Science calculations
Maths questions often start with the command words 'Calculate...' or 'Determine...'. They will then have a blank space for you to show 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 incorrect.
In some maths questions you will be required to give the units. This may earn you an additional mark. Don't forget to check whether you need to do this.
Maths questions might include graphs and tables as well as calculations. Don't forget to take a ruler and calculator.
If drawing graphs, make sure you:
- put the independent variable on the x-axis and the dependant variable on the y-axis
- construct regular scales for the axes
- label the axes appropriate
- plot each point accurately
- decide whether the origin should be used as a data point
- draw a straight or curved line of best fit
If you are asked to calculate an answer and it has lots of decimal places, don't forget to use 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 would also be to two significant figures. Don’t forget to check your rounding.
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
Two students recorded the number of birds they saw in one hour in two gardens.
The owners of garden A put out food on their bird table every day for five days. The owners of garden B moved out a month ago. No food has been put out in garden B in the last month. On day 5 they couldn't get into garden B so no results were recorded.
| Day 1 | Day 2 | Day 3 | Day 4 | Day 5 | |
| Garden A | 7 | 5 | 4 | 5 | 4 |
| Garden B | 1 | 2 | 1 | 2 | No results |
| Garden A | |
|---|---|
| Day 1 | 7 |
| Day 2 | 5 |
| Day 3 | 4 |
| Day 4 | 5 |
| Day 5 | 4 |
| Garden B | |
|---|---|
| Day 1 | 1 |
| Day 2 | 2 |
| Day 3 | 1 |
| Day 4 | 2 |
| Day 5 | No results |
Calculate the mean for both gardens. [2 marks]
To calculate a mean all the values must be added up and then divided by the total number of values.
Garden A: 7 + 5 + 4 + 5 + 4 = \(\frac{25}{5}\) = 5
Garden B: 1 + 2 + 1 + 2 = \(\frac{6}{4}\) = 1.5. To use the same number of significant figures as the original data the answer 1.5 should be rounded up to 2
Sample question 2 - Foundation
Question
The table shows the results from student A.
| Quadrat | Number of species counted |
| 1 | 1 |
| 2 | 3 |
| 3 | 4 |
| 4 | 2 |
| 5 | 2 |
| 6 | 1 |
| Quadrat | 1 |
|---|---|
| Number of species counted | 1 |
| Quadrat | 2 |
|---|---|
| Number of species counted | 3 |
| Quadrat | 3 |
|---|---|
| Number of species counted | 4 |
| Quadrat | 4 |
|---|---|
| Number of species counted | 2 |
| Quadrat | 5 |
|---|---|
| Number of species counted | 2 |
| Quadrat | 6 |
|---|---|
| Number of species counted | 1 |
What is the median result? Tick one box. [1 mark]
| A | 1 |
| B | 2 |
| C | 3 |
| D | 4 |
| A |
|---|
| 1 |
| B |
|---|
| 2 |
| C |
|---|
| 3 |
| D |
|---|
| 4 |
| A | 1 | |
| B | 2 | ✔ |
| C | 3 | |
| D | 4 |
| A |
|---|
| 1 |
| B |
|---|
| 2 |
| ✔ |
| C |
|---|
| 3 |
| D |
|---|
| 4 |
To calculate this to place the set of numbers in increasing order of size. The median is the middle number. In increasing order of size: 1,1,2,2,3,4. The answer is therefore 2.
Sample question 3 - Higher
Two students are investigating the effect of temperature on the rate of decay of fresh milk by measuring pH change. The following table shows their results at 25°C.
| Time (hours) | pH of milk |
| 0 | 6.5 |
| 24 | 6.0 |
| 48 | 5.2 |
| 72 | 4.7 |
| Time (hours) | 0 |
|---|---|
| pH of milk | 6.5 |
| Time (hours) | 24 |
|---|---|
| pH of milk | 6.0 |
| Time (hours) | 48 |
|---|---|
| pH of milk | 5.2 |
| Time (hours) | 72 |
|---|---|
| pH of milk | 4.7 |
Question
Calculate the rate of change per hour between the time the experiment started and ended. [1 mark]
\(\text{Rate of change} = \frac{\text{change in value}}{\text{change in time}}\)
\(\text{Change in value} = 6.5 - 4.7 = 1.8 \text{ pH units / hour}\)
\(\text{Change in time} = 72 ~\text{hours}\)
\(\text{So the rate of change} = \frac{1.8}{72} = 0.025 \text{ pH units / hour}\)
The question asks for the rate change per hour. So make sure you don't divide calculate the rate of change per day instead. You would do this by: \(\frac{1.8}{3} = 0.6\).
Question
Calculate the percentage change in the first 24 hour period (0 - 24 hours). [1 mark]
\(\text{Percentage change} = \frac{\text{change in value}}{\text{original value}} \times 100\)
\(\text{Change in value} = 6.5 - 6.0 \text{ pH units}\)
\(0.5 \text { pH units}\)
\(\text{Original value} = 6.5 \text { pH units}\)
\(\text{Percentage change} = \frac{0.5}{6.5} \times 100\)
\(7.7\%\)
Question
Calculate the percentage change in the last 24 hour period (48 - 72 hours). [1 mark]
\(\text{Percentage change} = \frac{\text{change in value}}{\text{original value}} \times 100\)
\(\text{Change in value} = 5.2 - 4.7 \text { pH units}\)
\(0.5 \text { pH units}\)
\(\text{Original value} = 5.2 \text{ pH units}\)
\(\text{Percentage change} = \frac{0.5}{5.2} \times 100\)
\(9.6\%\)
Question
Comment on the difference in the percentage change between the first and last 24 hour period. [1 mark]
The pH changed by the same amount (0.5 pH units) in each of the 24 hour periods, but the percentage change was greater in the second period so the rate of change was speeding up.