configuration (LTI 1.1 only) or a global college-wide configuration (LTI 1.1 or 1.3). Use of LTI 1.3 is highly recommended.

LTI 1.1

Key Types

For a course-level configuration, your LTI key will take the form LTKkey_###_#. The first number, ###, is your course ID. The last number determines how authentication is handled. If that last digit is 0, then when the student accesses the LTI placement, the first time they will be asked to sign into their IMathAS account or create one, and that account will be linked with the account at the host LMS. From then on, when the same student accesses any LTI placement, they will not need to sign in again. They will be able to sign in directly to IMathAS as well.

If the last digit of your LTI key is 1, then a student account will automatically be created the first time a student accesses the LTI placement, and that account will be linked with the host LMS account. The student will not be provided an IMathAS username or password, so they will only be able to access IMathAS resources through the LMS LTI placements.

Note that grade return ONLY works reliably with the _1 type keys, so that type of key is recommended.

LTI Connection Options

IMathAS supports several types of LTI integration, including whole course single-signon, and new links created from the LMS.

The recommended integration technique is to setup individual LTI links for each assessment. This is necessary if you want the grade to be returned from IMathAS to your LMS. The easiest way to set up LTI links in the LMS is to use the Export feature in IMathAS to create links and import those into your LMS. To do this, go to Course Items -> Export, select the items you want to export, your LMS, and Download the CC Export. Then follow the appropriate instructions below.

Alternatively, you can manually create individual links to assignments, or you can create a single link that launches your entire IMathAS course. Be aware that in many LMSs, manually created links to assignments will lose their association with IMathAS assessments when the course is copied in the LMS, so using the Import process is recommened when supported by the LMS.

IMathAS can also be an LTI 1.1 consumer, using the External Tool option for Link items.

LTI 1.3

LTI 1.3 must be installed by the LMS administrator.

There are two general ways to set up an LTI connection:

Dynamic Registration: Supported by Canvas, Moodle, and D2L, amongst others. The dynamic registration URL is https://yourIMathASsite/lti/dynreg.php.
Manually: Using the platform registration page: https://yourIMathASsite/lti/admin/platforms.php

The easiest way to set up LTI links in the LMS is to use the Export feature in IMathAS to create links and import those into your LMS. To do this, go to Course Items -> Export, select the items you want to export, your LMS, and Download the CC Export. Then follow the appropriate instructions below.

Alternatively, you can setup individual links to assignments, using your LMS's "deep linking" feature. The specific process varies by LMS.

Note that LTI 1.3 does not support a "whole course link" option, since that option does not allow grade passback.

Canvas Integration - Using Import

Go to Course Items → Export, select the items you want to export, select your LMS, and Download the Export Cartridge

To import the cartridge in Canvas:

Go to Settings, then Import Course Content
For Content Type, select Canvas Course Export Package. Select the export file from your computer, and select All Content. Click Import.
If you have an LTI 1.3 connection or global LTI 1.1 college-wide key and secret, you do not need to set up a course-level configuration. If you need to set up a course level configuration, in your Canvas course:
- Go to Settings, then Apps, then View App Configurations
- Locate for the IMathAS App. Use the gear icon dropdown to select Edit
- For the Consumer Key, enter: LTIkey_####_1, where #### is your Course ID
- For Shared Secret enter the secret you set up in your Course Settings
- If Target URL is required, enter: https://yourIMathASsite/bltilaunch.php
- Click Submit

Next you will need to establish the connection between your IMathAS course and Canvas course

In Canvas, click one of the assessment links in your course.
If this is your first time using this key and secret, IMathAS will ask you, the teacher, to sign into your IMathAS account. This is necessary to establish a connection between your LMS account and your IMathAS account. You will not need to do this step again, and students will not be asked to sign in and will not need a IMathAS account.
Follow the prompts to associate the LMS course with your existing IMathAS course or create a copy.
Once complete, all the LTI links in your LMS should work.
Be aware:
- Links, files, forums, and and text items were imported into your LMS. Changing them in IMathAS will not change them in your LMS
- If you change assessment settings or the questions in an assessment in IMathAS, those changes will show up when the assessment is launched from the LMS
- If you change due dates in IMathAS, they will be enforced by IMathAS, but the due dates in the LMS will not automatically be updated. However, there is a course setting to allow Canvas to set the due dates in IMathAS.
- Any new items added in IMathAS, including new assessments, will not automatically show up in the LMS; you would need to repeat the export/import process.
- If configured, grades will be sent from IMathAS to the LMS immediately every time the student completes a question, but the LMS may delay updating the grade.

Note: When configuring a course-level configuration, the use of a key in the form LTIkey_###_1 is recommended. With this type of key, students will not have or need a username for IMathAS, and they must access assignments via the LMS. This is usually desired when doing integration, and is necessary to ensure grades are passed from IMathAS back to the LMS. If, however, you are not interested in grade return, and simply want to provide single-signon from your LMS into IMathAS while allowing direct login to IMathAS as well, then you can use a key of the form LTIkey_###_0 instead. This will require students to have or create an account on IMathAS, which they'll have to log into once to establish the connection.

Canvas Integration - Manual Process

If you have an LTI 1.3 connection or global LTI 1.1 college-wide key and secret, you do not need to set up a course-level configuration. If you need to set up a course level configuration, in your Canvas course:

Go to Settings, then click the Apps tab
Click on View App Configurations, then the +App button
For Configuration type, select "By URL"
For Name, enter IMathAS, or whatever you'd like
For Consumer Key, enter: LTIkey_####_1, where #### is your Course ID
For Shared Secret enter the secret shown in your IMathAS Course Settings
For the Config URL, enter https://yourIMathASsite/canvas.php
Click Submit

To create a link to an individual assessment, in Canvas:

Go to the Assignments page, and click +Assignment
Under Submission Type, select "External Tool"
Click on the "Find" button, then on the IMathAS tool (or whatever name you used when you created the tool)
If this is your first time using this key and secret, IMathAS will ask you, the teacher, to sign into your IMathAS account. This is necessary to establish a connection between your LMS account and your IMathAS account. You will not need to do this step again, and students will not be asked to sign in and will not need a IMathAS account.
If this is your first link from this course, IMathAS will ask you to select the IMathAS course you want to connect your LMS course with.
Select the assignment you want to link to, and click Make Placement.
Click the Select button
Finish setting up the assignment in Canvas
Assignments set up this way will receive grade return from IMathAS

To create a single link to your entire IMathAS course, in Canvas:

On the Modules page, click on the + button inside a module
In the "Add" dropdown, select "External Tool"
Click on the IMathAS tool (or whatever name you used when you created the tool)
If this is your first time using this key and secret, IMathAS will ask you, the teacher, to sign into your IMathAS account. This is necessary to establish a connection between your LMS account and your IMathAS account. You will not need to do this step again, and students will not be asked to sign in and will not need a IMathAS account.
If this is your first link from this course, IMathAS will ask you to select the IMathAS course you want to connect your LMS course with.
Select "Whole Course Placement" and click Make Placement.
Click Add Item
Note that there is no grade return from IMathAS from a whole course placement.

Blackboard Integration - older Common Cartridge Instructions

Go to Course Items → Export, select the items you want to export, select your LMS, and Download the Export Cartridge

To import the cartridge in BlackBoard:

Go to Packages and Utilities, then Import Package
Click Import Package
Select the export file from your computer, click Select All to select all course materials, then click Submit.
If you have an LTI 1.3 connection or global LTI 1.1 college-wide key and secret, skip ahead. If you need to set up a course-level configuration, follow these steps.
- To to Packages and Utilities, then Manage LTI Links
- If the links are listed as Working, then you have an existing configuration, and do not need to continue.
- For one of the links with status listed as Broken, use the drop-down menu that shows when hovering over the link name and select Edit Credentials.
- For the Tool Provider Key, enter: LTIkey_####_1, where #### is your Course ID
- For the Tool Provider Secret enter the secret you set up in your Course Settings
- Check the box "Apply these credentials to all links"
- Click Submit
To enable grade return, Blackboard requires some additional steps:
- Return to the main course page in Blackboard.
- For each assessment link that was imported, use the drop-down menu and select Edit
- Set the Enable Evaluation option to Yes, specify the points possible (it does not need to match the points possible in IMathAS), and set a Due Date if desired.

Next you will need to establish the connection between your IMathAS course and BlackBoard course

In BlackBoard, click one of the assessment links in your course.
If this is your first time using this key and secret, IMathAS will ask you, the teacher, to sign into your IMathAS account. This is necessary to establish a connection between your LMS account and your IMathAS account. You will not need to do this step again, and students will not be asked to sign in and will not need a IMathAS account.
Follow the prompts to associate the LMS course with your existing IMathAS course or create a copy.
Once complete, all the LTI links in your LMS should work.
Be aware:
- Links, files, forums, and and text items were imported into your LMS. Changing them in IMathAS will not change them in your LMS
- If you change assessment settings or the questions in an assessment in IMathAS, those changes will show up when the assessment is launched from the LMS
- If you change due dates in IMathAS, they will be enforced by IMathAS, but the due dates in the LMS will not automatically be updated.
- Any new items added in IMathAS, including new assessments, will not automatically show up in the LMS; you would need to repeat the export/import process.
- If configured, grades will be sent from IMathAS to the LMS immediately every time the student completes a question, but the LMS may delay updating the grade.

Blackboard Integration - Using Import

Go to Course Items → Export, select the items you want to export, select your LMS, and Download the Export Cartridge

To import the cartridge in BlackBoard:

Go to Packages and Utilities, then Import Package
Click Import Package
Select the export file from your computer, click Select All to select all course materials, then click Submit.
If you have an LTI 1.3 connection or global LTI 1.1 college-wide key and secret, skip ahead. If you need to set up a course-level configuration, follow these steps.
- To to Packages and Utilities, then Manage LTI Links
- If the links are listed as Working, then you have an existing configuration, and do not need to continue.
- For one of the links with status listed as Broken, use the drop-down menu that shows when hovering over the link name and select Edit Credentials.
- For the Tool Provider Key, enter: LTIkey_####_1, where #### is your Course ID
- For the Tool Provider Secret enter the secret you set up in your Course Settings
- Check the box "Apply these credentials to all links"
- Click Submit
If importing a Common Cartridge, to enable grade return Blackboard requires some additional steps:
- Return to the main course page in Blackboard.
- For each assessment link that was imported, use the drop-down menu and select Edit
- Set the Enable Evaluation option to Yes, specify the points possible (it does not need to match the points possible in IMathAS), and set a Due Date if desired.

Next you will need to establish the connection between your IMathAS course and BlackBoard course

In BlackBoard, click one of the assessment links in your course.
If this is your first time using this key and secret, IMathAS will ask you, the teacher, to sign into your IMathAS account. This is necessary to establish a connection between your LMS account and your IMathAS account. You will not need to do this step again, and students will not be asked to sign in and will not need a IMathAS account.
Follow the prompts to associate the LMS course with your existing IMathAS course or create a copy.
Once complete, all the LTI links in your LMS should work.
Be aware:
- Links, files, forums, and and text items were imported into your LMS. Changing them in IMathAS will not change them in your LMS
- If you change assessment settings or the questions in an assessment in IMathAS, those changes will show up when the assessment is launched from the LMS
- If you change due dates in IMathAS, they will be enforced by IMathAS, but the due dates in the LMS will not automatically be updated.
- Any new items added in IMathAS, including new assessments, will not automatically show up in the LMS; you would need to repeat the export/import process.
- If configured, grades will be sent from IMathAS to the LMS immediately every time the student completes a question, but the LMS may delay updating the grade.

Blackboard Integration - Manual Process

To manually create a link to IMathAS, in Blackboard:

Under the Build Content dropdown, select Web Link
Give the link a Name
For URL, enter https://yourIMathASsite/bltilaunch.php
Click the checkbox for "This link is to a Tool Provider"
If you have an LTI 1.3 connection or global LTI 1.1 college-wide key and secret, you will not see or need to fill out the following two entries.
- For Key, enter LTIkey_####_1, where #### is your Course ID
- For Secret, enter the secret shown in your IMathAS Course Settings
If you are setting up a link to an individual assessment, set "Enabled Evaluation" to Yes, and enter the points possible. Whole course links to not return grades, so there is no need to enabled evaluation for those.
Click Submit
If the link you just created shows "(invalid link)" next to the name, they you'll need to ask your BlackBoard administrator to approve LTI connections to IMathAS.
Click on the link you just created.
If this is your first time using this key and secret, IMathAS will ask you, the teacher, to sign into your IMathAS account. This is necessary to establish a connection between your LMS account and your IMathAS account. You will not need to do this step again, and students will not be asked to sign in and will not need a IMathAS account.
If this is your first link from this course, IMathAS will ask you to select the IMathAS course you want to connect your LMS course with.
Select the assignment you want to link with, or select "Whole Course Placement" if you want a single link to your entire IMathAS course, then click Make Placement.

Be aware assessment links created manually in this way will lose their association with IMathAS assessments when the course is copied in BlackBoard, so using the Export/Import process is recommened if you are creating individual assessment links.

D2L Brightspace Integration

Go to Course Items → Export, select the items you want to export, select your LMS, and Download the Export Cartridge

To import the cartridge in Brightspace:

Go to Course Admin, and select Import/Export/Copy Components.
Select Import Components, and "from a course package"
Choose the export file and click Import All Components.
If you have an LTI 1.3 connection or global LTI 1.1 college-wide key and secret, you can skip ahead. If you need to set up a course-level configuration, follow these steps.
- Go to Course Admin, and click External Learning Tools
- Click on Manage Tool Providers. If you do not see this link, then your LMS administrators have blocked your ability to self-configure the connection. You will need to ask for them to set up a global tool provider.
- Click New Tool Provider
- For the Launch Point enter the address shown on the Export page
- For the Secret enter the secret you set up in your Course Settings
- Click the "Use custom tool information" box if needed
- For the Key, enter: LTIkey_####_1, where #### is your Course ID
- For the name name, enter: IMathAS
- Click the "Allow users to use this tool provider" if that option is available.
- Under Security Settings, make sure the following options are checked (it is OK to check other ones as well):
  - Send tool consumer information to tool provider
  - Send context information to tool provider
  - Send course information to tool provider
  - Send LTI user ID and LTI role to tool provider
  - Send user name to tool provider
  - Send user email to tool provider (optional, but recommended)
- Save

Next you will need to establish the connection between your IMathAS course and Brightspace course

In Brightspace, click one of the assessment links in your course.
If this is your first time using this key and secret, IMathAS will ask you, the teacher, to sign into your IMathAS account. This is necessary to establish a connection between your LMS account and your IMathAS account. You will not need to do this step again, and students will not be asked to sign in and will not need a IMathAS account.
Follow the prompts to associate the LMS course with your existing IMathAS course or create a copy.
Once complete, all the LTI links in your LMS should work.
Be aware:
- LTI assessments may not show in the gradebook columns until a student started working on an assignment.
- Links, files, forums, and and text items were imported into your LMS. Changing them in IMathAS will not change them in your LMS
- If you change assessment settings or the questions in an assessment in IMathAS, those changes will show up when the assessment is launched from the LMS
- If you change due dates in IMathAS, they will be enforced by IMathAS, but the due dates in the LMS will not automatically be updated.
- Any new items added in IMathAS, including new assessments, will not automatically show up in the LMS; you would need to repeat the export/import process.
- If configured, grades will be sent from IMathAS to the LMS immediately every time the student completes a question, but the LMS may delay updating the grade.

Moodle Integration

Go to Course Items → Export, select the items you want to export, select your LMS, and Download the Export Cartridge

To import the cartridge in Moodle:

Under Course Administration (in some versions, the big gear icon in the upper right), select Restore.
Choose the export file and select Restore.
Follow the prompts to import the content.
Turn on editing for your course.
For one of the assessment, use the Edit dropdown and select Edit Settings.
If the Launch URL does not display the warning Tool configuration not found for this URL, then you must have an existing LTI 1.3 connection or LTI 1.1 key and secret set up, and can skip ahead. If you do see that warning, then follow these steps.
- Click the + sign located directly after the External tool type pulldown (in some versions, this is labeled Preconfigured Tool)
- Give the tool a name, like IMathAS
- For Tool base URL enter the address shown on the Export page
- For Consumer Key, enter: LTIkey_####_1, where #### is your Course ID
- For Shared Secret enter the secret you set up in your Course Settings
- Under Privacy, it is recommended to set all options to Always, but it is fine to leave it as Delegate to teacher instead.
- Save changes
- The Launch URL should now indicate Using tool configuration IMathAS. Click Save.

Next you will need to establish the connection between your IMathAS course and Moodle course

In Moodle, click one of the assessment links in your course.
If this is your first time using this key and secret, IMathAS will ask you, the teacher, to sign into your IMathAS account. This is necessary to establish a connection between your LMS account and your IMathAS account. You will not need to do this step again, and students will not be asked to sign in and will not need a IMathAS account.
Follow the prompts to associate the LMS course with your existing IMathAS course or create a copy.
Once complete, all the LTI links in your LMS should work.
Be aware:
- LTI assessments may not show in the gradebook columns until a student started working on an assignment.
- Links, files, forums, and and text items were imported into your LMS. Changing them in IMathAS will not change them in your LMS
- If you change assessment settings or the questions in an assessment in IMathAS, those changes will show up when the assessment is launched from the LMS
- If you change due dates in IMathAS, they will be enforced by IMathAS, but the due dates in the LMS will not automatically be updated.
- Any new items added in IMathAS, including new assessments, will not automatically show up in the LMS; you would need to repeat the export/import process.
- If configured, grades will be sent from IMathAS to the LMS immediately every time the student completes a question, but the LMS may delay updating the grade.

LTI Integration for Other LMSs - Using Import

Go to Course Items → Export, select the items you want to export, select your LMS, and Download the Export Cartridge. The cartridge is an IMS Common Cartridge format.

Import the cartridge into your LMS. If you have an LTI 1.3 connection or global LTI 1.1 college-wide key and secret, skip ahead. Otherwise, you'll likely need to configure the LTI connection by providing the key and secret, which can be found on the Course Settings page.

Next you will need to establish the connection between your IMathAS course and LMS course

In your LMS, click one of the assessment links in your course.
If this is your first time using this key and secret, IMathAS will ask you, the teacher, to sign into your IMathAS account. This is necessary to establish a connection between your LMS account and your IMathAS account. You will not need to do this step again, and students will not be asked to sign in and will not need a IMathAS account.
Follow the prompts to associate the LMS course with your existing IMathAS course or create a copy.
Once complete, all the LTI links in your LMS should work.
Be aware:
- Links, files, forums, and and text items were imported into your LMS. Changing them in IMathAS will not change them in your LMS
- If you change assessment settings or the questions in an assessment in IMathAS, those changes will show up when the assessment is launched from the LMS
- If you change due dates in IMathAS, they will be enforced by IMathAS, but the due dates in the LMS will not automatically be updated.
- Any new items added in IMathAS, including new assessments, will not automatically show up in the LMS; you would need to repeat the export/import process.
- If configured, grades will be sent from IMathAS to the LMS immediately every time the student completes a question, but the LMS may delay updating the grade.

LTI Integration for Other LMSs - Manual Process

If you have an LTI 1.3 connection or global LTI 1.1 college-wide key and secret, you do not need to set up a course-level configuration. Otherwise, you will need to set up a course-level LTI configuration. Consult your LMS's help for how to do this; some LMSs configure an LTI took at the course settings level, while some have you enter the credentials with each link.

If you need to set up a course-level LTI configuration, you will need:

A Consumer/Tool Key: LTIkey_####_1, where #### is your Course ID
A Secret: use the LTI secret shown in your IMathAS Course Settings
Launch/Tool URL: https://yourIMathASsite/bltilaunch.php

The process to set up LTI links varies by LMS, so consult your LMS for details.

Be aware assessment links created manually in this way will lose their association with IMathAS assessments when the course is copied in the LMS, so using the Export/Import process is recommened if you are creating individual assessment links and your LMS supports it.

Writing Questions

The IMathAS question format is based on PHP.

Question Parts

A question is formed in several parts:

Description: A description of the question. This is not shown to students
Use Rights: The rights you wish to grant other people (you always have full rights). Options are:
- Private: Only you can see the question in question searches.
- Allow use by all: Anyone can use the problem, but only you can modify the problem. The question will appear in question searches if it's assigned to a library. Anyone can add library assignments, but cannot remove assignments.
- Allow use by all and modifications by group: Like above, but anyone in your instructor group can modify the question. Use with caution.
- Allow use by all and modifications by all: Like above, but anyone can modify the question. In general, do not use this. This is meant for temporary use where you're getting help from someone outside your group.
License: The permission license to apply to the question.
My libraries assignments: The question libraries you wish to include this question in.
Question type: The type of question.
Common control: The coding that defines variables, defines question behavior, and generates anything needed for display.
Question text: The actual question display. This section should be HTML based, but can include variables defined in the common or question control. For convenience, a blank line is automatically interpreted to be a paragraph break. Use of < and > signs are usually handled ok, but use of the HTML < and > are recommended in their place. You can use the Toggle Editor button to enable the rich-text editor if that is easier than working in raw HTML.
Detailed solution: An optional place to define a detailed solution that display with the answer key, or a popup written example. This section should be HTML based. There are options for whether the solution uses the variables from the question, and for whether to show the solution as a popup written example, with the "show answer" answer key, or both
Image files: This provides a place to upload static images (.png, .jpg, .gif) and assign them to a variable for use in the question code or question text. Be sure to provide a description for accessiblity. If you're only using an image in the question text, it can be simpler to Toggle Editor in the question text and use the insert image tool there.
Help buttons: Use these to provide help buttons for videos or links to reading material. These will show below the question, and can be toggled off in the assessment settings.
Use accessible alternative: This is only needed if your question cannot be made accessible through normal means. You probably don't need this. Read the accessible alternative help section for more details.

Basic Control Syntax

Lines of the common control, question control, and answer sections usually take the form of variable definition. In IMathAS, variables are identified with a dollarsign ($) prefix. For example, $a is the variable a. Most lines will take one of these forms:

$var = number. Example: $a = 3
$var = calculation. Example: $a = 3*$b*$c
$var = function. Example: $a = showplot("sin(x)")
$var = randomizer. Example: $a = rand(-5,5)

Variable Types

There are a few types of variables:

A number: $a = 15. A calculation like $a = 3^2 will also result in a number
An array: $a = array(6,8,10) or $a = [6,8,10]. This is a collection of variables. You can reference the parts using an index (note that arrays are zero-indexed), so $a[0] = 6.
An associative array: $a = array('x'=>3, 'y'=>5) or $a = ['x'=>3, 'y'=>5]. This is a collection of variables, referenced by keys. You can reference the parts using the key as index so $a['x'] = 3.
A string: $a = "hi there", or $b = "2/3".
Boolean: $a = true

Note that numbers are not in quotes, and strings are in quotes. When you use the double-quote mark (") to define a string, you can interpolate variables into the string. Example:

$a = 3
$b = 5
$str = "What is $a/$b"

In this example, $str now contains "What is 3/5".

If you need to insert a variable adjacent to text, you can wrap it in curly braces:

$a = rand(2,10)
$str = "The height is {$a}ft"

Note that strings in single quotes will not interpolate variables

As a warning, strings are interpolated literally, so if you had $a = -4 and then defined $b = "$a^2" you would end up with "-4^2", which may not be what you intended. Use explicit parentheses in these cases.

Warning: Strings that we as mathematicians think of as numbers are not numbers. If $a = "3/4", that defines a string, and if you try to compute $b = $a*5, that's going to give an error, because you can't multiply a string by a number. Usually there is an easy workaround, but if you really need to evaluate something like that, you'll need to use hte evalnumstr function.

Array assignment

In some cases you want to define several variables at once. There are two ways to do this:

$var1,$var2 = arrayfunction. Example: $a,$b = diffrands(-5,5,2)
$ar = arrayfunction. Example: $ar = diffrands(-5,5,2)

In the first example, variables $a and $b each take on a single value. In the second example, the variable $ar is an array; the elements can be accessed as $ar[0] and $ar[1] (note that arrays are zero-indexed). If you use this approach, enclose the variable reference in parenthesis in calculations, like $new = ($ar[0])^2, and in curly brackets inside strings, like $string = "there were {$ar[0]} people".

You can also literally define an array using the "array" function. Examples: $ar = array(2,3,4,5), or $ar = array("red","green","blue")

You can also use a shorthand notation for an array, using square brackets. Example: $ar = [2,3,4,5].

Working with Strings

If needed, you can concatenate (combine) two strings using the . operator. Example:

$a = "string one "
$b = "string two"
$both = $a . $b

Here, $both now contains the string "string one string two"

If you have a long command to type, you can put a "&" at the end of a line to specify it continues on the next line. Example:

$questions = array("this is choice 1",&
"this is choice 2")

If defining a string for display, you can put a "&&" at the end of a line to specify it continues on the next line and insert an HTML line break. Example:

$showanswer = "Do this first. &&
Then do this."

will be interpreted as:

$showanswer = "Do this first. <br/>Then do this."

For more ways to work with strings, see the string macros section.

Comments

You can insert comments in your code by starting the comment with two forward slashes: //this is a comment. Typically it's best to put comments on their own line, but they can also be placed after a line of code.

Conditionals

Any assignment line can be followed by one of two conditional: "where" or "if".

where

"where" is used to repeat the previous assignment if the condition provided is not met. The "where" condition is almost exclusively used with array randomizers. Example: to select two different numbers that are not opposites:

$a,$b = diffrands(-5,5,2) where ($a+$b!=0)

Beware that the system will give up if it's unable to meet the specified conditions after 200 tries, so be sure your where condition has fairly high probability of success, ideally at least 10%. If it doesn't, you should consider where there are other ways to generate your values. Alternatively, you can specify a fallback value to use if the condition fails using else:

$a = rand(1,100) where (gcd($a,$b)==1) else ($a = 7)

"where" can also be applied to a block of code:

{
  $a = rand(-5,-1)
  $b = rand(1,5)
} where ($a+$b !==0)

or with a fallback

{
  $a = rand(-5,-1)
  $b = rand(1,5)
} where ($a+$b !==0) else {
  $a = -3
  $b = 5
}

Note that where can also be used for looping. See the help on Loops for examples.

if

"if" is used to make an assignment conditional. For example:

$a = rand(0,1)
$b = "sin(x)" if ($a==0)
$b = "cos(x)" if ($a==1)

Note the use of double equal signs (==) for testing equality. A single equal sign (=) will make an assignment (change the value of $a in this example) and return "true", which is probably not what you intended to do.

