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

The graph below shows the results for an investigation into the volume of gas produced during the reaction between dilute hydrochloric acid and magnesium.

Graph of volume of gas produced by time

The table shows the results which were collected when the concentration was two times greater than the results shown in the graph.

Time in secondsVolume of gas produced in cm3
00
1035
1552
2080
3087

Plot the results from the table onto the graph paper. Draw a line of best fit. [3 marks]

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

  • all points plotted correctly [2]
  • best fit line drawn correctly, eg with approximately equal number of points on either side of the line [1]

Sample question 2 - Foundation

Question

Looking at the graph in the previous question, give one conclusion about how the rate of reaction changed when the concentration of hydrochloric acid was changed. [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.

When the concentration of acid increases, the rate of reaction increases [1].

Sample question 3 - Higher

Question

The graph below shows the volume of gas produced against time for the reaction between magnesium and hydrochloric acid.

Graph of volume of gas produced by second

Draw a tangent to the curve at 20 seconds. Determine the rate of reaction at 20 seconds by calculating the gradient of the tangent. Give the unit. [4 marks]

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

Tangent drawn correctly at 20 [1]

Correct values used for change in x and change in y (eg 8 and 3) [1]

Correct calculation of the gradient, eg 3/8 = 0.375 [1]

Correct unit: cm3/s [1]

Sample question 4 - Higher

Question

A student investigated the rate of a chemical reaction which produced a gas by measuring the change in mass over time. The results are shown on the graph below.

Mass of flask and its contents over time

Calculate the mean rate of reaction up to the time the reaction is complete. Give your answer to three significant figures. [4 marks]

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

Mass lost = 2.2 g [1]

Time taken = 270 s [1]

Mean rate of reaction = \frac{2.2}{270}= 0.00814814 [1]

Mean rate of reaction = 0.00815 g/s (to 3 significant figures) [1] (or given as 8.15 x 10-3)