How do I...

This section largely draws from the “How-tos” project on the numbas.mathcentre.ac.uk editor, where we gather example questions created to demonstrate authoring techniques.

If you’ve got a question that isn’t answered here, try asking on the Numbas users mailing list.

Images, diagrams and other media

Include an image

It’s best practice to attach images to questions so that they’re distributed with the final compiled exam, rather than linking to images stored on a webserver.

When editing a content area, click on the Insert/Edit Image button. You can then either pick an image you’ve already uploaded, or click the Choose file button to upload an image from your computer.

You can resize images and add a title attribute by selecting the image in the content area and clicking on the Insert/Edit Image button.

Embed a video

Upload your video to somewhere like YouTube or Vimeo. Including videos in downloaded exam packages is a terrible idea, so we discourage that. Click the Embed image/video button (it’s a blue cloud), and paste in the URL of your video.

Include an interactive diagram

There are a couple of ways of including an interactive diagram in a Numbas question. You can either embed a GeoGebra applet, or use JSXGraph.

For JSXGraph diagrams, there is an extension which takes care of most of the setup. You will need to write a fair amount of JavaScript code to create a diagram using JSXGraph.

GeoGebra applets are much easier to create and use, but are loaded from geogebra.org so the student must have internet access in order to use any questions containing GeoGebra applets.

The screencast below explains how to use a GeoGebra applet in a question. For more information, see the page on the geogebra extension.

Display a random line in a GeoGebra applet

A neat way to create a random line is to randomly pick the positions of two points on the line.

Create two points in your GeoGebra worksheet, and a line between those two points. Set the positions of the points in the parameters to the geogebra_applet function.

See this example question.

Use student input in a JSXGraph diagram

This question shows how to construct a line corresponding to an equation given by the student.

Appearance and display

Change how the question looks

You can use the formatting tools in the question editor to style your text. However, if you repeat the same styles over and over, or want to change aspects of the layout such as space between elements or decoration, you’ll need to write some CSS.

CSS is a language for defining how things should look - there’s a good introduction at Khan Academy. In the Numbas editor, you can add CSS rules to a question in the Preamble section.

The following questions demonstrate how to use CSS to change the look of a Numbas question:

Reveal the answer to a single part after submitting an answer

Someone wanted to know how to reveal the answer to one part of a question as soon as the student submits an answer, because the following part depends on having the correct answer to the first part.

This example question shows a few different ways of doing this.

Think very carefully before using this: by revealing the answer, you are removing the opportunity for the student to later on realise they’ve got that step wrong, as a consequence of some further work. It’s often possible to use adaptive marking to use the student’s answer in place of the correct answer in later parts.

Set an attribute on an HTML element based on the value of a question variable

Use the Source code view in a content area to edit its HTML code. You can set the value of an attribute on an HTML tag to the result of a JME expression by prefixing the attribute’s name with eval-. Variables are substituted into the attribute’s value using curly braces.

For example, this tag will have its class attribute set to the value of the variable classes:

<div eval-class="{classes}">

See this example question.

Question text

Show one of several blocks of text based on a random variable

Suppose you have a random variable a, which has the value 1,2 or 3, corresponding to three different scenarios. First, write out the text for each scenario.

_images/conditional_visibility.png

There is a button in the content editor labelled Conditional visibility. This allows you to give an expression (in JME syntax) which dictates whether or not the selected text is shown. For each scenario, select the corresponding text and click on the Conditional visibility button. Enter a=1 for the first block, a=2 for the second, and a=3 for the third.

When you run the question, only the block of text corresponding to the value of a is shown.

You can see an example of this technique in the question Conditional visibility.

Display a dollar sign

Because the dollar symbol is used to delimit portions of LaTeX maths, you need to escape dollar signs intended for display by placing a backslash before them – that is, write \$. See this example question.

Use random names for people in question statements

Whenever you have a named person in a question, you should try to randomise the name. It doesn’t really matter what people are called in word problems, but it can have a bad effect on students’ perceptions of the world if the plumber’s always called Gary and the nurse is always called Julie.

We’ve written a “random person” extension which makes it easy to randomly pick a name for a person, and use the correct pronouns.

There’s documentation on the extension’s GitHub repository, and an example question showing how to use it most effectively.

Randomise the names of variables in an expression

Suppose you want the student to solve an equation in terms of some variables, but you want to change the names of those variables each time the question is run. There are a couple of ways of achieving this.

One straightforward method is to use the expression command to substitute variable names, randomly generated as strings, into JME expressions as variables. See this example question.