The "if" condition can also be used before or after a code block like this:

$a = rand(0,1)
if ($a==0) {
   $b = 1
   $c = 2
}

$a = rand(0,1)
{
   $b = 1
   $c = 2
} if ($a==0)

When "if" is used before a block of code, it can optionally be followed with "elseif" and/or an "else" statement, like this:

$a = rand(0,5)
if ($a==0) {
   $b = 1
} elseif ($a==2) {
   $b = 3
} else {
   $b = 2
}

Other conditional operators and functions

For very simple if/else cases, you can use the shorthand condition ? then : else ternary syntax. For example:

$b = ($a > 0) ? "increasing" : "decreasing"

An equivalent but potentially friendlier looking option is the ifthen(condition,trueval,falseval) macro (see General Macros)

$b = ifthen($a > 0, "increasing", "decreasing")

For situations where you want to do a series of conditions based on the value options of a variable, you can use the cases macro (see General Macros). For example, these two code blocks do the same thing:

$a = rand(0,5)
if ($a==0) {
   $b = "AA"
} elseif ($a==2) {
   $b = "BB"
} else {
   $b = "CC"
}

$a = rand(0,5)
$b = cases($a, [0, 2], ["AA", "BB"], "CC")

Comparison operators

Comparison operators available for "if" and "where" statements:

== Equal to
!= Not equal to
> Greater than
< Less than
>= Greater than or equal to
<= Less than or equal to
isset($v) Whether $v is defined

To do compound conditionals, use || for "or", and && for "and". For example:

$a = nonzerorand(-9,9) where ($a!=1 && $a!=-1)

Conditionals in Question Text

Within the question text, it's possible to have a section of text display based on the value of a variable. If the text is a single string, it's preferable to define the string conditionally in the question code, then insert the variable for the string in the question text. Putting a conditional direclty in the question text is primarily intended for cases where there is a large block of text to control.

To do conditional text, wrap the text in [if variable==value][/if]. Note that the variable name should be given without the preceeding dollar sign here. You can use other simple comparisons like != or <, but not more complicated expressions. The value should not be in quotes, even if it is text. It is fine to have things like $answerbox inside two conditionals, so long as only one will display at at time.

Example:

[if graphdispmode==0]
Given f(x)=$func, estimate f'(x) at x=$x.  $answerbox
[/if]
[if graphdispmode>0]
$graph
Given the graph above, estimate f'(x) at x=$x.  $answerbox
[/if]

Loops

There are several looping macros (such as calconarray) that can meet most needs. For more general use there is a "for" loop:

for

for ($i=a..b) { action }

Here a and b represent whole numbers, variables, or simple expressions.

Examples:

$f = 0
for ($i=1..5) { $f = $f + $i }

$a = rands(1,5,5)
$b = rands(1,5,5)
for ($i=0..4) {
  $c[$i] = $a[$i]*$b[$i]
}

foreach

For associative arrays (arrays with non-numeric or non-consecutive keys) you can use a "foreach" loop:

foreach ($arr as $k=>$v) { action }

Here $arr is the associative array, and as it loops the keys will be assigned to $k and the values to $v.

Example:

$arr = ['red' => 3, 'green' => 5, 'blue' => 2]

$str = ''
foreach ($arr as $color=>$num) {
  $str .= "There are $num balls that are $color. "
}

where

where can be used in the same way a do...until loop might used in other languages. Example:

{
  $a = rand(1,10)
  $b = rand(-10,-1)
} where ($a+$b != 0)

while

while loops are similar to where loops, but evaluate the condition at the start rather than at the end. Example:

$index = 0
$a = $str[$index]
while ($a == '') {
  $index = $index + 1
  $a = $str[$index]
}

Notes

Conditions after the statement can be used inside a for loop, but not outside without explicit blocking

for ($i=1..5) {$a = $a+$i if ($i>2) }     WORKS
for ($i=1..5) {$a = $a+$i} if ($a>2)     DOES NOT WORK
{for ($i=1..5) {$a = $a+$i} } if ($a>2)    WORKS

Conditions using blocking inside a loop are fine

for ($i=1..5) { if ($i>2) {$a = $a+$i} }   WORKS

Inside a for or foreach loop, break can be used to break out of the loop, and continue can be used to move on to the next iteration without executing any further code in the block.

Randomizers

Note on macros: The descriptions below explain macros available and the arguments the functions should be called with. Arguments in [square brackets] are optional arguments, and can be omitted.

For all randomizers, all bounds (min,max) are inclusive.

Single result randomizers:

rand(min,max): Returns an integer between min and max

Example

$a = rand(1,10)        // $a might be 7
$b = rand(-5,5)        // $b might be -2

rrand(min,max,p): Returns a number between min and max in steps of p

Example

$a = rrand(2,5,.1)     // $a might be 3.4
$b = rrand(2,5,.01)    // $b might be 3.27
$c = rrand(2,8,2)      // $c might be 2, 4, 6, or 8

nonzerorand(min,max): Returns a nonzero integer between min and max
Example
```
$a = nonzerorand(-5,5) // $a might be -3 or 4, but never 0
```
nonzerorrand(min,max,p): Returns a nonzero real number between min and max in steps of p
Example
```
$a = nonzerorrand(-2,2,.5) // $a might be -1.5 or 3, but never 0
```

randfrom(list or array): Return an element of the list/array

Example

$color = randfrom("red,green,blue");  // might return "green"
$n = randfrom("2,4,6,8")             // might return 4

$arr = [10,20,30]
$val = randfrom($arr)                // might return 20

randname(),randmalename(),randfemalename(): Returns a random first name

Example

$name = randname()       // might return "Sofia"
$name = randmalename()   // might return "Carlos"
$name = randfemalename() // might return "Aisha"

randnamewpronouns([option]): Returns a random first name with pronouns in the order: subjective, objective, possessive (singular), possessive (plural), reflexive. Can set option to 'neutral' for they/them/their/theirs/themself pronouns. Use: $name,$heshe,$himher,$hisher,$hishers,$himherself = randnamewpronouns()

Example

$name,$heshe,$himher,$hisher,$hishers,$himherself = randnamewpronouns()
// might give: $name="Carlos", $heshe="he", $himher="him", $hisher="his"...
$str = "$name went to the store to buy a gift for $hisher friend"

$name,$heshe,$himher,$hisher,$hishers,$himherself = randnamewpronouns('neutral')
// always gives they/them pronouns

uniqid(): Generates a random unique string, useful for giving a unique id to elements.

Example

$id = uniqid()   // might return "a64f3a2b1c"
// Typical use: creating unique HTML element ids in question markup
// <div id='graph$id'>

Array randomizers (return multiple results):

rands(min,max,n,[order]): Returns n integers between min and max. Can set order to 'inc' or 'dec' to sort the values, but be aware there may still be duplicate values.

Example

$a,$b,$c = rands(1,10,3)        // might give 3, 7, 1 (duplicates possible)
$a,$b,$c = rands(1,10,3,'inc')  // sorted ascending, e.g. 1, 3, 7
$arr = rand(1,10,2) // reference using $arr[0] and $arr[1]

rrands(min,max,p,n,[order]): Returns n real numbers between min and max in steps of p. Can set order to 'inc' or 'dec' to sort the values.
Example
```
$a,$b,$c = rrands(0,1,.25,3)        // might give 0.25, 0.75, 0.5
$a,$b,$c = rrands(0,1,.25,3,'dec')  // sorted descending, e.g. 0.75, 0.5, 0.25
```
nonzerorands(min,max,n,[order]): Returns n nonzero integers between min and max. Can set order to 'inc' or 'dec' to sort the values.
Example
```
$a,$b = nonzerorands(-3,3,2)       // might give -1, 2 (never 0)
$a,$b = nonzerorands(-3,3,2,'inc')  // sorted: -1, 2
```
nonzerorrands(min,max,p,n,[order]): Returns n nonzero real numbers between min and max in steps of p. Can set order to 'inc' or 'dec' to sort the values.
Example
```
$a,$b = nonzerorrands(-3,3,.5,2) // might give -2.5, 1 (never 0)
```

randsfrom(list/array,n,[order]): Return n elements of the list/array. Can set order to 'inc' or 'dec' to sort the values.

Example

$a,$b = randsfrom("red,green,blue,yellow", 2)  // e.g. "blue", "red"
$arr = [2,4,6,8]
$a,$b = randsfrom($arr, 2, 'inc');         // sorted ascending, e.g. 2, 6

jointrandfrom(list/array,list/array,[list/array,...]): Returns one element from each list, where the location used in each list is the same

Example

$first,$last = jointrandfrom("Alice,Bob,Carlos", "Smith,Jones,Rivera")
// picks the same index from each list, so names stay paired:
// e.g. $first="Bob", $last="Jones"

// can be used to randomly pick a question prompt and answer from corresponding arrays:
$prompt,$answer = jointrandfrom($questionprompts, $allanswers)

diffrands(min,max,n,[order]): Returns n different integers between min and max. Can set order to 'inc' or 'dec' to sort the values.

Example

$a,$b,$c = diffrands(1,6,3)        // three distinct values, e.g. 4, 1, 6
$a,$b,$c = diffrands(1,6,3,'inc')  // sorted ascending, e.g. 1, 4, 6

diffrrands(min,max,p,n,[order]): Returns n different real numbers between min and max in steps of p. Can set order to 'inc' or 'dec' to sort the values.
Example
```
$a,$b = diffrrands(0,1,.1,2) // two distinct values, e.g. 0.3, 0.7
```
diffrandsfrom(list/array,n,[order]): Return n different elements of the list/array. Can set order to 'inc' or 'dec' to sort the values.
Example
```
$a,$b = diffrandsfrom("red,green,blue,yellow", 2) // two distinct colors, e.g. "green", "red"
```
nonzerodiffrands(min,max,n,[order]): Returns n different nonzero integers between min and max. Can set order to 'inc' or 'dec' to sort the values.
Example
```
$a,$b = nonzerodiffrands(-3,3,2) // two distinct nonzero values, e.g. -2, 3
```
nonzerodiffrrands(min,max,p,n,[order]): Returns n different nonzero real numbers between min and max in steps of p. Can set order to 'inc' or 'dec' to sort the values.
Example
```
$a,$b = nonzerodiffrrands(-1,1,.5,2) // e.g. -0.5, 1.0 (distinct and nonzero)
```
jointshuffle(list/array1,list/array2,[n1,n2]): Shuffles two lists/arrays in a way that retains respective order. In n1 is provided, n1 elements from each shuffled array will be returned (like a joint version of diffrandsfrom). If n2 is also provided, n1 elements of list/array1 and n2 elements of list/array2 will be returned.
Example
```
// Shuffle names and scores together so they stay paired:
$names,$scores = jointshuffle("Alice,Bob,Carlos", array(95,82,71))
// e.g. $names=array("Bob","Carlos","Alice"), $scores=array(82,71,95)

// Pick 2 from each:
$names,$scores = jointshuffle("Alice,Bob,Carlos", array(95,82,71), 2)
// e.g. $names=array("Bob","Alice"), $scores=array(82,95)
```
singleshuffle(list/array,[n]): returns a shuffled version of a list/array. If n is provided, it behaves identically to diffrandsfrom, and picks n items from the list/array.
Example
```
$shuffled = singleshuffle("1,2,3,4,5")    // e.g. array(3,1,5,2,4)
$two = singleshuffle("1,2,3,4,5", 2)      // pick 2: e.g. array(4,2)
```

randnames(n),randmalenames(n),randfemalenames(n): Returns n random first names

Example

$a,$b,$c = randnames(3)      // e.g. "Sofia", "Carlos", "Aisha"
$a,$b = randmalenames(2)     // e.g. "Marcus", "Eli"
$a,$b = randfemalenames(2)   // e.g. "Priya", "Helena"

randcity([country]),randcities(n, [country]): Returns one or n random US or Canadian city names. Argument country can be set to "USA" or "Canada". The default is "USA".
Example
```
$city = randcity()             // e.g. "Portland"
$city = randcity("Canada")    // e.g. "Calgary"
$c1,$c2 = randcities(2)      // e.g. "Austin", "Denver"
```
randstate([country]),randstates(n, [country]): Returns one or n random US state or Canadian province names. Argument country can be set to "USA" or "Canada". The default is "USA".
Example
```
$state = randstate()           // e.g. "Oregon"
$prov = randstate("Canada")   // e.g. "Alberta"
$s1,$s2 = randstates(2)      // e.g. "Texas", "Ohio"
```

randcountry(),randcountries(n): Returns one or n random country names

Example

$c = randcountry()            // e.g. "Brazil"
$c1,$c2 = randcountries(2)   // e.g. "Japan", "Mexico"

randpythag([min,max]): Return a Pythagorean triple. min/max default to 1 to 100

Example

$a,$b,$c = randpythag()        // e.g. 3, 4, 5  (satisfies a^2+b^2=c^2)
$a,$b,$c = randpythag(5,20)   // triple with values between 5 and 20

Graph/Table Macros

The following macros create graphs or tables:

showarrays(string,array,[string,array]...,[options]): Creates a tabular display of the data in the array(s) as column(s), with the strings as column headers.
Parameters

Alternate call form: showarrays(array of column headers, array of data arrays, [options]).
Options can be a string "c", "l", or "r" to center, left-align, or right-align data, or an array with $opts["align"] for alignment, $opts["tablealign"]="center" to center the whole table, and $opts["caption"] to add a caption. To align each column differently use a character-per-column string like "rcc".
Example
```
$xs = array(1,2,3)
$ys = array(1,4,9)
$table = showarrays("x", $xs, "y", $ys)

// all columns centered
$table = showarrays("x", $xs, "y", $ys, 'c')

// With alignment and caption:
$opts["align"] = "rc"
$opts["caption"] = "Squares"
$table = showarrays("x", $xs, "y", $ys, $opts)
// or equivalently
$table = showarrays("x", $xs, "y", $ys, ['align'=>"rc", 'caption'=>"Squares"])

// Array-of-arrays alternate call form:
$table = showarrays(array("x","y"), array($xs,$ys))
```
showdataarray(array,[columns,options]): Creates a tabular display of the data in the array with no headers.
Parameters

Data is presented in one column unless a column count is provided. Options can be a string "c", "l", or "r" to align data, or an array with $opts["align"], $opts["tablealign"]="center", and $opts["caption"].
Example
```
$data = array(10,20,30,40,50,60)
$table = showdataarray($data)         // single column
$table = showdataarray($data, 3)      // spread across 3 columns
$table = showdataarray($data, 2, "c") // 2 columns, centered
$table = showdataarray($data, 2, ['align'=>'c', 'caption'=>"Scores"]) // 2 columns, centered, with caption
```
horizshowarrays(string,array,[string,array]...,[options]): Creates a tabular display of the data in the array(s) as row(s), with the strings as row labels. Does not text wrap, so only use for small data sets.
Parameters

Options can be a string "c", "l", or "r" to align data, or an array with $opts["align"], $opts["tablealign"]="center", and $opts["caption"].
Example
```
$xs = array(1,2,3,4)
$ys = array(1,4,9,16)
$table = horizshowarrays("x", $xs, "y", $ys)
// Creates a two-row table: "x" row and "y" row, values in columns
```
showrecttable(data array of arrays,columnlabels,rowlabels,[options]): Creates a tabular display of a rectangular data table, where $data[0] is the first row.
Parameters

rowlabels and columnlabels are arrays of label strings. Options can be a string "c", "l", or "r" to align data, or an array with $opts["align"], $opts["tablealign"]="center", and $opts["caption"].
Example
```
$data = array(array(10,20), array(30,40))
$cols = array("A","B")
$rows = array("Row1","Row2")
$table = showrecttable($data, $cols, $rows)
// table with column headers A and B, row headers Row1 and Row2, first row 10, 20
```
showplot(funcstrings,[xmin,xmax,ymin,ymax,labels,grid,width,height]): Creates a graph from one or more function strings.
Parameters
- funcstrings is a single string or an array of strings each having at least the first of the following list:
  "function,color,min,max,startmarker,endmarker,width,dash"
  - Function: a single function of x, like cos(x), or a parametric function of t, entered like [sin(t),cos(t)], or x=c for a vertical line, entered like x=1
  - color: a color designator: black,red,orange,yellow,green,blue,purple
  - min,max: the min and max values for the input variable for which you wish to see this graph. You can also exclude point discontinuities; for example -5,5!0!2 for min,max would include all values from -5 to 5, excluding 0 and 2.
  - startmarker,endmarker: can be "open" or "closed" (dots), "arrow", or anything else for none
  - width: a pixel width for the line
  - dash: enter "dash" if you want a dashed line, otherwise the line is solid
  - Examples: "cos(x),red" or "x^2,,-2,2,open,closed" or "[t^2,t/3],blue,0,5,,,2,dash" or "1/x,black,-5,5!0" or "x=1,red,,,,,,dash"
  - Dots and Labels: There are two alternate funcstrings formats:
    - dots: For drawing dots. A string containing at least the first three of: "dot,x,y,style,color,label,labelloc"
      
      dot: the literal word dot
      
      x,y: the coordinates of the dot
      
      style: open or closed
      
      color: a color designator: black,red,orange,yellow,green,blue,purple
      
      label: a text string to put as a label on the dot
      
      labelloc: label location: above, left, right, below, aboveleft, etc.
      
      Examples:: "dot,3,4", "dot,1,1,open", "dot,3,3,,blue,A"
    - text: For placing text labels. A string containing at least the first four of: "text,x,y,label,color,location,angle,graphassoc"
      
      text: the literal word text
      
      x,y: the coordinates of the label
      
      label: the text string to display
      
      color: a color designator: black,red,orange,yellow,green,blue,purple
      
      location: label location: above, left, right, below, aboveleft, etc.
      
      angle: a rotation angle in degrees for the label (0,90,180,270)
      
      graphassoc: If this text is a label for a graph, the index in funcstrings for the graph it labels. This is used by the accessible alt text.
      
      Examples:: "text,2,4,Cars", "text,4,0,Hours,below"
- xmin,xmax,ymin,ymax: Graphing window. Defaults to -5 to 5 for both. Use "0:-n" (for some value of n) for xmin or ymin to only have gridlines and labels after 0, while still using -n to adjust spacing. This is an alternative to using addplotborder to create first quadrant graphs.
- labels: spacing of axes labels. Defaults to 1. Set to "off" or 0 for none. Use "xlbl:ylbl" for different spacing on each axis. Use "xlbl:ylbl:xname:yname" to put a named label on the axes.
- grid: spacing of grid lines. Defaults to 1. Set to "off" or 0 for none. Use "xgrid:ygrid" for different spacing on each axis.
- width,height: The width and height (in pixels) of the graph. Defaults to 200x200
Example
```
// Single function:
$graph = showplot("x^2")

// With window
$graph = showplot("x^2,blue", -3, 3, -1, 9, 1, 1, 300, 300)

// Drawn larger, 300x300
$graph = showplot("x^2", -5, 5, -5, 5, 1, 1, 300, 300)

// With window and scaling, labels spaced at 2 in x and 20 in y, 
// grid spaced at 1 in x, 10 in y.
$graph = showplot("2^x", -3, 12, -20, 200, "2:20", "1:10")

// dashed line, with axes labeled x and y, no grid lines
$graph = showplot("3-x,blue,,,,,,dash", -5, 5, -5, 5, "1:1:x:y", 0)

// Multiple functions with dot and label:
$funcs = array("x^2,blue", "2*x+1,red", "dot,1,1,closed,blue", "text,1,1,A,blue,above")
$graph = showplot($funcs, -4, 4, -2, 10)

// Parametric curve:
$graph = showplot("[cos(t),sin(t)],blue,0,6.28", -1.5, 1.5, -1.5, 1.5)

// Domain with hole:
$graph = showplot("1/x,black,-5,5!0", -5, 5, -5, 5)

// Piecewise, first line ends at closed dot, second starts at open dot
$funcs = ["3-x,blue,-6,1,,closed","-2+x,blue,1,6,open"]
$graph = showplot($funcs)
```
mergeplots($plot1, $plot2, [$plot3, $plot4, ...]): Merges multiple plots into one. Usually not necessary since showplot accepts an array of funcstrings, but useful when combining graphs generated by different functions. The grid and border from the first graph is used; ensure all plots use the same grid.
Example
```
$g1 = showplot("x^2,blue")
$g2 = showplot("2*x,red")
$combined = mergeplots($g1, $g2)
```
invertplot($plot): Inverts a plot by swapping x and y coordinates of every point. Useful for drawing curves where x is a function of y. Note: use replacealttext after inverting, since the auto-generated alt text will not be accurate.
Example
```
// Draw x = y^2 by drawing y = x^2 then inverting:
$g = showplot("x^2,blue")
$g = invertplot($g)
$g = replacealttext($g, "Graph of x equals y squared")
```
addfractionaxislabels(plot,step,[axis]): Adds fraction or pi-multiple labels along an axis of a showplot graph.
Parameters

Set axis to "y" for the y-axis; defaults to x-axis.
Step can be a fraction like "1/4" or a pi multiple like "pi/4" or "2pi".
Example
```
// Trig graph with pi/2 labels on x-axis:
$g = showplot("sin(x),blue", 0, 6.3, -1.2, 1.2)
$g = addfractionaxislabels($g, "pi/2")
// x-axis now shows 0, pi/2, pi, 3pi/2, 2pi
```
addlabel(plot,x,y,label,[color,loc,angle,size,alt]): Adds a text label at graph coordinates (x,y) to a showplot graph.
Parameters
- color: Label color. Defaults to black.
- loc: Position relative to the point — "above", "below", "left", "right", "aboveleft", etc. Defaults to centered.
- angle: Rotation angle in degrees.
- size: Font size for the label.
- alt: Alt text for the label, replacing the default.
Example
```
$g = showplot("x^2,blue")
$g = addlabel($g, 1, 1, "A", "red", "above")
$g = addlabel($g, -2, 4, "(-2,4)", "blue", "left")
```
addlabelabs(plot,x,y,label,[color,loc,angle,alt]): Like addlabel, but x and y are pixel coordinates on the image rather than graph coordinates.
Example
```
$g = showplot("x^2,blue")
$g = addlabelabs($g, 0, 200, "My Graph", "black", "belowright")
```

addplotborder(plot,left,[bottom,right,top]): Changes the pixel border width (default 5) around a plot. Labels show within the border; typically used to add room for axis labels.

Example

$g = showplot("x^2,blue", 0, 10, 0, 10)
$g = addplotborder($g, 30)           // 30px border all sides
$g = addplotborder($g, 30, 30, 5, 5) // wide left and bottom border for axis labels

adddrawcommand(plot,commands): Inserts arbitrary ASCIIsvg drawing commands into an existing plot.
Example
```
$g = showplot("x^2,blue")
$g = adddrawcommand($g, "stroke='green'; line([0,0],[1,1]);")
```
showasciisvg(string,[width,height,alttext]): Renders an ASCIIsvg script directly as an SVG. Always include alttext for accessibility.
Example
```
$g = showasciisvg("initPicture(0,10,0,10);path([[0,0],[0,10],[10,10],[0,0]]);", 100, 100, "A Triangle")
```
replacealttext(image or graph, alttext): Replaces the auto-generated alt text on a graph or image with the specified text.
Example
```
$g = showplot("x^2,blue")
$g = replacealttext($g, "Graph of y equals x squared, a parabola opening upward")
```

changeimagesize(image, width, [height]): Changes the display size of an image. Does not resize the underlying file.

Example

// assuming $img is an attached image
$img = changeimagesize($img, 300)        // 300px wide
$img = changeimagesize($img, 300, 400)   // 300x400px

textonimage(img,text,left,top[,text,left,top,...]): Overlays text strings over an image at given pixel offsets from the top-left corner.

Parameters

Image can be a URL or an uploaded image variable. Not screenreader-friendly — provide alt text on the image. Put "centerelements" anywhere after the image to center subsequent labels at their coordinates instead of using top-left anchoring. Alternate form: textonimage(img, array("Label A", 50, 30, "Label B", 150, 30)). You can use this helper tool to help you form the inputs.

Example

// $img is an uploaded image variable
$img = replacealttext($img, "A diagram of a field with width $w ft and height $h ft.")
$result = textonimage($img, "$w ft", 50, 30, "$h ft", 150, 80)

// Centered labels:
$result = textonimage($img, "centerelements", "A", 100, 50, "B", 200, 50)

// answerboxes on image. use [AB0], [AB1] etc for multipart 
// define $readerlabel for each to describe what its the input for
$img = replacealttext($img, "A right triangle with legs $a and $b. The hypotenuse is unknown.")
$res = textonimage($img, $a,50,80, $b,20,50, "[AB]",60,60)
$readerlabel = "The hypotenuse of the triangle"

addimageborder(image, [border width, margin]): Adds a border to an uploaded image. Border width defaults to 1px, margin defaults to 0.
Example
```
$img2 = addimageborder($img)         // default 1px border
$img2 = addimageborder($img, 2, 5)   // 2px border, 5px whitespace margin
```

arraystodoteqns(xarray,yarray,[color]): Converts arrays of x and y values into a dot funcstring for use in showplot.

Example

$xs = array(1,2,3,4)
$ys = calconarray($xs, "x^2")
$dots = arraystodoteqns($xs, $ys, "blue")
$g = showplot($dots, "0:-1", 5, "0:-2", 20, "1:2", "1:2")

connectthedots(xarray,yarray,[color,thickness,startmarker,endmarker]): Converts arrays of x and y values into a connected-line funcstring for showplot.
Example
```
$xs = array(0,1,2,3)
$ys = array(0,2,1,3)
$lines = connectthedots($xs, $ys, "red")
$g = showplot($lines, -1, 4, -1, 4)
```

arraystodots(xarray,yarray): Converts arrays of x and y values into a form suitable for use as the answer to a Drawing question.

Example

$answerformat = "twopoint,dot"
$xs = array(1,2,3)
$ys = array(1,4,9)
$answers = arraystodots($xs, $ys) // an $answers for a Drawing question

gettwopointlinedata(stuans, [xmin, xmax, ymin, ymax, drawing width, drawing height]) or gettwopointlinedata(stuans, [grid, snaptogrid]): Extracts two-point line data from a Drawing question student answer. Returns an array of lines, each as array(x1,y1,x2,y2).

