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
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)
Take extra care when converting between units.
This page contains AQA material which is reproduced by permission of AQA.
Question 1 - Foundation
The table below shows the blood sugar levels for two people after eating a meal.
| Time after eating in hours | Person A | Person B |
| 0 | 70 | 130 |
| 1 | 150 | 230 |
| 2 | 90 | 185 |
| 3 | 80 | 165 |
| 4 | 75 | 140 |
| Time after eating in hours | 0 |
|---|---|
| Person A | 70 |
| Person B | 130 |
| Time after eating in hours | 1 |
|---|---|
| Person A | 150 |
| Person B | 230 |
| Time after eating in hours | 2 |
|---|---|
| Person A | 90 |
| Person B | 185 |
| Time after eating in hours | 3 |
|---|---|
| Person A | 80 |
| Person B | 165 |
| Time after eating in hours | 4 |
|---|---|
| Person A | 75 |
| Person B | 140 |
Use data from the table to complete the graph below.
Question
a) Plot the points for person A.
The first two points have been plotted for you.
Draw a line through all the points. [3 marks]
b) How long after the meal is person B's insulin production at its peak? [1 mark]
a) All three points correct [2].
Suitable line drawn [1].
b) 1 hour [1]
Sample question 2 - Foundation
The table below shows how the count rate of a radioactive substance changes with time.
| Time in seconds | 0 | 40 | 80 | 120 | 160 |
| Count rate in counts/second | 600 | 463 | 300 | 221 | 150 |
| Time in seconds |
|---|
| 0 |
| 40 |
| 80 |
| 120 |
| 160 |
| Count rate in counts/second |
|---|
| 600 |
| 463 |
| 300 |
| 221 |
| 150 |
Question
a) Describe the relationship shown in the table. [2 marks]
b) Use the information from the table to predict the count rate after 200 seconds. [2 marks]
a) Include the following points to gain all marks:
- as time increases the count rate decreases [1]
- count rate halves every 80 seconds [1]
b) Half-life is 80 seconds [1]
75 ÷ 2 = 37.5
150 – 37.5 = 112.5 seconds
After 200 seconds, the count rate = 113 [1]
Sample question 3 - Higher
Question
The activity of a radioactive isotope changes over an 8 hour period of time. This can be seen in the graph below.
Predict how long it will take for the count rate to fall from 100 to 1.56 Becquerels. [2 marks]
Half-life read from graph = 2 hours [1]
Time to fall to 1.56 is six half-lives = 6 × 2 (hours) [1]
Sample question 4 - Higher
Question
Lead-210 is a radioactive isotope that decays to an isotope of mercury by alpha decay.
Complete the nuclear equation to show the alpha decay of lead-210. [3 marks]
\(_{...}^{210}\textrm{Pb} \rightarrow _{80}^{...}\textrm{Hg} + _{...}^{...}\textrm{...}\)
\(_{82}^{210}\textrm{Pb} \rightarrow _{80}^{206}\textrm{Hg} + _{2}^{4}\textrm{He}\)
