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.

Take extra care when converting between units.

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)

These questions have been written by Bitesize consultants as suggestions to the types of questions that may appear in an exam paper.

Sample question 1 - Foundation

Question

The overall energy change is 386 kJ.

What percentage of 1370 kJ is this? Give your answer to two significant figures. [2 marks]

\frac{386}{1370} × 100 [1]

= 28% [1]

Sample question 2 - Foundation

Question

A student investigated the energy released during the combustion of ethanol. Her results are shown in the table below.

Table 1 shows his results.

Table 1

Experiment 1Experiment 2Experiment 3
Initial temperature19°C21°C20°C
Final temperature39°C42°C39°C

Calculate the mean temperature difference in the water. [2 marks]

Temperature differences: 20, 21, 19 [1]

Mean = 20°C [1]

Sample question 3 - Higher

Question

Combustion is an exothermic reaction.

Molecular structure of methane oxygen combustion
BondBond energy in kJ/mol
C–H413
O=O498
C=O805
O–H464

Calculate the overall energy change for the complete combustion of one mole of methane in oxygen. [3 marks]

(4 × 413) + (2 × 498) = 2648 [1]

(2 × 805) + (4 × 464) = 3466 [1]

2646 - 3466 = -818 kJ/mol [1]

Sample question 4 - Higher

Question

A student pours dilute copper sulfate solution into a polystyrene cup, and measures the temperature of the acid.

He adds magnesium powder.

He stirs and measures the temperatures again.

He repeats the test two more times.

His results for the three runs are shown in the tables below.

Run 1

MetalTemperature at start (°C)Temperature at end (°C)Temperature change (°C)
Magnesium2036+16

Run 2

MetalTemperature at start (°C)Temperature at end (°C)Temperature change (°C)
Magnesium2037

Run 3

MetalTemperature at start (°C)Temperature at end (°C)Temperature change (°C)
Magnesium2136

a) Complete the tables by writing in the missing values. [2 marks]

b) Calculate the mean temperature change for the three runs. [1 mark]

a)

Run 2

MetalTemperature at start (°C)Temperature at end (°C)Temperature change (°C)
Magnesium2037+17

Run 3

MetalTemperature at start (°C)Temperature at end (°C)Temperature change (°C)
Magnesium2136+15

[1] for each correct answer.

b) \frac{16 + 17 + 15}{3} = 16 °C [1]