Example

$answerformat = "twopoint,line"
$grid = "-5,5,-5,5"
$snaptogrid = .5
if (stuansready($stuanswers, $thisq, null, 'draw')) {
  $lines = gettwopointlinedata($stuanswers[$thisq], $grid, $snaptogrid)
  if (count($lines)==1) {
    // $lines[0] = array(x1, y1, x2, y2) for the first line drawn
    $slope = ($lines[0][3] - $lines[0][1]) / ($lines[0][2] - $lines[0][0])
  }
}

gettwopointdata(stuans, type, [xmin, xmax, ymin, ymax, drawing width, drawing height]) or gettwopointdata(stuans, type, [grid, snaptogrid]): Extracts two-point control data from a Drawing question for a specific curve type. Returns an array of curves, each as array(x1,y1,x2,y2).
Parameters

Type should be one of: 'line', 'lineseg', 'ray', 'parab', 'halfparab', 'horizparab', 'sqrt', 'cubic', 'cuberoot', 'rational', 'exp', 'genexp', 'log', 'genlog', 'sin', 'cos', 'abs', 'vector', 'circle', 'ellipse', 'rect'. Points are returned in click order — for 'parab', the first point is the vertex; for 'rect', the two opposite corners. 'genexp'/'genlog' return a 5th array entry for the asymptote value. Use 'circlerad' to return array(x-center, y-center, radius), 'ellipserad' for array(x-center, y-center, x-radius, y-radius), or 'rectdim' for array(width, height).
Example
```
$answerformat="twopoint,parab"
if (stuansready($stuanswers, $thisq, null, 'draw')) {
  $curves = gettwopointdata($stuanswers[$thisq], 'parab');
  // For a parabola: $curves[0] = array(x_vertex, y_vertex, x_point, y_point)
  if (count($curves)>0) {
	$vx = $curves[0][0];
	$vy = $curves[0][1];
  }
}
```
gettwopointformulas(stuans, type, [xmin, xmax, ymin, ymax, drawing width, drawing height]) or gettwopointformulas(stuans, type, [grid, snaptogrid]): Returns algebraic formulas for curves drawn in a Drawing question. Returns an array of expression strings (functions of x).
Parameters

Type should be one of: 'line', 'lineseg', 'ray', 'parab', 'halfparab', 'horizparab', 'sqrt', 'cubic', 'cuberoot', 'rational', 'exp', 'genexp', 'log', 'genlog', 'sin', 'cos', 'abs', 'circle', 'ellipse'. For 'horizparab', output is in terms of y. For 'circle'/'ellipse', output is an expression in x and y equaling 1. Add a final argument 'showequation' (optionally with custom variable names like 'showequation,x,y') to return implicit equations.
Example
```
$answerformat = "twopoint,sqrt"
$grid = "-5,5,-5,5"
$snaptogrid = .5
if (stuansready($stuanswers, $thisq, null, 'draw')) {
  $formulas = gettwopointformulas($stuanswers[$thisq], 'sqrt', $grid, $snaptogrid)
  // $formulas[0] is a string like "3*sqrt(x-2)"
  $eqns = gettwopointformulas($stuanswers[$thisq], 'sqrt', $grid, $snaptogrid, 'showequation,t,y')
  // $eqns[0] is a string like "y=2*sqrt(t+1)"
}
```
getdotsdata(stuans, [xmin, xmax, ymin, ymax, drawing width, drawing height]) or getdotsdata(stuans, [grid, snaptogrid]): Extracts the closed dots from a Drawing question. Returns an array of dots, each as array(x, y).
Example
```
if (stuansready($stuanswers, $thisq, null, 'draw')) {
  $dots = getdotsdata($stuanswers[$thisq]);
  // $dots[0] = array(x, y) of the first closed dot
}
```
getopendotsdata(stuans, [xmin, xmax, ymin, ymax, drawing width, drawing height]) or getopendotsdata(stuans, [grid, snaptogrid]): Extracts the open dots from a Drawing question. Returns an array of dots, each as array(x, y).
Example
```
if (stuansready($stuanswers, $thisq, null, 'draw')) {
  $dots = getopendotsdata($stuanswers[$thisq]);
  // $dots[0] = array(x, y) of the first open dot
}
```
getlinesdata(stuans, [xmin, xmax, ymin, ymax, drawing width, drawing height]) or getlinesdata(stuans, [grid, snaptogrid]): Extracts freehand line or polygon data from a Drawing question. Returns an array of curves, where each curve is an array of array(x,y) points.
Example
```
if (stuansready($stuanswers, $thisq, null, 'draw')) {
  $lines = getlinesdata($stuanswers[$thisq]);
  // $lines[0] = array of points for the first curve
  // $lines[0][0] = array(x, y) of the first point on that curve
}
```
getineqdata(stuans, [type, xmin, xmax, ymin, ymax, drawing width, drawing height]) or getineqdata(stuans, [grid, snaptogrid]): Extracts inequality data from a Drawing question. Returns an array of curves, each as array(style, x1, y1, x2, y2, x3, y3).
Parameters

Type should be 'linear' or 'quadratic'. style will be 'ne' for strict inequality (dashed border) or 'eq' for inequality with equality (solid border).
Example
```
if (stuansready($stuanswers, $thisq, null, 'draw')) {
  $ineqs = getineqdata($stuanswers[$thisq], 'linear', $grid, $snaptogrid);
  // $ineqs[0][0] = 'ne' or 'eq' (dashed or solid border)
  // $ineqs[0][1..6] = x1,y1,x2,y2,x3,y3 of the three control points:
  //   (x1,y1) and (x2,y2) for the line, (x3,y3) for the shading point
}
```
getsnapwidthheight(xmin, xmax, ymin, ymax, drawing width, drawing height, snaptogrid): Returns an adjusted drawing width and height that guarantees snap-to-grid values fall on exact pixel boundaries.
Example
```
$dims = getsnapwidthheight(-5, 5, -5, 5, 200, 200, 0.5)
// Use $dims[0] as width and $dims[1] as height where you need the actual width and height
```
Note: You generally can avoid needing to use this function by passing $grid and $snaptogrid to any of the get___data functions above, rather than passing the width and height. In some cases you might want to use this function to determine a more exact width and height to use in the $grid to ensure pixel-perfect snapping.

Format Macros

The following macros help with formatting values for display:

makepretty(string or array of strings): Changes double add/subtract signs to a single sign (e.g. "3+-2" → "3-2", "5--3" → "5+3").
Example
```
$a = rand(-5,5)
$nice = makepretty("x+$a")    // "x+3" or "x-2" depending on sign of $a
```
makeprettydisp(string or array of strings): Does makepretty and wraps the result in backticks for math display.
Example
```
$a = rand(-5,5)
$disp = makeprettydisp("(x+$a)/7");  // e.g. "`(x-3)/7`"
```
polymakepretty and polymakeprettydisp: Like makepretty but for polynomials — also cleans up 0*, 1*, ^1, and ^0. Test carefully; can behave unexpectedly with non-polynomial expressions.
Example
```
$a = rand(1,5)
$poly = "$a x^2 + 0 x + 1 x^0"
$nice = polymakepretty($poly);    // e.g. "3x^2+1" or "x^2+1"
$disp = polymakeprettydisp($poly); // backtick-wrapped math display version
```
makexpretty and makexprettydisp: (deprecated — use makexxpretty instead) Like makepretty but also cleans up 1*, 0*, etc. Can cause unexpected results; test carefully.
makexxpretty and makexxprettydisp: Like makepretty but also cleans up 1*, 0*, x^1, x^0, etc. Cannot handle |x| notation — use abs(x) instead. Test carefully.
Example
```
$expr = "1*x^2+0*x^1+1*x^0"
$nice = makexxpretty($expr)     // "x^2+1"
$disp = makexxprettydisp($expr) // math display version
```
simplifyexpr(expr,[vars,level,implicit]) Cleans up an expression and can do some simplification.
Parameters
- expr: the expression to simplify
- vars: (default "x") comma-separated list of variables.
- level: (default 0) the level of simplification:
  - 0 (default): Basic cleanup. Removes 1*, 0*, ^0, ^1, /1, cleans up +-. Also removes un-needed parens. (e.g. (1)(x^1)sin(x) -> x sin(x))
  - 1: Combine like terms with integer/decimal coefficients (e.g. 3x+x+3+5/2 -> 4x+3+5/2)
  - 2: Combine like terms, evaluating powers and adding fractional coefficients. (e.g. 3x+x+3+5/2 -> 4x+11/2)
  - 3: Also simplifies products/quotients with the same base. (e.g. 5x^2*2x^5 -> 10x^7, x/x^2 -> 1/x)
- implicit: (default true) whether to use implicit multiplication. Set false to add explicit *.
Example
```
simplifyexpr("1x^2+0x+(3)")              // "x^2+3"
simplifyexpr("2x+5+3y+(4x-1)","x,y",1)   // "6x+4+3y"
simplifyexpr("1/2x+1/4x+1+1/2^2","x",2)  // "3/4x+5/4"
simplifyexpr("(6xy)/(8y^3)","x,y",3)     // "(3x)/(4y^2)"
```
makepretynegative(string): Wraps negative terms in parentheses — e.g. "3+-4" → "3+(-4)" and "3--4" → "3-(-4)". Note: "3-+4" becomes "3-4".
Example
```
$b = rand(-5,-1)  // a negative number
$expr = "3+$b"      // like "3+-4"
$nice = makepretynegative($expr) // "3+(-4)"
```

numtowords(number,[addth, numwithTh, addcommas]): Converts a number to its word representation.

Example

numtowords(1203)              // "one thousand two hundred three"
numtowords(1203, true)        // "one thousand two hundred third"  (ordinal)
numtowords(1203, false, true) // "1203rd"  (numeric with ordinal suffix)
numtowords(1203, false, false, true) // "one thousand, two hundred three"  (with comma)

fractowords(numerator,denominator,[options]): Converts a fraction to its word representation. By default reduces to integers if possible.

Parameters

Options is a string combining any of: 'mixed' (mixed number output), 'literal' (suppress simplifications), 'over' or 'by' (connect with that word), 'hyphen' (hyphenate the fraction). If both 'over' and 'by' are given, 'over' wins. If both 'mixed' and 'literal' are given, 'mixed' wins.

Example

fractowords(5, -2)             // "negative five halves"
fractowords(6, 3)              // "two"  (reduced to integer)
fractowords(6, 3, 'literal')  // "six thirds"  (no simplification)
fractowords(2, 3, 'hyphen')   // "two-thirds"
fractowords(3, 4, 'by')       // "three by four"
fractowords(3, 4, 'over')       // "three over four"
fractowords(-7, 4, 'mixed')   // "negative one and three fourths"
fractowords(-7, 4, 'mixed over') // "negative one and three over four"

numtoroman(number,[uppercase]): Converts a number (0.5–3999.5) to a Roman numeral string. Defaults to uppercase; pass false for lowercase.
Example
```
numtoroman(14)        // "XIV"
numtoroman(14, false) // "xiv"
numtoroman(1999)      // "MCMXCIX"
```
prettyint(number): Formats an integer with comma thousands separators. Returns a string for display only, not for calculations.
Example
```
prettyint(1234567)  // "1,234,567"
prettyint(1000)     // "1,000"
```
prettyreal(number,decimals,[comma]): Formats a number with comma thousands separators and a fixed number of decimal places. Returns a string for display only. Set comma to "" to suppress the thousands separator.
Example
```
prettyreal(1234.567, 2)     // "1,234.57"
prettyreal(1.8, 3)          // "1.800"
prettyreal(1234.5, 2, "")   // "1234.50"  (no comma)
```
prettyreal_instring(string,decimals,[comma]): Applies prettyreal formatting to every number found within a string.
Example
```
prettyreal_instring("The value is 1234.567 dollars", 2)
// "The value is 1,234.57 dollars"
```
round_instring(string,[decimals]): Rounds every number within a string to the specified decimal places (nearest whole number if omitted).
Example
```
round_instring("Pi is about 3.14159", 3) // "Pi is about 3.142"
round_instring("roughly 3.7 people", 0)  // "roughly 4 people"
```
prettysmallnumber(number, [space]): Displays very small numbers in decimal form instead of scientific notation. Set space to true to add spaces every 3 decimal places.
Example
```
prettysmallnumber(0.0000002)       // "0.0000002"  (not "2E-7")
prettysmallnumber(0.0000002, true) // "0.000 000 2"
```
prettysigfig(number,sigfigs,[comma,choptrailingzeros,scinot,sigfigbar]): Rounds a number to the specified significant figures for display. For rounding for calculations, use roundsigfig instead.
Parameters
- comma: By default adds comma thousands separators; set comma to "" to suppress.
- choptrailingzeros: set true to remove trailing decimal zeros even if significant.
- scinot: set true to display in scientific notation.
- sigfigbar: set true to put an overline on the last significant zero (e.g. 4200 for 3 sig figs) — use in math display only.
Example
```
prettysigfig(12345.6, 3)              // "12,300"
prettysigfig(0.00456, 2)             // "0.0046"
prettysigfig(123, 4)                 // "123.0"
prettysigfig(123, 4, ",", true)      // "123"
prettysigfig(12345.6, 3, "", false, true) // "1.23*10^4"  (sci notation)
```
prettysigfig_instring(string,sigfigs,[comma,choptrailingzeros,scinot,sigfigbar]): Applies prettysigfig rounding to every number found within a string.
Example
```
prettysigfig_instring("The mass is 1234.56 kg", 3) // "The mass is 1,230 kg"
```
makescinot(number,[decimals,format]): Converts a number to scientific notation. Optionally rounds the mantissa to the given decimal places. Format can be "*" or "E" as alternatives to the default multiplication cross.
Example
```
makescinot(1234.5)       // "1.2345 xx 10^3"
makescinot(1234.5, 2, '*')   // "1.23*10^3"
makescinot(1234.5, 2, "E") // "1.23E3"
```

prettytime(value,informat,outformat): Converts a time value to a readable string. informat is 'h', 'm', or 's' (the unit of the input). outformat is any combination of 'h', 'm', 's', or 'clock'/'sclock'.

Example

prettytime(90, 'm', 'hm')     // "1 hour and 30 minutes"
prettytime(3661, 's', 'hms')  // "1 hour, 1 minute, and 1 second"
prettytime(754, 'm', 'clock') // "12:34pm"
prettytime(754, 'm', 'sclock') // includes seconds: "12:34:00pm"

dispreducedfraction(numerator,denominator,[doubleslash,variable in numerator]): Returns a reduced fraction already formatted for display (wrapped in backticks). Set doubleslash to true for "3//4" format. Set variable in numerator to include a variable like pi.
Example
```
dispreducedfraction(6, 9)         // "`2/3`"
dispreducedfraction(3, 4, true)   // "`3//4`"
dispreducedfraction(2, 3, false, 'pi') // "`(2pi)/3`"
```
makereducedfraction(numerator,denominator,[doubleslash,variable in numerator]): Same as dispreducedfraction but returns a value suitable for use in $answer (not pre-formatted for display). Pass 'parts' as the third argument to get an array of [numerator, denominator] instead.
Example
```
makereducedfraction(6, 9)           // "2/3"
makereducedfraction(3, 4, true)     // "3//4"
makereducedfraction(6, 9, false, 'pi') // "(2pi)/3"

// Get reduced parts as separate values:
$num,$den = makereducedfraction(6, 9, 'parts'); // $num=2, $den=3
```
decimaltofraction(decimal,[format,maxden]): Converts a decimal to a fraction string. Can use format="mixednumber" to get a mixed number rather than improper fraction. Only works for denominators up to maxden (default 5000).
Example
```
decimaltofraction(0.75)                  // "3/4"
decimaltofraction(1.5)                   // "3/2"
decimaltofraction(1.5, 'mixednumber')    // "1 1/2"
```
htmldisp(string,[variables]): Uses HTML superscripts/subscripts and italics for simple math display, without invoking the full math typesetter.
Example
```
htmldisp("x_1^2 + x_2^2")        // renders subscripts and superscripts in HTML
htmldisp("x^2 + y^2", "x,y")    // also italicizes the variables x and y
```
Note: It's usually better for accessibility to use the math renderer (wrap the expression in backticks).

formatcomplex(real,imag): Creates a display string for a complex number from its real and imaginary parts.

Example

formatcomplex(2, 3)   // "2+3i"
formatcomplex(2, -3)  // "2-3i"
formatcomplex(0, 1)   // "i"
formatcomplex(3, 0)   // "3"

rawurlencode(string): Encodes a string for safe use in a URL query string.
Example
```
rawurlencode("hello world!") // "hello%20world%21"
```

String Macros

These macros help with working with strings:

stringappend(value,string): Appends string to value. If value is an array, string is appended to each element.
Example
```
stringappend("hello", " world")    // "hello world"
stringappend(array("cat","dog"), "s") // array("cats","dogs")
```
stringprepend(value,string): Prepends string to value. If value is an array, string is prepended to each element.
Example
```
stringprepend("world", "hello ")    // "hello world"
stringprepend(["A","B"], "$")  // array("$A","$B")
```
today([string]): Returns today's date. Defaults to "Month D, YYYY" format. See PHP date format codes for custom formats.
Example
```
today()          // "July 3, 2026"
today("Y-m-d")  // "2026-07-03"
today("D, M j") // "Tue, Jul 3"
```
stringpos(needle,haystack): Returns the position (0-indexed) of needle in haystack. Returns -1 if not found.
Example
```
stringpos("lo", "hello")   // 3
stringpos("xyz", "hello")  // -1  (not found)
```
stringlen(string): Returns the number of characters in the string.
Example
```
stringlen("hello")  // 5
stringlen("")       // 0
```
stringclean(string,[mode]): Cleans up a string. Mode 0 (default): trim whitespace. Mode 1: remove all whitespace. Mode 2: remove all non-alphanumeric characters.
Example
```
stringclean("  hello  ")     // "hello"
stringclean("h e l l o ", 1) // "hello"
stringclean("hi there! 2", 2) // "hithere2"
```
substr(string,start,[length]): Extracts a portion of the string. Negative start counts from the end. Negative length omits that many characters from the end.
Example
```
substr("hello abc", 6)      // "abc"
substr("hello abc", 0, 5)   // "hello"
substr("hello abc", -3)     // "abc"
substr("hello abc", 6, -1)  // "ab"
```
strtoupper(string): Converts all characters to uppercase.
Example
```
strtoupper("hello")  // "HELLO"
```
ucfirst(string): Capitalizes the first character of the string.
Example
```
ucfirst("hello world")  // "Hello world"
```
strtolower(string): Converts all characters to lowercase.
Example
```
strtolower("HELLO")  // "hello"
```
lcfirst(string): Lowercases the first character of the string.
Example
```
lcfirst("Hello World")  // "hello World"
```
substr_count(haystack,needle): Counts how many times needle appears in haystack.
Example
```
substr_count("hello world", "l")  // 3
substr_count("aababc", "ab")      // 2
```

str_replace(search,replace,string): Replaces all occurrences of search in string with replace. Search and replace can be arrays for bulk replacement.

Example

str_replace("cat", "dog", "I have a cat")  // "I have a dog"

// Array replacement:
str_replace(array("cat","dog"), array("feline","canine"), "I have a cat and a dog")
// "I have a feline and a canine"

preg_match(pattern,subject,[matches]): Tests subject against a regular expression. Returns true/false, and stores the full match and capture groups in matches.
Example
```
$found = preg_match("/\d+/", "abc123", $m);
// $found = true, $m[0] = "123"

$found = preg_match("/^[a-z]+$/", "hello", $m);
// $found = true (all lowercase letters)
```
preg_match_all(pattern,subject,[matches, flags, offset]): Finds all matches of a regular expression in subject. Returns the count of matches. See PHP help for optional flags.
Example
```
$count = preg_match_all("/\d+/", "abc 12 def 34", $m);
// $count = 2, $m[0] = array("12","34")
```

preg_replace(pattern,replacement,subject,[limit]): Replaces all regex matches in subject with replacement.

Example

preg_replace("/\s+/", "_", "hello world foo")  // "hello_world_foo"
preg_replace("/\d+/", "NUM", "abc 12 def 34")  // "abc NUM def NUM"

levenshtein(string1,string2): Finds the Levenshtein distance between two strings.
Example
```
levenshtein("hello","help")  // 2; one deletion, one replacement
```

Array Macros

These macros are for working with arrays:

listtoarray(list, [tonum]): Converts a comma-separated list string to an array. Set tonum to true to ensure numeric values are treated as numbers.

Example

listtoarray("1,2,3,4")         // array("1","2","3","4")
listtoarray("red,green,blue")  // array("red","green","blue")
listtoarray("1,2,3,4", true)   // array(1,2,3,4)  (as numbers)

calclisttoarray(list): Converts a list of calculation expressions to an array, evaluating each one.
Example
```
calclisttoarray("2^2,3^2,4^2")  // array(4,9,16)
calclisttoarray("pi,3/2")      // array(3.14159..., 1.5)
```

explode(symbol, string): Splits a string into an array using the given delimiter.

Example

explode(",", "a,b,c")   // array("a","b","c")
explode(":", "x:y:z")   // array("x","y","z")

arraytolist(array, [space]): Converts an array to a comma-separated string. Set space to true to add a space after each comma.
Example
```
arraytolist(array(1,2,3))        // "1,2,3"
arraytolist(array(1,2,3), true)  // "1, 2, 3"
```

joinarray(array,[symbol,ksort]): Joins array elements into a string using the given symbol (default: comma). Set ksort to true to sort by key first, useful if elements were defined out of order.

Example

joinarray(array("a","b","c"))          // "a,b,c"
joinarray(array("a","b","c"), " + ")   // "a + b + c"
joinarray(array("x","y"), " and ")     // "x and y"

$a[2]="c";$a[0]="a";$a[1]="b";
$g = joinarray($a)    // "c,a,b" in order defined
$g = joinarray($a,",",true)  // "a,b,c" ordered by key/index

stringtoarray(string, [tonum]): Converts a string to an array of individual characters. Set tonum to true if all characters are digits.
Example
```
stringtoarray("abc")         // array("a","b","c")
stringtoarray("123", true)   // array(1,2,3)
```

fillarray(value,num,[start]): Creates an array filled with the same value. Indexing starts at 0 unless start is specified. num can also be an array of indices to set.

Example

fillarray(0, 5)              // array(0,0,0,0,0)
fillarray("x", 3, 2)        // array(2=>"x", 3=>"x", 4=>"x")
fillarray(1, array(0,2,4))  // array(0=>1, 2=>1, 4=>1)

// for a multipart question with 5 number parts:
$anstypes = fillarray("number",5)

consecutive(min,max,[step]): Creates an array of evenly spaced numbers from min to max.

Example

consecutive(1, 5)        // array(1,2,3,4,5)
consecutive(0, 1, .25)  // array(0, 0.25, 0.5, 0.75, 1)
consecutive(2, 10, 2)   // array(2,4,6,8,10)

arraysetvalues(array,keyarray,value/valuearray): Sets values in an existing array at the specified keys. Returns the modified array.

Example

// Set a single value at multiple keys:
$arr = fillarray(0, 5);  // array(0,0,0,0,0)
$arr = arraysetvalues($arr, array(1,3), 99);    // array(0,99,0,99,0)

// Set different values at each key:
$arr = fillarray(0, 5);  // array(0,0,0,0,0)
$arr = arraysetvalues($arr, array(0,2), array(10,20)); // array(10,0,20,0,0)

// If you had 10 large inputs and two small ones at parts 3 and 7:
$answerboxsize = fillarray(20, 10)  // 10 inputs, size 20
$answerboxsize = arraysetvalues($answerboxsize, [3,7], 5)  // set index 3 and 7 to size 5.

sortarray(list/array,[type, maxkey]): Sorts an array from lowest to highest. Use second argument "rev" for descending by value, "key" to sort by key, or "keyfill" to sort by key and fill missing keys with empty string. When using "keyfill" you can optionally provide a maxkey to fill past the existing range.
Example
```
sortarray(array(3,1,4,1,5))          // array(1,1,3,4,5)
sortarray(array(3,1,4,1,5), "rev")  // array(5,4,3,1,1)

$a = ['c'=>1, 'a'=>4, 'b'=>5]
sortarray($a, 'key')  // array("a" => 4, "b" => 5, "c" => 1)

$b[0]=3; $b[5]=2; $b[2]=5; 
sortarray($b, 'keyfill', 7) // array(3,"",5,"","",2,"","")
```
jointsort(array,array,[array,...]): Reorders two or more arrays together based on a lowest-to-highest sort of the first array's values.
Example
```
$xs = array(3,1,2)
$ys = array(9,1,4)
$xs,$ys = jointsort($xs,$ys)  // $xs=array(1,2,3), $ys=array(1,4,9)
```
calconarray(array,calculation): Applies a calculation to each element of an array. Use "x" to represent each element.
Example
```
$a = consecutive(1,4)
$b = calconarray($a, "x^2")    // array(1,4,9,16)
$c = calconarray($a, "2*x+1")  // array(3,5,7,9)
```
multicalconarray(calculation,varslist,var1array,var2array,...): Like calconarray but supports multiple variables, one per array.
Example
```
$xs = array(1,2,3)
$ys = array(4,5,6)
$zs = multicalconarray("x*y", "x,y", $xs, $ys)  // array(4,10,18)
```

calconarrayif(array,calculation,ifcondition): Like calconarray but only applies the calculation to elements that satisfy the condition; others are left unchanged.

Example

$a = array(1,2,3,4,5)
$b = calconarrayif($a, "x^2", "x>3")  // array(1,2,3,16,25)
// Only squares elements greater than 3

$b = calconarrayif($a,"x+.1","floor(x)==x")
// will add .1 to add whole numbers in the array, and leave the other elements unchanged.

keepif(array,condition): Filters an array, returning only elements that satisfy the condition. Use "x" for each element.

Example

$a = array(1,2,3,4,5,6);
keepif($a, "x%2==0")  // array(2,4,6)  — keep only even numbers
keepif($a, "x>3")     // array(4,5,6)

subarray(array,params): Creates a new array as a subset of the original.
Parameters
The params can take several forms:
- subarray($a,2,4,6): picks $a[2], $a[4], $a[6]
- subarray($a,"1:3","6:8"): picks $a[1] through $a[3] and $a[6] through $a[8]
- subarray($a,$b): picks entries from $a at the indices listed in array $b
Example
```
$a = array(10,20,30,40,50);
subarray($a, 1, 3)       // array(20,40)
subarray($a, "1:3")      // array(20,30,40)
subarray($a, array(0,2,4)) // array(10,30,50)
```

splicearray(array,offset,length,[replacement]): Removes elements at offset for length positions, optionally replacing them with new values.

