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

Question

Calculate the energy transferred to the surroundings as 0.40 kg of stearic acid changed state from liquid to solid.

The specific latent heat of fusion of stearic acid is 199,000 J/kg.

Use the correct equation from the Physics Equations Sheet. [2 marks]

Energy = m × l [1]

= 0.40 × 199,000

Energy = 79,600 J [1]

Write out the equation in full and show all stages of the calculation. Include units in the answer.

Sample question 2 - Foundation

Question

The helium in a balloon has a mass of 0.00254 kg.

The balloon has a volume of 0.0141 m3.

Calculate the density of the helium and give the correct unit. [3 marks]

Density = mass ÷ volume [1]

= 0.00254 ÷ 0.0141 [1]

Density = 0.18 kg/m3 [1]

Write out the equation in full and show all stages of the calculation. Include units in the answer.

Sample question 3 - Higher

Question

Water vapour is a gas.

Gases change state when they cool.

A volume of 2.5 × 10-5 m3 of condensation forms on a bathroom mirror.

Density of water = 1,000 kg/m3.

Specific latent heat of vaporisation of water = 2.26 x 106 J/kg.

Calculate the energy released when the condensation forms. [5 marks]

1,000 = m ÷ 2.5 × 10-5 [1]

m = 2.5 × 10-5 × 1,000 [1]

m = 0.025 kg [1]

E = 0.025 × 2,260,000 [1]

E = 56,500 J [1]

Write out the equation in full and show all stages of the calculation. Include units in the answer.