Maths questions

Maths questions often start with the command words ‘calculate’ or ‘determine’. They will then have a blank space for you to show your working. It is important that you show your working, don’t just write the answer down. You might earn marks for your working even if you get the answer incorrect. Calculation errors carried forward are worked through to give credit for later working.

In some maths questions you will be required to give the units. This may earn you an additional mark. Don’t forget to check whether you need to do this. Take extra care when converting between units.

Maths questions might include graphs and tables as well as calculations. Don’t forget to take a ruler and scientific calculator into the exam.

If drawing graphs, make sure you:

  1. put the independent variable on the x-axis and the dependent variable on the y-axis
  2. construct regular scales for the axes
  3. label the axes appropriately
  4. plot each point accurately
  5. draw a straight or curved line of best fit

If you are asked to calculate an answer and it has lots of significant figures, you should try to round it to the same number of significant figures you were given in the data in the question. Don’t forget to check your rounding.

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

Sample question 1 - Foundation


The signals for a monitor unit are transmitted as electromagnetic waves with a wavelength of 0.125 m.

Wave speed of electromagnetic waves = 3 × 108 m/s

Calculate the frequency of the signal in Hertz (Hz). [3 marks]

3 × 108 = f × 0.125 [1]

f = 3 × 108 ÷ 0.125 [1]

frequency = 2.4 × 109 (Hz) [1]

Sample question 2 - Foundation


Waves made by a machine in a swimming pool.

In 10 seconds 5 complete waves go past a person standing in the pool.

Determine the time period and frequency of water waves and give the units. [4 marks]

  • time period = 10 ÷ 5 = 2 seconds
  • frequency = 1 ÷ time period
  • frequency = ½ = 0.5 Hz

One mark for each of time period and frequency values correctly calculated. Another mark for both seconds and Hertz as units and a final mark for use of frequency = 1 ÷ time period. An alternative could determine frequency first and then use time period = 1 ÷ frequency.


Sample question 3 - Higher


A student uses a ripple tank where all the water is the same depth.

She measures the wavelength of each wave as 0.34 m.

The period of each wave is 0.42 s.

Calculate the speed of the wave.

Use the correct equation from the Physics Equation Sheet.

Give the unit.

Give your answer to three significant figures. [5 marks]

This calculation must be done in two parts. Use the time period to find the frequency then use the frequency and wavelength to find the wave speed. Do not forget to give the unit and to give the answer to three significant figures.

Time period = 1 ÷ frequency

0.42 = 1 ÷ frequency [1]

frequency = 1 ÷ 0.42 [1]

= 2.38 Hz [1]

wave speed = frequency × wavelength

= 2.38 × 0.34 [1]

wave speed = 0.809 m/s [1]

Sample question 4 - Higher


The speed of a wave is calculated using the following equation:

wave speed = frequency × wavelength

The water waves in a ripple tank have a wavelength of 1.2 cm and a frequency of 18.5 Hz.

How does the speed of these water waves compare to the typical speed of a person walking? [4 marks]

1.2 cm = 0.012 m [1]

Wave speed = frequency × wavelength

= 18.5 × 0.012 [1]

= 0.22 m/s [1]

Typical walking speed = 1.5 m/s so the water waves are much slower (than a typical walking speed) [1].

In this question, it is important to convert centimetres into metres and to remember to make the final comparison with walking speed.