Maths questions

Don't forget to take a ruler and calculator into the exam.

Maths questions 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 may be given for working, including substitution and rearrangement
  • 'errors carried forward' are worked through to give credit for later working

Errors are carried forward if a later working depends on an earlier answer. You could still get marks 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. 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, 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)

Sample question 1 - Foundation

Question

The table shows the percentages of the fractions in crude oil from three different oil wells.

FractionOil well AOil well BOil well C
Gases1%6%9%
Petrol2%15%24%
Kerosene6%14%20%
Diesel oil7%10%16%
Fuel oil26%28%30%
Bitumen58%27%1%

a) State which oil well produces a crude oil containing the highest percentage of the high boiling point fractions.

[1 mark]

A barrel of crude oil from oil well B weighs 130 kg.

b) Calculate the mass of kerosene in this barrel. [1 mark]

Edexcel question courtesy of Pearson Education Ltd.

a) Oil well C [1]

b) mass of kerosene = 130 × (14 ÷ 100) = 18.2 kg [1]

Sample question 2 - Foundation

Question

The graph shows the concentration of carbon dioxide in the atmosphere above Hawaii from 1960 to 2010.

A rising curve graph of the amount of carbon dioxide in the atmosphere since 1960.

Use the graph to calculate the increase in the volume of carbon dioxide in 1 m3 of atmosphere from 1960 to 2010. [2 marks]

Edexcel question courtesy of Pearson Education Ltd.

  • 384 and 315 used from graph [1]
  • 384 - 315 = 69 cm3 [1]

Sample question 3 - Higher

Question

In an experiment, dry air is passed backwards and forwards over hot, excess copper in the apparatus shown.

A blue flame from a bunsen burner is underneath a piece copper within dry air.

The oxygen in the air reacts with the hot copper to form copper oxide, CuO.

When the copper has reacted with all the oxygen, the apparatus is allowed to cool.

The initial volume of dry air in the apparatus was 50.0 cm3, measured at room temperature and pressure.

During the experiment the volume of gas in the apparatus decreased.

The percentage of oxygen in dry air is 21%. Calculate the final volume of gas remaining in the apparatus after allowing it to cool to room temperature. [2 marks]

Edexcel question courtesy of Pearson Education Ltd.

  • volume of oxygen in 50.0 cm3 = 50.0 × (21 ÷ 100) = 10.5 cm3 [1]
  • volume of gas remaining = (50.0 - 10.5) = 39.5 cm3 [1]

Sample question 4 - Higher

Question

Methane, CH4, undergoes incomplete combustion.

Write a balanced equation in which the incomplete combustion of methane produces water vapour, and equal amounts of carbon and carbon monoxide. [3 marks]

This question has been written by a Bitesize consultant as a suggestion to the type of question that may appear in an exam paper.

4CH4 + 5O2 → 8H2O + 2C + 2CO

or 2CH4 + 2½O2 → 4H2O + C + CO

  • correct formulae [1]
  • equal balancing numbers for C and CO on right hand side [1]
  • correctly balanced [1]