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
curriculum-key-fact
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

Question

a) The kinetic energy of a moving car depends on the car's mass and speed.

Write down the equation that links kinetic energy, mass and speed. [1 mark]

b) A car has a mass of 1,650 kg.

Calculate the kinetic energy of the car moving at 30 m/s.

Give your answer in kilojoules (kJ). [2 marks]

a) Kinetic energy = 0.5 × mass × speed2 [1]

b) 0.5 × 1,650 × 302 [1]

= 742500 J [1]

= 742.5 kJ [1]

Sample question 2 - Foundation

Question

A heater has a power rating of 2,500 W.

The heater is turned on for 180 seconds.

Calculate the energy transferred by the heater.

Use the equation:

energy transferred = power × time

Give your answer in kilojoules (kJ). [3 marks]

energy = 2,500 × 180 [1]

= 450,000 [1]

= 450 kJ [1]

Sample question 3 - Higher

Question

A skater with a mass of 70 kg stands on the ice.

a) Write down the equation that links acceleration, change in velocity and time. [1 mark]

b) As the skater pushes away across the ice there is a small frictional force.

After pushing, the skater starts to move with a velocity of 5 m/s.

He slows to 3 m/s in 6 seconds.

Calculate the acceleration of the skater. [2 marks]

a) \text{acceleration} = \frac{\text{change in velocity}}{\text{time taken}} [1]

b) \frac{5 - 3}{6} [1]

= -0.33 (m/s2 ) [1]

Sample question 4 - Higher

Question

In an electrolysis cell the current is 1.5 × 105 A , at a potential difference of 4 V.

Calculate the energy transferred by the electrolysis cell in 24 hours. [5 marks]

power = 1.5 × 105 × 4 [1]

= 6.0 × 105 [1]

24 hours = 24 × 60 × 60 [1]

= 8.64 × 104 seconds

energy transferred = 6.0 × 105 × 8.64 × 104 [1]

5.184 × 1010 (J) [1]