Maths questions
Maths questions will appear throughout both exams papers (Breadth and Depth), and at both Foundation Tier and Higher Tier.
Don't forget to take a ruler and a calculator into the exams.
Maths questions often start with the command word 'calculate', followed by a blank space for your working. It is important that you show your working – don't just write the answer down. You might earn marks for your working even if you get the answer wrong.
Always include the correct units for your answer, unless they are already given on the answer line. This may earn you an additional mark.
Check carefully to see if the question tells you to round your answer to a particular number of significant figures or decimal places. And don't forget to check your rounding!
If the question does not tell you to round your answer but it has lots of decimal places, you should give your answer to the same number of significant figures as the data in the question. For example, if two significant figures are used in the question, then usually your answer should also be given to two significant figures.
Other command words you might see in maths question include:
- 'predict' (look at some data and suggest an outcome – don't just guess, look at trends in the data and use your scientific knowledge and understanding to make a sensible suggestion)
- 'estimate' (suggest a rough value without doing a calculation – don't just guess, use your scientific knowledge and understanding to make a sensible suggestion)
- 'show' (write down the details, steps or calculations to prove that an answer is correct)
Maths questions might include tables and graphs as well as calculations. When drawing a graph, make sure you:
- put the independent variable (the factor you changed) on the x-axis
- put the dependent variable (the factor you measured) on the y-axis
- construct regular scales for the axes
- label each axis with the quantity and units, eg time (s)
- plot each point accurately
- decide whether the origin (0,0) should be used as a data point
- draw a straight or curved line of best fit if appropriate
Sample question 1 - Foundation
Question
A student counted the number of limpets found on three parts of the rocky shore. The data is shown in the table below.
| Part of shore | Test A | Test B | Test C | Mean |
| Low shore (closest to sea) | 15 | 16 | 17 | |
| Mid shore | 45 | 47 | 49 | |
| High shore (farthest from sea) | 2 | 1 | 8 |
| Part of shore | Low shore (closest to sea) |
|---|---|
| Test A | 15 |
| Test B | 16 |
| Test C | 17 |
| Mean |
| Part of shore | Mid shore |
|---|---|
| Test A | 45 |
| Test B | 47 |
| Test C | 49 |
| Mean |
| Part of shore | High shore (farthest from sea) |
|---|---|
| Test A | 2 |
| Test B | 1 |
| Test C | 8 |
| Mean |
Calculate the mean number of limpets found on the mid shore.
Show your working. [2 marks]
OCR 21st Century, GCE Biology, Paper J257 - Higher, 2016.
(45 + 47 + 49) ÷ 3 [1 mark]
= 47 [1 mark]
Note how the question asks you to show your working. It is important that you always do this in calculation questions. There is a mark for your working. Make sure you read the question carefully so that you calculate the mean for the correct sample (Mid shore). You must add up the numbers from each test then divide by the number of tests to calculate the mean.
Sample question 2 - Foundation
Question
Study the graph.
Estimate how many more amphibians are threatened compared to reptiles. [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.
One mark for reading the graph correctly:
Amphibians = ~1,900 threatened (give or take 50)
Reptiles = ~250 threatened (give or take 50)
Second mark for calculation:
1,900 – 250 = 1,650 more amphibians are threatened compared to reptiles
The symbol ~ means 'about this number' so it is often used in questions that are about estimating.
Sample question 3 - Higher
Question
New body cells are created as part of the cell cycle.
This is represented in the diagram below.
The whole cell cycle in this example takes 141 minutes.
Calculate the length of time spent in mitosis.
Give your answer to 2 decimal places. [2 marks]
See how the examiners ask you to give your answer to 2 decimal places. You should also show your working.
OCR 21st Century, GCE Biology, Paper J257 - Higher, 2016.
(141 ÷ 360) × 70 [1 mark for the calculation]
27.42 minutes [1 mark for correct decimal places]
Sample question 4 - Higher
Question
Use the graph to calculate the percentage increase in global carbon dioxide emissions from fossil fuels from 1900 to 2010. [4 marks]
To calculate percentage increase, work out the difference (increase) between the two numbers you are comparing. Then divide the increase by the original number and multiply the answer by 100.
This question has been written by a Bitesize consultant as a suggestion to the type of question that may appear in an exam paper.
Carbon dioxide in 1900 = 500 million tons [1 mark]
Carbon dioxide in 2010 = 9,000 million tons [1 mark]
Increase = 8,500 million tons [1 mark]
Percentage increase = [8,500 ÷ 500] × 100 = 1700% [1 mark]
