Maths questions

Don't forget to take a ruler and calculator into the exam.

Maths questions often start with 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 if you make a small slip, you can still get marks for your working)
  • marks may be given for working, including substitution and rearrangement
  • 'errors carried forward' are worked through to give credit for later working

Errors are carried forward if a later working depends on an earlier answer. You could still get marks 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. 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, 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


A student investigates the rate of reaction between zinc and excess dilute hydrochloric acid. The student uses the following method:

  1. place a known mass of granulated zinc into a conical flask
  2. connect a gas syringe to a bung
  3. pour 25 cm3 of dilute hydrochloric acid (an excess) into the conical flask and fit the bung quickly into the neck of the flask
  4. measure the volume of gas produced every 20 seconds until after the reaction finishes

The table shows the results.

TimeVolume of hydrogen
0 s0 cm3
20 s42 cm3
40 s66 cm3
60 s75 cm3
70 s80 cm3
100 s72 cm3
120 s82 cm3
140 s82 cm3
A blank graph.

Draw a graph of the volume of hydrogen gas produced against time using the grid. [3 marks]

Edexcel question courtesy of Pearson Education Ltd.

  • axes with linear scale that use more than half of each edge of the grid and labelled with units from the table [1]
  • all points correctly plotted to ± half a square [1]
  • a single curved line starting at the origin and passing through all points on the graph [1]

Sample question 2 - Foundation


Refer to the table of results in question 1.

Calculate the mean rate of reaction until the reaction finishes. [2 marks]

Edexcel question courtesy of Pearson Education Ltd.

  • reaction time = 100 s [1]
  • mean rate = 82 ÷ 100 = 0.82 [1]

Sample question 3 - Higher


A student investigates the rate of reaction between dilute hydrochloric acid and marble chips (calcium carbonate):

CaCO3(s) + 2HCl(aq) → CaCl2(aq) + H2O(l) + CO2(g)

The student investigates the rate by using different sizes of marble chips. This is done by using the same mass of marble chips in each experiment and measuring the volume of gas given off.

The graph shows the results.

Graph of volume of gas by time, with two curved lines and a tangent.

a) State how the graph shows that line B gives the results for the larger marble chips. [1 mark]

b) A tangent has been drawn on line A. Calculate the rate of reaction at this point. Give your answer to two significant figures, and include the units. [3 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.

a) Line B is less steep/flattens later. [1]

b) Gradient = change in volume of gas ÷ change in time:

  • = (90 - 30) ÷ (72 - 0)
  • gradient = 60 ÷ 72 [1]
  • = 0.83 [1]
  • cm3/s or cm3 s-1 [1]

Sample question 4 - Higher


The energies of some bonds are shown in the table.

BondEnergy of bond
H–H436 kJ mol-1
Cl–Cl243 kJ mol-1
H–Cl432 kJ mol-1

Hydrogen reacts with chlorine to form hydrogen chloride:

H2(g) + Cl2(g) → 2HCl(g)

Calculate the energy change, in kJ mol-1, for the reaction of 1 mol of hydrogen gas, H2, with 1 mol of chlorine gas, Cl2, to form 2 mol of hydrogen chloride gas, HCl. [4 marks]

Edexcel question courtesy of Pearson Education Ltd.

  • bonds broken = 436 + 243 = 679 kJ mol-1 [1]
  • bonds formed = 2 × 432 = 864 kJ mol-1 [1]
  • energy change = 679 - 864 = -185 kJ mol-1 [2]