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
Always show working in calculation questions. You can get marks for correct working, even if the answer is wrong.

Take extra care when converting between units.

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)

These questions have been written by Bitesize consultants as suggestions to the types of questions that may appear in an exam paper.

Sample question 1 - Foundation


Lithium chloride is an ionic compound. It is made up of lithium ions and chloride ions.

The diameter of a lithium ion is 0.120 nm.

The diameter of a chloride ion is 0.362 nm.

Calculate how many times bigger the diameter of the chloride ion is than the diameter of the lithium ion. Give your answer to three significant figures. [2 marks]

\(\frac{diameter \\ of \\ chloride \\ ions}{diameter \\ of \\ lithium \\ ions} = \frac{0.362 \\ nm}{0.120 \\ nm}\) [1]

= 3.02 [1]

Sample question 2 - Foundation


Some types of solder are alloys of tin and lead.

Some solder was made by mixing 22.5 g of lead with 15.0 g of tin.

Calculate the percentage of tin in this solder. [2 marks]

Percentage of tin \(\frac{15.0~g}{(15.0 + 22.5)~g}\) × 100 [1]

= 40.0% [1]

Sample question 3 - Higher


Gold is mixed with other metals to make jewellery.

Figure 1 shows the composition of different carat values of gold.

Figure 1

Two bar charts showing the percentage of metals in 9 and 18 carat gold.

An 18 carat gold ring has a mass of 5 g.

Calculate the masses of gold and copper in the ring. [2 marks]

Mass of gold = \(\frac{75}{100}\) × 5 g

= 3.75 g [1]

Percentage of copper = 100 - 80 = 20%

Mass of copper = \(\frac{20}{100}\) × 5 g

= 1 g [1]

Sample question 4 - Higher


A sodium chloride crystal has a cubic shape. The length of its sides is 0.5 mm.

Calculate the surface area and volume of the crystal. [2 marks]

Surface area = 6 × 0.5 mm × 0.5 mm

= 1.5 mm2[1 mark]

Volume = (4 nm)3 = 64 nm3

Volume = (0.5 mm)3 [1]

= 0.125mm3 [1]