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 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 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 question part 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


Sodium chlorate, NaClO3, is used to bleach paper.

Calculate the relative formula mass (Mr) of sodium chlorate. [2 marks]

  • 23 + 35.5 + (3 × 16) [1]
  • = 106.5 [1]

Sample question 2 - Foundation


When 36 g of water is broken down into its elements, 4 g of hydrogen is produced. Calculate the mass of oxygen produced. [1 mark]

32 g [1]

Sample question 3 - Higher


The overall equation for the extraction of aluminium is as follows.

2Al2O3 → 4Al + 3O2

a) Calculate how many tonnes of aluminium can be obtained from 2040 tonnes of aluminium oxide. [3 marks]

b) Calculate the volume of oxygen in m3 that could be formed from 2040 tonnes of aluminium oxide. The volume of 1 mol of gas at room temperature and pressure is 0.024 m3. [3 marks]

a)Mr Al2O3 = 102 [1]

Mass ratio 204 : 108 [1]

Answer = 1080 tonnes [1]

b) Mass ratio 2040 : 960 [1]

Number of moles oxygen = (960 × 106) ÷ 32 [1]

Volume = (3 × 107) × 0.024 = 7.2 × 105 m3 [1]

Sample question 4 - Higher


Sulfur dioxide can be produced by heating sulfide ores such as iron(II) sulfide, FeS2, in oxygen.

4FeS2(s) + 11O2(g) → 2Fe2O3(s) + 8SO2(g)

a) Calculate the number of moles in 176 tonnes of SO2.

1 tonne = 1 × 106 g [3 marks]

b) Use your answer to part (a) to calculate the minimum mass of iron sulfide, FeS2, required to produce 176 tonnes of SO2. [2 marks]

a)Mr(SO2) = 64 [1]

Indication of 176/64 or 2.75 [1]

2.75 × 106 mol [1]

b) 1.375 × 106 mol or indication that mass in grams multiplied by 120 [1]

165 tonnes [1]