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)

Take extra care when converting between units.

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

Question 1 - Foundation

The table below shows the blood sugar levels for two people after eating a meal.

Time after eating in hoursPerson APerson B

Use data from the table to complete the graph below.


a) Plot the points for person A.

The first two points have been plotted for you.

Draw a line through all the points. [3 marks]

The blood sugar of person B over seven hours is monitored in this graph

b) How long after the meal is person B's insulin production at its peak? [1 mark]

a) All three points correct [2].

Suitable line drawn [1].

b) 1 hour [1]

Sample question 2 - Foundation

The table below shows how the count rate of a radioactive substance changes with time.

Time in seconds04080120160
Count rate in counts/second600463300221150

a) Describe the relationship shown in the table. [2 marks]

b) Use the information from the table to predict the count rate after 200 seconds. [2 marks]

a) Include the following points to gain all marks:

  • as time increases the count rate decreases [1]
  • count rate halves every 80 seconds [1]

b) Half-life is 80 seconds [1]

75 ÷ 2 = 37.5

150 – 37.5 = 112.5 seconds

After 200 seconds, the count rate = 113 [1]

Sample question 3 - Higher


The activity of a radioactive isotope changes over an 8 hour period of time. This can be seen in the graph below.

The graph shows that the count rate decreases as time goes on

Predict how long it will take for the count rate to fall from 100 to 1.56 Becquerels. [2 marks]

Half-life read from graph = 2 hours [1]

Time to fall to 1.56 is six half-lives = 6 × 2 (hours) [1]

Sample question 4 - Higher


Lead-210 is a radioactive isotope that decays to an isotope of mercury by alpha decay.

Complete the nuclear equation to show the alpha decay of lead-210. [3 marks]

_{...}^{210}\textrm{Pb} \rightarrow _{80}^{...}\textrm{Hg} + _{...}^{...}\textrm{...}

_{82}^{210}\textrm{Pb} \rightarrow _{80}^{206}\textrm{Hg} + _{2}^{4}\textrm{He}