Mathematical 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. 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.

If drawing graphs, make sure you:

  1. put the independent variable on the x-axis and the dependant variable on the y-axis
  2. construct regular scales for the axes
  3. label the axes appropriate
  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 decimal places, don't forget to only use one more than the data in the question. For example, if whole numbers are given in the question, then your answer would be to one decimal place. Don't forget to check your rounding.

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

Sample question 1 – Foundation


A table of results for the ruler-drop reaction test is given below.

AttemptDistance without caffeine (cm)Distance with caffeine (cm)

Calculate the mean distance with and without caffeine. [2 marks]

Without caffeine: 32.5 cm

With caffeine: 19.75 cm

Sample question 2


Students investigated body temperature in the class. The bar chart shows the results.

A graph showing the number of students and there body temperature.

One student used the bar chart to calculate the mean body temperature of the class. The student calculated the mean body temperature as 37.0°C. How did the student use the bar chart to calculate the mean? [2 marks]

Multiply temperature by number of students at that temperature and add them up divide by number of students.

(36.8 × 5) + (36.9 × 3) + (37.0 × 6) + (37.1 × 7) + (37.2 × 3) = 888 [1]

888 divided by 24 = 37.0°C [1]

Sample question 3 – Higher


Both athletes were training to run a marathon. Which athlete, A or B, would be more likely to complete the marathon? Use information from the graph to explain your answer. [4 marks]

A graph showing the concentration of glycogen in muscles in mmol per kilogram of muscle mass.

Tip – compare the different athletes' data. Consider how glycogen can be used?

Athlete A is more likely to complete the marathon. (no mark)

This is because athlete A had more glycogen or athlete B had less glycogen (only awarded if athlete A was chosen to complete marathon). [1]

Glycogen or glucose is very important because it is used in respiration. [1]

More respiration means more energy is released or more energy is available to athlete A. [1]

This energy can be used for movement or muscle action or to run during the marathon or extra glycogen in the body means more glucose can be released for respiration during exercise. [1]

Sample question 4 – Higher

Two clinics, R and S, used IVF treatment on women in 2007. Doctors at each clinic used the results of the treatments to predict the success rate of treatments in 2008.

The table shows the total number of IVF treatments in 2007 and then the amount of treatments resulting in pregnancy. The table's left column shows the predicted percentage of successful IVF treatments in 2008.

Total '07'07 successPredicted '08
Clinic R100420018% to 23%
Clinic S98203% to 56%

Compare the success rates of the two clinics in 2007. [1 mark]

Tip – use the data in the table to determine this.

Any from the following: [1]

Both clinic R and S produced almost identical values or they both were approximately at 20% success rates.

Also possible to accept that clinic S is slightly more successful than clinic R.

In clinic R a total of 1004 IVF treatments were undertaken, and this resulted in 200 successful pregnancies. Calculation for clinic R - 200 pregnancies divided by 1004 treatments = 200 ÷ 1004 × 100 = 19.9% (round up to 20%)

In clinic S a total of 98 IVF treatments were undertaken, which is much lower than in clinic R and this resulted in 20 successful pregnancies. Calculation for clinic S - 20 pregnancies divided by 98 treatments = 20 ÷ 98 × 100 = 20.4% (round down to 20%)


The range of the predicted success rate in 2008 for clinic R's much smaller than the range of the predicted success rate for clinic S. Suggest why. [2 marks]

Tip – refer to table again.

Larger numbers of overall IVF treatments were recorded in clinic R in 2007 with a total of 1004. This can be compared to the 98 treatments in clinic S, which has a low number of treatments but a high success rate. [1]

The successful results are likely to be more repeatable or allow more reliable results in the following year in 2008. [1]

Do not accept more reproducible or accurate or precise.