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


A car travels a distance of 2,040 metres in 2 minutes.

Use the following equation to calculate the mean speed of the car:

mean \ speed = \frac{distance}{time}

[2 marks]

mean \ speed = \frac{distance}{time}

= \frac{2,040}{120} [1]

mean speed = 17 m/s [1]

Write out the equation in full and show all stages of the calculation. Remember to convert the time into seconds. Include units in the answer.

Sample question 2 - Foundation


A force of 13.8 N was used to lift a mass 30 cm vertically through a liquid.

Use the following equation to calculate the work done in lifting the mass.

work done = force × distance

Choose the correct unit from the box:


[3 marks]

work done = force × distance

= 13.8 × 0.30 [1]

work done = 4.14 J [2]

Write out the equation in full and show all stages of the calculation and remember to include units in the answer. Remember to convert 30 cm into 0.3 m. Work done is an amount of energy transferred from one store to another so the unit is Joules (J).

Sample question 3 - Higher


During a journey, a car accelerates from 9 m/s to 18 m/s in 6 s.

Use the following equation to calculate the acceleration of the car:

acceleration = \frac{\text{change in velocity}}{\text{time taken}}

[2 marks]

acceleration = \frac{\text{change in velocity}}{\text{time taken}}

= \frac{(18 - 9)}{6} [1]

= \frac{9}{6}

acceleration = 1.5 m/s2 [1]

Sample question 4 - Higher


The figure shows how the velocity of the train changes with time as the train travels along a straight section of the journey:

A graph shows velocity over time for a train.

Estimate the distance travelled by the train along the section of the journey shown in the figure.

To gain full marks you must show how you worked out your answer. [3 marks]

number of squares below line = 17

each square represents 500 m

distance = number of squares × value of each square [1]

= 17 × 500 [1]

distance = 8,500 m [1]