Maths questions
Maths questions will appear throughout both exam 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 questions 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
The nervous system consists of billions of neurons.
The speed an electrical impulse can travel down a neuron can differ.
| Neuron | Length (m) | Time taken for impulse to travel (s) | Speed (m/s) |
| A | 1.3 | 0.027 | 48.15 |
| B | 1.3 | 0.014 | |
| C | 0.8 | 0.022 |
| Neuron | A |
|---|---|
| Length (m) | 1.3 |
| Time taken for impulse to travel (s) | 0.027 |
| Speed (m/s) | 48.15 |
| Neuron | B |
|---|---|
| Length (m) | 1.3 |
| Time taken for impulse to travel (s) | 0.014 |
| Speed (m/s) |
| Neuron | C |
|---|---|
| Length (m) | 0.8 |
| Time taken for impulse to travel (s) | 0.022 |
| Speed (m/s) |
Calculate the speed of the electrical impulse travelling down neuron B and neuron C.
OCR 21st Century, GCE Biology, Paper J257, 2016.
\(\text{speed} = \frac{\text{distance}}{\text{time}}\)
B - speed = 1.3 ÷ 0.014 = 92.86 m/s
C - speed = 0.8 ÷ 0.022 = 36.36 m/s
Sample question 2 - Foundation
Question
Blood is made up of cells, plasma and platelets.
The picture below is of blood cells as seen down a microscope.
There are more red blood cells than white blood cells in the blood sample shown above.
Estimate the ratio of red blood cells to white blood cells. [1 mark]
OCR 21st Century, GCE Biology, Paper J257, 2016.
10:1 OR 8:1
Sample question 3 - Higher
Question
A student does an experiment to find out more about how the process of osmosis works.
She was given five dishes each containing a different unknown concentration of sugar solution.
The student put two pieces of potato in each dish and left them for 30 minutes. She then removed the potato pieces and re-measured their length.
The student recorded the results in this table.
| Dish | Original length (cm) | Piece 1 after 30 min (cm) | Piece 2 after 30 min (cm) | Mean after 30 min (cm) | Change in mean length (cm) | Percentage change |
| 1 | 4.9 | 5.0 | 5.4 | 5.2 | +0.3 | |
| 2 | 5.1 | 4.3 | 4.1 | 4.2 | -0.9 | -18.4 |
| 3 | 5.0 | 4.8 | 4.4 | 4.6 | -0.4 | -8.0 |
| 4 | 5.2 | 5.7 | 5.9 | 5.8 | +0.6 | +11.5 |
| 5 | 4.9 | 4.8 | 4.8 | 4.8 | -0.1 | -2.0 |
| Dish | 1 |
|---|---|
| Original length (cm) | 4.9 |
| Piece 1 after 30 min (cm) | 5.0 |
| Piece 2 after 30 min (cm) | 5.4 |
| Mean after 30 min (cm) | 5.2 |
| Change in mean length (cm) | +0.3 |
| Percentage change |
| Dish | 2 |
|---|---|
| Original length (cm) | 5.1 |
| Piece 1 after 30 min (cm) | 4.3 |
| Piece 2 after 30 min (cm) | 4.1 |
| Mean after 30 min (cm) | 4.2 |
| Change in mean length (cm) | -0.9 |
| Percentage change | -18.4 |
| Dish | 3 |
|---|---|
| Original length (cm) | 5.0 |
| Piece 1 after 30 min (cm) | 4.8 |
| Piece 2 after 30 min (cm) | 4.4 |
| Mean after 30 min (cm) | 4.6 |
| Change in mean length (cm) | -0.4 |
| Percentage change | -8.0 |
| Dish | 4 |
|---|---|
| Original length (cm) | 5.2 |
| Piece 1 after 30 min (cm) | 5.7 |
| Piece 2 after 30 min (cm) | 5.9 |
| Mean after 30 min (cm) | 5.8 |
| Change in mean length (cm) | +0.6 |
| Percentage change | +11.5 |
| Dish | 5 |
|---|---|
| Original length (cm) | 4.9 |
| Piece 1 after 30 min (cm) | 4.8 |
| Piece 2 after 30 min (cm) | 4.8 |
| Mean after 30 min (cm) | 4.8 |
| Change in mean length (cm) | -0.1 |
| Percentage change | -2.0 |
The student has not finished working out the results.
Calculate the missing value. [2 marks]
OCR 21st Century, GCE Biology, Paper J257, 2016.
(0.3 ÷ 4.9) × 100 [1 mark for working]
+6.1 [1 mark for the correct answer]
Sample question 4 - Higher
Question
In coeliac disease, the patient may have a reduced number of villi in their small intestine. Calculate the density villi in the small intestine in both a healthy individual and a coeliac patient.
Villi in the small intestine increase the surface area for absorption of food molecules into the blood.
Give your answer to 2 decimal places. [2 marks]
| Patient | Number of villi | Area (square µm) | Villi per square µm |
| Healthy | 150,000 | 5,540 | |
| Coeliac disease | 50,000 | 7,200 |
| Patient | Healthy |
|---|---|
| Number of villi | 150,000 |
| Area (square µm) | 5,540 |
| Villi per square µm |
| Patient | Coeliac disease |
|---|---|
| Number of villi | 50,000 |
| Area (square µm) | 7,200 |
| Villi per square µm |
This question has been written by a Bitesize consultant as a suggestion to the type of question that may appear in an exam paper.
To find the number of villi per µm3 divide the number of villi by the area that was used to count the villi. Remember to follow the instructions in the question and give your answer to two decimal places.
Healthy person - 150,000 ÷ 5540 = 27.08 villi per µm2
Coeliac disease - 50,000 ÷ 7200 = 6.94 villi per µm2
More guides on this topic
- How do substances get into, out of and around our bodies?
- How does the nervous system help us respond? - OCR 21st Century
- Why do we need to maintain a constant internal environment?
- What role do hormones play in human reproduction? - OCR 21st Century
- What can happen when organs & control systems stop working?
