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)

Sample question 1 - Foundation

Question

A student measured the melting point of a solid hydrocarbon four times. The student’s results are in the table below.

Trial 1Trial 2Trial 3Trial 4
Melting point in oC35483737

Calculate the mean melting point of the hydrocarbon, leaving out any anomalous result. Give your answer to two significant figures. [2 marks]

This question is AQA material which is reproduced by permission of AQA.

\frac{(35+37+37)}{3}\ =\ 36.33 [1]

= 36 (to 2 significant figures) [1]

Sample question 2 - Foundation

Question

The hydrocarbon C16H34 can be cracked.

C16H34 → ______ C2H4 + C8H18

Balance the equation for this cracking reaction. [1 mark]

This question is AQA material which is reproduced by permission of AQA.

4 [1]

Sample question 3 - Higher

Question

In a cracking reaction, an alkane with 14 carbon atoms breaks down to produce two smaller hydrocarbon molecules. One is an alkane with 8 carbon atoms and the other is an alkene. Write a balanced symbol equation for this reaction. [1 mark]

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

C14H30 → C8H18 + C6H12 [1]

Sample question 4 - Higher

Question

The boiling points of some alkanes are shown in table 1.

Table 1

AlkaneNumber of carbon atoms Boiling point in °C
Methane1-162
Ethane2-89
Propane3-42
Butane4
Pentane5+36
Hexane6+69

Plot a graph to show how boiling point changes as the number of carbon atoms increases.

Use your graph to estimate the boiling point of butane. [4 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.

Line graph drawn with number of C atoms on x axis and boiling point on y axis [1]

All points plotted correctly [1]

Line of best fit drawn [1]

Correct value read from graph for an alkane with four carbon atoms (≈−0.5°C) [1]