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 the 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 graph below shows how the temperature changes when acids A and B are added separately to 25 cm3 of sodium hydroxide solution.

Two acids and how their temperature rises as more acid is added

Use the graphs to find:

a) the volume of acid required to neutralise the sodium hydroxide solution in both experiments. [1 mark]

b) the maximum temperature rise for acid B. [1 mark]

a) 25 ± 1 cm3 [1]

b) 1.5°C [1]

Sample question 2 - Foundation


A student measured out 25 cm3 of a sodium carbonate solution. The sodium carbonate solution had a concentration of 1.06 g/dm3.

Calculate the mass of sodium carbonate (Na2CO3) that was in 25 cm3 of this solution.

Give your answer in units of g and mg. [3 marks]

  • mass = 1.06 × 25/1000 [1]
  • = 0.0265 g [1] and 26.5 mg [1]

Sample question 3 - Foundation


Bethany adds water to some dilute hydrochloric acid.

The concentration of hydrogen ions decreases by a factor of 1000.

Predict the effect on the pH. [2 marks]

The pH increases [1]

It increases by 3 [1]

Sample question 4 - Higher


Iain prepared a solution of sodium hydroxide, NaOH, by dissolving 1.50 g of sodium hydroxide pellets in 500cm3 of water.

Calculate the concentration of the sodium hydroxide solution in g/dm3 [2 marks]

concentration = \frac {1.50 \ g}{0.500 \ dm^{3}} [1]

= 3.00 g/dm3 [1]