Maths questions
Don't forget to take a ruler and scientific calculator into the exam.
Maths questions often start with the command word calculate. You need to use numbers given in the question to work out the answer.
When an answer to a maths question is marked:
- full marks are given for the right answer
- marks may be given for working, including substitution and rearrangement
- calculation errors carried forward are worked through to give credit for later working
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.
Take extra care when converting between units.
Make sure you give answers to a suitable number of significant figures.
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)
These questions have been written by Bitesize consultants as suggestions to the types of questions that may appear in an exam paper.
Sample question 1 - Foundation
Question
The overall energy change is 386 kJ.
What percentage of 1370 kJ is this? Give your answer to two significant figures. [2 marks]
\(\frac{386}{1370}\) × 100 [1]
= 28% [1]
Sample question 2 - Foundation
Question
A student investigated the energy released during the combustion of ethanol. Her results are shown in the table below.
Table 1 shows his results.
Table 1
| Experiment 1 | Experiment 2 | Experiment 3 | |
| Initial temperature | 19°C | 21°C | 20°C |
| Final temperature | 39°C | 42°C | 39°C |
| Initial temperature | |
|---|---|
| Experiment 1 | 19°C |
| Experiment 2 | 21°C |
| Experiment 3 | 20°C |
| Final temperature | |
|---|---|
| Experiment 1 | 39°C |
| Experiment 2 | 42°C |
| Experiment 3 | 39°C |
Calculate the mean temperature difference in the water. [2 marks]
Temperature differences: 20, 21, 19 [1]
Mean = 20°C [1]
Sample question 3 - Higher
Question
Combustion is an exothermic reaction.
| Bond | Bond energy in kJ/mol |
| C–H | 413 |
| O=O | 498 |
| C=O | 805 |
| O–H | 464 |
| Bond | C–H |
|---|---|
| Bond energy in kJ/mol | 413 |
| Bond | O=O |
|---|---|
| Bond energy in kJ/mol | 498 |
| Bond | C=O |
|---|---|
| Bond energy in kJ/mol | 805 |
| Bond | O–H |
|---|---|
| Bond energy in kJ/mol | 464 |
Calculate the overall energy change for the complete combustion of one mole of methane in oxygen. [3 marks]
(4 × 413) + (2 × 498) = 2648 [1]
(2 × 805) + (4 × 464) = 3466 [1]
2646 - 3466 = -818 kJ/mol [1]
Sample question 4 - Higher
Question
A student pours dilute copper sulfate solution into a polystyrene cup, and measures the temperature of the acid.
He adds magnesium powder.
He stirs and measures the temperatures again.
He repeats the test two more times.
His results for the three runs are shown in the tables below.
Run 1
| Metal | Temperature at start (°C) | Temperature at end (°C) | Temperature change (°C) |
| Magnesium | 20 | 36 | +16 |
| Metal | Magnesium |
|---|---|
| Temperature at start (°C) | 20 |
| Temperature at end (°C) | 36 |
| Temperature change (°C) | +16 |
Run 2
| Metal | Temperature at start (°C) | Temperature at end (°C) | Temperature change (°C) |
| Magnesium | 20 | 37 |
| Metal | Magnesium |
|---|---|
| Temperature at start (°C) | 20 |
| Temperature at end (°C) | 37 |
| Temperature change (°C) |
Run 3
| Metal | Temperature at start (°C) | Temperature at end (°C) | Temperature change (°C) |
| Magnesium | 21 | 36 |
| Metal | Magnesium |
|---|---|
| Temperature at start (°C) | 21 |
| Temperature at end (°C) | 36 |
| Temperature change (°C) |
a) Complete the tables by writing in the missing values. [2 marks]
b) Calculate the mean temperature change for the three runs. [1 mark]
a)
Run 2
| Metal | Temperature at start (°C) | Temperature at end (°C) | Temperature change (°C) |
| Magnesium | 20 | 37 | +17 |
| Metal | Magnesium |
|---|---|
| Temperature at start (°C) | 20 |
| Temperature at end (°C) | 37 |
| Temperature change (°C) | +17 |
Run 3
| Metal | Temperature at start (°C) | Temperature at end (°C) | Temperature change (°C) |
| Magnesium | 21 | 36 | +15 |
| Metal | Magnesium |
|---|---|
| Temperature at start (°C) | 21 |
| Temperature at end (°C) | 36 |
| Temperature change (°C) | +15 |
[1] for each correct answer.
b)\(\frac{16 + 17 + 15}{3}\) = 16 °C [1]
