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
A company extracts iron from rock that contains 30% iron by mass.
Calculate the mass of iron in 200 kg of the rock. [2 marks]
Mass of iron = \(\frac{30}{100} \times 200 \ kg\) [1]
= 60 kg [1]
Sample question 2 - Foundation
Question
A student electrolysed copper sulfate solution for five minutes.
Table 1 shows his results.
Table 1
| 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 on the cathode. [2 marks]
Mass deposited = 1.57 - 1.28 [1]
= 0.29 g [1]
Sample question 3 - Higher
Question
Use the formulae in table 2 to deduce the formulae of the salts named in table 3.
Table 2
| Name of ion | Chemical formula |
| Aluminium | Al3+ |
| Carbonate | CO32- |
| Magnesium | Mg2+ |
| Nitrate | NO3- |
| Phosphate | PO43- |
| Sodium | Na+ |
| Sulfate | SO42- |
| Name of ion | Aluminium |
|---|---|
| Chemical formula | Al3+ |
| Name of ion | Carbonate |
|---|---|
| Chemical formula | CO32- |
| Name of ion | Magnesium |
|---|---|
| Chemical formula | Mg2+ |
| Name of ion | Nitrate |
|---|---|
| Chemical formula | NO3- |
| Name of ion | Phosphate |
|---|---|
| Chemical formula | PO43- |
| Name of ion | Sodium |
|---|---|
| Chemical formula | Na+ |
| Name of ion | Sulfate |
|---|---|
| Chemical formula | SO42- |
Use the formulae in table 1 to deduce the formulae of the salts named in table 2. [5 marks]
Table 3
| Name of salt | Chemical formula of salt |
| Sodium carbonate | |
| Magnesium nitrate | |
| Aluminium phosphate | |
| Aluminium sulfate | |
| Magnesium phosphate |
| Name of salt | Sodium carbonate |
|---|---|
| Chemical formula of salt |
| Name of salt | Magnesium nitrate |
|---|---|
| Chemical formula of salt |
| Name of salt | Aluminium phosphate |
|---|---|
| Chemical formula of salt |
| Name of salt | Aluminium sulfate |
|---|---|
| Chemical formula of salt |
| Name of salt | Magnesium phosphate |
|---|---|
| Chemical formula of salt |
| Name of salt | Chemical formula of salt |
| Sodium carbonate | Na2CO3 |
| Magnesium nitrate | Mg(NO3)2 |
| Aluminium phosphate | AlPO4 |
| Aluminium sulfate | Al2(SO4)3 |
| Magnesium phosphate | Mg3(PO4)2 |
| Name of salt | Sodium carbonate |
|---|---|
| Chemical formula of salt | Na2CO3 |
| Name of salt | Magnesium nitrate |
|---|---|
| Chemical formula of salt | Mg(NO3)2 |
| Name of salt | Aluminium phosphate |
|---|---|
| Chemical formula of salt | AlPO4 |
| Name of salt | Aluminium sulfate |
|---|---|
| Chemical formula of salt | Al2(SO4)3 |
| Name of salt | Magnesium phosphate |
|---|---|
| Chemical formula of salt | Mg3(PO4)2 |
Sample question 4 - Higher
Question
A student adds water to a sample of dilute hydrochloric acid.
The concentration of hydrogen ions decreases by a factor of 100.
Predict the effect on the pH. [2 marks]
The pH increases. [1]
It increases by 2. [1]