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 a 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


1.50 g of manganese(IV) oxide powder was accurately weighed and put into 20 cm3 of hydrogen peroxide solution. After the reaction had stopped, the reaction mixture was filtered into a pre-weighed filter paper.

The filtered manganese(IV) oxide and filter paper was dried in an oven.

The mass readings are shown below.

Filter paper1.26 g
Manganese(IV) oxide and filter paper after drying2.74 g
Recovered manganese(IV) oxide1.48 g

Calculate the percentage (%) mass of manganese(IV) oxide recovered to one decimal place. [3 marks]

  • 1.48 ÷ 1.5 × 100 [1]
  • 98.66 [1]
  • 98.7 [1]

Sample question 2 - Foundation


The activity of an enzyme at various temperatures is shown in the graph.

Graph of enzyme activity by temperature

a) State the temperature at which the enzyme activity is highest. [1 mark]

b) Calculate the difference between the enzyme activity at 10°C and 30°C. [2 marks]

a) Temperature = 36(±1)°C [1]

b) 5.2 - 1.8 [1]

= 3.4 units [1]

Sample question 3 - Higher


The graph below shows how the percentage yield of sulfur trioxide changes with temperature between 300°C and 800°C.

Percentage yield of sulfur trioxide by temperature

Use the graph to find the increase in percentage yield if the temperature is reduced from 650°C to 450°C. [2 marks]

  • 86 and 56 read from graph [1]
  • 30% increase [1]

Sample question 4 - Higher


Sodium thiosulfate solution reacts with dilute hydrochloric acid forming a yellow precipitate. This reaction can be investigated using a light sensor. The yellow precipitate formed during the reaction causes a reduction in the amount of light reaching the light sensor.

5 cm3 of dilute hydrochloric acid was added separately to 10 cm3 sodium thiosulfate solutions at four different temperatures. All other factors were kept the same. The results are shown on the graph below.

Graph of light intensity by time

a) Give the letter A, B, C or D of the graph which represents the reaction carried out at the highest temperature and give the reason for your choice. [1 mark]

The rate of reaction can be calculated using the formula: rate = 1 / time.

b) The reaction is considered to be complete when the percentage light intensity reaches 30%. Use the formula to find the mean rate for experiment A. [2 marks]

a) A, as it has the steepest line/finishes in the shortest time [1]

b) Time = 22 seconds [1]

Rate = 0.045/0.0455/0.04545 [1]