Maths 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. Calculation errors carried forward are worked through to give credit for later working.

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. Take extra care when converting between units.

Maths questions might include graphs and tables as well as calculations. Don’t forget to take a ruler and scientific calculator into the exam.

If drawing graphs, make sure you:

  1. put the independent variable on the x-axis and the dependent variable on the y-axis
  2. construct regular scales for the axes
  3. label the axes appropriately
  4. plot each point accurately
  5. 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.

Sample Question 1 - Foundation

Question

This table shows how the count rate from a radioactive source changes with time:

Time (seconds)04080120160
Count rate (counts/second)400283200141100

Use the data in the table to calculate the count rate after 200 seconds. [2 marks]

Half-life = 80 s [1]

Counts/second after 200 s = 71 [1]

From the table it can be seen that the half-life is 80 seconds as it takes 80 seconds for count rate to fall from 400 to 200 and from 200 to 100. The count rate at 200 seconds will be half the count rate measured 80 seconds earlier, ie at 120 seconds. Half of 141 = 70.5, so answers of 70 or 71 are both acceptable.

Sample Question 2 - Foundation

Question

This graph shows how the activity of a sample of potassium-40 changes over time:

A graph which shows the mass of sample against time. The curve shows gradual decrease in mass over time.

Use the graph to determine the half-life of potassium-40. [2 marks]

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 [1], the time taken for the mass to decrease by half is 1.3 billion years [1].

Sample Question 3 - Higher

Question

An atom of radium-228 decays by emitting a beta (β) particle from the nucleus.

A beta particle is in fact an electron (symbol 0-1e).

The effect of this is to change a neutron into a proton.

An atom of actinium remains.

This type of decay can also be represented by an equation:

_{88}^{228}\textrm{Ra} \rightarrow _{-1}^{0}\textrm{e} + _{89}^{228}\textrm{Ac}

This isotope of actinium is radioactive.

An atom of actinium-228 also decays by emitting a beta particle.

An isotope of thorium is left behind.

Complete the equation for this decay:

_{89}^{228}\textrm{Ra} \rightarrow

[2 marks]

_{89}^{228}\textrm{Ra} \rightarrow _{-1}^{0}\textrm{e} + _{90}^{228}\textrm{Th}

_{-1}^{0}\textrm{e} [1]

_{90}^{228}\textrm{Th} [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} +

_{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 [1]. The total mass numbers on each side of the equation should be equal [1]. You should know that an alpha particle could also be described as a Helium nucleus [1].