Determine the correct parametric representation of a given curve.  Curve is randomly chosen from a set of 20.

The graph of the curve was not displayed on my machine.

Given linear programming problems in standard form, write down the dual problem.

Given $f(x)=(x+b)^n$. Find the gradient and equation of the chord between $(a,f(a))$ and $(a+h,f(a+h))$ for randomised values of $a$, $b$ and $h$.

Multiple choice. Students need to select the correct simplification for a given expression. 

This question has four versions. Skills required are: using Pythagorean identities, converting to sine or cosine. Some also require fraction division.

Multiple choice question. Given a randomised polynomial select the possibe ways of writing the domain of the function.

Part (a) - dividing a total quantity given a ratio

Part (b) - given the value of one part of the ratio to find the total quantity.

MCQ to calculate selling price when given cost price and VAT rate.

MCQ - Pick the correct cost price when given the selling price and rate of VAT.

Identifying y=mx+b given two points

Given one point and the gradient determine the equation of the line.

Given the graph of the line determine the equation of the line.

Given an equation or a worded formula determine if it is a function or not

The student must calculate the carbon footprint given electricity and gas energy usage.

Convert a number given in base 10 to a different base.

Convert a number given in base 10 to a different base.

Example showing how to mark a "choose one from a list" part where the student has to pick the range a given number lies in.

Given price, marginal cost and fixed cost, find the quantity that maximises profits.

This question assesses the learner's ability to compute a confidence interval for a difference of two means, given two samples.

Randomized variables: sample raw data and confidence level. 

Adapted from section 7.3.1 in OpenIntro Statistics (4th ed).

Given a graph of the form either a.cos(bx) or a.sin(bx), identify the amplitude and period.

Drag a point into the specified quadrant. Uses jsxgraph

Choosing whether given random variables are qualitative or quantitative.

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

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.

An application of quadratic functions based on the Golden Gate Bridge in San Francisco, USA. Student is given an equation representing the suspension cable of the bridge and asked to find the width between the towers and the minimum height of the cable above the roadway. Requires and understanding of the quadratic function and where and how to apply correct formulae.

Multiple choice questions. Given randomised trig functions select the possible ways of writing the domain of the function.

Given a 3 x 3 matrix, and two eigenvectors find their corresponding eigenvalues. Also fnd the characteristic polynomial and using this find the third eigenvalue and a normalised eigenvector $(x=1)$.

Example of an explore mode question. Student is given a 3x3 matrix and is asked to find the characteristic polynomial and eigenvalues, and then eigenvectors for each eigenvalue. The part asking for eigenvectors can be repeated as often as the student wants, to be used for different eigenvalues.

Assessed: calculating characteristic polynomial and eigenvectors.

Feature: any correct eigenvalue will be recognised by the marking algorithm, even multiples of the obvious one(s) (which can be read off from the reduced row echelon form)

Randomisation: Not randomised, just using particular matrices. I am still working on how to randomise this for 3x3; a randomised 2x2 version exists. I have several different versions for 3x3 (not all published yet), so I could make a random choice between these in a test.

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

Given $5$ vectors in $\mathbb{R^4}$ determine if a spanning set for $\mathbb{R^4}$ or not by looking for any simple dependencies between the vectors.

Real numbers $a,\;b,\;c$ and $d$ are such that $a+b+c+d=1$ and for the given vectors $\textbf{v}_1,\;\textbf{v}_2,\;\textbf{v}_3,\;\textbf{v}_4$ $a\textbf{v}_1+b\textbf{v}_2+c\textbf{v}_3+d\textbf{v}_4=\textbf{0}$. Find $a,\;b,\;c,\;d$.