$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

Solve linear equations with unkowns on both sides. Including brackets and fractions.

Used for LANTITE preparation (Australia). MG = Measurement & Geometry strand. NC = Non-Calculator strand. Students are shown an image of a thermometer calibrated in both degrees Celsius and degrees Fahrenheit. Student must answer a question using the thermometer. The image is randomly selected from a pool of 3. There are two different potential questions for each thermometer. Hence 6 questions in total.

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

Manipulate fractions in order to add and subtract them. The difficulty escalates through the inclusion of a whole integer and a decimal, which both need to be converted into a fraction before the addition/subtraction can take place. 

Manipulate fractions in order to add and subtract them. The difficulty escalates through the inclusion of a whole integer and a decimal, which both need to be converted into a fraction before the addition/subtraction can take place. 

Solve linear equations with unkowns on both sides. Including brackets and fractions.

Solve linear equations with unkowns on both sides. Including brackets and fractions.

Solve linear equations with unkowns on both sides. Including brackets and fractions.

Manipulate fractions in order to add and subtract them. The difficulty escalates through the inclusion of a whole integer and a decimal, which both need to be converted into a fraction before the addition/subtraction can take place. 

Simplify the sum of two algebraic fractions where spotting factorising of both numerators and denominators can reduce the work massively.

Solve a simple linear equation algebraically. The unknown appears on both sides of the equation.

Solve linear equations with unkowns on both sides. Including brackets and fractions.

$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

Simplify an algebraic fraction where both numerator and denominator must first be factorised. Part of HELM Book 1.4

Use a calculator to evaluate a number to the power of a fractional index. Both the number (a positive integer) and the index (a rational) are randomised.

Part of HELM Book 1.2

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

An A-frame structure supporting a load at the top.  Simple because both legs are two force bodies.

Calculating the original amount when told that $p\%$ is $x$. The value given and the original values are both integers.

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

Students are given 2 right-angle triangles - two ramps of differing steepness up a step, and are asked to find one of a selection of randomly chosen lengths. The height of the step is given - it is randomised. Students are also given either the angle of incline of the steeper ramp or its length, both of which are randomised. They are also given the angle of incline of the shallower ramp, which is also randomised.

This question assesses

• the students ability to apply both theoretical and experimental probability to calculate expected values 
• the students understanding of how to calculate the relative frequency of an outcome

The question also helps to show students how using experimental probability and theoretical probability results in different expected values of an outcome.

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

A graph shows both the speed and acceleration of a car. Identify which line corresponds to which measurement, and calculate the acceleration during a portion of time.

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

A question testing the application of the Cosine Rule when given two sides and an angle. In this question, the triangle is always obtuse and both of the given side lengths are adjacent to the given angle (which is the obtuse angle).

Two questions testing the application of the Cosine Rule when given two sides and an angle. In these questions, the triangle is always acute and both of the given side lengths are adjacent to the given angle.

Calculate the distance between two points along the surface of a sphere using the cosine rule of spherical trigonometry. Context is two places on the surface of the Earth, using latitude and longitude.

The question is randomised so that the numerical values for Latitude for A and B will be positive and different (10-25 and 40-70 degrees). As will the values for Longitude (5-25 and 50-75). The question statement specifies both points are North in latitude, but one East and one West longitude, This means that students need to deal with angles across the prime meridian, but not the equator.

Students first calculate the side of the spherical triangle in degrees, then in part b they convert the degrees to kilometers. Part a will be marked as correct if in the range true answer +-1degree, as long as the answer is given to 4 decimal places. This allows for students to make the mistake of rounding too much during the calculation steps.

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve.