Maths questions

Remember that you will need to take a ruler and calculator into the exam.

Questions that test mathematical skills will often start with the command words like 'Calculate...' 'Determine...', 'Estimate...' and 'Measure...'. They will then include blank space for you to show your working.

When an answer to a maths question is marked:

  • full marks are given for the right answer (but it is very important to show your working, so you can check your answer and so that, if you make a small slip, you can still get marks for your working)
  • marks are given for working, including substitution and rearrangement
  • if you make a small mistake, the examiner will give you credit for your 'error carried forward'

An 'error carried forward' means that, in questions with more than one part, your answer to a later part of the question will be marked according to your answer for the earlier part, even if you got this wrong. So, you could still get full marks in the later answer if your working is correct but you use the incorrect earlier answer.

If your answer has many decimal places or figures, make sure you give it to an appropriate number of decimal places or significant figures. If in doubt, match the number of decimal places or significant figures to the data given in the question.

You may be asked to give units. This may earn you an additional mark, so don’t forget to check whether you need to do this.

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

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 (the one that is being changed in the experiment) on the x-axis and the dependent variable (the one that changes as a result) on the y-axis
  • make sensible scales so that the plotted points cover at least half of the area of the graph
  • label the axes with their quantity and unit, eg time (s)

Questions courtesy of Eduqas.

Sample question 1 - Foundation


A pupil carried out an investigation to find the temperature change which occurs when dilute hydrochloric acid reacts with dilute sodium hydroxide solution.

Volume of acid addedTemperature
0 cm321.0°C
10 cm322.7°C
20 cm324.0°C
30 cm325.1°C
40 cm326.0°C
50 cm326.5°C
60 cm326.0°C
70 cm325.0°C
80 cm324.0°C

Plot the volume of acid added against the temperature and draw a suitable line. [3 marks]

Your answer should include:

  • all points plotted correctly [2]
  • curve of best fit - judgement by eye, ie smooth, continuous single line [1]

Sample question 2 - Foundation


Use the graph in Sample question 1 to find the:

a) maximum temperature rise during the experiment. [1 mark]

b) volume of acid needed to neutralise all the alkali. [1 mark]

a) 5.5°C [1]

b) 50 ± 1 cm3 [1]

Sample question 3 - Higher


Hydrogen sulfide (H2S) burns in air to give sulfur dioxide and water.

The following equation shows the rearrangement of atoms as hydrogen sulfide burns.

2 H-S-H + 3 O=O → 2 O=S=O + 2 H-O-H

The relative energies of these bonds are given in the table below.

BondBond energy
H - S339 kJ
O = O ______ kJ
S = O523 kJ
O - H463 kJ

The overall relative energy change during the reaction is -1103 kJ, which shows that the reaction is exothermic.

Use the information given above to calculate the energy needed to break the O=O bond. [5 marks]

  • energy released in forming bonds = (4 × 523) + (4 × 463) [1]
  • 3944 kJ [1]
  • total energy needed to break bonds = 3944 - 1103 = 2841 kJ [1]
  • 2841 = (4 × 339) + (3 × O=O) [1]
  • (O=O) = 495 [1]

Sample question 4 - Higher


Hefin 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 are in Table 1.

Table 1

Temp at start (°C)Temp at end (°C)Temp change (°C)
Run 12036+16
Run 22037
Run 32136

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

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

a) [1] for each correct value.

Temp at start (°C)Temp at end (°C)Temp change (°C)
Run 12036+16
Run 22037+17 [1]
Run 32136+15 [1]

b) \frac {16 \ + \ 17 \ + \ 15}{3} = 16 °C [1]