The student is shown two labelled graphs. They are asked:

• Number of vertices in each
• Number of edges in each
• Degree sequences for each
• Is there an isomorphism between them? If so, write one.

The number of vertices is always equal, so this is a gimme.

If the edges or degree sequences are different, the student is expected to realise that there cannot be an isomorphism.

If these values are the same, then there will be an isomorphism (else the question is a bit too tricky).

Numbas expects a particular isomorphism, but there may be more than one, all of which would be accepted.

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Example of an explore mode question. Student is given a 2x2 matrix with eigenvalues and eigenvectors, and is asked to decide if the matrix is invertible. If yes, second and third parts are offered where the student should give the eigenvalues and eigenvectors of the inverse matrix.

Assessed: remembering link between 0 eigenvalue and invertibility. Remembering link between eigenvalues and eigenvectors of matrix and its inverse.

Randomisation: a random true/false for invertibility is created, and the eigenvalues a and b are randomised (condition: two different evalues, and a=0 iff invertibility is false), and a random invertible 2x2 matrix with determinant 1 or -1 is created (via random elementary row operations) to change base from diag(a,b) to the matrix for the question. Determinant 1 or -1 ensures that we keep integer entries.

The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".

This question assesses learners' ability to:

- construct a confidence interval for a proportion given corresponding summarised data;

- predict the sample size required to limit the margin of error to a given value.

Face, Place and actual value, adding, subtracting, multiplying, dividing and rounding decimals.

Compute a table of values for a quadratic function. A JSXgraph plot shows the curve going through the entered values.

Read a value from a table. There are 36 possible questions.

Substitute a given value into a formula, and substitute an expression in terms of $x$ into a formula.

Looking at gradients and values for x and y for straight-line graphs

A resource for Business students to practise calculating Normal probabilities and finding $Z$-values. 

This question assesses the students ability to find the expected number of times an event occurs given the probability of the event occurring for a single trial and the total number of trials.

This exercise will help you rearrange a linear equation to find the value of a given variable

This exercise will help you rearrange a linear equation to find the value of a given variable

Compute a table of values for a quadratic function. A JSXgraph (the graph paper) plot shows the curve going through the entered values. The student input is now disconnected from the graph so that they slide the points usually after they input the values and the answer fields are not updated.

This question shows how to pick a GeoGebra worksheet to show to the student from a list, based on the value of a question variable.

Compute a table of values for a quadratic function. A JSXgraph plot shows the curve going through the entered values.

Substitute values into formulae for the area or volume of various geometric objects.

Determine for which value of \(t\) two vectors are parallel. In the first part, there is no real number \(t\) to make it work. In the second part, a value can be worked out.

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Given an ascending sequence of numbers, finds the index in the sequence of the first number greater than or equal to a given value.

Because JavaScript numbers lose precision as they get bigger, you get some unexpected results.

See the variable "two" - the difference should be 2, but because the JavaScript representation of each of the two numbers is the same, it thinks the difference is 0.

Using the decimal data type, there's no loss of precision, so the correct value is produced.

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Simple probability question. Counting number of occurrences of an event in a sample space with given size and finding the probability of the event.

Asks to determine whether or not 6 statements are propositions or not i.e. we can determine a truth value or not.