This allows the student to input a linear system in augmented matrix form (max rows 5, but any number of variables). Then the student can decide to swap some rows, or multiply some rows, or add multiples of one row to other rows. The student only has to input what operation should be performed, and this is automatically applied to the system. This question has no marks and no feedback as it's just meant as a "calculator".

Solving a system of three linear equations in 3 unknowns using Gaussian Elimination (or Gauss-Jordan algorithm) in 5 stages. Solutions are all integers. Introductory question where the numbers come out quite nice with not much dividing. Set-up is meant for formative assessment. Adapated from a question copied from Newcastle.

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.

Finding a matrix from a formula for each entry, which involves the row and column numbers of that entry. Randomized size of the matrices and formula.

First compute matrix times vector for specific vectors. Then determine domain and codomain and general formula for the matrix transformation defined by the matrix.

Randomising the number of rows in the matrix, m, makes the marking algorithm for part c) slightly complicated: it checks whether it should include the third gap or not depending on the variable m. For the correct distribution of marks, it is then necessary to do "you only get the marks if all gaps are correct". Otherwise the student would only get 2/3 marks when m=2, so the third gap doesn't appear.

Easy true/false questions to check if the meaning of a size of a matrix is understood, in terms of numbers of rows and columns.

give the negative of each of two vectors. One always has 5 entries, the other has a random number of entries.

Finding a matrix from a formula for each entry, which involves the row and column numbers of that entry. Not randomized because it's the same as in our workbook. But the variables are made in a way that it should be easy to randomise the size of the matrix, and the to change the formula for the input in not too many places.

Finding a matrix from a formula for each entry, which involves the row and column numbers of that entry. Randomized size of the matrices and formula.

Questions on addition, subtraction, multiplication and powers of negative numbers.

A question designed to demonstrate the exam-level variable overrides feature. The student must work out the median of a given sample. The exam can override size of the sample, the range of numbers to pick, and whether the sample should be shown to the student in increasing order.

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A graph (of a cubic) is given. The question is to determine the number of roots and number of stationary points the graph has. Non-calculator. Advice is given.

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.

Pick from the range -5..5, but make 0 more likely.

Demonstrates how to set up a "choose one from a list" part where the number of choices is randomised.

The part is given a list of labels for the choices as well as a list specifying the marks to award for each choice.

Should not be used: there's now a built-in function frequencies.

This question randomly generates a list of 100 items, each chosen from a list of strings.

It then computes the number of occurrences of each distinct item in the list. The statement shows the frequencies in a table.

Shows how to use the JME function lpad to add zeros to the beginning of a number so it's always displayed using two digits.

The student is asked to write a number with a certain property, or tick a box labelled "this is impossible" if it can't be done.

A custom marking algorithm on the gap-fill part first checks if the student ticked the box. If they did, their answer is marked correct if it really is impossible. If they didn't tick it, their number is checked against the required property.

This demonstrates how to render a set of tuples such as $\{(1,2),(3,4)\}$ in LaTeX, starting with a list of pairs of numbers.

Ask for the squares of five randomly-chosen numbers between 0 and 15.

The shuffle function puts a list in random order.

This question shows how to display a number like "1234" as "1,234", or "1 234", using the formatNumber function.

Do not use this: alternative answers are the best way of accepting multiple correct answers.

A couple of different ways of asking the student to enter a large number, to get around the floating point imprecision problem.