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 30 W light bulb uses 600 J of electrical energy in a certain period of time. In that time, it produces 450 J of light energy. The rest of the energy is wasted.

Calculate the energy wasted by the light bulb in this period of time. [1 mark]

150 J [1]

600 J is used. 450 J of that is transferred usefully. The remaining energy must be wasted. 600 J - 450 J = 150 J

Sample question 2 - Foundation


A student does a bungee jump. At the lowest point in the jump when the student is stationary, the extension of the bungee cord is 35 metres.

The bungee cord behaves like a spring with a spring constant of 40 N/m.

Calculate the energy stored in the stretched bungee cord.

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

\frac{1}{2} \times \text{40} \times \text{35}^{2} [1]

24,500 J [1]

A sensible way to approach a question like this is to write out the numbers so you can see what you are working with. For example:

Extension = 35 m

Spring constant = 40 N/m

It then makes it more obvious as to which equation needs to be used. In this case, \text{E}_{e} = \frac{1}{2}\text{k}\text{e}^{2}. You can then substitute the numbers in and calculate.

Sample question 3 - Higher


The mass of water in a cup is 200 g.

Calculate the energy, in joules, transferred from the water in a cup when the temperature of the water falls by 8°C.

Specific heat capacity of water = 4,200 J / kg°C. [3 marks]

6,720 J

This requires a similar approach to Sample Question 2. However, there is an added complication. The mass of 200 g needs to be converted into kg (0.2 kg). Failing to convert the mass results in an answer of 6,720,000 J.

Sample question 4 - Higher


A remote control car has a top speed of 12 m/s and a mass of 800 g.

Calculate the maximum kinetic energy of the car. [3 marks]

kinetic energy = 0.5 × mass × (speed)2 [1]

0.5 × 0.8 × 122 [1]

= 57.6 J [1]

Be sure to show the equation, the working and the final answer for all calculation questions.