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:

a) plot each point accurately

b) 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)

Take extra care when converting between units.

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

Sample question 1 – Foundation


Phosphorus has a mass number of 31 and has 16 neutrons.

What percentage of the mass number of phosphorus is the number of neutrons?

Give your answer to two significant figures. [2 marks]

(16 ÷ 31) × 100 = 51.6 [1]

= 52 [1]

Incorrect number of significant figures gains a maximum of 1 mark.

Sample question 2 – Foundation

The image shows a water wave.

A cut through of a water wave

a) Write down the equation that links frequency, wave speed and wavelength. [1 mark]

b) The wave shown above has a wavelength of 75 cm.

The wave moves at a speed of 1.6 m/s.

Calculate the frequency of the wave. [4 marks]

a) wave speed = frequency × wavelength [1]

b) 75 cm = 0.75 m [1]

1.6 = \text{f} × 0.75 [1]

\text{f} = 1.6 ÷ 0.75 [1]

= 2.13 (Hz) [1]

Sample question 3 – Higher


A student investigated the specific heat capacity of metals.

The table shows the student's results.

Use data from the table to calculate the temperature change for copper.

MetalMass of material in kgTime in minutesTemperature change in °CChange in thermal energy in JCalculated specific heat capacity of material in J/kg °C

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

4,600 = 1 × 657 × temperature change [1]

temperature change = 4,600 ÷ 657 [1]

= 7°C [1]

Question 4 – Higher


According to modern measurements:

  • the radius of an atom is about 1 × 10-10 m
  • the radius of an atomic nucleus is about 1 × 10-14 m

Show that these values fit with the nuclear model of the atom. [2 marks]

The figures show that the radius of an atom is 10,000 times bigger than the nucleus [1].

This is consistent with the nuclear model, which says that the atom has a tiny nucleus at the centre of the atom [1].