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 so that, 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)
Edexcel questions courtesy of Pearson Education Ltd.
Learn maths skills with Dr Alex Lathbridge
Listen to the full series on BBC Sounds.
Brush up on the maths you need for your exam - percentages, averages and converting units.
Sample question 1 - Foundation
Question
Alcohols and carboxylic acids are important organic compounds.
The table shows the names and formulae of three alcohols in a homologous series.
| Name | Formula |
| Methanol | CH3OH |
| Ethanol | C2H5OH |
| Propanol | C3H7OH |
| Name | Methanol |
|---|---|
| Formula | CH3OH |
| Name | Ethanol |
|---|---|
| Formula | C2H5OH |
| Name | Propanol |
|---|---|
| Formula | C3H7OH |
(a) Predict the formula of the alcohol that has five carbon atoms in its molecule, using the information in the table.
[1 mark]
(b) Calculate the relative formula mass of ethanol, C2H5OH.
[2 marks]
(Relative atomic masses: H = 1, C = 12, O = 16)
- (a) C5H11OH [1]
- (b) (2 × 12) + (5 × 1) + 16 + 1 [1]
- = 46 [1]
Sample question 2 - Foundation
Question
A student compares the temperature rise produced in the water when propanol burns with the temperature rise produced when ethanol burns.
The table shows the results for the two alcohols.
| Alcohol | Mass of alcohol burned | Temperature rise |
| Ethanol | 0.33 g | 20°C |
| Propanol | 0.28 g | 20°C |
| Alcohol | Ethanol |
|---|---|
| Mass of alcohol burned | 0.33 g |
| Temperature rise | 20°C |
| Alcohol | Propanol |
|---|---|
| Mass of alcohol burned | 0.28 g |
| Temperature rise | 20°C |
Explain, using only the information in the table, why propanol might be the better fuel.
[2 marks]
- The same temperature rise is achieved [1]
- Using a lower mass of alcohol/propanol [1]
Sample question 3 - Higher
Question
The use of nanoparticles has increased in recent years.
The length of the sides of a cube of silver is 2 cm.
Calculate the surface area to volume ratio of this cube of silver.
[3 marks]
- Surface area = 6 × 2 × 2 = 24 cm2 [1]
- Volume = 2 × 2 × 2 = 8 cm3 [1]
- Surface area to volume ratio = 24 ÷ 8 = 3 : 1 [1]
Sample question 4 - Higher
Question
When sodium hydroxide solution is mixed with a solution containing copper ions, Cu2+, copper hydroxide, Cu(OH)2, is formed.
Write the ionic equation for this reaction.
[3 marks]
Cu2+ + 2OH- → Cu(OH)2
- Cu2+ and Cu(OH)2 on correct sides [1]
- OH- on left hand side [1]
- (Correct formulae) correctly balanced [1]