Example

$a = array(5,6,7,8,9);
splicearray($a, 1, 2)                      // array(5,8,9)  (removed 2 elements at index 1)
splicearray($a, 1, 2, array(20,30))        // array(5,20,30,8,9)

mergearrays(array,array,[array,...]): Concatenates two or more arrays into one.
Example
```
$a = array(1,2,3)
$b = array(4,5,6)
mergearrays($a, $b)  // array(1,2,3,4,5,6)
```
unionarrays(array,array): Combines two arrays, removing duplicate values.
Example
```
unionarrays([1,2,3], [2,3,4])  // array(1,2,3,4)
```
intersectarrays(array,array): Returns elements that appear in both arrays.
Example
```
intersectarrays(array(1,2,3,4), array(2,4,6))  // array(2,4)
```
diffarrays(array1,array2): Returns elements from array1 that do not appear in array2.
Example
```
diffarrays(array(1,2,3,4), array(2,4))  // array(1,3)
```
array_unique(array): Removes duplicate values from an array. Note: does not re-index — follow with array_values if you need consecutive keys.
Example
```
array_unique([1,2,2,3,3,3])  // array(1,2,3)  (possibly non-consecutive keys)
array_values(array_unique(array(1,2,2,3,3,3)))  // re-indexed: [0,1,2]
```
array_values(array): Returns array values re-indexed with consecutive numeric keys starting at 0.
Example
```
array_values(array(2=>"a", 5=>"b", 8=>"c"))  // array(0=>"a", 1=>"b", 2=>"c")
```
array_keys(array): Returns the keys of an array as a new array.
Example
```
array_keys(array("x"=>1, "y"=>2, "z"=>3))  // array("x","y","z")
```
count(array): Returns the number of elements in the array.
Example
```
count(array(10,20,30,40))  // 4
```
is_array(variable): Returns true if the variable is an array, false otherwise.
Example
```
is_array(array(1,2,3))  // true
is_array(5)             // false
```
sumarray(array): Returns the sum of all elements in the array.
Example
```
sumarray(array(1,2,3,4,5))  // 15
```
in_array(needle,haystack): Returns true if needle is found anywhere in the haystack array.
Example
```
in_array(3, array(1,2,3,4,5))          // true
in_array("red", array("blue","green"))  // false
```

arrayfindindex(needle,haystack): Returns the index of the first occurrence of needle in haystack.

Example

arrayfindindex("green", array("red","green","blue"))  // 1
$a = arrayfindindex(4, [3,4,5,4]) // 1, since that is the index of the first 4

arrayfindindices(needle,haystack): Returns an array of all indices where needle appears in haystack.

Example

arrayfindindices("x", array("x","y","x","z","x"))  // array(0,2,4)
$a = arrayfindindex(4, [3,4,5,4]) // array(1,3)

array_flip(array): Swaps keys and values in a one-to-one array.

Example

array_flip(array("a"=>1, "b"=>2, "c"=>3))  // array(1=>"a", 2=>"b", 3=>"c")

print_r(array, [return]): Outputs an array in readable form for debugging. Pass true as second argument to return the output as a string instead of printing it.
Example
```
print_r($a)              // prints array structure in question warning output
$s = print_r($a, true);  // store as string, then include $s in question text
```

General Macros

These macros are fairly general purpose:

ifthen(condition,trueval,falseval): Returns trueval if condition is true, falseval otherwise. Useful for inline conditionals without a full if/else block.
Example
```
$a = rand(1,10);
$desc = ifthen($a > 5, "large", "small");  // "large" or "small"
$sign = ifthen($a >= 0, "positive", "negative");
```
cases(testvalue,comparearray,outputarray,[defaultoutput, tolerance]): Looks up testvalue in comparearray and returns the corresponding entry from outputarray. Returns defaultoutput if no match is found. Numeric comparisons use tolerance; string comparisons are exact.
Parameters

Tolerance defaults to 0.0015 relative error. Prefix with | for absolute tolerance, like "|0.1". String comparison is exact — "0.5" will not match 1/2.
Example
```
$n = rand(1,4);
$word = cases($n, array(1,2,3,4), array("one","two","three","four"));
// if $n=3, returns "three"

// With default fallback:
$result = cases($n, array(1,2), array("yes","no"), "other");
// returns "other" if $n is neither 1 nor 2
```

formhoverover(label,tip): Creates a word or phrase with a tooltip that appears on hover.

Example

$def = formhoverover("compound interest", "Interest calculated on principal and accumulated interest");
// Place $def in question text to show a tooltip on hover

formpopup(label,content,[width,height,style,scrollbars]): Creates a link or button that opens a popup window. Content can be a URL or HTML string. Style can be "link" or "button"; scrollbars defaults to false.
Example
```
$popup = formpopup("See formula", "A = P(1 + r/n)^(nt)");
$popup = formpopup("Help", "https://example.com/help", 400, 300, "button");
```
forminlinebutton(label,content,[style,outputstyle]): Creates a link or button that reveals hidden content inline. Style can be "link" or "button". Outputstyle can be "inline" (stays on same line) or "block" (new line, allows any HTML).
Example
```
$hint = forminlinebutton("Show hint", "Try factoring the numerator.", "button");
$note = forminlinebutton("Note", "Remember to simplify.", "link", "inline");
```

makenumberrequiretimes(array/list): Generates a $requiretimes string ensuring every number in the array must appear in the student answer.

Example

$requiretimes = makenumberrequiretimes(array(2, 3, 3, 12)) // "#2,=1,#3,=2,#12,=1"
// $requiretimes ensures 2, 3, and 12 all appear in the student's answer

ABarray(start, num): Produces an array of [AB#] placeholders that get replaced with answer boxes in question text. Often used with showarrays to embed answer boxes in a table.

Example

$boxes = ABarray(5, 3);  // array("[AB5]","[AB6]","[AB7]")

// Embed answer boxes in a table:
$anstypes = fillarray("number", 3)
$xs = array(1,2,3);
$table = showarrays("x", $xs, "y", ABarray(0,3));

getntupleparts(string, [expected number of components, checknumeric]): Extracts the components from an N-tuple student answer string, returning them as an array. Returns false if the input is not a valid n-tuple. Does not work on lists of n-tuples. It is recommended to provide a second argument of the number of components expected, and if the values are expected to be numeric, put true as the third argument.

Example

if (stuansready($stuanswers, $thisq, null)) {
  $parts = getntupleparts($stuanswers[$thisq], 2, true)
  // For student answer "(3,4)": $parts = array(3,4)
  // Returns false if input is not a valid ntuple
  if ($parts !== false) {
    $x = $parts[0]
    $y = $parts[1]
  }
}

// for calculated n-tuple question, use $stuanswervals to get decimal values
// if student entered "(3/4, 5)" 
getntupleparts($stuanswers[$thisq],2)          // array("3/4", "5")
getntupleparts($stuanswersval[$thisq],2,true)  // array(0.75, 5)

scoremultiorder(stua, answer, swap, type, [weights, options]): In a multipart question, allows specified parts to be answered in any order. Works for types 'number', 'string', 'calculated', 'numfunc', 'complex', 'calccomplex', 'ntuple', and 'calcntuple'. Note: The "list" option on individual question types is strongly preferred for most multi-answer situations.
Parameters
- stua: For numeric types, use $stuanswers[$thisq]. For calculated types, use $stuanswersval[$thisq].
- answer: Always $answer. Must be called after $answer is defined.
- swap: Which answer indices are interchangeable. Examples:
  - '0;1' — parts 0 and 1 are swappable
  - '0;1;2' — parts 0, 1, and 2 are all swappable
  - ['0;1','2;3'] — 0↔1 and 2↔3 independently
  - '0,1,2;3,4,5' — the group [0,1,2] is swappable with the group [3,4,5]. Comparison is only made on the first entry to decide whether to swap the groups.
- type: The part type short name, like 'number' or 'calccomplex'. When swapping groups, use the part type for the first entry in the group.
- weights: Optionally pass $answeights to have weights swapped along with answers (set weights to null to skip).
- options: Array of extra options. Use ['variables'=>$variables] when type is 'numfunc'.
Example
```
// Allow parts 0 and 1 to be answered in either order:
$answer = scoremultiorder($stuanswers[$thisq], $answer, '0;1', 'number');

// With weights also swapped:
$answer,$answeights = scoremultiorder($stuanswers[$thisq], $answer, '0;1', 'number', $answeights)

// numfunc with variables:
$answer = scoremultiorder($stuanswers[$thisq],$answer,'0;1','numfunc',null,['variables'=>$variables])

// based on choice in calculated part at index 0 and 3, swap groups 
$answer = scoremultiorder($stuanswersval[$thisq], $answer, '0,1,2;3,4,5', 'calculated');
```

scoreperiodic(answer, stuanswer, variable, [tolerance]): Helps score "all solutions" periodic answers (e.g. "pi/6+2pik") by accepting equivalent forms with a shifted base value (like "-11pi/6+2pik"). Returns a value to replace $answer. Always define $showanswer separately first so a clean answer shows in the key.

Example

// Single-part algebraic expression question:
$answerformat = "list";
$variables = "k";
$answer = "pi/6 + 2pik, pi/3+2pik";
$showanswer = "`$answer`";
$answer = scoreperiodic($answer, $stuanswers[$thisq], "k");
// "-11pi/6+2pik" will now be accepted as equivalent

// Multipart (part index 3, numfunc type):
$answer[3] = "pi/12 + pi/3*n";
$variables[3] = "n";
$showanswer[3] = "`$answer[3]`";
$answer[3] = scoreperiodic($answer[3], getstuans($stuanswers,$thisq,3), "n");

setupmathquillfillin(asciimath format, alt format): Creates fill-in answer boxes embedded inside a rendered math expression. Use in multipart questions: write the expression in ASCIIMath with [AB#] at each fill-in point, and provide a plain-text fallback for accessibility.
Parameters

Place the returned string in question text instead of $answerboxes. To show a single combined answer key, define $showanswer[lastpart] and place [SAB0-N] after the entry in the question text. Use $answerboxsize[part] to adjust box size. Set $showanswerstyle = "inline" to keep the key on the same line. The alt format string should be a plain text string using the same [AB#] inputs, which will be used for students who have disabled the equation editor for accessibility
Example
```
// Integral with three fill-in areas (lower limit, upper limit, integrand):
$anstypes = "number,number,numfunc"
$entry = setupmathquillfillin(
  "int_([AB0])^([AB1]) [AB2] dx",
  "The integral from [AB0] to [AB1] of [AB2] dx"
);
$showanswer[2] = "`int_$a^$b $func dx`"
// Place $entry in question text where the expression goes, [SAB0-2] after it
```

Math Macros

These macros are used for mathematical calculations:

sin(t), cos(t), tan(t), sec(t), csc(t), cot(t): The standard trig functions (input in radians).
Example
```
$a = sin(pi/6);  // 0.5
$b = cos(0);     // 1
$c = tan(pi/4);  // 1
```
arcsin(v), arccos(v), arctan(v), atan2(y,x): The inverse trig functions (output in radians). atan2 handles the full circle using the signs of both arguments.
Example
```
arcsin(0.5)   // pi/6 ≈ 0.5236
arccos(1)     // 0
arctan(1)     // pi/4 ≈ 0.7854
atan2(1, 1)   // pi/4  (first quadrant)
atan2(-1, 0)  // -pi/2
```
abs(v): Absolute value.
Example
```
abs(-5)  // 5
abs(3)   // 3
```

sqrt(t), root(n)(t): Square root and nth root.

Example

sqrt(16)    // 4
root(3)(8)  // 2  (cube root of 8)
root(4)(81) // 3

gcd(a,b,[c,d,...]): Greatest common divisor of two or more integers.
Example
```
gcd(12, 8)     // 4
gcd(12, 8, 6)  // 2
```
lcm(a,b,[c,d,...]): Least common multiple of two or more integers.
Example
```
lcm(4, 6)      // 12
lcm(3, 4, 6)   // 12
```
sign(a,[option]): Returns the sign of a. Without option: returns 1 or -1. With option true: returns "+" or "-". With option "onlyneg": returns "-" if negative, "" otherwise.
Example
```
sign(-7)           // -1
sign(3)            // 1
sign(-7, true)     // "-"
sign(3, true)      // "+"
sign(-7, "onlyneg") // "-"
sign(3, "onlyneg")  // ""
```
sgn(a): Returns -1, 0, or 1 depending on the sign of a (unlike sign, returns 0 for zero).
Example
```
sgn(-7)  // -1
sgn(0)   //  0
sgn(3)   //  1
```
hexdec(a): Converts a hexadecimal string to a decimal number.
Example
```
hexdec("1F")   // 31
hexdec("FF")   // 255
```
dechex(a): Converts a decimal integer to a hexadecimal string.
Example
```
dechex(31)   // "1f"
dechex(255)  // "ff"
```
v!: Factorial operator. Write as a postfix operator on a variable.
Example
```
$n = 5
$result = $n!  // 120
$result = 0!   // 1
```
evalfunc(func,vars,val1,val2,...,[falseonerror]): Evaluates a function string at given variable values. Returns false on invalid parameters; returns empty string (or false if falseonerror=true) on syntax errors.
Example
```
evalfunc("x^2", "x", 3)          // 9
evalfunc("x^2*y", "x,y", 2, 3)  // 12
evalfunc("x^2+x", "x", "sin(x)")  // (sin(x))^2+(sin(x))
```
evalnumstr(expr, [complex]): Evaluates a numerical expression string to a decimal. Useful when you already have a string for display and need its value, but avoid using this in place of direct calculation in most cases. Set complex to true for complex number expressions.
Example
```
evalnumstr("(2*pi)/3")  // ≈ 2.0944
evalnumstr("sqrt(2)+1") // ≈ 2.4142
evalnumstr("3/2+3i", true) // array(1.5,3)
```
See also: calconarray and multicalconarray in the Array Macros section

Conditional Test Macros

These macros are used to test various conditions. They typically return true or false, depending on whether the desired condition is met.

getstuans($stuanswers or $stuanswersval, $thisq, [part number]): Safely retrieves a student answer. Preferred over direct array access because it handles undefined values without triggering errors. Omit the part number for single-part questions.
Example
```
$ans = getstuans($stuanswers, $thisq)       // single-part question
$ans = getstuans($stuanswersval, $thisq, 2)  // numerical part index 2 of a calculated multipart
```
stuansready($stuanswers, $thisq, array of part numbers, [anstypes, answerformat]): Checks that the student has submitted non-blank answers for all specified parts. Wrap any code that uses student answers in an if block with this as the condition.
Parameters
- part numbers array
  - Use null for part numbers on a single-part question
  - Prefix a part number with ~ to allow a blank for that part.
  - Use "1 or 2" as a part number if either is sufficient.
- anstypes: Pass $anstypes as 4th argument to handle special cases like matrices, and to enable answerformat checks. For a single part question you can pass a string like 'number'
- answerformat: Pass $answerformat to check the student answer meets the answerformat (currently only checks Calculated and Calculated N-tuple questions, and no lists). Pass 'checknumeric' to also verify the answer is numeric (use $stuanswersval for the first argument for calculated/calcntuple types).
Example
```
// Single-part question:
if (stuansready($stuanswers, $thisq, null)) {
  // safe to use $stuanswers[$thisq]
}

// Multipart — require parts 0 and 1, allow part 2 to be blank:
if (stuansready($stuanswers, $thisq, array(0,1,"~2"), $anstypes)) {
  // process answers
}

// verify $stuanswers[$thisq] is a matrix with numeric entries
if (stuansready($stuanswers, $thisq, null, 'matrix', 'checknumeric')) {
  // verified
}

// verify a calculated answer represented a valid number 
if (stuansready($stuanswersval, $thisq, null, 'calculated', 'checknumeric')) {
  // $stuanswerval[$thisq] is a number
}
```

comparenumbers(a,b,[tol]): Compares two numbers or numerical expressions. Returns true if they are equivalent within the given tolerance. Set tol for relative tolerance (default 0.001) or prefix with | for absolute.

Example

comparenumbers(0.3333, 1/3)         // true  (within default 0.1% tolerance)
comparenumbers(1.001, 1, .01)      // true  (within 1% relative tolerance)
comparenumbers(1.5, 1.49, "|0.02") // true  (within 0.02 absolute)
comparenumbers("sqrt(4)", 2)       // true  (evaluates expressions)

comparenumberswithunits(a,b,[tol]): Compares two quantities that include units. Units do not have to match; "100 cm" and "1 m" are considered equivalent.
Parameters

Each value must be of the form: [number]*[unit]^[power]*[unit]^[power].../[unit]^[power].... 'per' may be used for division. 'unit squared', 'square unit', 'unit cubed', 'cubic unit' are accepted. Tolerance defaults to 0.1% (0.001) relative; prefix with | for absolute.
Example
```
comparenumberswithunits("3.45 feet", "3.5 feet", "|.1")      // true to .1 absolute tolerance
comparenumberswithunits("9.8 meters per second squared", "9.8 m/s^2") // true
comparenumberswithunits("100 cm", "1 m")      // true
comparenumberswithunits("100 cm", "100")      // false
```
comparecomplex(a,b,[tol]): Compares complex number expressions for equivalence. Handles any representation, so 'sqrt(-4)' equals '2i', 'e^(pi*i)' equals '-1'. Tolerance defaults to 0.001 relative; prefix with | for absolute.
Example
```
comparecomplex("2+3i", "2+3i")     // true
comparecomplex("sqrt(-4)", "2i")   // true
comparecomplex("e^(pi*i)", "-1")   // true
```
comparentuples(a,b,[tol],[option]): Compares two n-tuples for equivalence. By default also checks that the bracket type matches; pass option "ignoreparens" to treat (a,b) and [a,b] as equivalent. Tolerance defaults to 0.001 relative; prefix with | for absolute. Can make tol an array (or list) to apply by element to the ntuple.
Example
```
comparentuples("(1,2,3)", "(1,2,3)")                     // true
comparentuples("(1,2)", "[1,2]")                         // false  (brackets differ)
comparentuples("(1,2)", "[1,2]", .001, "ignoreparens")  // true
comparentuples("(1.005,2.02)", "(1,2)", array(.01,.1))          // true. different tol per element
```
comparefunctions(a,b,[vars,tol,domain]): Tests whether two algebraic expressions are equivalent.
Parameters
- a, b: the functions
- vars: a list of variables in the function (default "x")
- tol: defaults to 0.001 relative; prefix with | for absolute.
- domain: Set "xmin,xmax" to specify a domain for comparison, or "xmin,xmax,integers" to restrict to integer values.
Example
```
comparefunctions("x^2+2*x+1", "(x+1)^2")         // true
comparefunctions("sin(t)^2+cos(t)^2", "1", "t")       // true
comparefunctions("x*y", "y*x", "x,y")            // true  (multivariable)
comparefunctions("sqrt(x)", "x^(1/2)", "x", .001, "0,5")   // true, test domain adjusted
```
comparesameform(a,b,[vars]): Checks whether two expressions are in the same structural form, identical except for commutativity of +/*, multiplying by 1, implicit multiplication, and extra parentheses. This is picky, so use with caution.
Example
```
comparesameform("x+2", "2+x")        // true  (commutation ok)
comparesameform("2*(x+1)", "2*x+2")  // false  (expanded vs factored)
comparesameform("(t+2)(t+3)", "(t+3)(t+2)", "t")        // true 
```

comparelogic(a,b,vars): Compares two propositional logic statements for equivalence. Uses ^^ (and), vv (or), ~ (not), -> or => (conditional), <-> or <=> (biconditional).

Example

comparelogic("p^^q", "q^^p", "p,q")           // true  (and is commutative)
comparelogic("~(p^^q)", "~p vv ~q", "p,q")   // true  (De Morgan's law)
comparelogic("p->q", "~p vv q", "p,q")        // true  (material conditional)

isset($var): Returns true if the variable has been defined, false otherwise.
Example
```
$a = 5
isset($a)  // true
isset($b)  // false  ($b not yet defined)
```
is_numeric(str): Returns true if the string represents an integer or decimal number (not fractions or expressions).
Example
```
is_numeric("3.14")  // true
is_numeric("3/4")   // false
is_numeric("abc")   // false
```
are_numeric(v1,v2,v3,...): Returns true only if all arguments are numeric values or strings. Can also pass a single array.
Example
```
are_numeric(1, 2.5, 3)   // true
are_numeric(1, "x", 3)  // false
are_numeric([3,"3/2"])  // false
```
is_nan(val): Returns true if the value is NaN (not a number), such as the result of sqrt(-1). Only works on calculated values, not expression strings.
Example
```
$a = sqrt(-1)
is_nan($a)  // true
is_nan(5)   // false
is_nan("sqrt(-1)")   // triggers an error; cannot use on strings
```
scorestring($answer,$showanswer,words,$stuanswers,$thisq,[partn, highlight]): Checks whether all required words appear in a student's text answer. If they do, redefines $answer to mark the student correct and highlights the matched words in $showanswer. Set highlight to false to disable highlighting.
Example
```
$words = array("slope", "negative")

// Single-part question:
$answer,$showanswer = scorestring($answer, "", $words, $stuanswers, $thisq);

// Multipart question (part 2):
$answer,$showanswer = scorestring($answer, $showanswer, $words, $stuanswers, $thisq, 2);
```
checkanswerformat(string, answerformat): Checks whether a numerical expression string meets the specified answer format (e.g. "fraction", "reducedfraction", "decimal").
Example
```
checkanswerformat("3/4", "fraction")  // true
checkanswerformat("0.75", "fraction") // false
checkanswerformat("6/8", "reducedfraction")   // false
```

getsigfigs(value, [expected sigfigs]): Returns the number of significant figures in value. Provide the expected count to resolve ambiguity on values like 1200.

Example

getsigfigs("0.0450")     // 3
getsigfigs(0.0450)     // 2 because it's not a string so the 0 gets lost
getsigfigs("1.234")      // 4
getsigfigs("1200")       // 2, but is ambiguous without hint
getsigfigs("1200", 3)    // 3  (resolves ambiguity)

Feedback Macros

These macros are used to select and format feedback messages to students. They return a string which can be placed in the question text.

getfeedbackbasic(correct msg, incorrect msg, $thisq, [partnum]): Returns a feedback string based on whether the question was scored correct or not. For multipart questions pass a part number (or an array of part numbers — the correct message only shows if all parts are correct).

Example

//single part
$feedback = getfeedbackbasic("Great job!", "Not quite — try again.", $thisq);

// Part 2 of a multipart:
$feedback = getfeedbackbasic("Correct!", "Check your work.", $thisq, 2);

// Correct message only shows when all three parts are right:
$feedback = getfeedbackbasic("All correct!", "Review your answers.", $thisq, [0,1,2]);

getfeedbacktxt(stuans, feedbacktxt, ans): Returns per-choice feedback for multiple choice questions. feedbacktxt is an array whose indices correspond to the $questions array, so feedbacktxt[1] shows when the student picks $questions[1].
Example
```
$feedbacktxt = array(
  "That's too small.",
  "Correct!",
  "That's too large.",
  "Way off."
);
$feedback = getfeedbacktxt($stuanswers[$thisq], $feedbacktxt, $answer);
```
getfeedbacktxtessay(stuans, feedbacktxt): Returns feedbacktxt once the student has entered any response to an essay question. The answer is not evaluated — it only checks for a non-blank response.
Example
```
// for part 2 of a multipart 
$feedback = getfeedbacktxtessay(
  getstuans($stuanswers, $thisq, 2)
  "Thank you for your response. The key concepts to include are..."
);
```
getfeedbacktxtnumber(stuans, partialcredit, feedbacktxt, defaultfeedback, [tol]): Returns targeted feedback for numeric questions, with correct/incorrect marks based on the partialcredit.
Parameters
- For Calculated questions use $stuanswersval instead of $stuanswers.
- partialcredit is array(value, score, value, score, ...) where scores are in [0,1].
- feedbacktxt is an array of messages corresponding to each value/score pair.
- defaultfeedback shows when no value matches.
- Tolerance defaults to 0.001 relative; prefix with | for absolute.
Example
```
$partialcredit = array(10, 1, 10.3, 0.5) // answer 10 = full credit, 10.3 = half credit
$feedback = getfeedbacktxtnumber(
  $stuanswers[$thisq],
  $partialcredit,          
  array("Correct!", "Close, but check your rounding."),
  "Incorrect, the answer is 10."
)
```
getfeedbacktxtcalculated(stuans, stuansval, partialcredit, feedbacktxt, defaultfeedback, [answerformat, requiretimes, tol]): Like getfeedbacktxtnumber but for Calculated question types, supporting answerformat and requiretimes checks.
Parameters
- stuans from $stuanswers[$thisq], stuansval from $stuanswersval[$thisq]
- partialcredit is array(value, score, value, score, ...) where scores are in [0,1].
- feedbacktxt is an array of messages corresponding to each value/score pair.
- defaultfeedback shows when no value matches.
- answerformat can be a single answerformat to apply to all expressions, or an array with each element applied to the corresponding expression
- requiretimes can be a single requiretimes to apply to all expressions, or an array with each element applied to the corresponding expression
- Tolerance defaults to 0.001 relative; prefix with | for absolute.
Example
```
// Check the answer "1/2" twice: once requiring fraction format, once without:
$partialcredit = array("1/2", 1, "1/2", 0.5)
$answerformat = ["fraction", ""] // different answerformat per check in $partialcredit
$feedback = getfeedbacktxtcalculated(
  $stuanswers[$thisq],
  $stuanswersval[$thisq],
  $partialcredit,
  array("Correct!", "Right value, but give your answer as a fraction"),
  "Incorrect",
  $answerformat 
)
```
getfeedbacktxtnumfunc(stuans, partialcredit, feedbacktxt, defaultfeedback, [vars, requiretimes, tol, domain]): Targeted feedback for algebraic expression (numfunc) questions.
Parameters
- stuans from $stuanswers[$thisq]
- partialcredit is array(expr, score, expr, score, ...) where scores are in [0,1].
- feedbacktxt is an array of messages corresponding to each value/score pair.
- defaultfeedback shows when no value matches.
- vars is a list of variables in the expressions, like "x,y" (default "x")
- requiretimes can be a single requiretimes to apply to all expressions, or an array with each element applied to the corresponding expression
- Tolerance defaults to 0.001 relative; prefix with | for absolute.
- Set domain to limit the test domain. Defaults to "-10,10"
Example
```
$partialcredit = array("x+1", 1, "x^2+1", 0.5)
$feedback = getfeedbacktxtnumfunc(
  $stuanswers[$thisq],
  $partialcredit,
  array("Correct!", "Close, check whether that's linear or quadratic."),
  "Incorrect, the answer is x+1."
)
```

Using Other Macros

If an IMathAS administrator has installed other Macro Libraries, you can load a macro library by entering the line loadlibrary("list of library names") at the beginning of the Common Control section.

Examples: loadlibrary("stats") or loadlibrary("stats,misc")

Click on the "Macro Library Help" link in the question editor to get a list of installed macro libraries and the macros available in each library

Math Entry

IMathAS uses ASCIIMath for math entry. In question text or inside strings that will be displayed in the question text, wrap expressions to be rendered in the backtick/grave symbol, like `x^2`. That key is usually located on the same keyboard button as the tilde.

For calculations, a limited subset is available:

Symbol	Meaning
* / + -	Multiply, divide, add, subtract
^	Powers. 2^3 = 8.
e, pi	The standard constants
%	Modulus of integers (remainder after division. 5%2 = 1)
mod(p,n)	Modulus of integers. This version gives positive results for modulus of negative numbers.
fmod(p,n)	Modulus of decimal values. May give negative results from negative inputs.
!	Factorial
sqrt	Square root
sin,cos,tan,cot,sinh,cosh	Standard trig function. Be sure to enter as sin(2), not sin 2
arcsin,arccos,arctan,arcsinh,arccosh	Inverse trig functions.
sin^-1, cos^-1, tan^-1	Alternative entry for inverse trig functions. Use like sin^-1(0.5)
ln	Natural Logarithm base e
log	Common Logarithm base 10
abs	Absolute Value. Note that while abs() is used for calculations, you may prefer to use \| brackets for display
round(n,d)	round number n to d decimal places
roundsigfig(n,s)	round number n to s significant digits. This is for calculations; if you need a value for display and want to ensure trailing 0's display, use prettysigfig
floor,ceil	floor/ceiling: integer below/above given number
min,max	min or max of the passed values. Can be used as min($a,$b,$c) or min($arrayvariable).

