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. You will still get marks for your working even if you make an error)
- 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)
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
Copper sulfate solution was electrolysed for five minutes using copper electrodes.
The table shows the mass of the anode and of the cathode before electrolysis and after electrolysis.
| Anode | Cathode | |
| Mass of electrode before electrolysis | 1.16 g | 1.28 g |
| Mass of electrode after electrolysis | 0.85 g | 1.57 g |
| Mass of electrode before electrolysis | |
|---|---|
| Anode | 1.16 g |
| Cathode | 1.28 g |
| Mass of electrode after electrolysis | |
|---|---|
| Anode | 0.85 g |
| Cathode | 1.57 g |
Calculate the mass of copper deposited.
[2 marks]
Edexcel question courtesy of Pearson Education Ltd.
- Copper is deposited on the cathode, therefore mass deposited = 1.57 - 1.28 [1]
- = 0.29 (g) [1]
Sample question 2 - Foundation
Question
To find the exact amount of dilute hydrochloric acid that reacts with 25.0 cm3 of the sodium hydroxide solution, a titration is carried out. The table shows the results for the titrations.
| 1st titration | 2nd titration | 3rd titration | 4th titration | |
| Final burette reading | 37.60 cm3 | 36.20 cm3 | 39.15 cm3 | 38.40 cm3 |
| Initial burette reading | 0.40 cm3 | 0.00 cm3 | 3.95 cm3 | 2.10 cm3 |
| Volume of acid used | 37.20 cm3 | 36.20 cm3 | 35.20 cm3 | 36.30 cm3 |
| Final burette reading | |
|---|---|
| 1st titration | 37.60 cm3 |
| 2nd titration | 36.20 cm3 |
| 3rd titration | 39.15 cm3 |
| 4th titration | 38.40 cm3 |
| Initial burette reading | |
|---|---|
| 1st titration | 0.40 cm3 |
| 2nd titration | 0.00 cm3 |
| 3rd titration | 3.95 cm3 |
| 4th titration | 2.10 cm3 |
| Volume of acid used | |
|---|---|
| 1st titration | 37.20 cm3 |
| 2nd titration | 36.20 cm3 |
| 3rd titration | 35.20 cm3 |
| 4th titration | 36.30 cm3 |
In this titration, the accurate volumes of acid used that are within 0.20 cm3 of each other are considered concordant volumes.
Identify the concordant results and use them to calculate the mean volume of hydrochloric acid required.
[1 mark]
Edexcel question courtesy of Pearson Education Ltd.
Mean volume = \(\frac{36.20 + 36.30}{2}\) [1]
36.25 cm3 [1]
Sample question 3 - Higher
Question
Copper is purified by the electrolysis of copper sulfate solution using an impure copper anode and a pure copper cathode.
Write the half equation for the formation of a copper atom from a copper ion.
[2 marks]
Edexcel question courtesy of Pearson Education Ltd.
Cu2+ + 2e- → Cu
- All species [ions, electrons, atoms]. [1]
- Correctly balanced. [1]
Sample question 4 - Higher
Question
Water is added to a sample of dilute hydrochloric acid. The concentration of hydrogen ions decreases by a factor of 100.
Predict the effect on the pH of the solution.
[2 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.
The pH increases [1] by 2. [1]
