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 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 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


The table below shows information about some of the fractions obtained from crude oil.

FractionBoiling point rangeNumber of carbon atoms in the hydrocarbons
Paraffin (kerosene)150-250°CC11-C15
Diesel oil (gas oil)250-350°CC15-C19

Pentane is a hydrocarbon found in crude oil and has the formula C5H12. Suggest a value for the boiling point of pentane. [1 mark]

A value in the region 40 to 100 °C. [1]

Sample question 2 - Foundation


Dodecane is an alkane with 12 carbon atoms. Calculate the number of hydrogen atoms present in a molecule of dodecane. [1 mark]

26 [1]

Sample question 3 - Higher


Calculate the percentage by mass of carbon in butane, an alkane containing four carbon atoms.

Ar(H) = 1, Ar(C) = 12 [2 marks]

  • C4H10 has formula mass of 58 [1]
  • % carbon = 48 ÷ 58 × 100 = 82.8 % [1]

Sample question 4 - Higher


Crude oil can be separated into simpler mixtures, called fractions, which contain hydrocarbon compounds with boiling points within a similar range.

The graph below shows the boiling points of hydrocarbons containing 1 to 12 carbon atoms.

Boiling points of carbon atoms

a) Give the number of carbon atoms in the hydrocarbon which has the lowest boiling point. [1 mark]

b) State how the boiling point changes as the number of carbon atoms increases. [1 mark]

a) 1 carbon atom [1]

b) it increases [1]