For display only, the full ASCIIMath language is available (which includes support for a limited subset of LaTeX). For more info, see the ASCIIMath syntax.

Solver

While writing a question, it can be handy to quickly solve a formula for a variable. For example, if you're writing a question that asks students to solve y=($a x + $b)/($b x - $a) for x, where $a and $b are randomized variables. You might need to calculate the correct answer. The Solver tool can help solve or check the solution.

Solver Input

Tips:

Select your code from the Common Control box, then either drag-drop or copy-paste it to the box below, or
Highlight an expression in Common Control and press Ctrl-M to update the Solver code, or
Highlight an expression in your code before clicking Solver.
Select an operation to perform: Solve, Differentiate, Integrate, Plot.
You may need to change the colored Sage code below to solve for the correct variable or to adjust the plot window etc. See the help icon below for examples.

Solver: Sage Syntax

SageMath examples:

#create symbolic variables x,y,a,b,c,d = var('x,y,a,b,c,d') # solve the equation for x solve( y==(a*x+b)/(c*x-d) , x ) x = var('x') #Differentiate diff( 3*x^4 , x ) x = var('x') #Plot in a standard window plot( -x^2+4 , (x,-10,10) ) x = var('x') #Simplify simplify( 5*x+7*(-3*x-4) )

Tips:

Declare any variables using var() as above. By default, x is a variable.
Use two equal signs for math equations.
With solve() diff() integral() give the independent variable after a comma.
With plot() a range for the independent variable must be specified, e.g. (x, -10, 10).
Select a new operation or click Go to calculate.

Solver Output

Tips:

Drag the result above to the Common Control box where you define the $answer or any other location, or
Click Insert in Common Control to append the result to the end of the Common Control, or
Click Insert as $answer to append $answer = result to the Common Control (not available if $answer is already defined).
Note: Touchscreens might not be supported by the drag operation.

Accessible Alternative

The accessible alternative option, near the bottom of the question editor, allows you to specify an alternative question ID to display if the student has accessibility settings enabled.

You most likely should not use this feature. It is intended for the rare case where a question cannot be made accessible using the built-in accessibility features, like some questions using jsxgraph, Geogebra, etc. If your question uses static images, graphs generated using showplot, or is a standard Drawing type question, you DO NOT NEED this feature, and will make things worse by using it.

The system automatically generates textual alternatives for graphs generated using showplot, histogram, etc., and displays those when the student has the visual text alternatives setting enabled. If the default text alternative is insufficient or inappropriate, use replacealttext to replace the default with a custom-written alternative. If using a non-interactive jsxgraph visual, you can use the description> option in jsxBoard to add alternative text. To check what is generated and shown, you can test the question with different accessibility settings in the question Preview. Note you may need to use the browser's inspector to "see" alt-text added to static images.

Likewise, the system automatically provides a keyboard-based alternative for drawing questions when the student has the keyboard based drawing setting enabled.

It is always preferable to make the original question accessible when possible rather than specifying an alternative. But if your question cannot be reasonably made accessible, this option allows you to specify a different question ID to show the student instead. Your goal should be to pick a question that assesses equivalent concepts but in a different way.

For the "Use accessible alternative", you can select to have the alternative displayed:

"visual alt": when the student has Graph Display set to text alternatives. This is the appropriate option if your question relies on visual information but does not involve any user interaction that requires a mouse (cannot be performed with a keyboard alone). In this case, rather than provide an accessible alternative, it might be better to wrap the visual in <div aria-hidden=true></div> to hide it from a screenreader, and add a <div class="sr-only"></div> after it containing a textual description of the visual element, which will be visually hidden but available to a screenreader.
"mouse alt": when the student has Drawing Entry set to Keyboard and text-based. If your question has an element that requires a mouse to operate and cannot be operated with keyboard, but does not contain any visual elements that don't have alt-text, then use this option.
"visual or mouse alt": if the question has both visual elements and elements that require a mouse, then select this option. The alternative will be used if the student has either accessibility setting enabled.

Common options to all types

All question types can support these options:

Hints

For a single question (not multipart), to use hints, in the common control (or question control) section define the array $hints where:

$hints[attempt number] = "hint text"

For example:

$hints[0] = "This will show on first display"
$hints[1] = "This will show on second attempt (after 1 missed attempt)"
$hints[2] = "This will show on third and subsequent attempts, since no later values have been defined"

It is fine, for example, to not define $hints[0] if you want nothing to display initially.

Then in the question text, place the location of the hint using the variable $hintloc.

In multipart questions, you can follow the process above if you just want a single strand of hints for the entire problem. If you want per-part hints, define the $hints array as:

$hints[question part number][attempt number] = "hint text"

Then in question text, place each hint using $hintloc[question part number]

To have the hint to display based on a set of previous answers, you can use:

$hints[question part number][attempt number] = array("hint text", [part num1, part num 2])

This will display the hint after all the parts listed have had the required attempts or are correct.

To override the default Hint: text, set $hintlabel.

Help references

To provide help of some sort for a question (typically, links to videos, book references, etc), define $helptext in the common control section. Any text assigned to this variable will show at the bottom of the question. The display of this text is controlled by the same "show hints?" option that controls the display of hints described above.

Referencing Student Answers

To create multipart questions that are graded on consistency, or to create a set of lab-type problems that rely on student-provided data, you can reference students' previous answers in your question code. You will only be able to reference the student answer to some question types

$stuanswers[N] will refer to the student's answer on question N (not zero-indexed: N=1 is question 1)
$stuanswers[N][P] will refer to the student's answer on question N, part P (if multipart)
$stuanswers[$thisq][P] will refer to the student's answer on the current question, part P
$stuanswers[$thisq-1] will refer to the student's answer on the previous question
$stuanswersval[$thisq] or $stuanswersval[$thisq][P] will contain the numerical value of Calculated question types.
$stulastentry or $stulastentry[P] will contain the student's entered answer on the current question. While $stuanswers will only contain submitted answers, $stulastentry will also include autosaved entries.

Notes (important!):

1) If the student has not answered the question, then $stuanswers[N] === null, with the exception of drop-down select questions, where $stuanswers[N] == "NA" if no selection is made. To prevent divide-by-zero errors and other issues and to prevent students from exploiting this, it is highly recommended that you do something like:

if (stuansready($stuanswers, $thisq, [0])) {
	// stuff using $stuanswers[$thisq][0]
}

2) If you use $stuanswers in your $answer, $showanswer will not be defined until the student answers. If you follow the advice in #1 above, then your $showanswer will reflect the random number assigned to $a. For this reason, it is highly recommended that you custom define the $showanswer.

3) If using the $stuanswers array in a string or in the Question Text, you must enclose it with curly brackets: Your answer was {$stuanswers[$thisq][0]}. If using it directly in a calculation, enclose it in parentheses just to be safe.

4) $stuanswers[$thisq] is defined for question scoring, but may not be for question display.

5) You can use the function getstuans($stuanswers,N,P) to retrieve a student answer value. This method bypasses some strange things that happen when there is a multipart question with only one part, so is recommended.

6) You can use the function stuansready($stuanswers,$thisq,[p1,p2,...]) to determine if the parts have been answered, instead of checking for null. It also provides options for checking format or if the entry is numeric, so is highly recommended.

Other Reference Variables

A few other special purpose variables can be referenced:

$scorenonzero: This variable is only available on display, not during scoring. $scorenonzero[$thisq] (or $scorenonzero[$thisq][partindex] for multipart) will be -1 if the question is unanswered, 0 if the score is zero, and 1 if the score is anything above 0.
$scoreiscorrect: This variable is only available on display, not during scoring. $scoreiscorrect[$thisq] (or $scoreiscorrect[$thisq][partindex] for multipart) will be -1 if the question is unanswered, 1 if the score (before any penalties) is perfect, and 0 otherwise.
$attemptn: This variable holds the attempt number of the current attempt. 0 is the initial attempt, 1 is the next attempt, etc.
$partattemptn[part number]: For multipart questions, this holds the attempt number on each part.
$requestclearla: If you set $requestclearla=true in your code, it will request the display to clear out the student's last answer. This might be useful if your question branches based on attempt count. Example: $requestclearla = true if ($attemptn==2 && !$scoreiscorrect[$thisq])
$graphdispmode: This will be 0 if the student has text-based alternatives for graph display enabled, and 1 or 2 if an image-based mode is enabled.
$drawentrymode: This will be 0 if the student has keyboard-based alternatives for drawing entry enabled, or 1 for mouse-based entry.

Reusing Code

You can import in the Common Control code from another question using

includecodefrom(questionid)

where questionid is the ID number of the question you want to import the code of. In the source question, the variable $included will automatically be set to true when the question has been included, so it can be used to determine if the question has been imported into another question, or is running independently.

For example, in the master/source question, you might use the code:

if (!$included) {
 $type = rand(0,4)
}
do stuff here

In a question using this code, you could limit to a specific type using:

$type = 0
includecodefrom(1234)

Question text can be also brought in from another question by using

includeqtextfrom(questionid)

somewhere in the Question Text portion of the question.

Teacher Notes

In the question text, you can add a note that will only be viewable by the teacher while grading. Do this by wrapping the teacher note in the [teachernote] shortcode like this: [teachernote]This is the note[/teachernote]

Hiding/Toggling content

If you need to hide content from view, you can wrap it in <div class="hidden"></div>. Be aware the content is still in the page, so a student can still view the hidden content using the browser inspector, so don't use this to hide secret info, but it can be helpful if you need to hide an answerbox that is being populated by some other means.

If you want to toggle a block of content, one option for shorter content is to use forminlinebutton. For longer content, you can wrap the content in a block using <div data-toggler="Title for button"></div>. That will hide the wrapped content, and add a button with the specified title for toggling the content. You can optionally add a data-toggler-hide attribute as well if you want a different button label once the content is showing.

Question Types

The question types available are:

Number

The student is asked to enter a number (integer, decimal, or scientific notation). The answer is compared to a given tolerance. Can also accept DNE, oo (Infinity), and -oo (Negative Infinity) as answers.

Examples

// a question asking for the mean of 3 numbers
$a,$b,$c = diffrands(1,20,3)
$answer = ($a+$b+$c)/3

// a rounding question 
$a = rand(1,9) + rand(2,9)/10 + rand(5,9)/100
$answer = round($a,1)
$abstolerance = 0  // require an exact answer, no tolerance

// a money question
$answer = $initial*(1+$rate/100)^$years
$reqdecimals = 2   // require accurate to cents; allows more than 2
// $reqdecimals = "=2"  // would require exactly 2 decimals 

// a list of answers 
$answerformat = "list"
$answer = "$root1,$root2"

Required Variables

$answer = a number or calculation resulting in a number, like $answer = 5: Defines the answer. Define multiple acceptable answers in a string separated by or: $answer = "3 or 5 or 7". Alternatively, you can provide an interval notation range of acceptable answers, like $answer = "(2,5]". Providing a range will override any tolerances set. If $answerformat is set for list answers, then this should provide a list of correct answers, like $answer = "1,2,3".

Optional Variables

$reltolerance = a decimal value

Defines the largest relative error that will be accepted. If this is not set, a relative error of .001 (.1%) is used by default.

$abstolerance = a number

Defines the largest absolute error that will be accepted. This will override the use of $reltolerance

$reqdecimals = a number

Defines the minimum decimal accuracy required (ie 2 for two decimal places). This will put a message in the answer tips stating the decimals required. If neither $abstolerance or $reltolerance is set, this will set the tolerance, otherwise the provided tolerance will be used (even if it doesn't agree with the $reqdecimal setting).

$reqdecimals = "=2" can be used to require exactly 2 decimal places in the answer, regardless of how the value rounds (so 3.5 would get marked wrong when the answer is 3.50 if "=2" is used). If you use the "=2" form, it will also round your $answer if needed for the $showanswer.
$reqdecimals = "r2" can be used to require rounding to 2 decimal places in the answer, not checking for trailing zeros (so 3.5 would get marked correct when the answer is 3.50 if "r2" is used). If you use the "r2" form, it will also round your $answer if needed for the $showanswer.
When the "=2" or "r2" form is used, it overrides both $reltolerance and $abstolerance, and by default tests that the student answer exactly matches the correct answer ($abstolerance=0).
To override the tolerance use +- in the setting, like this:
$reqdecimals = "=2+-.01" checks for exactly 2 decimals, but allows the answer to have an absolute error of .01
$reqdecimals = "=2+-1%" checks for exactly 2 decimals, but allows the answer to have an relative error of 1% (equivalent to $reltolerance = .01)

$reqsigfigs = a number

Defines the significant figure accuracy required. Use $reqsigfigs = 2 for at least 2 sig fig accuracy, or $reqsigfigs = "=2" to require exactly 2 sig figs in the answer, or $reqsigfigs = "[2,4]" to require between 2 to 4 sigfigs. This will put also a message in the answer tips stating the significant figures required. If you use the "=2" form, it will also round your $answer if needed for the $showanswer.
This setting overrides both $reltolerance and $abstolerance, and by default tests that the student answer rounded to the specified sigfigs matches the correct answer. To override the tolerance use +- in the setting, like this:
$reqsigfigs = "=2+-.01" checks for exactly 2 sigfigs, but allows the answer to have an absolute error of .01
$reqsigfigs = "=2+-1%" checks for exactly 2 sigfigs, but allows the answer to have an relative error of 1% (equivalent to $reltolerance = .01)

$answerformat = "list", "exactlist", "orderedlist", "set", "integer, "units", "nosoln", or "nosolninf"

Answerformats can be combined, like $answerformat = "nosoln,list"
$answerformat = "list", "exactlist", or "orderedlist" specifies that a list of answers is expected.
If $answerformat="list", then duplicate values are ignored.
If $answerformat="exactlist", then duplicate values are not ignored.
If $answerformat="orderedlist", the list must be in the same order and contain identical counts of values.
$answerformat = "set" behaves like "list", but expects the answer list to be wrapped in curly braces as a set.
$answerformat = "integer" changes the entry hint to only indicate integers, and rejects answers that contain decimals (except it does allow 2.0 instead of 2)
$answerformat = "units" adds unit checking. Supply the answer like $answer = "3 kg/m^2". The student's answer can be in other equivalent units, so "300 cm" is considered equivalent to "3 m". The answer must be in the format [decimal number]*[unit]^[power]*[unit]^[power].../[unit]^[power]*[unit]^[power]..., though multiplication can be implied. Also, 'per' may be used for division of units, and 'unit squared', 'square unit', 'unit cubed' and 'cubic unit' may be used. Note that the units do not require mathematically-proper parens around the denominator. The decimal number can include basic scientific notation in 3E5 or 3*10^5 formats. Examples: 4 cm, and 3.5E4 feet per second squared Note that tolerances are scaled to the unit, so $answer = "3m" with $abstolerance = .1 would mean .1 meters, so "310cm" would still be within tolerance. If $reqsigfigs is set, the specified number of sigfigs will need to be present in the student's answer, regardless of units.
$answerformat = "nosoln" or "nosolninf" adds a list radio buttons for "no solutions" and optionally "infinite solutions". $ansprompt can override the default statements like this: $ansprompt = "One value, x=;No values;Many values"

$requiretimes = a list, like "E,=0"

Adds format checking to the student's answer. The list can include multiple checks, which come in pairs. The first is the symbol to look for. The second describes what is acceptable. For example, in the string shown above, the symbol "E" would be required to show up exactly 0 times.
Be aware that if you search for "5,=1", it will match both 5 and 15 and 2.5, since all three strings contain a 5. When searching for numbers, you can avoid this by putting a "#" before the number, like "#5,=1", which would match the 5 but not 15 or 0.5. Beware this type of search ignores signs.
You can use just "#" in the symbol location to match any number (including decimal values); 3.2^5 would match twice.
You can match either of two symbols by putting || between them, like ".5||1/2,>0"
You can use a regular expression by putting in the symbol location "regex:expression"
You can put "ignore_commas,true" at the beginning of the $requiretimes to ignore commas in the answer

$requiretimeslistpart = a list, in the same format as $requiretimes

Similar to $requiretimes, but this check is applied to each element of the answer list when a list $answerformat is used, where $requiretimes would be applied to the entire list of answers.

$partialcredit = array(number,score,[number,score,...])

Allows you to specify partial credit for other answers. The array should be given in the form array(number,score,number,score,...), where number is the value to compare to the student answer, and score is a proportion between 0 and 1 to award as partial credit. Note this currently only works for single number answers; "or" and list answers are not supported.

$ansprompt = string

A string that will be displayed in front of the input box. Example: $ansprompt="y="

$displayformat = "alignright"

Aligns the text in the answer box to the right side

$answerboxsize = number

Determines the number of characters space provided for entry of an answer. Defaults to 20.

$readerlabel = string

A string that will be used as a visually hidden label on the input box for screenreaders.

$answerbox (In Question Text)

Using the variable $answerbox in the Question Text will place the question input box in that location

$showanswer

The answer to show to students (if option if available). Defaults to $answer. Use this to give a detailed answer, or a rounded off answer.

$hidetips = true

Hides the question entry tips that display by default. This should only be used when a question type is being used in an unintentional way, or if the question type gives away critical info to the student.

Calculated

A student is asked to enter a number or a calculation, like 2/3, 5^2, or sin(2). Can also accept DNE, oo (Infinity), and -oo (Negative Infinity) as answers.

Examples

// an answer expecting a reduced fraction answer to a/b+c/d
$answer = makereducedfraction($a*d+$c*$b, $b*$d)
$answerformat = "reducedfraction"  // check the stu answer is reduced

// require two answers to x^2=$a
$answerformat = "list"
$answer = "sqrt($a),-sqrt($a)"

// have student evaluate sin(pi/6)
$answerformat = "notrig"  // prevents them just typing sin(pi/6)
$answer = "1/2"

Required Variables

$answer = a number or calculation resulting in a number: Defines the answer. Define multiple acceptable answers in a string separated by or: $answer = "3 or 5 or 7". Alternatively, you can provide an interval notation range of acceptable answers, like $answer = "(2,5]". Providing a range will override any tolerances set

To have the answer display as a rendered expression, provide the answer as a string. For example, if you want the answer to show as 2⁴ then you'd specify $answer = "2^4". If you specified $answer = 2^4, the answer would display as 16.

Optional Variables

$answerformat = "fraction", or one of the other options below.

Specifies answer format options. Some can be combined in a list, like this: $answerformat="nodecimal,notrig".

Base format types: only use at most one of these at a time
- fraction: requires the answer to be a single fraction (like 10/6, 1/3, or 5)
- reducedfraction: a reduced fraction (like 5/3 or 5)
- mixednumber: a reduced mixed number (like 2 1/2 or 2_1/2, or 2/3 or 5)
- mixednumberorimproper: a reduced mixed number or improper fraction (like 2 1/2 or 5/2)
- sloppymixednumber: a mixed number (will take 5/2, 2 1/2, even 1 3/2)
- scinot: scientific notation (like 2.3*10^4)
- scinotordec: scientific notation (like 2.3*10^4) or decimal value
- fracordec: a single fraction or decimal value. Can be combined with "allowmixed" to also allow mixed numbers.
- decimal: requires the answer to be an integer or decimal value
Mix-ins: You can add these as needed to modify what's allowed
- allowunreduced: can be combined with "mixednumber" or "mixednumberorimproper" to allow unreduced fractional parts
- allowxtimes: allows the use of x for multiplication (like 23x10^2 for 23*10^2), typically in combo with the "scinot" format
- allowplusminus: allow use of +- in the answer. Will enable the 'list' option if not already included.
- nodecimal: require an answer without decimals (also disallows 10^-2 and 3E-2)
- notrig: require an answer without trig functions (sin,cos,tan,sec,csc,cot)
- allowmixed: will enable support for mixed numbers (like 2 1/2) in answers
- allowdegrees: will enable the use of the degree symbol to designate degrees, so sin(30degree)=1/2.
- noval: tells the answer preview to not compute a decimal equivalent (deprecated - this option is now enabled by default)
- showval: tells the answer preview to display a decimal equivalent
- sameform: requires the student's answer be in the "same form" as the correct answer. This means exactly the same, except for commutation of addition and multiplication, multiplication by 1, implicit multiplication, and extra parentheses. Use with caution.
List options: only use at most one of these at a time
- list: a list of answers is expected - ignores duplicate values (1,1,2 is equivalent to 1,2)
- exactlist: a list of answers is expected - does not ignore duplicates
- orderedlist: a list of answers is expected - order is important, and duplicates are not ignored
Special options:
- nosoln: adds radio buttons for "no solutions". Use $answer="DNE" if the answer is no solutions.
- nosolninf: adds radio buttons for "no solutions" and "infinite solutions". Use $answer="DNE" or $answer="oo" respectively if needed.
- To override the default "no solutions" and "infinite solutions" wording, you can define $ansprompt as a list of semicolon-delimited strings to override the default wording. For example,
  $ansprompt = "One value, x=;No values;Many values"

$formatfeedbackon = true

Turns on "right answer, wrong format" feedback on the question

$reltolerance = a decimal value

Defines the largest relative error that will be accepted. If this is not set, a relative error of .001 (.1%) is used by default.

$abstolerance = a number

Defines the largest absolute error that will be accepted. This will override the use of $reltolerance

$reqdecimals = a number

Defines the decimal accuracy required (ie 2 for two decimal places). This will put a message in the answer tips stating the decimals required. If neither $abstolerance or $reltolerance is set, this will set the tolerance, otherwise the provided tolerance will be used (even if it doesn't agree with the $reqdecimal setting).

$reqsigfigs = a number

Defines the significant figure accuracy required. Only valid for "decimal", "scinot", and "scinotordec" $answerformat options. Use $reqsigfigs = 2 for at least 2 sig fig accuracy, or $reqsigfigs = "=2" to require exactly 2 sig figs in the answer, or $reqsigfigs = "[2,4]" to require 2 to 4 sigfigs. This will put also a message in the answer tips stating the significant figures required. If you use the "=2" form, it will also round your $answer if needed for the $showanswer.
This setting overrides both $reltolerance and $abstolerance, and by default tests that the student answer rounded to the specified sigfigs matches the correct answer. To override the tolerance use +- in the setting, like this:
$reqsigfigs = "=2+-.01" checks for exactly 2 sigfigs, but allows the answer to have an absolute error of .01
$reqsigfigs = "=2+-1%" checks for exactly 2 sigfigs, but allows the answer to have an relative error of 1% (equivalent to $reltolerance = .01)

$requiretimes = a list, like "^,=3,cos,<2"

Adds format checking to the student's answer. The list can include multiple checks, which come in pairs. The first is the symbol to look for. The second describes what is acceptable. For example, in the string shown above, the symbol "^" would be required to show up exactly 3 times, and "cos" would be required to show up less than 2 times.
Be aware that if you search for "5,=1", it will match both 5 and 15 and 2.5, since all three strings contain a 5. When searching for numbers, you can avoid this by putting a "#" before the number, like "#5,=1", which would match the 5 but not 15 or 0.5. Beware this type of search ignores signs.
You can use just "#" in the symbol location to match any number (including decimal values); 3.2^5 would match twice.
You can match either of two symbols by putting || between them, like ".5||1/2,>0"
You can use a regular expression by putting in the symbol location "regex:expression"
You can put "ignore_commas,true" at the beginning of the $requiretimes to ignore commas in the answer
You can put "ignore_spaces,true" at the beginning of the $requiretimes to ignore spaces in the answer
You can put "ignore_symbol,$" (or some symbol other than $) at the beginning of the $requiretimes to ignore that symbol in the answer

$requiretimeslistpart = a list, in the same format as $requiretimes

Similar to $requiretimes, but this check is applied to each element of the answer list when a list $answerformat is used, where $requiretimes would be applied to the entire list of answers. To apply different $requiretimes to each element of the $answer list, separate them with semicolons, like "pi,=1;/,=1;;"

$partialcredit = array(answer,score,[answer,score,...])

Allows you to specify partial credit for other answers. The array should be given in the form array(answer,score,answer,score,...), where answer is the numerical or string expression to compare to the student answer, and score is a proportion between 0 and 1 to award as partial credit. Note this currently only works for single answers; "or" answers and lists are not supported. If needed, you can make $requiretimes and/or $answerformat an array, with the first entry to be applied to the $answer, and subsequent entries to apply to the $partialcredit answers.

$ansprompt = string

A string that will be displayed in front of the input box. Example: $ansprompt="y="

$answerboxsize = number

Determines the number of characters space provided for entry of an answer. Defaults to 20.

$hidepreview = true

Hides the Preview button. Could be useful in multipart questions, or if you're only asking for a simple response, like a fraction

$readerlabel = string

A string that will be used as a visually hidden label on the input box for screenreaders.

$answerbox (In Question Text)

Using the variable $answerbox in the Question Text will place the question input box in that location

$showanswer

The answer to show to students (if option if available). Defaults to $answer. Use this to give a detailed answer, or a rounded off answer.

$previewloc (In Question Text)

Where you want the preview button to be located. Defaults to after the entry box if not placed in question text.

$hidetips = true

Multiple-Choice

A student is asked to select the correct answer from those given. The order of choices is automatically randomized.

Examples

// select the what function to use
$questions = ['sin','cos','tan']
$answer = 0  // index 0, so the answer is 'sin'

// define one option at a time 
$questions[0] = "There is exactly one solution"
$questions[1] = "There are no solutions"
$questions[2] = "There are infinitely many solutions"
$answer = 1  // index 1: There are no solutions 
$noshuffle = "all"  // don't shuffle option order

// Make a dropdown for completing an expression 
$questions = ['&gt;','&lt;','=']
$answer = 0
$displayformat = "select" // display as drop-down

Required Variables

$questions (or $choices) = an array of choices: Defines the choices. If you use $choices, don't define $questions
$answer = the index into $questions that contains the correct answer: Defines the answer. Remember that arrays are zero-indexed, so if $questions = array("correct","wrong","wrong"), then $answer=0. Define multiple acceptable answer indices in a string separated by or: $answer = "0 or 1".

