Maths questions

Don't forget to take a ruler and scientific calculator into the exam.

Maths questions often start with the command word 'calculate'. You need to use numbers given in the question to work out the answer.

When an answer to a maths question is marked:

  • full marks are given for the right answer
  • marks may be given for working, including substitution and rearrangement
  • calculation errors carried forward are worked through to give credit for later working
Always show working in calculation questions. You can get marks for correct working, even if the answer is wrong.

Make sure you give answers to a suitable number of significant figures.

Maths questions might ask you to plot or complete a graph or table. When you draw a graph, make sure you:

  • plot each point accurately
  • draw a best fit straight line or curve, where appropriate

You may be given a grid with axes labelled and scales already given. Sometimes you may be given an empty grid for you to supply your own axes. When you do this:

  • put the independent variable on the x-axis and the dependent variable on the y-axis
  • choose even scales and make sure that the points cover at least half the given grid
  • label the axes with their quantity and unit, eg time (s)

You will complete 21 required practical activities if you are studying GCSE combined science: Synergy. You could be asked questions about the apparatus, methods, safety precautions, results, analysis and evaluation of these experiments.

This page contains AQA material which is reproduced by permission of AQA.

Sample question 1 - Foundation


An object has a weight of 6.4 N.

Calculate the mass of the object, giving your answer to 2 significant figures. [1 mark]

Use the equation:

mass = weight ÷ gravitational field strength (g)

gravitational field strength = 9.8 N/kg

6.4 ÷ 9.8 = 0.65 (kg) [1]

Sample question 2 - Foundation

A student investigates rolling a marble down a track.

The diagram below shows how he sets up the investigation.

A marble is placed on a curved track between two rulers.

The student lets go of the marble from different heights.

He records:

  • the height from which he drops the marble (the drop height)
  • the height the marble rolls up the other side (the roll height)

The table shows the student's results.

Drop height in cmTest 1 - roll heightTest 2 - roll heightTest 3 - roll heightMean

a) Calculate the mean roll height of the marble when it is dropped from 40 cm. [1 mark]

b) The student calculated the mean roll height for a drop height of 60 cm.

He did not include the result for Test 2 in his calculation.

Why did the student leave out the result for Test 2? [1 mark]

a) (29 + 33 + 32) ÷ 3 = 31 (cm) [1]

b) The result was anomalous [1].

Sample question 3 - Higher

This question is about forces.


a) Write down the equation that links gravitational field strength, mass and weight. [1 mark]

b) A small ball weighs 1.4 N

gravitational field strength, g = 9.8 N/kg

Calculate the mass of the ball.

Give your answer to 3 significant figures. [3 marks]

a) weight = mass × gravitational field strength [1]

b) mass = weight ÷ g [1]

= 1.4 ÷ 9.8 [1]

= 0.143 (kg) [1]

Sample question 4 - Higher


The image shows an exercise device called a chest expander. The three springs are identical.

A working force model, shown using a spring chest expander

A person pulls outwards on the handles and does work to stretch the springs.

The graph shows how the extension of a single spring from the chest expander depends on the force acting on the spring.

An extension against force graph

Use data from the graph to calculate the spring constant of the spring.

Give the unit.

Use the correct equation from the Physics Equations Sheet. [3 marks]

400 [2].

One mark allowed for correct substitution of any pair of numbers correctly taken from the graph, eg 160 = k × 0.40.

Newtons per metre or N/m [1].