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.

Some maths questions might ask you to 'show that' something is true. These questions often require you to prove something mathematically. For example, you might have to calculate two values and then compare them.

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:

  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 (you can use a special best fit line ruler to help with this)

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.

Edexcel questions courtesy of Pearson Education Ltd.

Sample question 1 - Foundation


An isotope of technicium, technicium-99, has a half-life of 6 hours.

A hospital has a sample which contains 40 mg of technicium-99.

Calculate how much technicium-99 will be in this sample after 12 hours. [2 marks]

After 1 half life (6 hours) the amount of technicium-99 will have halved from 40 mg to 20 mg [1]. After another 6 hours, it will have halved again to 10 mg [1].

Make sure to show each step of your working clearly.

Sample question 2 - Higher


Plutonium-238 is used in spacecraft to provide heat to power generators.

One of these generators contains 925 g of plutonium-238 when it is manufactured.

One gram of plutonium-238 has a power density of 0.54 W/g.

Plutonium-238 has a half-life of 87.7 years.

Calculate the average energy released per second by the generator after 263 years. [4 marks]

Make sure to show each step of your working clearly and include the unit in the final answer.

First, calculate the number of half lives which have passed in 263 years.

263 ÷ 87.7 = 3 half lives [1]

Now calculate the mass of plutonium left after 87.7 years. Do this by finding 925 divided by 2, three times:

925 ÷ 2 = 462.5

462.5 ÷ 2 = 231.25

231.25 ÷ 2 = 115.625 g [1]

Finally, calculate the total power by using the power density as 0.54 W/g.

To find the number of watts, multiply by the number of grams.

115.625 × 0.54 [1] = 62.4 Joules [1]