Optional Variables

$displayformat = "horiz", "select", "2column, "3column", or "inline": Will lay out the choices horizontally, as a select box, in multiple columns, or inline with text rather than using the default vertical layout
$noshuffle = "all" or "last" or "last2": If $noshuffle="all", then the $questions array will not be randomized (shuffled). If $noshuffle = "last", then the $questions array will be randomized, except for the last element. This is for options like "None of the above". You can use "last2" or "last3" to randomize all but the last 2 or 3 elements.
$partialcredit = array(index,score,[index,score,...]): Allows you to specify partial credit for other answers. The array should be given in the form array(index,score,index,score,...), where index is the index in $questions, and score is a proportion between 0 and 1 to award as partial credit. For example, if $answer = 0 and $partialcredit = array(2,.3), then the student would get full credit for selecting the item corresponding with $questions[0], and 30% credit for selecting the item corresponding with $questions[2]. All other answers would receive 0 credit.
$readerlabel = string: A string that will be used as a visually hidden label on the input box for screenreaders.
$ansprompt = string: When $displayformat = "select" is used, this allows you to override the default "Select an answer" text that displays. Do not use this unless there's a really strong reason to.
$answerbox (In Question Text): Using the variable $answerbox in the Question Text will place the choice list in that location
$showanswer: The answer to show to students (if option if available). Defaults to the text of the correct answer. Use this to substitute a detailed answer.
$hidetips = true: Hides the question entry tips that display by default. This should only be used when a question type is being used in an unintentional way, or if the question type gives away critical info to the student.

Multiple-Answer

A student is asked to select all the choices given that are correct. The order of choices is automatically randomized.

Examples

// select all the functions with period 2pi 
$questions = ['sin','cos','tan']
$answers = "0,1"  // indexes 0 and 1 are both correct

Required Variables

$questions (or $choices)= an array of questions: Defines the choices. If you use $choices, don't define $questions
$answers = a list of the indexes into $questions that contain the correct answer: Defines the answers. Remember that arrays are zero-indexed, if $questions = array("correct","correct","wrong"), then $answers="0,1". Or there are more than one correct combination, separate with or, like $answers = "0,1 or 0,3"

Optional Variables

$scoremethod = "answers" or "allornothing" or "takeanything": By default, the total points possible are divided by the number of questions, and partial credit is lost for each correct answer missed and each wrong answer selected. If $scoremethod="answers" is set, then the total points possible are divided by the number of answers (tougher grading scheme). If $scoremethod="allornothing", then the student will only get credit if every piece is correct (no partial credit). if $scoremethod="takeanything", full credit will be given for any response.
$displayformat = "horiz", "2column, "3column", or "inline": Will lay out the choices horizontally, in multiple columns, or inline with text rather than using the default vertical layout
$noshuffle = "all" or "last": If $noshuffle="all", then the $questions array will not be randomized (shuffled). If $noshuffle="last", then the last element of $questions will not be randomized (shuffled) but the others will.
$answerformat = "addnone": Adds "None of these" to the options. This is added automatically if $answers="", and you can add "None of these" yourselv to $questions, but this provides another way to always include the "None of these" option.
$readerlabel = string: A string that will be used as a visually hidden label on the input box for screenreaders.
$answerbox (In Question Text): Using the variable $answerbox in the Question Text will place the choice list in that location
$showanswer: The answer to show to students (if option if available). Defaults to the text of the correct answers. Use this to substitute a detailed answer.
$hidetips = true: Hides the question entry tips that display by default. This should only be used when a question type is being used in an unintentional way, or if the question type gives away critical info to the student.

Matching

A student is asked to match answers with questions

Examples

// match each function with its derivative
$questions = ['sin(x)','cos(x)','x^2','e^x']
$answers = ['cos(x)','-sin(x)','2x','e^x']

// matchlist when one answer matches with multiple questions 
$questions=array("34","`2/3`","3+4i")
$answers=array("real","complex")
$matchlist = "0,0,1"
$displayformat = "select" // puts the $answers in dropdowns next to each $question

Required Variables

$questions = an array of questions: Defines the questions - these will be on the left with entry boxes
$answers = an array of answers: Defines the answers - these will be on the right and lettered

Optional Variables

$matchlist = a list of the indexes into $answers that contain the match to each question.: Defines correct matches. By default, it is assumed that each element of $questions is matched one-to-one with the corresponding element of $answers (in other words, that $answers[0] is the answer to $questions[0]).
$matchlist allows you to define one-to-many matches. Example: if $questions=array("cat","dog","quartz") and $answers=array("animal","mineral"), then $matchlist = "0,0,1"
$questiontitle = string: Displays a title above the list of questions. For example, if $questions was a list of states, then $questiontitle="States" would be appropriate
$answertitle = string: Displays a title above the list of answers
$noshuffle = "questions" or "answers": Retains original order of questions or answers, and only shuffles the other. By default, both lists are shuffled
$displayformat = "select" or "2columnselect": Only displays the $questions, with select boxes next to each containing the $answers. This should only be used with pure text $answers.
$scoremethod = "allornothing": Setting "allornothing" will mean no partial credit is given, and the student must match all parts correctly to get credit.
$ansprompt = string: This allows you to override the default "-" that displays in the dropdowns when no selection has been made, for example to replace it with "?". It's recommended to not use this unless there's a really strong reason to.
$readerlabel = string: A string that will be used as a visually hidden label on the input box for screenreaders.
$answerbox (In Question Text): Using the variable $answerbox in the Question Text will place matching questions and answers in that location
$showanswer: The answer to show to students (if option if available). Defaults to the list of correct matches. Use this to substitute a detailed answer.
$hidetips = true: Hides the question entry tips that display by default. This should only be used when a question type is being used in an unintentional way, or if the question type gives away critical info to the student.

Function (Algebraic Expression/Equation)

A student is asked to enter a function (algebraic expression or equation).

Examples

// basic expression in x. System will accept anything algebraically equivalent
$answer = "$a(x-$h)^$k"

// an equation answer 
$variables = "x,y"
$answerformat = "equation"
$answer = "y=$m x + $b"

// multiple expressions 
$answerformat = "list"
$answer = "x+$a,x+$b"

// require "same form" 
$variables = "t"
$answer = "$g(t-$a)(t-$b)"
$answerformat = "sameform"

// check for something specific in answer 
$answer = "$a(x-$b)^2+$c"
// make sure there 1 $a and 0 sqrt in the student answer
$requiretimes = "#$a,=1,sqrt,=0" 

// specify domain, to prevent evaluation issues 
$answer = "sqrt(x-$a)"
$domain = "$a,$a+10"

// calc integral answer; allow anything +c 
$answer = "x^3+4"
$answerformat = "toconst"

Required Variables

$answer = string: Defines the answer function, entered as a string. For example, $answer="2sin(x)". You can specify multiple acceptable answers by separating with "or", like $answer="x^2 or x^4"
Note: The system will accept any algebraically equivalent answer. To only allow answers of a specific format, you'll also need to define $requiretimes (see below).

Optional Variables

$variables = string: A list of all variables in the function (including letters representing constants). Defaults to "x". Can use "f()" to indicate a symbol represents a function.
$domain = "inputmin,inputmax": Defines the domain on which to compare the given answer and correct answer functions. The same domain applies to all variables. An option third list element "integers" can be given, which limits the domain to integer values. The domain defaults to real numbers from -10 to 10. If using multiple variables, can extend domain to define domain for each variable separately. Example: $variables = "x,y"; $domain = "0,5,20,25"
$requiretimes = a list, like "^,=3,cos,<2": Adds format checking to the student's answer. The list can include multiple checks, which come in pairs. The first is the symbol to look for. The second describes what is acceptable. For example, in the string shown above, the symbol "^" would be required to show up exactly 3 times, and "cos" would be required to show up less than 2 times. You can use "#" in the symbol location to match any number (including decimal values); 3.2x+42y would match twice.
You can use a regular expression by putting in the symbol location "regex:expression"
You can match either of two symbols by putting || between them, like "x^-3||/x^3,>0"
Include "ignore_case,false" to make the search case sensitive.
You can put "ignore_spaces,true" at the beginning of the $requiretimes to ignore spaces in the answer
Include "ignore_symbol,$" (or some symbol other than $) at the beginning of the $requiretimes to ignore that symbol in the answer
Note that commas are ignored by default with Function type, and a basic exponent like x^(-3) is converted to x^-3 before the check.
$answerformat = "equation" or "inequality" or "doubleinequality" or "generalcomplex" or "toconst" or "scalarmult" or "nosoln" or "nosolninf" or "sameform" or "list" or "casesensitivevars" (can combine, like "equation,nosoln"): By default, the student answer is expected to be an expression, and be equivalent (at points) to the specified answer. This option changes this behavior.
"equation": Specifies that the answer expected is an equation rather than an expression. The given answer should also be an equation. Be sure to specify all variables in the equation in $variables. This may fail on equations that are near zero for most values of the input; this can often be overcome by changing the $domain
"inequality": Specifies that the answer is expected to be an inequality rather than an expression. The given answers should also be an inequality. Be sure to specify all variables in the equation in $variables. This may fail on equations that are near zero for most values of the input; this can often be overcome by changing the $domain
"doubleinequality": Specifies that the answer is expected to be a compound inequality like 3<2x+3≤5 rather than an expression. The given answers should also be a compound inequality.
"generalcomplex": Specifies the answer is a complex function, involving i.
"list": Allow a list of expressions or equations to be entered. Does not ignore duplicates. You cannot use this in combination with $partialcredit. $requiretimes will apply to each element of the list.
"toconst": Specifies that the answer provided by the student is allowed to differ from the specified answer by a constant for all inputs. Appropriate for comparing antiderivatives. This may fail on expressions that evaluate to very large values or raise numbers to very large powers.
"scalarmult": Specifies that the answer provided by the student is allowed to differ from the specified answer by a scalar multiple.
"allowplusminus": allow use of +- in the answer. Will enable the 'list' option if not already included.
"nosoln" or "nosolninf" adds a list radio buttons for "no solutions" and optionally "infinite solutions". $ansprompt can override the default statements like this: $ansprompt = "One function, f(x)=;No such function exists"
"sameform": requires the student's answer be in the "same form" as the correct answer. This means exactly the same, except for commutation of addition and multiplication, multiplication by 1, implicit multiplication, and extra parentheses. (2x-3)(5-x) would be "sameform" as (-1x+5)(2*x-3), but 2/4x and 1/2x and 0.5x would not be "sameform". Use with caution.
"casesensitivevars": By default answers with incorrect case variables (like X instead of x) will be accepted. Add this option to not ignore case on variables.
$partialcredit = array(string,score,[string,score,...]): Allows you to specify partial credit for other answers. The array should be given in the form array(string,score,string,score,...), where string is the expression to compare to the student answer, and score is a proportion between 0 and 1 to award as partial credit. Note this currently only works for single expression answers; "or" answers are not supported.
$formatfeedbackon = true: Turns on "right answer, wrong format" feedback on the question
$reltolerance = a decimal value: Defines the largest relative error that will be accepted. If this is not set, a relative error of .001 (.1%) is used by default.
$abstolerance = a number: Defines the largest absolute error that will be accepted. This will override the use of $reltolerance
$ansprompt = string: A string that will be displayed in front of the input box. Example: $ansprompt="y="
$answerboxsize = number: Determines the number of characters space provided for entry of an answer. Defaults to 20.
$hidepreview = true: Hides the Preview button. Could be useful in multipart questions, but generally not recommended
$readerlabel = string: A string that will be used as a visually hidden label on the input box for screenreaders.
$answerbox (In Question Text): Using the variable $answerbox in the Question Text will place the question input box in that location
$showanswer: The answer to show to students (if option if available). Defaults to makeprettydisp($answer).
$previewloc (In Question Text): Where you want the preview button to be located. Defaults to after the entry box if not placed in question text.
$hidetips = true: Hides the question entry tips that display by default. This should only be used when a question type is being used in an unintentional way, or if the question type gives away critical info to the student.

String

A student is asked to enter a string (a word or list of letters).

Examples

// basic vocab question 
$answer = "categorical"

// scoring logic expressions
$variables = "p,q"
$answer = "p vv q"

Required Variables

$answer = a string: Defines the answer. Multiple acceptable answers can be entered using "or". Example: $answer = "dog or cat"

Optional Variables

$strflags = string of flags, like "ignore_case=1,trim_whitespace=0"

Determines how the string will be compared. Set to 1 to turn on, 0 for off. Flags are:

ignore_case: ignores capitol/lowercase differences
trim_whitespace: trims leading and ending whitespace (spaces)
compress_whitespace: compresses multiple spaces to one space and trims
remove_whitespace: removes all whitespace (spaces)
ignore_order: treats ABC and CBA as equivalent
ignore_commas: removes commas
partial_credit: awards partial credit based on Levenshtein distance between strings
all_words: gives credit the student answer contains a list of key words. $answer should provide a comma-separated list of words to look for, and partial credit will be given for each word found. Cannot be combined with $answerformat="list" or $partialcredit.
allow_diff=n: gives full credit for answers with Levenshtein distance between strings ≤ n
in_answer: gives credit if $answer is contained anywhere in the student answer
regex: interprets $answer as a regular expression (pattern) to evaluate the student's answer. For example, $answer="cost.*increas" will give credit if the word cost appears before increas in the student's answer. $answer="increas|ris" will accept any of the following: increasing, increases, rising, or risen etc.
special_or: use *or* for separating answers rather than or.
ignore_symbol=sym: Unlike the other flags, this is not an on/off flag. Set this equal to a symbol to ignore that symbol in student answers. This flag can be used multiple times with different symbols.

By default, compress_whitespace and ignore_case are On. Only one of partial_credit, allow_diff, in_answer or regex may be used at a time.

$scoremethod = "takeanything" or "takeanythingorblank" or "submitblank"

"takeanything" or "takeanythingorblank" sets the problem to give full credit for any answer. "takeanythingorblank" also counts blank answers as correct. "submitblank" will cause blank answers to get submitted for scoring (new system only).

$answerformat = "list" or "logic" or "setexp"

"list" specifies that a list of answers is expected. Renders ignore_commas unnecessary. Cannot be used with partial_credit flag. Duplicates are not ignored.

"logic" enables a separate grading algorithm for logic statements, ignoring $strflags. The $answer should be given using vv for or, ^^ for and, neg for not, xor for exclusive or, => for conditional, and <=> for biconditional. Parens are supported, but no other symbols. The variables used in the logic expression must be declared by defining $variables.

"setexp" enables a separate grading algorithm for set expression statements, ignoring $strflags. The $answer should be given using 'nn' for intersection, 'uu' for union, '-' for set difference, '^c' for set complement, and 'oplus' for symmetric difference.

$partialcredit = array(string,score,[string,score,...])

Allows you to specify partial credit for other answers. The array should be given in the form array(string,score,string,score,...), where string is the value to compare to the student answer, and score is a proportion between 0 and 1 to award as partial credit. Note this only works for single string answers; list answers and "all_words" are not supported.

$ansprompt = string

$displayformat = "usepreview" or "typeahead" or "usepreviewnomq"

"usepreview" enables mathquill entry for mathematical answers.
"usepreviewnomq" adds a preview button for previewing mathematical answers in asciimath.
"typeahead" will enable an auto-suggest list of options once the student has typed at least two letters of the word. Provide the auto-suggest list in the variable $questions.

$variables

When $answerformat="logic" or "setexp" is used, define the $variables in the logic statement, like "p,q"

$requiretimes = a list, like "^,=3,cos,<2"

Adds format checking to the student's answer. Usually not needed for string questions, but can be useful when the "logic" or "setexp" answerformat is used. The list can include multiple checks, which come in pairs. The first is the symbol to look for. The second describes what is acceptable. For example, in the string shown above, the symbol "^" would be required to show up exactly 3 times, and "cos" would be required to show up less than 2 times.

$ansprompt = string

A string that will be displayed in front of the input box. Example: $ansprompt="type: "

$answerboxsize = number

Determines the number of characters space provided for entry of an answer. Defaults to 20.

$readerlabel = string

A string that will be used as a visually hidden label on the input box for screenreaders.

$answerbox (In Question Text)

Using the variable $answerbox in the Question Text will place the answer entry box in that location

$showanswer

The answer to show to students (if option if available). Defaults to the text of the correct answer. Use this to substitute a detailed answer.

$hidetips = true

Essay

A student is asked to enter a free-response answer. The essay type is not automatically graded.

Examples

// enable the text editor on the essay box
$answerformat = "editor"

// give credit for any non-blank answer 
$scoremethod = "takeanything"

Required Variables

None - the essay type is not computer graded.

Optional Variables

$answerboxsize = "rows" or $answerboxsize = "rows,columns": Determines size of space provided for entry of an answer. Defaults to 5 rows, 50 columns.
$displayformat = "editor" or "editornopaste" or "pre": "editor" to use the rich text editor for the essay answer box, or "editornopaste" for the rich text editor with paste disabled.
"pre" to use standard text entry, and to display in gradebook as preformatted text.
$scoremethod = "takeanything" or "takeanythingorblank" or "nomanual": The first two sets the problem to give full credit for any answer. The second also counts blank answers as correct. The "nomanual" option will give no credit for any answer, but doesn't mark the question as needing manual grading.
$readerlabel = string: A string that will be used as a visually hidden label on the input box for screenreaders.
$answerbox (In Question Text): Using the variable $answerbox in the Question Text will place the essay box in that location
$showanswer: The answer to show to students (if option if available). Defaults to the text of the correct answer. Use this to substitute a detailed answer.
$hidetips = true: Hides the question entry tips that display by default. This should only be used when a question type is being used in an unintentional way, or if the question type gives away critical info to the student.

Drawing

Drawing questions require the student to draw one or more lines/curves or dots. Dots are graded right/wrong. Lines/curves are graded based on the deviation of the drawn line from the correct line.

Examples

// have students graph a parabola on a standard grid
$answerformat = "twopoint"
$snaptogrid = 0.5
$answers = "$a(x-$h)^2+$k"

// have students graph an exponential on a modified grid 
$grid = "-2,10,-2,10"
$answerformat = "twopoint,exp,genexp,log,genlog"
$answers = "$a*$b^x"
$snaptogrid = 0.25

// have students draw a tangent line to a drawn parab 
$answerformat = "twopoint,line"
$background = "x^2,red"
$answers = "2x-1"
$snaptogrid = 0.5

// have students plot points in the first quadrant
$grid = "0:-1,10,0:-10,100,2,10"
$answerformat = "twopoint,dot"
$answers = ["$x1,$y1","$x2,$y2"]
$snaptogrid = "1:5"

// graph on a number line 
loadlibrary("interval")
$answerformat = "numberline"
$answers = intervalstodraw("(-2,3]")

Required Variables

$answers = a string or array of strings describing the points or curves to be drawn: Curves: "f(x)" like "x^2+3".
Line segments or rays: "f(x),xmin,xmax", like "x+1,-3,2" or "x+1,-oo,3"
Dots: "x,y" for closed dots, "x,y,open" for open dots, like "2,3"
See below for additional entry formats for other curves when using "twopoint" drawing.
When using twopoint drawing, you can preface an answer with "optional", like "optional,2,3", to indicate that drawing element is not required, but shouldn't mark down the score if present.

Recommended Variables

$answerformat = "twopoint", "polygon", "inequality", "numberline", "freehand", or (for the older tools), "line,lineseg,dot,opendot"

Limits the drawing tools available to students. Defaults to the older drawing tools "line,dot,opendot".

$answerformat="twopoint" will use a different set of drawing tools for specific shapes that all use two control points to define the shape. It is strongly recommended you use these instead of the older tools.

$answerformat="twopoint" will use a default tool set of line, parabola, absolute value, circle, and dot tools
You can limit or expand the tools by specifying them: e.g. $answerformat = "twopoint,line,parab". Valid values are:
- line (lines)
- dashedline (dashed lines)
- lineseg (line segment)
- ray (rays)
- parab (vertical parabolas)
- horizparab (horizontal parabolas)
- halfparab (half a vertical parabola)
- 3pointparab (parabola given 3 points)
- cubic (a(x-h)^3+k style cubics)
- abs (absolute value)
- circle (circles)
- dot (closed dots)
- opendot (open dots)
- sqrt (square root)
- cuberoot (cube root)
- trig (sin and cos)
- tan (tan and cot function)
- sec (sec and csc function)
- vector (position or displacement vectors)
- exp (exponential with horizontal asymptote at y=0)
- genexp (exponential with any horizontal asymptote)
- log (logarithm with vertical asymptote at x=0)
- genlog (logarithm with any vertical asymptote)
- rational (linear/linear rational)
- ellipse (ellipses)
- hyperbola (vertical or horizontal hyperbolas)
- rect (rectangles)
For lines, vertical parabolas, absolute values, square roots, cubics, cuberoots, sines, cosines, exponentials, logs, and rationals (linear/linear only) give $answers as a function of x, like "2(x-1)^2+3"
For line segments and rays, given $answers as a function with domain, like "2x+4,-oo,3", or for vertical line segments use x= and give the range, like "x=4,-2,3"
For dashed lines, give $answers as "dashedline,function" like "dashedline,2/3x+4"
For dots give $answers as "x,y", or "x,y,open" for open dots
For circles, give $answers as "circle,x,y,radius", like "circle,2,-1,3".
For ellipses, give $answers as "ellipse,x,y,x_radius,y_radius", like "ellipse,1,2,4,2"
For hyperbolas of form (x-h)^2/a^2-(y-k)^2/b^2=1, give $answers as "horizhyperbola,h,k,a,b"
For hyperbolas of form (y-k)^2/a^2-(x-h)^2/b^2=1, give $answers as "verthyperbola,h,k,a,b"
For horizontal parabolas give $answers as "x=equation", like "x=2(y-1)^2-3".
For half parabolas give $answers as "equation,>xvertex", like "(x-1)^2-3,>1". Note only half parabolas are supported, not arbitrary segments.
For rectangles, give $answers as "rect,x1,y1,x2,y2", providing two diagonal corners.
For vertical lines give $answers as "x=number", like "x=3".
For vectors, give $answers as "vector, x_start, y_start, x_end, y_end" for position vectors, or "vector, dx, dy" for displacement vectors. Note you can use $scoremethod to change how vectors are scored.

$answerformat = "polygon" can be used for drawing a single polygon; give $answer as array of points in order joined with edges.

$answerformat = "closedpolygon" can be used for drawing a single polygon that is closed; the enclosed area will be shaded and the drawing terminate when the shape is closed. The format is the same as "polygon", except make sure the first and last entry of your $answers array are identical.

$answerformat="inequality" will use a set of drawing tools for graphing linear inequalities in two variables. Give $answers for non-vertical lines in form like ">=3x+4", "<5x+4", and "x<=3" for vertical lines.

$answerformat="inequality,parab" will use a set of drawing tools for graphing quadratic inequalities in two variables. Give $answers in form like ">=x^2-4", "<x^2+1". Use $answerformat="inequality,both" to turn on lines and parabolas.

$answerformat="inequality,abs" will use a set of drawing tools for graphing absolute value inequalities in two variables. Give $answers in form like ">=abs(x-3)+4", "<3abs(x)". Use $answerformat="inequality,line,abs,parab" or some combo to turn on multiple tools.

$answerformat="numberline" will use a set of drawing tools for graphing inequalities or points in one variable on a number line. Give $answers as dots and line segments, or use the intervalstodraw function from the interval macro library to form the $answers array.

$answerformat="freehand" will allow freehand drawing without any drawing tools. This mode can NOT be autograded, and should only be used for manually graded answers.

$answerformat can also be used to limit the older tools: $answerformat = "line", or $answerformat = "line,dot"

$snaptogrid = spacing

Turns on snapping, where points will jump to a grid. $snaptogrid = 1 will jump to the nearest integer. $snaptogrid = 0.5 will jump to the nearest .5. $snaptogrid = "2:4" will jump to the nearest 2 in the x and 4 in the y. Does not have to match the actual grid line spacing. Be aware that due to pixelation, the snapping may not land on exact values correctly. This is usually corrected for automatically, but it sometimes fails if the correction would be too large. In that case, use the getsnapwidthheight macro to compute an imagewidth and imageheight that will be pixel accurate.

Optional Variables

$grid = "xmin,xmax,ymin,ymax,xscl,yscl,imagewidth,imageheight": Defines the grid to be drawn on. Defaults to "-5,5,-5,5,1,1,300,300". You can set all or just some of the values. For example, to just set the window, you could use "0,10,0,10"
If using $answerformat="numberline", set ymin and ymax to 0.
If desired, you can set separate label and grid spacing using "xmin,xmax,ymin,ymax,xlabelspacing:xgridspacing,ylabelspacing:ygridspacing,imagewidth,imageheight". You can specify axis labels using "xmin,xmax,ymin,ymax,xlabelspacing:xgridspacing:xaxislabel,ylabelspacing:ygridspacing:yaxislabel,imagewidth,imageheight". To create first quadrant graphs, use "0:-n" (for some value of n) for xmin and/or ymin to only have gridlines and labels after 0, while still using -n to adjust spacing.
$background = equation or array of equations, using the showplot macro format: Define a graph to display in the background, to be drawn on top of. Example: $background = "x^2,red".
You can also set $background a string of asciisvg commands prefaced with "draw:", like "draw:line([1,1],[3,3]);". Note that initPicture and axes will already have been called, so do not include them.
You can also set $background to "none" to remove axes and the grid.
To specify alt-text for the background, add an element to the background array, like $background = ["x^2,red","alt:a parabola"]. For a background using draw, add the alt at the end of your commands, like: "draw:line([1,1],[3,3]);alt:a line segment". Note that this provided alt will replace everything, including the basic window information.
$partweights = array or list of weights: Defines grading weight for each line or dot in $answers. Example: $partweights = ".5,.25,.25". Defaults to equal weights on each line or dot.
$reltolerance = tolerance scaling factor: Scales the grading tolerance. Defaults to 1. Set $reltolerance = 2 to make the grading twice as tolerant; $reltolerance = 0.5 to make grading half as forgiving
$abstolerance = grading cutoff: Sets all-or-nothing grading. If score < $abstolerance, the student receives 0 for the question (note: score is between 0 and 1). Otherwise the student will receive full credit. Not set by default.
$scoremethod = "takeanything", "direction", "relativelength", "ignoreoverlap", "ignoreextradots": When "takeanything" is used, this will give full credit for any non-blank answer. This might be of use with the freehand drawing option.
"direction" and "relativelength" are only used for vectors. "direction" will score the initial point and direction for position vectors, but not length, and will only score direction for displacement vectors. "relativelength" will score like "direction", but will also check that the drawn vectors have correct lengths relative to each other.
"ignoreoverlap" only works with $answerformat="line", and will not deduct for overlapped lines.
"ignoreextradots" only works with $answerformat="polgon" and "closedpolygon", and will ignore any extra dots drawn along a side of the polygon.
$readerlabel = string: A string that will be used as a visually hidden label on the input box for screenreaders.
$answerbox (In Question Text): Using the variable $answerbox in the Question Text will place the question input drawing tool in that location
$showanswer: The answer to show to students (if option if available). Defaults to the text of the correct answer. Use this to substitute a detailed answer.
$hidetips = true: Hides the question entry tips that display by default. This should only be used when a question type is being used in an unintentional way, or if the question type gives away critical info to the student.

