Maths questions
Maths questions often start with the command words ‘C²¹±ô³¦³Ü±ô²¹³Ù±ð...’ or ‘D±ð³Ù±ð°ù³¾¾±²Ô±ð...’. 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 dependent variable on the y-axis
- construct regular scales for the axes
- label the axes appropriately
- 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 significant figures, you should try to round it to the same number of significant figures you were given in the data in the question. Don’t forget to check your rounding.
This page contains AQA material which is reproduced by permission of AQA.
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Sample Question 1 - Foundation
Question
The table shows how the count rate from a radioactive source changes with time.
| Time (seconds) | 0 | 40 | 80 | 120 | 160 |
| Count rate (counts / second) | 400 | 283 | 200 | 141 | 100 |
| Time (seconds) |
|---|
| 0 |
| 40 |
| 80 |
| 120 |
| 160 |
| Count rate (counts / second) |
|---|
| 400 |
| 283 |
| 200 |
| 141 |
| 100 |
Use the data in the table to calculate the count rate after 200 seconds. [2 marks]
Half-life = 80 s, counts/second after 200 s = 71
From the table it can be seen that the half-life is 80 seconds as it takes 80 s for count rate to fall from 400 to 200 and from 200 to 100.
The count rate at 200 s will be half the count rate measured 80 s earlier ie at 120 s.
Half of 141 = 70.5, so answers of 70 or 71 are both acceptable.
Sample Question 2 - Foundation
Question
The graph shows how the activity of a sample of potassium-40 changes over time.
Figure 2
Use the graph to determine the half-life of potassium-40. [2 marks]
1.3 billion years.
The initial mass is 1,100 mg. Half of this will be 550 mg. Draw a line from 550 mg across to the curve of the graph and another down to the time scale bar, the time taken for the mass to decrease by half is 1.3 billion years.
Sample Question 3 - Higher
Question
This graph shows how the power output of the nuclear reactor would change if the control rods were removed.
Calculate the rate of increase of power output at 10 minutes. [2 marks]
Rate of increase between 240 and 276 MW/minute.
The rate of increase is given by the gradient of the curve at 10 minutes. To find the gradient of a curve, draw a tangent and divide the change in power output by the change in time.
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]
\(_{}^{210}\textrm{Pb} \rightarrow _{80}^{}\textrm{Hg} + \)
\(_{82}^{210}\textrm{Pb} \rightarrow _{80}^{206}\textrm{Hg} + _{2}^{4}\textrm{He}\)
The total atomic (proton) numbers on each side of the equation should be equal. The total mass numbers on each side of the equation should be equal. You should know that an alpha particle could also be described as a Helium nucleus.