How-tos

The student is asked to enter a given matrix, but they're only required to fill in the upper triangle.

A custom marking algorithm fills in any empty cells in the lower triangle of the student's answer with the corresponding cell in the upper triangle.

The student is still warned if they leave any cells empty in the upper triangle.

This demonstrates how to:

• Generate a fixed number of observations of data in two categories.
• Display the data in a table, with row and column totals.
• Ask the student to enter the data in a spreadsheet which is automatically marked.

The CSS preamble adds a vertical line down the input for part b, to separate the two parts of the matrix.

The student has to enter `diff(y,x,2)`, equivalent to $\frac{\mathrm{d}^2y}{\mathrm{d}x^2}$, as their answer. It's marked by pattern matching, using a custom marking algorithm.

The student has to enter three different letters of the alphabet in the three gaps. Their answer is marked as a set: repeated answers only count as one answer.

Each gap has the same custom marking algorithm which marks that gap as correct if the student's answer is in the set of acceptable answers.

This question models an experiment: the student must collect some data and enter it at the start of the question, and the expected answers to subsequent parts are marked based on that data.

The student's values of the variables width, depth and height are stored once they move on from the first part.

This question models an experiment: the student must collect some data and enter it at the start of the question, and the expected answers to subsequent parts are marked based on that data.

A downside of working this way is that you have to set up the variable replacements on each part of the question. You could avoid this by using explore mode.

In the first part, the student must write any linear equation in three unknowns. Each distinct variable can occur more than once, and on either side of the equals sign. It doesn't check that the equation has a unique solution.

In the second part, they must write three equations in two unknowns. It doesn't check that they're independent or that the system has a solution. The marking algorithm on each of the gaps just checks that they're valid linear equations, and the marking algorithm for the whole gap-fill checks the number of unknowns.

The student must solve a pair of simultaneous equations in $x$ and $y$.

The variables are generated backwards: first $x$ and $y$ are picked, then values for the coefficients of the equations are chosen satisfying those values.

Shows how to use JSXGraph to make a sine graph with amplitude, frequency and phase controlled by sliders.

This shows how to define a list of LaTeX strings, and pick a couple of them at random to display.

The "JSON data" type is used to define the available strings, so they're automatically marked as "safe" and curly braces aren't interpreted as variable substitution.

This question shows how to generate a random set of $(x,y)$ samples, where $y = mx + c + \mathrm{noise}$.

The JSXGraph extension is used to show a scatter plot of the data. This isn't necessary if you just want to generate the data.

This shows how to use a variable name annotation to put a hat on a variable name inside the \simplify command.

A mathematical expression part with a pattern restriction to ensure that the student has extracted the highest common factor of two terms.

The answer must be of the form $a(b+cx)$, where $b$ and $c$ are coprime.

The student is asked to give the roots of a quadratic equation. They should be able to enter the numbers in any order, and each correct number should earn a mark.

When there's only one root, the student can only fill in one of the answer fields.

This is implemented with a gap-fill with two number entry gaps. The gaps have a custom marking algorithm to allow an empty answer. The gap-fill considers the student's two answers as a set, and compares with the set of correct answers.

The marking corresponds to this table:

The expected answer involves the logarithm of a negative number, which doesn't have a unique solution.

The part's marking algorithm evaluates the exponential of the student's answer and the expected answer, and compares those.

The expected answer involves the logarithm of a negative number, which doesn't have a unique solution.

The part's marking algorithm checks that the student's answer differs from the expected answer by a multiple of $2\pi$.

This shows one way of laying out matrix cells in a table, so that some cells can be filled in by the student.

At the time this was written, there's an open issue for allowing some entries in the matrix entry part to be filled-in, which would make this technique redundant.

Some CSS in the preamble adds the brackets around the table - it has to have the attribute class="matrix-gaps"

The student is given a quadratic formula and asked to fill in a table of values of $f(x)$ for a given range of $x$.

There is also a plot of the points, which updates when the table is filled in, or the student can move the points to fill in the table.

The table uses the spreadsheet and JSXgraph extensions.

The student is given a quadratic formula and asked to fill in a table of values of $f(x)$ for a given range of $x$.

The table uses the spreadsheet extension.

This question shows how to use the question's JavaScript preamble to request data from an external source, and use that data in question variables.

Note that this means the question only works when the external source is available. Use this very carefully, and avoid it if you possibly can!

This question shows how explore mode can be used to loop through several versions of the same question. The variables for each version are stored in a list of "scenarios", and a counter works through that list each time the student moves on to the next part, labelled "try the next version of this question".

Shows that you can embed a 3D GeoGebra applet in a content area.

The student is shown a passage of code in the prompt to a "choose several from a list" part.

A random proper fraction $a/b$ with denominator in the range 2 to 30 is picked, and the student must write $\frac{a}{b} \pi$.

The point of this question is to demonstrate that the correct answer is shown as a multiple of $\pi$ rather than a decimal.

The number entry part in this question has an alternative answer which is marked correct if the student's number satisfies an equation specified in the custom marking algorithm.

A custom marking algorithm picks out the names of the constants of integration that the student has used in their answer, and tries mapping them to every permutation of the constants used in the expected answer. The version that agrees the most with the expected answer is used for testing equivalence.

If the student uses fewer constants of integration, it still works (but they must be wrong), and if they use too many, it's still marked correct if the other variables have no impact on the result. For example, adding $+0t$ to an expression which otherwise doesn't use $t$ would have no impact.

Should not be used: this relies on a custom JavaScript which is not guaranteed to continue working.

Wrap the student's answer in set() so it's marked as a set.

The answer to this question is a differential equation involving $y''$, $y'$ and $y$.

A variable value generator for $y$ ensures that the right values are tested to check that the student's answer is equivalent to the expected equation.

This question includes a JavaScript preamble which defines 'hbar' as a special variable name to be rendered in LaTeX as \hbar.