Solving an inequality of the form ax+b < c where a is negative.

Expanding two linear brackets multiplied together.

Expanding two linear brackets multiplied together.

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. 

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.

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

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

Solving linear equations with unknowns on both sides

Covering 1-3 step linear equations but not introducing brackets or an unknown on both sides.

Finding equivalent fractions, and expressing fractions in other equivalent forms.

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. 

$A,\;B$ $2 \times 2$ 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.

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

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.