N-Tuple

N-Tuple questions require the student to enter an n-tuple or list of n-tuples. This can be used for coordinate points, vectors, or any other n-tuple of numbers.

Examples

// enter two points 
$displayformat = "pointlist"
$answer = "($a,$b),($c,$d)"

// enter a vector 
$displayformat = "vector"
$answerformat = "dimensionhint"
$answer = "<$a,$b,$c>"

Required Variables

$answer = a string containing an n-tuple or list of n-tuples: Defines the answer n-tuple or list of n-tuples. N-tuples can be any dimension, but must be surrounded by any of: (), [], {}, <>. Examples: $answer = "(1,2)", $answer = "<2,3,4>,<1,5,7>", $answer = "(1,2) or (1,3)"

Optional Variables

$displayformat = "point", "pointlist", "vector", "vectorlist", "list", "set", "setlist": Changes the answer entry tips (does NOT change how the question is graded). For points, entry like (2,3) is specified. For vectors, entry like <2,3> is specified.
$answerformat = "scalarmult", "anyorder", "nosoln", "nosolninf", "dimensionhint": "scalarmult" will accept any answer that is a scalar multiple of the correct answer.
"anyorder" will accept elements in any order, so (2,1) would be treated equivalent to (1,2)
"dimensionhint" will show a warning to students if they enter the wrong number of components.
$answerformat = "nosoln" or "nosolninf" adds a list radio buttons for "no solutions" and optionally "infinite solutions". $ansprompt can override the default statements like this: $ansprompt = "One value, x=;No values;Many values"
$scoremethod = "byelement": By default, the whole n-tuple must be correct to receive any credit. Set $scoremethod = "byelement" to give partial credit if only some elements of the n-tuple are correct.
$partweights = ".2,.8": Can be used with $scoremethod = "byelement" to change the value of each part of the ntuple
$reltolerance = a decimal value: Defines the largest relative error that will be accepted. If this is not set, a relative error of .001 (.1%) is used by default.
$abstolerance = a number: Defines the largest absolute error that will be accepted. This will override the use of $reltolerance
$readerlabel = string: A string that will be used as a visually hidden label on the input box for screenreaders.
$answerbox (In Question Text): Using the variable $answerbox in the Question Text will place the question input drawing tool in that location
$showanswer: The answer to show to students (if option if available). Defaults to the text of the correct answer. Use this to substitute a detailed answer.
$hidetips = true: Hides the question entry tips that display by default. This should only be used when a question type is being used in an unintentional way, or if the question type gives away critical info to the student.

Calculated N-Tuple

Calculated N-Tuple questions require the student to enter an n-tuple or list of n-tuples. This can be used for coordinate points, vectors, or any other n-tuple of numbers. This is identical the the N-tuple answer type, but allows students to enter mathematical expressions rather than just numbers, such as (5/3, 2/3).

Examples

// enter a point with fraction components
$displayformat = "point"
$fx = makereducedfraction($nx,$dx)
$fy = makereducedfraction($ny,$dy)
$answers = "($fx,$fy)"
$answerformat = "fraction"

Required Variables

$answer = a string containing an n-tuple or list of n-tuples: Defines the answer n-tuple or list of n-tuples. N-tuples can be any dimension, but must be surrounded by any of: (), [], {}, <>. Examples: $answer = "(1/3,2)", $answer = "<2,3,4>,<1,5,7>", $answer = "(1,2) or (1,3)"

Optional Variables

$displayformat = "point", "pointlist", "vector", "vectorlist", "list", "set", "setlist": Changes the answer entry tips (does NOT change how the question is graded). For points, entry like (2,3) is specified. For vectors, entry like <2,3> is specified.
$answerformat = "scalarmult", "anyorder", "dimensionhint", "fraction", "reducedfraction", "mixednumber", "scinot", "fracordec", "nodecimal", "notrig", "nosoln", "nosolninf", "sameform": "scalarmult" will accept any answer that is a scalar multiple of the correct answer.
"anyorder" will accept elements in any order, so (2,1) would be treated equivalent to (1,2)
"dimensionhint" will show a warning to students if they enter the wrong number of components.
The other options require each component of the answer to be a single fraction (like 10/6), a reduced fraction (like 5/3), a reduced mixed number (like 2_1/2), scientific notation (like 2.3*10^4), a single fraction or decimal, an answer without decimals (also disallows 10^-2 and 3E-2), or an answer without trig functions (sin,cos,tan,sec,csc,cot). Multiple options can be specified like $answerformat="nodecimal,notrig".
$answerformat = "nosoln" or "nosolninf" adds a list radio buttons for "no solutions" and optionally "infinite solutions". $ansprompt can override the default statements like this: $ansprompt = "One value, x=;No values;Many values"
$scoremethod = "byelement": By default, the whole n-tuple must be correct to receive any credit. Set $scoremethod = "byelement" to give partial credit if only some elements of the n-tuple are correct.
$partweights = ".2,.8": Can be used with $scoremethod = "byelement" to change the value of each part of the ntuple
$reltolerance = a decimal value: Defines the largest relative error that will be accepted. If this is not set, a relative error of .001 (.1%) is used by default.
$abstolerance = a number: Defines the largest absolute error that will be accepted. This will override the use of $reltolerance
$readerlabel = string: A string that will be used as a visually hidden label on the input box for screenreaders.
$answerbox (In Question Text): Using the variable $answerbox in the Question Text will place the question input drawing tool in that location
$showanswer: The answer to show to students (if option if available). Defaults to the text of the correct answer. Use this to substitute a detailed answer.
$hidetips = true: Hides the question entry tips that display by default. This should only be used when a question type is being used in an unintentional way, or if the question type gives away critical info to the student.

Complex N-Tuple

Complex N-Tuple questions require the student to enter an n-tuple or list of n-tuples of complex numbers. This can be used for coordinate points, vectors, or any other n-tuple of complex numbers. This will require the student to enter each complex number in a+bi form.

Examples

// enter a complex point
$displayformat = "point"
$answer = "(2+3i,4-5i)"

Required Variables

$answer = a string containing an n-tuple or list of n-tuples of complex numbers in a+bi form.: Defines the answer n-tuple or list of n-tuples. N-tuples can be any dimension, but must be surrounded by any of: (), [], {}, <>. Examples: $answer = "(1,2+i)", $answer = "<i,3+i,4>,<1+i,5-i,7>", $answer = "(1,2i) or (1+i,3)"

Optional Variables

$displayformat = "point", "pointlist", "vector", "vectorlist", "list", "set", "setlist": Changes the answer entry tips (does NOT change how the question is graded). For points, entry like (2,3) is specified. For vectors, entry like <2,3> is specified.
$answerformat = "allowjcomplex", "dimensionhint", "nosoln", "nosolninf": "allowjcomplex" allows 2+3j instead of 2+3i
"dimensionhint" will show a warning to students if they enter the wrong number of components.
$answerformat = "nosoln" or "nosolninf" adds a list radio buttons for "no solutions" and optionally "infinite solutions". $ansprompt can override the default statements like this: $ansprompt = "One value, x=;No values;Many values"
$scoremethod = "byelement": By default, the whole n-tuple must be correct to receive any credit. Set $scoremethod = "byelement" to give partial credit if only some elements of the n-tuple are correct.
$partweights = ".2,.8": Can be used with $scoremethod = "byelement" to change the value of each part of the ntuple
$reltolerance = a decimal value: Defines the largest relative error that will be accepted. If this is not set, a relative error of .001 (.1%) is used by default.
$abstolerance = a number: Defines the largest absolute error that will be accepted. This will override the use of $reltolerance
$readerlabel = string: A string that will be used as a visually hidden label on the input box for screenreaders.
$answerbox (In Question Text): Using the variable $answerbox in the Question Text will place the question input drawing tool in that location
$showanswer: The answer to show to students (if option if available). Defaults to the text of the correct answer. Use this to substitute a detailed answer.
$hidetips = true: Hides the question entry tips that display by default. This should only be used when a question type is being used in an unintentional way, or if the question type gives away critical info to the student.

Calculated Complex N-Tuple

Calculated Complex N-Tuple questions require the student to enter an n-tuple or list of n-tuples of complex numbers. This can be used for coordinate points, vectors, or any other n-tuple of complex numbers. This is identical the the Complex N-tuple answer type, but allows students to enter mathematical expressions rather than just numbers, such as (5/3+sqrt(2)i, 2/3+1/4i).

Examples

// enter a complex point
$displayformat = "point"
$answer = "(2/3+3i,1/2-5i)"
$answerformat = "reducedfraction"

Required Variables

$answer = a string containing an n-tuple or list of n-tuples: Defines the answer n-tuple or list of n-tuples. N-tuples can be any dimension, but must be surrounded by any of: (), [], {}, <>. Examples: $answer = "(1/3+i,2)", $answer = "<2i,3,i>,<1+i,5,7>", $answer = "(1,2i) or (i,3)". Each complex number must be in a+bi format unless $answerformat="sloppycomplex" or "generalcomplex" is used.

Optional Variables

$displayformat = "point", "pointlist", "vector", "vectorlist", "list", "set", "setlist": Changes the answer entry tips (does NOT change how the question is graded). For points, entry like (2,3) is specified. For vectors, entry like <2,3> is specified.
$answerformat = "sloppycomplex", "generalcomplex", "allowjcomplex", "dimensionhint", "fraction", "reducedfraction", "mixednumber", "scinot", "fracordec", "nodecimal", "notrig", "nosoln", "nosolninf", "sameform": Use "sloppycomplex" to allow the student to enter complex numbers in forms other than a+bi (allows (4+sqrt(3)i)/5 for example). Student answer must still only contain one i.
Use "generalcomplex" to allow students to enter complex expressions that may involve calculations, like (e^(3i),4).
"allowjcomplex" allows for use of j instead of i as the imaginary unit.
"dimensionhint" will show a warning to students if they enter the wrong number of components.
The other options require each component of the answer to be a single fraction (like 10/6), a reduced fraction (like 5/3), a reduced mixed number (like 2_1/2), scientific notation (like 2.3*10^4), a single fraction or decimal, an answer without decimals (also disallows 10^-2 and 3E-2), or an answer without trig functions (sin,cos,tan,sec,csc,cot). Multiple options can be specified like $answerformat="nodecimal,notrig". Note that component-based answerformats won't be checked for sloppycomplex or generalcomplex.
$answerformat = "nosoln" or "nosolninf" adds a list radio buttons for "no solutions" and optionally "infinite solutions". $ansprompt can override the default statements like this: $ansprompt = "One value, x=;No values;Many values"
$scoremethod = "byelement": By default, the whole n-tuple must be correct to receive any credit. Set $scoremethod = "byelement" to give partial credit if only some elements of the n-tuple are correct.
$partweights = ".2,.8": Can be used with $scoremethod = "byelement" to change the value of each part of the ntuple
$reltolerance = a decimal value: Defines the largest relative error that will be accepted. If this is not set, a relative error of .001 (.1%) is used by default.
$abstolerance = a number: Defines the largest absolute error that will be accepted. This will override the use of $reltolerance
$readerlabel = string: A string that will be used as a visually hidden label on the input box for screenreaders.
$answerbox (In Question Text): Using the variable $answerbox in the Question Text will place the question input drawing tool in that location
$showanswer: The answer to show to students (if option if available). Defaults to the text of the correct answer. Use this to substitute a detailed answer.
$hidetips = true: Hides the question entry tips that display by default. This should only be used when a question type is being used in an unintentional way, or if the question type gives away critical info to the student.

Algebraic N-Tuple

Algebraic N-Tuple questions require the student to enter an n-tuple or list of n-tuples of algebraic expressions. This can be used for parameterized points or vectors, or any other n-tuple of algebraic expressions. This is similar to the other N-tuple answer types, but allows students to enter algebraic expressions rather than just numbers, such as (x, x^2, 4-x).

Examples

// enter a vector of functions
$displayformat = "vector"
$variables = "t"
$answer = "<cos(t),sin(t),t>"

Required Variables

$answer = a string containing an n-tuple or list of n-tuples: Defines the answer n-tuple or list of n-tuples. N-tuples can be any dimension, but must be surrounded by any of: (), [], {}, <>. Examples: $answer = "(x,x^2)", $answer = "<t,4-t,2+3t>,<t,3t,8t>", $answer = "(x,x^2) or (sqrt(x),x)". .

Optional Variables

$displayformat = "point", "pointlist", "vector", "vectorlist", "list", "set", "setlist": Changes the answer entry tips (does NOT change how the question is graded). For points, entry like (2,3) is specified. For vectors, entry like <2,3> is specified.
$variables = string: A list of all variables in the function (including letters representing constants). Defaults to "x". Can use "f()" to indicate a symbol represents a function.
$domain = "inputmin,inputmax": Defines the domain on which to compare the given answer and correct answer functions. The same domain applies to all variables. An option third list element "integers" can be given, which limits the domain to integer values. The domain defaults to real numbers from -10 to 10. If using multiple variables, can extend domain to define domain for each variable separately. Example: $variables = "x,y"; $domain = "0,5,20,25"
$answerformat = "generalcomplex", "dimensionhint", "nosoln", "nosolninf", "sameform": Use "generalcomplex" to allow students to enter complex functions involving i.
"dimensionhint" will show a warning to students if they enter the wrong number of components.
"sameform" requires the student's answer be in the "same form" as the correct answer. This means exactly the same, except for commutation of addition and multiplication, multiplication by 1, implicit multiplication, and extra parentheses. (2x-3)(5-x) would be "sameform" as (-1x+5)(2*x-3), but 2/4x and 1/2x and 0.5x would not be "sameform". Use with caution.
$answerformat = "nosoln" or "nosolninf" adds a list radio buttons for "no solutions" and optionally "infinite solutions". $ansprompt can override the default statements like this: $ansprompt = "One value, x=;No values;Many values"
$requiretimes = a list, like "^,=3,cos,<2": Adds format checking to the student's answer. The list can include multiple checks, which come in pairs. The first is the symbol to look for. The second describes what is acceptable. See the Function question type for more details. Note the $requiretimes applies to the student's entire answer.
$requiretimeslistpart = a list, in the same format as $requiretimes: Similar to $requiretimes, but this check is applied to each ntuple when the answer is a list of ntuples.
$scoremethod = "byelement": By default, the whole n-tuple must be correct to receive any credit. Set $scoremethod = "byelement" to give partial credit if only some elements of the n-tuple are correct.
$partweights = ".2,.8": Can be used with $scoremethod = "byelement" to change the value of each part of the ntuple
$reltolerance = a decimal value: Defines the largest relative error that will be accepted. If this is not set, a relative error of .001 (.1%) is used by default.
$abstolerance = a number: Defines the largest absolute error that will be accepted. This will override the use of $reltolerance
$readerlabel = string: A string that will be used as a visually hidden label on the input box for screenreaders.
$answerbox (In Question Text): Using the variable $answerbox in the Question Text will place the question input drawing tool in that location
$showanswer: The answer to show to students (if option if available). Defaults to the text of the correct answer. Use this to substitute a detailed answer.
$hidetips = true: Hides the question entry tips that display by default. This should only be used when a question type is being used in an unintentional way, or if the question type gives away critical info to the student.

Complex

Complex questions require the student to enter a complex number in a+bi form.

Examples

// basic answer
$answer = "$a + $b i"

Required Variables

$answer = a string containing a complex number or list of complex numbers: Defines the answer. Example: $answer="3+2i"

Optional Variables

$answerformat = "list" or "allowjcomplex": "list" Specifies that the answer will be a list of complex numbers. "allowjcomplex" allows 2+3j instead of 2+3i
$reltolerance = a decimal value: Defines the largest relative error that will be accepted. If this is not set, a relative error of .001 (.1%) is used by default.
$abstolerance = a number: Defines the largest absolute error that will be accepted. This will override the use of $reltolerance
$readerlabel = string: A string that will be used as a visually hidden label on the input box for screenreaders.
$answerbox (In Question Text): Using the variable $answerbox in the Question Text will place the question input drawing tool in that location
$showanswer: The answer to show to students (if option if available). Defaults to the text of the correct answer. Use this to substitute a detailed answer.
$hidetips = true: Hides the question entry tips that display by default. This should only be used when a question type is being used in an unintentional way, or if the question type gives away critical info to the student.

Calculated Complex

Calculated Complex questions require the student to enter a complex number in a+bi form. This is identical to the Complex answer type, but allows students to enter mathematical expressions rather than just numbers, such as 1/3+sqrt(2)i.

Examples

// basic answer
$answer = "1/2 + 3/4 i"

// to allow non-"a+bi" form 
$answerformat = "sloppycomplex"
$answer = "(5+3i)/2"

// allow plus/min
$answerformat = "sloppycomplex,allowplusminus"
$answer = "(3+-sqrt(2)i)/2"

// allow complex-equivalent
$answerformat = "generalcomplex"
$answer = -1 // will accept e^(i pi)

Required Variables

$answer = a string containing a complex number or list of complex numbers: Defines the answer. Example: $answer="3+2i", $answer="2/3+1/3i". The answer must be given in a + bi format (so 2+3isqrt(2) or 5/2+i/3 will not work) unless $answerformat="sloppycomplex" is used.

Optional Variables


$answerformat = "sloppycomplex", "generalcomplex", "allowjcomplex" "fraction", "reducedfraction", "mixednumber", "scinot", "fracordec", "nodecimal", "notrig", or "sameform": Use "sloppycomplex" to allow the student to enter complex numbers in forms other than a+bi (allows 2+3isqrt(2) for example). Student answer must still only contain one i.
Use "generalcomplex" to allow students to enter complex expressions that may involve calculations.
"allowjcomplex" allows for use of j instead of i as the imaginary unit.
The other options requires the real and imaginary parts of the answer to be a single fraction (like 10/6), a reduced fraction (like 5/3), a reduced mixed number (like 2_1/2), scientific notation (like 2.3*10^4), a single fraction or decimal, an answer without decimals (also disallows 10^-2 and 3E-2), or an answer without trig functions (sin,cos,tan,sec,csc,cot). Multiple options can be specified like $answerformat="nodecimal,notrig".
$answerformat = "list" specifies that the answer will be a list of complex numbers.
allowplusminus allow use of +- in the answer. Will enable the 'list' option if not already included.
$answerformat = "nosoln" or "nosolninf" adds a list radio buttons for "no solutions" and optionally "infinite solutions". $ansprompt can override the default statements like this: $ansprompt = "One value, x=;No values;Many values"
$reltolerance = a decimal value: Defines the largest relative error that will be accepted. If this is not set, a relative error of .001 (.1%) is used by default.
$abstolerance = a number: Defines the largest absolute error that will be accepted. This will override the use of $reltolerance
$readerlabel = string: A string that will be used as a visually hidden label on the input box for screenreaders.
$answerbox (In Question Text): Using the variable $answerbox in the Question Text will place the question input drawing tool in that location
$showanswer: The answer to show to students (if option if available). Defaults to the text of the correct answer. Use this to substitute a detailed answer.
$hidetips = true: Hides the question entry tips that display by default. This should only be used when a question type is being used in an unintentional way, or if the question type gives away critical info to the student.

Numerical Matrix

The student is asked to enter a matrix of numbers (integer, decimal, or scientific notation). The entries are compared to a given tolerance.

Examples

// standard entry; student will use equation editor 
$answer = "[(1,2),(3,4)]"

// provide a 2x3 grid of boxes to fill in 
$answersize = "2,3"
$displayformat = "augmented" // put augment lines in entry
$answer = "[(1,2,3),(4,5,6)]"

Required Variables

$answer = string describing a matrix of numbers, or calculations leading to numbers: Defines the answer. Example: $answer = "[(1,2,3),(8/2,5,6)]" is a 2x3 matrix with first row: 1,2,3

Optional Variables

$answersize = "rows,cols": Defines the size of the answer matrix. If this is supplied, the student will be provided with a grid of entry boxes in which to input the matrix. If this is not supplied, they will be required to enter the matrix using the ASCIIMath notation, like "[(1,2,3),(4,5,6)]"
$answerformat = "scalarmult" or "ref" or "rowequiv" or "anyroworder": If "scalarmult" used, any scalar multiple of the correct matrix will be accepted.
If "ref" is used, any row echelon form matrix that is row equivalent will be accepted.
If "rowequiv" is used, any matrix that is row equivalent will be accepted.
If "anyroworder" is used, any matrix equivalent up to row interchanges will be accepted.
$reltolerance = a decimal value: Defines the largest relative error that will be accepted. If this is not set, a relative error of .001 (.1%) is used by default.
$abstolerance = a number: Defines the largest absolute error that will be accepted. This will override the use of $reltolerance
$scoremethod = "byelement": By default, the whole matrix must be correct to receive any credit. Set $scoremethod = "byelement" to give partial credit if only some elements of the matrix are correct.
$displayformat = "det" or "inline" or "augmented": When $answersize is used, by default square brackets are used around the entry array. Set $displayformat = "det" to use vertical bars instead.
Normally matrices with $answersize set are displayed on their own line. Set $displayformat = "inline" to display it inline with text. Note that if the text is in a <p>, you may need to change that to a <div> wrapper for the matrix to stay inline.
Use $displayformat = "augmented" to display the usual augment bar before the last column.
$ansprompt = string: A string that will be displayed in front of the input box. Example: $ansprompt="y="
$answerboxsize = number: Determines the number of characters space provided for entry of an answer. Defaults to 20. Will only be used if $answersize is not supplied.
$readerlabel = string: A string that will be used as a visually hidden label on the input box for screenreaders.
$answerbox (In Question Text): Using the variable $answerbox in the Question Text will place the question input box in that location
$showanswer: The answer to show to students (if option if available). Defaults to $answer. Use this to substitute a detailed answer.
$hidetips = true: Hides the question entry tips that display by default. This should only be used when a question type is being used in an unintentional way, or if the question type gives away critical info to the student.

Calculated Matrix

The student is asked to enter a matrix of numbers or calculations, like 2/3 or 5^2. The entries are compared to a given tolerance.

Examples

// standard entry; student will use equation editor 
$answer = "[(1/2,2),(sqrt(3),4)]"

// provide a 2x3 grid of boxes to fill in 
$answersize = "2,3"
$answer = "[(1/2,2,5),(-1/3,5,6)]"
$answerformat = "fraction" // require entries be fractions

Required Variables

$answer = string describing a matrix of numbers, or calculations leading to numbers: Defines the answer. Example: $answer = "[(1,2,3),(8/2,5,6)]" is a 2x3 matrix with first row: 1,2,3

Optional Variables

$answersize = "rows,cols": Defines the size of the answer matrix. If this is supplied, the student will be provided with a grid of entry boxes in which to input the matrix. If this is not supplied, they will be required to enter the matrix using the ASCIIMath notation, like "[(1,2,3),(4,5,6)]"
$answerformat = "scalarmult","ref","rowequiv","anyroworder",fraction", "reducedfraction", "mixednumber", "scinot", "fracordec", "nodecimal", or "notrig": Requires the entries of the answer to be a single fraction (like 10/6), a reduced fraction (like 5/3), a reduced mixed number (like 2_1/2), scientific notation (like 2.3*10^4), a single fraction or decimal, an answer without decimals (also disallows 10^-2 and 3E-2), or an answer without trig functions (sin,cos,tan,sec,csc,cot). Multiple options can be specified like $answerformat="nodecimal,notrig".
If "scalarmult" used, any scalar multiple of the correct matrix will be accepted.
If "ref" is used, any row echelon form matrix that is row equivalent will be accepted.
If "rowequiv" is used, any matrix that is row equivalent will be accepted.
If "anyroworder" is used, any matrix equivalent up to row interchanges will be accepted.
$reltolerance = a decimal value: Defines the largest relative error that will be accepted. If this is not set, a relative error of .001 (.1%) is used by default.
$abstolerance = a number: Defines the largest absolute error that will be accepted. This will override the use of $reltolerance
$scoremethod = "byelement": By default, the whole matrix must be correct to receive any credit. Set $scoremethod = "byelement" to give partial credit if only some elements of the matrix are correct.
$displayformat = "det" or "inline" or "augmented": When $answersize is used, by default square brackets are used around the entry array. Set $displayformat = "det" to use vertical bars instead.
Normally matrices with $answersize set are displayed on their own line. Set $displayformat = "inline" to display it inline with text. Note that if the text is in a <p>, you `may need to change that to a <div> wrapper for the matrix to stay inline.
Use $displayformat = "augmented" to display the usual augment bar before the last column.
$ansprompt = string: A string that will be displayed in front of the input box. Example: $ansprompt="y="
$answerboxsize = number: Determines the number of characters space provided for entry of an answer. Defaults to 20. Will only be used if $answersize is not supplied.
$hidepreview = true: Hides the Preview button. Could be useful in multipart questions, but generally not recommended
$readerlabel = string: A string that will be used as a visually hidden label on the input box for screenreaders.
$answerbox (In Question Text): Using the variable $answerbox in the Question Text will place the question input box in that location
$showanswer: The answer to show to students (if option if available). Defaults to $answer. Use this to substitute a detailed answer.
$previewloc (In Question Text): Where you want the preview button to be located. Defaults to after the entry box if not placed in question text.
$hidetips = true: Hides the question entry tips that display by default. This should only be used when a question type is being used in an unintentional way, or if the question type gives away critical info to the student.

Complex Numerical Matrix

The student is asked to enter a matrix of complex numbers in a+bi form with decimal or integer coefficients.

Examples

// standard entry; student will use equation editor 
$answer = "[(1+i,2,3i),(8,5+i,6)]"

Required Variables

$answer = string describing a matrix of complex numbers: Defines the answer. Example: $answer = "[(1+i,2,3i),(8,5+i,6)]" is a 2x3 matrix with first row: 1+i,2,3i

Optional Variables

$answersize = "rows,cols": Defines the size of the answer matrix. If this is supplied, the student will be provided with a grid of entry boxes in which to input the matrix. If this is not supplied, they will be required to enter the matrix using the ASCIIMath notation, like "[(1+i,2,3i),(8,5+i,6)]" or using the equation editor palette.
$answerformat = "nosoln", "nosolninf": $answerformat = "nosoln" or "nosolninf" adds a list radio buttons for "no solutions" and optionally "infinite solutions". $ansprompt can override the default statements like this: $ansprompt = "One value, x=;No values;Many values"
$reltolerance = a decimal value: Defines the largest relative error that will be accepted. If this is not set, a relative error of .001 (.1%) is used by default.
$abstolerance = a number: Defines the largest absolute error that will be accepted. This will override the use of $reltolerance
$scoremethod = "byelement": By default, the whole matrix must be correct to receive any credit. Set $scoremethod = "byelement" to give partial credit if only some elements of the matrix are correct.
$displayformat = "det" or "inline" or "augmented": When $answersize is used, by default square brackets are used around the entry array. Set $displayformat = "det" to use vertical bars instead.
Normally matrices with $answersize set are displayed on their own line. Set $displayformat = "inline" to display it inline with text.
Use $displayformat = "augmented" to display the usual augment bar before the last column.
$ansprompt = string: A string that will be displayed in front of the input box. Example: $ansprompt="y="
$answerboxsize = number: Determines the number of characters space provided for entry of an answer. Defaults to 20. Will only be used if $answersize is not supplied.
$readerlabel = string: A string that will be used as a visually hidden label on the input box for screenreaders.
$answerbox (In Question Text): Using the variable $answerbox in the Question Text will place the question input box in that location
$showanswer: The answer to show to students (if option if available). Defaults to $answer. Use this to substitute a detailed answer.
$hidetips = true: Hides the question entry tips that display by default. This should only be used when a question type is being used in an unintentional way, or if the question type gives away critical info to the student.

