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

Question

Three groups of students investigated how the electric current passing through a sodium chloride solution depends on the concentration of the solution.

The test was carried out using 50 cm3 of each solution. The students were given a stock solution of concentration 0.5 M and asked to dilute this as required to make the other solutions.

ConcentrationGroup A currentGroup B currentGroup C current
0.1 mol/dm30.07 A0.06 A0.06 A
0.2 mol/dm30.14 A0.12 A0.13 A
0.3 mol/dm30.20 A0.19 A0.20 A
0.4 mol/dm30.28 A0.26 A0.27 A
0.5 mol/dm30.35 A0.33 A0.34 A

a) Calculate the mean value for the current using sodium chloride concentration with a value of 0.5 mol/dm3. [1 mark]

b) Use the formula below to calculate the percentage variation in the current measured using this solution. [1 mark]

\frac{\textup{(Furthest~value~from~the~mean~value - mean~value)}}{\textup{mean~value}}\times 100\%

a) 0.34 A [1]

b) 3.0% or 3% [1]

Sample question 2 - Foundation

Question

Rust is iron(III) oxide, Fe2O3. It is formed when iron comes into contact with water and oxygen.

Some iron nails were weighed before and after being exposed to water and oxygen for one week.

The mass before exposure was 28 g and after one week the mass was 40 g.

Use this information to calculate the percentage increase in mass of the nails after they had been exposed to water and oxygen. [2 marks]

  • increase of 12 g [1]
  • 12 ÷ 28 × 100 = 42.8% or 43% [1]

Sample question 3 - Foundation

Question

Electrolysis is used to break down water into hydrogen and oxygen using an electric current.

The table below shows the total volume of hydrogen formed over 10 minutes.

Time0 mins2 mins4 mins6 mins8 mins10 mins
Volume of hydrogen0 cm34 cm38 cm312 cm316 cm320 cm3

a) Plot the results from the table on a grid and draw a suitable line. Label this line 'hydrogen'. [2 marks]

b) Draw a second line on the grid to show the volume of oxygen that would be collected during the same 10 minutes. Label this line 'oxygen'. [2 marks]

a)

  • all points plotted correctly ± ½ square [1]
  • straight line through all points - ruler must be used [1]

b)

  • straight line (ruler used) from (0,0) to (10,10) [2]

or

  • straight line from (0,0) and anywhere below hydrogen line [1]

Sample question 4 - Higher

Question

Many metal ores contain sulfides. Chalcocite is an important copper ore which contains copper(I) sulfide, Cu2S.

Copper can be obtained from the ore by heating in air.

The equation for the reaction that takes place is as follows:

Cu2S + O2 → 2Cu + SO2

a) Use the above equation to calculate the mass of copper produced on heating 20.5 tonnes of copper(I) sulfide with an excess of oxygen. [3 marks]

RAM: Cu = 64, S = 32

When the extraction was carried out with 20.5 tonnes of chalcocite, only 12.3 tonnes of copper was formed.

b) Calculate the percentage of impurity present in the ore. [2 marks]

a)

  • Mr = 64 + 64 + 32 = 160 [1]
  • 1 mol of Cu2S produces 2 mol of Cu/160 tonnes of Cu2S produces 128 tonnes of Cu [1]
  • 20.5 tonnes of Cu2S produces 128/160 × 20.5 = 16.4 tonnes of Cu [1]

b)

  • 4.1 tonnes of 'missing product' [1]
  • 4.1 ÷ 16.4 × 100 = 25% [1]