This document will guide you through the process of writing an example IMathAS Question. This is meant to be an introduction. This is not a comprehensive guide; please refer to the help file for more detailed information.

Start out by clicking the "Manage Question Set" link from the grey control box on the course page. Click "Add New Question". This will take you to the question editor

A question has several parts:

- Description: What displays to the instructor in the question list. Be specific in your question descriptions.
- Use Rights: What you will allow others to do with this questions
- Author: This is automatically set by the system.
- Assign to Library: Which question library your question will be recorded in
- Question Type: What the question type is (number, function, matrix, etc)
- Common Control: Code common to both the question and the answer
- Question Control: Code only needed for the question text
- Question Text: Where you actually write the question to be displayed to students
- Answer: Code defining the answer

**Note:** It is not necessary to use the Question Control and Answer boxes; you can place all
your control code in the Common Control box. For short questions, using just
Common Control and Question Text is fine. For complicated questions, you may find using all four
boxes helpful.

Each question type has specific requirements. You can click the "Writing Questions Help" link above the Common Control box to pop up that section of the help file

For this example, let's write a question asking students to write the equation for a graphed parabola. In the description box, enter something like "Write equation for parabola, form y=a(x-b)^2+c"

Let's leave this as the default "Allow use, use as template, no modifications". This allows other to use your question or derive new questions based on this one, but they cannot modify this question itself.

If you have set up a scratch-work library, click the "Select Library" button and choose that library. Otherwise, it is fine to leave this as "Unassigned" for now

We want students to enter an equation for the curve, so select the type "Function" from the pull-down.

To write our question, we need to pick values for a, b, and c. In order for the question to change for each student, we need to have these values randomly chosen. Enter:

$b,$c = nonzerodiffrands(-3,3,2) $a = nonzerorand(-2,2) $eqn = makepretty("$a*(x-$b)^2+$c")

The first line defines two variables, $b and $c. Notice that variables start with a dollar sign. The randomizer we are using is "nonzerodiffrands" which, as you might guess, will return different, nonzero integers. We have specified that we want numbers between -3 and 3, and want 2 of them.

The second line defines the variable $a. The randomizer "nonzerorand" returns a single nonzero random number, in this case between -2 and 2.

If we simply entered the question as "$a*(x-$b)^2+$c", it will not display the way we want if $b or $c are negative. To fix this, we use the function "makepretty", which cleans up double sign problems. We put the equation in quotes because it is a string, not a calculation we want to perform.

We have not defined the variables in our equation or its domain. These default to "x" for the variable, and -5 to 5 for the domain, so we really don't need to in this case.

We want to display a graph to the student. We'll define the graph here:

$graph = showplot("$eqn,red",-6,6,-6,6)

"showplot" creates a graph. In quotes is the definition of the function to be graphed. It's equation is given by y=$eqn, and we want it graphed in red. Additional options allow defining a limited domain, open and closed dots, width, dashing, etc. The next numbers (-6,6,-6,6) define the viewing window. Additional options allow changing the axis labeling, grid spacing, and the display size of the graph

Time to actually write the question! Enter

Find an equation for the graph shown below. (<i>Hint</i>: use the form `y=a(x-h)^2+k`) $graph `y=` $answerbox

Notice the use of the HTML tag <i> to create italic text. All HTML tags are valid in IMathAS questions. An empty line, however, is automatically turned into a paragraph break.

Notice also that the equation in the hint is enclosed in backticks, \`. Anything enclosed in backticks is rendered as pretty math. Enter the math using standard calculator-style notation. There are also ways to display more advanced math (example: \`int_3^5 x^2 dx\` would display as `int_3^5 x^2 dx`)

On the last line, the variable $answerbox is used. This variable allows you to place the answer entry box anywhere in the question. It is not necessary to do so, but in this case, I wanted to preface the answer box with "y=" so the student would know they don't need to enter the "y=" part of the equation

Time to specify the answer. Enter:

$answer = $eqn $showanswer = "`y=$eqn`"

The first line defines the answer. In this case, the answer was just the equation we used for graphing. The second line defines the answer to show to students (if the show answers option is selected).

We could have given more detail in the $showanswer. For example, we could have written (without line breaks):

$testx = $b+1 $testy = $a*($testx - $b)^2+$c $showanswer = "Notice the vertex is at ($b,$c). Using the form `y=a(x-h)^2+k`, this gives `y=a(x-($b))^2+($c)`. Plugging in the point ($testx,$testy) for `x` and `y` allows us to solve for a, leading to `y=$eqn`"

Click the "Save and Test Question" button at the bottom of the page. This will save the question and pop up a window displaying the question. Try entering the answer and clicking "Submit". The system will display your score on the question, and display a new version of the question. Testing a question several times is essential to ensuring that it is behaving the way you want, and you didn't miss something (like not using nonzero random numbers).

When you are done, click "Update Question", or just navigate back to the Manage Question Set page. You should now see your question in the list (unless you assigned it to a different library than you're currently viewing).

To create a new question, it is often quickest to not start from scratch. If you click on the Template link next to any question, it will create a new question, starting with all the code from an existing question. This way you can create a similar but new question without starting from scratch and without losing the original question.

© 2006 David Lippman

This guide was written with development grant support from the WA State Distance Learning Council