Calculated Complex Matrix

The student is asked to enter a matrix of complex numbers or calculations, like 2/3+1/3i or 5^2.

Examples

// 2x2 grid of boxes to enter answer
$answersize = "2,2"
$answer = "[(1/2+i,3i),(8,5+i)]"
$answerformat = "nodecimal" // disallow decimal answers

Required Variables

$answer = string describing a matrix of complex numbers, or calculations leading to numbers: Defines the answer. Example: $answer = "[(1+i,2,3i),(3/2+i,3sqrt(2)i,6)]" is a 2x3 matrix with first row: 1+i,2,3i

Optional Variables

$answersize = "rows,cols": Defines the size of the answer matrix. If this is supplied, the student will be provided with a grid of entry boxes in which to input the matrix. If this is not supplied, they will be required to enter the matrix using the ASCIIMath notation, like "[(1+i,2,3i),(3/2+i,3sqrt(2)i,6)]" or use the equation editor palette
$answerformat = "sloppycomplex", "generalcomplex", "allowjcomplex", "fraction", "reducedfraction", "mixednumber", "scinot", "fracordec", "nodecimal", or "notrig", "nosoln","nosolninf": Use "sloppycomplex" to allow the student to enter complex numbers in forms other than a+bi (allows (4+sqrt(3)i)/5 for example). Student answer must still only contain one i.
Use "generalcomplex" to allow students to enter complex expressions that may involve calculations, like e^(3i).
"allowjcomplex" allows for use of j instead of i as the imaginary unit.
The other options require each of the coefficients of the entries of the answer to be a single fraction (like 10/6), a reduced fraction (like 5/3), a reduced mixed number (like 2_1/2), scientific notation (like 2.3*10^4), a single fraction or decimal, an answer without decimals (also disallows 10^-2 and 3E-2), or an answer without trig functions (sin,cos,tan,sec,csc,cot). Multiple options can be specified like $answerformat="nodecimal,notrig".
$answerformat = "nosoln" or "nosolninf" adds a list radio buttons for "no solutions" and optionally "infinite solutions". $ansprompt can override the default statements like this: $ansprompt = "One value, x=;No values;Many values"
$reltolerance = a decimal value: Defines the largest relative error that will be accepted. If this is not set, a relative error of .001 (.1%) is used by default.
$abstolerance = a number: Defines the largest absolute error that will be accepted. This will override the use of $reltolerance
$scoremethod = "byelement": By default, the whole matrix must be correct to receive any credit. Set $scoremethod = "byelement" to give partial credit if only some elements of the matrix are correct.
$displayformat = "det" or "inline" or "augmented": When $answersize is used, by default square brackets are used around the entry array. Set $displayformat = "det" to use vertical bars instead.
Normally matrices with $answersize set are displayed on their own line. Set $displayformat = "inline" to display it inline with text.
Use $displayformat = "augmented" to display the usual augment bar before the last column.
$ansprompt = string: A string that will be displayed in front of the input box. Example: $ansprompt="y="
$answerboxsize = number: Determines the number of characters space provided for entry of an answer. Defaults to 20. Will only be used if $answersize is not supplied.
$hidepreview = true: Hides the Preview button. Could be useful in multipart questions, but generally not recommended
$readerlabel = string: A string that will be used as a visually hidden label on the input box for screenreaders.
$answerbox (In Question Text): Using the variable $answerbox in the Question Text will place the question input box in that location
$showanswer: The answer to show to students (if option if available). Defaults to $answer. Use this to substitute a detailed answer.
$previewloc (In Question Text): Where you want the preview button to be located. Defaults to after the entry box if not placed in question text.
$hidetips = true: Hides the question entry tips that display by default. This should only be used when a question type is being used in an unintentional way, or if the question type gives away critical info to the student.

Algebraic Matrix

The student is asked to enter a matrix of algebraic expressions, like x^2 or 3t+1.

Examples

$answer = "[(x,x^2,3),(4,5+x,2)]"

Required Variables

$answer = string describing a matrix of algebraic expressions: Defines the answer. Example: $answer = "[(x,x^2,3),(4,5+x,2)]" is a 2x3 matrix with first row: x,x^2,3

Optional Variables

$answersize = "rows,cols": Defines the size of the answer matrix. If this is supplied, the student will be provided with a grid of entry boxes in which to input the matrix. If this is not supplied, they will be required to enter the matrix using the ASCIIMath notation, like "[(x,x^2,3),(4,5+x,2)]" or use the equation editor palette
$variables = string: A list of all variables in the function (including letters representing constants). Defaults to "x". Can use "f()" to indicate a symbol represents a function.
$domain = "inputmin,inputmax": Defines the domain on which to compare the given answer and correct answer functions. The same domain applies to all variables. An option third list element "integers" can be given, which limits the domain to integer values. The domain defaults to real numbers from -10 to 10. If using multiple variables, can extend domain to define domain for each variable separately. Example: $variables = "x,y"; $domain = "0,5,20,25"
$answerformat = "generalcomplex", "nosoln", "nosolninf", "sameform": Use "generalcomplex" to allow students to enter complex functions involving i.
"sameform" requires the student's answer be in the "same form" as the correct answer. This means exactly the same, except for commutation of addition and multiplication, multiplication by 1, implicit multiplication, and extra parentheses. (2x-3)(5-x) would be "sameform" as (-1x+5)(2*x-3), but 2/4x and 1/2x and 0.5x would not be "sameform". Use with caution.
$answerformat = "nosoln" or "nosolninf" adds a list radio buttons for "no solutions" and optionally "infinite solutions". $ansprompt can override the default statements like this: $ansprompt = "One value, x=;No values;Many values"
$reltolerance = a decimal value: Defines the largest relative error that will be accepted. If this is not set, a relative error of .001 (.1%) is used by default.
$abstolerance = a number: Defines the largest absolute error that will be accepted. This will override the use of $reltolerance
$scoremethod = "byelement": By default, the whole matrix must be correct to receive any credit. Set $scoremethod = "byelement" to give partial credit if only some elements of the matrix are correct.
$displayformat = "det" or "inline" or "augmented": When $answersize is used, by default square brackets are used around the entry array. Set $displayformat = "det" to use vertical bars instead.
Normally matrices with $answersize set are displayed on their own line. Set $displayformat = "inline" to display it inline with text.
Use $displayformat = "augmented" to display the usual augment bar before the last column.
$ansprompt = string: A string that will be displayed in front of the input box. Example: $ansprompt="y="
$answerboxsize = number: Determines the number of characters space provided for entry of an answer. Defaults to 20. Will only be used if $answersize is not supplied.
$hidepreview = true: Hides the Preview button. Could be useful in multipart questions, but generally not recommended
$readerlabel = string: A string that will be used as a visually hidden label on the input box for screenreaders.
$answerbox (In Question Text): Using the variable $answerbox in the Question Text will place the question input box in that location
$showanswer: The answer to show to students (if option if available). Defaults to $answer. Use this to substitute a detailed answer.
$previewloc (In Question Text): Where you want the preview button to be located. Defaults to after the entry box if not placed in question text.
$hidetips = true: Hides the question entry tips that display by default. This should only be used when a question type is being used in an unintentional way, or if the question type gives away critical info to the student.

Interval

A student is asked to enter an interval notation answer. Example: (2,5]U(7,oo)

Examples

// an interval notation answer
$answer = "(2,3]"

// two acceptable answers 
$answer = "(2,3) or [2,3]"

Required Variables

$answer = a string with the answer in interval notation: Defines the answer. Join multiple intervals with U for union. Example: $answer = "(-oo,4]U(3,oo)". Use DNE for empty set. Multiple acceptable answers can be entered using "or". Example: $answer = "(3,3) or [3,3]"

Optional Variables

$reltolerance = a decimal value: Defines the largest relative error that will be accepted. If this is not set, a relative error of .001 (.1%) is used by default.
$abstolerance = a number: Defines the largest absolute error that will be accepted. This will override the use of $reltolerance
$reqdecimals = a number: Defines the decimal accuracy required (ie 2 for two decimal places). This will put a message in the answer tips stating the decimals required. If neither $abstolerance or $reltolerance is set, this will set the tolerance, otherwise the provided tolerance will be used (even if it doesn't agree with the $reqdecimal setting).
$answerformat = "normalcurve" or "list" or "allowsloppyintervals": "normalcurve" Changes the question to use a "shade the area under the normal curve" widget. Define $answer using the open interval that should be shaded. Note that the shading tool only allows selection of z-values to 1 decimal place.
"list" will accept a list of comma-separated intervals like $answer="[2,3),(5,7)"
"allowsloppyintervals" will accept unsimplified unions, so will count [2,5)U(3,7) as equivalent to [2,7)
$scoremethod = "partialcredit": By default, interval answers will be marked all right or all wrong. Setting $scoremethod = "partialcredit" will changing the scoring mode to give partial credit. (new assessment system only).
$ansprompt = string: A string that will be displayed in front of the input box. Example: $ansprompt="`x in`"
$answerboxsize = number: Determines the number of characters space provided for entry of an answer. Defaults to 20.
$readerlabel = string: A string that will be used as a visually hidden label on the input box for screenreaders.
$answerbox (In Question Text): Using the variable $answerbox in the Question Text will place the entry box in that location
$showanswer: The answer to show to students (if option if available). Defaults to the text of the correct answer. Use this to substitute a detailed answer.
$hidetips = true: Hides the question entry tips that display by default. This should only be used when a question type is being used in an unintentional way, or if the question type gives away critical info to the student.

Calculated Interval

A student is asked to enter an interval notation answer. Example: (2,5]U(7,oo). Values can be entered as calculations rather than numbers, like [2/5,sqrt(8)]. Can use $answerformat="inequality" to require the student to use inequalities rather than interval notation.

Examples

// an interval notation answer
$answer = "(1/2,5]U(7,oo)"
$answerformat = "fraction" // require fraction answers

// inequality format answer
$answerformat = "inequality"
$variables = "t"
// $answer is still specified in interval notation, 
// but student will enter t>=2
$answer = "[2,oo)"

Required Variables

$answer = a string with the answer in interval notation: Defines the answer. Join multiple intervals with U for union, and oo for infinity. Example: $answer = "(-oo,4]U(9/2,oo)". Use DNE for empty set. Multiple acceptable answers can be entered using "or". Example: $answer = "(3,3) or [3,3]".

Optional Variables

$answerformat = "fraction", "reducedfraction", "mixednumber", "scinot", "fracordec", "nodecimal", "notrig", "list", "allowsloppyintervals", or "inequality": Requires the each value in the answer to be a single fraction (like 10/6), a reduced fraction (like 5/3), a reduced mixed number (like 2_1/2), scientific notation (like 2.3*10^4), a single fraction or decimal, an answer without decimals (also disallows 10^-2 and 3E-2), or an answer without trig functions (sin,cos,tan,sec,csc,cot). Multiple options can be specified like $answerformat="nodecimal,notrig".
$answerformat = "inequality" will require the student to enter an inequality rather than an interval. The instructor answer must still be given in interval notation (it will be reformatted to an inequality automatically for the Show Answer). Use $variables="y" to change the variable of the inequality.
"list" will accept a list of comma-separated intervals like $answer="[2,3),(5,7)". Does not work with "inequality".
"allowsloppyintervals" will accept unsimplified unions, so will count [2,5)U(3,7) as equivalent to [2,7)
$reltolerance = a decimal value: Defines the largest relative error that will be accepted. If this is not set, a relative error of .001 (.1%) is used by default.
$abstolerance = a number: Defines the largest absolute error that will be accepted. This will override the use of $reltolerance
$reqdecimals = a number: Defines the decimal accuracy required (ie 2 for two decimal places). This will put a message in the answer tips stating the decimals required. If neither $abstolerance or $reltolerance is set, this will set the tolerance, otherwise the provided tolerance will be used (even if it doesn't agree with the $reqdecimal setting).
$scoremethod = "partialcredit": By default, interval answers will be marked all right or all wrong. Setting $scoremethod = "partialcredit" will changing the scoring mode to give partial credit. Note that answers not meeting $answerformat requirements will have deductions in addition to correctness checks. (new assessment system only).
$ansprompt = string: A string that will be displayed in front of the input box. Example: $ansprompt="`x in`"
$answerboxsize = number: Determines the number of characters space provided for entry of an answer. Defaults to 20.
$readerlabel = string: A string that will be used as a visually hidden label on the input box for screenreaders.
$answerbox (In Question Text): Using the variable $answerbox in the Question Text will place the entry box in that location
$showanswer: The answer to show to students (if option if available). Defaults to the text of the correct answer. Use this to substitute a detailed answer.
$previewloc (In Question Text): Where you want the preview button to be located. Defaults to after the entry box if not placed in question text.
$hidetips = true: Hides the question entry tips that display by default. This should only be used when a question type is being used in an unintentional way, or if the question type gives away critical info to the student.

Chemical Equation

A student is asked to enter a chemical formula, or use $answerformat="reaction" to ask for a reaction equation.

Examples

// A basic molecule answer
$answer = "Ca (O H)_2"

// a reaction 
$answerformat = "reaction"
$answer = "2H+O->H_2O"
$variables = "H,O" // adds buttons to the editor

Required Variables

$answer = a string with the answer: Defines the answer, like "H_2O". Spaces are ignored. For reactions, use -> for a right arrow, and <-> for an equilibrium arrow, like "2H+O->H_2O".

Optional Variables

$answerformat = "reaction": Use "reaction" if you're asking for a reaction equation.
$variables = a list of atoms: Define this to populate the equation editor with the specified atoms.
$answerboxsize = number: Determines the number of characters space provided for entry of an answer. Defaults to 20.
$readerlabel = string: A string that will be used as a visually hidden label on the input box for screenreaders.
$answerbox (In Question Text): Using the variable $answerbox in the Question Text will place the entry box in that location
$showanswer: The answer to show to students (if option if available). Defaults to the text of the correct answer. Use this to substitute a detailed answer.

Chemical Molecule Drawing

A student is asked to enter a sketch a molecule, using the Kekule drawing tool. If the student has enabled the keyboard-based drawing accessibility option, they will be presented with a textbox for them to write out a description instead.

Required Variables

$answer = "SMILES~~~CML": Defines the answer, which includes the SMILES representation of the molecule, as well as the CML representation used for displaying the answer key. Use our answer generator to draw the answer and generate the $answer string. You can specify multiple acceptable answers separated by or, like "SMILES~~~CML or SMILES~~~CML"

Optional Variables

$displayformat (In Common Control): Set to "condensed" to display the atom labels on the drawing.
$answerbox (In Question Text): Using the variable $answerbox in the Question Text will place the entry box in that location
$showanswer: The answer to show to students (if option if available). Defaults to a drawing of the correct answer. Use this to substitute a detailed answer.

File Upload

A student is asked to upload a file. The file upload type is not automatically graded. The file must be an allowed file type, one of these extensions: @whitelist@.

Required Variables

None - the file upload type is not computer graded.

Optional Variables

$scoremethod = "takeanything" or "takeanythingorblank": Sets the problem to give full credit for any answer. The latter also counts blank answers as correct.
$answerformat = "images", "canpreview", or a list of file extensions: Set a list of preferred file formats for the file selector. "images" is a shorthand for .jpg,.gif,.png,.jpeg. "canpreview" is a shorthand for image files, office files, and pdfs, which can be previewed inline. If listing file extensions, provide a comma separated list with leading periods, like ".pdf,.docx,.doc"
$readerlabel = string: A string that will be used as a visually hidden label on the input box for screenreaders.
$answerbox (In Question Text): Using the variable $answerbox in the Question Text will place the file upload box in that location
$showanswer: The answer to show to students (if option if available).
$hidetips = true: Hides the question entry tips that display by default. This should only be used when a question type is being used in an unintentional way, or if the question type gives away critical info to the student.

Multipart

This type of question can contain multiple parts, where each part is one of the previous question types.

Examples

// A basic multipart question with an ntuple part and an expression
$anstypes = "ntuple,numfunc"
$displayformat[0] = "point" // sets displayformat on part index 0
// answer to the first part (index 0): coordinate of vertex
$answer[0] = "($h,$k)"
// answer to second part: equation of parab 
$answer[1] = "(x-$h)^2+$k"

// A multipart question with 3 number parts 
$anstypes = fillarray("number",3)
// the answers to the parts, defined as 
$answer[0] = $a 
$answer[1] = $b 
$answer[2] = $c 
// if we don't index an option, it will apply to all parts 
$answerboxsize = 3

Required Variables

$anstypes = an array or list of answer types

Defines the answer type for each part. Example: $anstypes = array("number","number","choices")
Refer to this list for the short names of each question type:

Number: "number"
Calculated: "calculated"
Multiple Choice: "choices"
Multiple Answer: "multans"
Matching: "matching"
Function/expression: "numfunc"
Drawing: "draw"
N-tuple: "ntuple"
Calculated N-tuple: "calcntuple"
Complex N-tuple: "complexntuple"
Calculated Complex N-tuple: "calccomplexntuple"
Algebraic N-tuple: "algntuple"
Matrix: "matrix"
Calculated Matrix: "calcmatrix"
Complex Matrix: "complexmatrix"
Calculated Complex Matrix: "calccomplexmatrix"
Algebraic Matrix: "algmatrix"
Complex: "complex"
Calculated Complex: "calccomplex"
Interval: "interval"
Calculated Interval: "calcinterval"
Chemical Equation: "chemeqn"
Chemical Molecule Drawing: "molecule"
Essay: "essay"
File Upload: "file"
String: "string"

Question part variables

For each question part, you will need to define the variables (like $answer, $questions, etc.) you would normally need to define. However, you will need to suffix the variable with a part designator. For example, based on $anstypes above, the first answer is a number. Instead of $answer = 5, enter $answer[0] = 5. This designates that this answer belongs to the first element of $anstypes. Likewise, to set the variables for the "numfunc" type, you'd set $variables[5] = "x". Note that if you do not index the variable, it will apply to all parts. See $defaults below for more info and other options.

$answerbox[partnum] (In Question Text)

The array $answerbox will contain the entry boxes for each answer type. In the question text, you will need to position these boxes within the question. For example: "Enter a number: $answerbox[0]. Now a function: $answerbox[1]". Alternatively, you can use [AB#]: "Enter a number: [AB0]. Now a function: [AB1]"

Optional Variables

$answeights = an array or list of weights for each question: By default the points for a problem are divided evenly over the parts. Use this option if you wish to weight parts differently. Example: $answeights = array(.2,.3,.5). Best practice is to use percents, but if other values are used, they will be converted to percents.
$scoremethod = "singlescore" or "allornothing": Instead of recording individual scores for each question part, these will cause a single score to be recorded for the question. "singlescore" totals the individual part scores, while "allornothing" will only give full credit or no credit. If you need to specify per-part indexed scoremethod values as well, you can define this as the array value $scoremethod['whole'] instead.
Question part options: You can define any optional variable for each question part. Like above, suffix the variable with the part designator.
$defaults: To set an optional variable to the same value for every question part, you can simply specify it without index, like $reqdecimals=1, and it will apply to all parts. But if you do this, you can't set an indexed value for one one/some parts. If you want to change the default value for most parts but have a different value for some, set $defaults['variable'] = value, like $defaults['answerboxsize'] = 5, and that will change the default value for that variable, and you can still override that default for specific parts, like $answerboxsize[2]=3. Be aware that using $defaults will generally apply the variable for ALL parts, which may cause some unexpected behavior. Note that defaults for abstolerance or reltolerance will not be applied to Drawing question parts, since those variables have special meaning in that context.
$disablePartsWhenCorrect: Indicates you want a question input disabled if it's correct, preventing changing existing answers. Set in general, or indexed for specific parts. Generally not necessary, but may be useful in certain cases where later answers depend on earlier ones.
$showanswer: You can either define $showanswer for individual question parts (ie, $showanswer[1]="`x^2`"), or you can set one $showanswer, which will be the only answer shown for the problem (ie, $showanswer = "x=$answer[0], y=$answer[1]")
$showanswerloc (In Question Text): Optionally, you can use $showanswerloc to place a single $showanswer "Show Answer" button, or $showanswerloc[part] to place "Show Answer" buttons for each part. You can also use short tags of the form [SAB] or [SABn] (like [SAB2]). Note that if you use this to place one Show Answer button, and have defined $showanswer[n] for only some parts, you must place [SABn] for all parts, or else the remainder will not show. To define a single Show Answer for a sequential set of parts, define $showanswer[n] using the last part number in the set, and put [SABn-n] in the question text to place the Show Answer button for that set of parts. For example, if you parts 2-4 were to have a single key, you'd define $showanswer[4] and put [SAB2-4] in the question text.
$showanswerstyle: Use $showanswerstyle = 'inline' to allow Show Answer buttons placed using $showanswerloc or [SABn] to be placed inline with text rather than on its own line.
[SAB#] (In Detailed Solution): To include the generated "show answer" values in the detailed solution, you can use short tags like [SAB2]. Note that this will place the "show answer" directly, not wrapped in a button like in question text.

Scaffolding

Scaffolded questions, also know as Sequential Multipart questions, allow you to break a question up into chunks, where the second chunk only shows after the first chunk is correctly answered or the student runs out of tries. This allows you to use the answer to the first chunk in the second without "giving away" the answer, and allows a student who gets stuck on the first chunk to move on to the rest of the question.

Note: scaffolding is only available in the new assessment interface. If you are using the old interface, the question will behave like a regular multipart question.

Scaffolded questions are an extension of Multipart questions. To turn a multipart question into a scaffolded question, just add an isolated line with three or more slashes in the Question Text where you want the chunks broken apart.

An example: (in the Question Text)

To simplify $a(x+$b) + $c, first we need to distribute:

$a(x+$b) = $answerbox[0]

///

Next, combine like terms:

$a x + $ab + $c = $answerbox[1]

Conditional

A variation on multipart questions, a conditional question can include multiple answer boxes, but assigns a single score. The score is based on applying some comparison or conditional test to the student answers, referenced through the $stuanswers array. This allows the question writer to essentially create their own question type.

Examples

// A simple "two numbers that add to 5"
$anstypes = "number,number"
if (stuansready($stuanswers,$thisq,[0,1],$anstypes,'checknumeric')) {
	$a = getstuans($stuanswers, $thisq, 0)
	$b = getstuans($stuanswers, $thisq, 1)
	$answer = comparenumbers($a+$b, 5) // answer can be true/false
}

Required Variables

$anstypes = an array or list of answer types

Defines the answer type for each part. Example: $anstypes = "number,number". See the Multipart help above for the list of short names

$answer = any of these:

A boolean (true/false) expression: Something that evaluates to true or false.
Example: $answer = ($a>3)
Example: $answer = comparefunctions($f,'x^2') && ($a!=0)
A single numerical value in the interval [0,1]: will award that percentage of the total possible points.
The string 'manual': will assign a score of 0 but treat the whole question as a manual-grade question.
array('function',$a,$b): Will compare the functions $a and $b and mark the question correct if they are equivalent. Can set $variables, $reltolerance, $abstolerance, and $domain as needed, like with Function type questions
array('number',$a,$b): Will compare the numbers or numerical expressions $a and $b and mark the question correct if they are equivalent. Can set $reltolerance or $abstolerance as needed, like with Number/Calculated type questions
Multiple comparisons: You can mix the two types above by creating an array of comparisons. All must be true for the question to be marked correct.
Example: $answer = array($a>3, array('function',$b,c), array('number',evalfunc($b,$a),5))

Question part variables

For each question part, you will need to define the variables (like $questions, etc.) you would normally need to define, except you should not define an $answer. However, you will need to suffix the variable with a part designator. For example, based on $anstypes above, the first answer is a number. Instead of $displayformat = "select", enter $displayformat[0] = "select". This designates that this setting belongs to the first element of $anstypes.

$answerbox[partnum] (In Question Text)

Optional Variables

Question part options: You can define any optional variable for each question part. Like above, suffix the variable with the part designator. Note that $variables, $domain, $reltolerance, and $abstolerance may be used for the comparison, and should not be set for individual parts.
$showanswer: By default the $showanswer for conditional types is "Answers may vary". Set $showanswer to override this.

Scaffolding

While not as simple as scaffolding multipart questions, you can add scaffolding to a Conditional question. As with multipart, put an isolated line with three slashes in the question text to indicate where the breaks occur. Then you will need to set $seqPartDone[pn] to true for each part index once that part should be considered completed. The scaffolding will move onto the next chunk when all parts in the previous chunk have $seqPartDone set to true.

IMathAS Help Documentation

Table of Contents

Administration

Creating Courses

Course Creation Settings

Adding Teachers

Transfering Ownership

Deleting

Question Set Management

Manage Question Set

Library Management

Manage Libraries

Export Libraries

Import Libraries

Install Macro File

Delete Old Users

Import Students from File

Manage Groups

Diagnostics

Managing Administrators and Teachers

Adding Administrators and Teachers

Rights

Resetting Admin Passwords

Deleting

Course Management

Course Page Layout

Adding Items

Blocks

Inline Text Items

Linked Text Items

Forum Items

Assessments

Assessment Settings

Adding Questions to an Assessment

Icons used in question listing

Adding an Introduction to a Question

After the Assessment has been Taken

Adding New Questions

Categorizing Questions

Making Print Copies

Quick View

Calendar

Question Set Management

Manage Question Set

Library Management

Manage Libraries

Export Libraries

Import Libraries

List Students

Exceptions

Resetting Passwords / Changing Info

Unenrolling

Import Students from File

Assigning Section and/or Code Numbers

Manage LatePasses

Manage Tutors

Gradebook

Gradebook Settings and Categories

Offline Grades

Gradebook Detail

Student Groups

Messages

Copy Course Items

Change Dates

Change Assessments

Import/Export Course Items (for another IMathAS system)

LTI Integration

LTI 1.1

LTI 1.3

Canvas Integration - Using Import

Canvas Integration - Manual Process

Blackboard Integration - older Common Cartridge Instructions

Blackboard Integration - Using Import

Blackboard Integration - Manual Process

D2L Brightspace Integration

Moodle Integration

LTI Integration for Other LMSs - Using Import

LTI Integration for Other LMSs - Manual Process

Writing Questions

Question Parts