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.

Sample question 1 - Foundation


In a power station 900 MJ of thermal energy were released by burning natural gas.

a) Write down the equation that links efficiency, useful input energy and useful output energy transfer. [1 mark]

b) In a power station 900 MJ of thermal energy were released by burning natural gas. Only 405 MJ was generated.

Calculate the efficiency of this energy transfer. [2 marks]

a) \text{efficiency} = \frac{\text{useful output energy transfer}}{\text{total input energy transfer}} [1]

b) = \frac{405}{900} [1]

= 0.45 [1]

Sample question 2 - Foundation


A car has an electric motor.

The electric motor has an input energy of 50,000 joules each second.

The motor transfers 35,000 joules of useful energy each second.

Calculate the efficiency of the electric motor. [2 marks]

Efficiency = 35,000 ÷ 50,000 [1]

0.7 or 70% [1]

Sample question 3 - Higher


Some power stations burn wood instead of fossil fuels to generate electricity.

A coal-burning power station burns 6 million tonnes of coal per year.

Coal has an average energy value of 29.25 MJ per kg.

Wood chip from willow trees has an energy value of 13 MJ per kg.

A hectare of agricultural land can produce 9 tonnes of dry willow wood per year.

If this power station burned dry willow wood instead of coal, how much agricultural land would be needed to grow the willow? [3 marks]

1 tonne is equal to 1,000 kg.

Coal consumption per year = 29.25 × 1,000 × 6 million

= 175,500,000,000 MJ [1]

1 hectare of willow will produce 9 × 13 × 1000

= 117,000 MJ per year [1]

So, 175,500,000,000 ÷ 117,000

= 1,500,000 (hectares) needed [1]

Sample question 4 - Higher


Iron is a metal that has many uses.

Iron is extracted from iron ore. Part of the process involves reduction of the ore with carbon monoxide.

Iron ore contains iron oxide (Fe2O3).

Write a balanced equation for the reaction of iron oxide with carbon monoxide. [3 marks]

Fe2O3 + 3CO → 2Fe + 3CO2

One mark will be awarded for correct formulae of reactants.

One mark will be awarded for correct formulae of products.

One mark will be awarded for correct balancing.