Use commas or spaces to separate powers of 1,000 in numbers

By default, numbers substituted into question text do not have any separators between powers of 1,000. When working with real-world data, separating blocks of figures can improve readability. Use the formatnumber function to render numbers following one of the supported Number notation styles.

This example question shows how the formatnumber function in use.

Show amounts of money with trailing zeros

Use the currency function to ensure that amounts of money are displayed as you’d expect: the figure is either a whole number or given to two decimal places, and the appropriate symbol for the unit of currency is shown before or after the figure.

See this example question.

LaTeX

Include a randomised LaTeX command

If you want to include a LaTeX command in a string variable, remember that backslashes and curly braces in strings must be escaped. That means you should type two backslashes where you’d normally type one, and add a backslash before each left or right curly brace, for example \\frac\{1\}\{2\} produces the LaTeX \frac{1}{2}. You need to do this because the backslash is used as an escape character in strings so you can include quote marks, which would normally end the string. (For example, "he said \"hello\" to me")

If you substitute a string variable into a mathematical expression using \var, it’s normally assumed to represent plain text and displayed using the plain text font. If your string is really a partial LaTeX expression, you must mark it as such by wrapping it in latex(), e.g. \var{latex(mystring)}.

See this example question.

Substituted randomised raw LaTeX into question text

The majority of the time, substituting raw LaTeX into a question is not the neatest way of achieving what you want. It’s often possible to achieve the desired effect by good use of the simplify command.

However, if you do need to substitute raw LaTeX code into question text for some reason, the latex command is normally what you want.

See this example question, which shows how different methods of substituting a string into question text end up being displayed.

Custom marking scripts

Use LaTeX in a comment created during a custom marking script

Remember that backslashes must be escaped in JavaScript strings, i.e. this.markingComment("$\\sqrt{x}$") instead of this.markingComment("$\sqrt{x}$").

See this example question.

Check that the student has simplified a polynomial fraction

This question uses pattern-matching to check that the student’s answer is in the form \(\frac{x+?}{?}\). In combination with the normal mathematical expression marking algorithm, this confirms that the student has simplified a fraction of the form \(\frac{x+a}{x+b}\).

Check that the student has factorised a quadratic expression

This question uses Pattern-matching mathematical expressions to check that the student’s answer is the product of two factors. In combination with the normal mathematical expression marking algorithm, this confirms that the student has factorised the expression.

Use data from a CSV file that the student has uploaded

This question uses some custom JavaScript to process a file that the student uploads, and use it to set the correct answers for the question’s parts.

Variable generation

Generate a random list of unique numbers

Suppose you want to pick a list of numbers from a given range, but don’t want any repeats.

Use the shuffle function to put the numbers in random order, then take as many as you need from the front of the resulting list. The example below picks three distinct numbers between 0 and 10:

shuffle(0..10)[0..3]

See this example question.

Assign several variables corresponding to a scenario

A simple way of randomising a question, particularly when working with real-world data, is to come up with a number of distinct scenarios. Use the dictionary data type to list the values of variables corresponding to each scenario, then pick randomly from a list of these dictionaries.

See this example question.

This more sophisticated example combines lists of names with JSON data to construct a table of data about people’s hobbies.

Load JSON data

JSON is a commonly-used format to store data in a way that is easy for both people and computers to read.

The following questions show how to use large JSON data sets in Numbas questions:

Maths

Find the factors of a number

If your number is small enough - as a rule of thumb, at most 5 digits - the easiest way to list all the factors of a number \(N\) is to check each lower number for divisibility by \(N\):

filter(x|n, x, 1..n)

See this example question.

Find the prime factorisation of a number

Primality testing is a difficult topic, but if your number is small enough it’s easiest just to check against a hard-coded list of prime numbers. The following produces a list of pairs [prime, power] for the prime-power factors of the number n:

filter(x[1]>0,x,zip(primes,factorise(n)))

See this example question, which also produces LaTeX code to show the factorisation.

Randomly give two of hypotenuse, opposite, and adjacent side of a triangle

This question shows how to randomly generate a Pythagorean triple - a right-angled triangle with integer-length sides - and randomly show two of the lengths to the student. The student is asked to calculate the length of the third side.

Take a logarithm to a randomly-chosen base.

The built-in JME functions ln and log compute logarithms to base \(e\) and \(10\), respectively. log can take a second parameter defining the base. For example:

log(x,3)

Computes \(\log_3(x)\).

This example question shows how to ask the student to enter a mathematical expression containing a logarithm to a randomly-chosen base, or with an unbound variable as the base.