Mathematical questions
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
- 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 only use one more than the data in the question. For example, if whole numbers are given in the question, then your answer would be to one decimal place. Don't forget to check your rounding.
This page contains AQA material which is reproduced by permission of AQA.
Sample question 1 - Foundation
A species of snail lived 400 million years ago. Scientists measured the width of 49 fossil shells of this snail. The bar chart shows the scientists' results.
Question
What is the range of the values for the width of the fossil shells for this species?
From ______ to ______ [1 mark]
Tip - a 'range' shows the lowest to the highest values in a data set.
From 18 to 30.
Question
The scientists cannot be sure that this is the full range of fossil shell widths for this species. Why? [1 mark]
Tip - the fossil record is not complete, so it cannot be assumed all have been found.
Only a small sample was examined, for example 49 shells in total. This was not a representative number and could not be considered enough evidence. It may also suggest that not all fossils have been found.
Sample question 2 - Foundation
Question
The diagram shows the inheritance of X and Y chromosomes.
What is the chance of having a female child? Give the reason for your answer. [2 marks]
Calculation explained - 4 possible offspring and 2 have XX therefore 2 divide by 4 = 0.5
You will be marked correctly for using equilvalent alternatives to 0.5, such as \(\frac{1}{2}\), 50%, 1:1, 50:50, or 1 in 2. [1 mark]
2 (out of 4) boxes are XX or half of the sperm contain an X-chromosome. [1 mark]
Sample question 3 - Higher
Question
Latitude is a measure of distance from the Earth's equator. Scientists investigated the effect of latitude on:
- the time taken for a new species to evolve
- the number of living species
The table shows the scientists' results.
| Latitude | Time | Number of species |
| 0 (at the equator) | 3 - 4 millions of years | 100 |
| 25 | 2 millions of years | 80 |
| 50 | 1 millions of years | 30 |
| 75 (in the Arctic) | 0.5 millions of years | 20 |
| Latitude | 0 (at the equator) |
|---|---|
| Time | 3 - 4 millions of years |
| Number of species | 100 |
| Latitude | 25 |
|---|---|
| Time | 2 millions of years |
| Number of species | 80 |
| Latitude | 50 |
|---|---|
| Time | 1 millions of years |
| Number of species | 30 |
| Latitude | 75 (in the Arctic) |
|---|---|
| Time | 0.5 millions of years |
| Number of species | 20 |
As latitude increases environmental conditions become more severe.
Describe the patterns shown by the data. [2 marks]
Tip - use your data table. Look at the number of living species as the latitude increases.
Marks will be awarded from any of the following points:
- there is an increase in latitude, which reduces the number of (living) species [1 mark]
- there is an increase in latitude, which reduces time for evolution (of new species) [1 mark]
- the less the time to evolve the fewer the number of (living) species [1 mark]
Ignore reference to severity of conditions
Sample question 4 - Higher
Question
The table gives information about the four species of bird in winter.
The information given in the table shows the mean body mass (in grams), the daily needed mean energy (in kilojoules) and the mean percentage of each day spent feeding
| Species | Mass | Energy | Spent feeding |
| Great tit | 21 g | 84.2 KJ | 75% |
| Blue tit | 12 g | 62.4 KJ | 81% |
| Coal tit | 9 g | 49.5 KJ | 88% |
| Long-tailed tit | 7 g | 42.0 KJ | 92% |
| Species | Great tit |
|---|---|
| Mass | 21 g |
| Energy | 84.2 KJ |
| Spent feeding | 75% |
| Species | Blue tit |
|---|---|
| Mass | 12 g |
| Energy | 62.4 KJ |
| Spent feeding | 81% |
| Species | Coal tit |
|---|---|
| Mass | 9 g |
| Energy | 49.5 KJ |
| Spent feeding | 88% |
| Species | Long-tailed tit |
|---|---|
| Mass | 7 g |
| Energy | 42.0 KJ |
| Spent feeding | 92% |
Calculate the energy needed per day per gram of body mass for the blue tit. [2 marks]
Tip - show your working out in these style of questions.
Blue tit needs 62.4 kJ of energy per day. It has 12 gram body mass.
Therefore: 62.4 divided by 12 = 62.4 ÷ 12 = 5.2
5.2 kJ per day per gram of body mass. (2 marks)
Question
Describe the trend for energy needed per day per gram of body mass for the four species of bird. [1 mark]
Tip - refer to data table again. You don't need data examples here, as it talks about the trend only.
The smaller the (mass of the) bird the more energy is needed (per gram of body mass) [1 mark] or accept the converse.
Question
Suggest an explanation for the trend you have described in part 2. [2 marks]
Explanation: Surface area to volume ratio is a tricky concept.
This diagram helps explain the difference between surface area (SA) to volume (vol) ratio. People assume a larger organism has a larger SA : Vol ratio, but it is in fact the opposite.
A smaller bird has a larger surface area to volume ratio. Or it can be considered that a smaller bird has a larger surface area to mass ratio. [1 mark]
Due to these ratios the amount of energy lost as heat occurs more quickly. [1 mark]