Maths questions

Don't forget to take a ruler and calculator into the exam.

Maths questions often start with command words like 'Calculate...' 'Determine...', 'Estimate...' and 'Measure...'. They will then include blank space for you to show your working.

When an answer to a maths question is marked:

  • full marks are given for the right answer (but it is very important to show your working, so you can check your answer and so that, if you make a small slip, you can still get marks for your working)
  • marks may be given for working, including substitution and rearrangement
  • 'errors carried forward' are worked through to give credit for later working

Errors are carried forward if a later working depends on an earlier answer. You could still get marks if your working is correct but you use the incorrect earlier answer.

If your answer has many decimal places or figures, make sure you give it to an appropriate number of decimal places or significant figures. You may be asked to give units. This may earn you an additional mark, so don’t forget to check whether you need to do this.

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)

Sample question 1 - Foundation

Question

Copper ore contains copper carbonate, CuCO3.

In the first stage of the extraction process, the copper carbonate is decomposed by heating to form copper oxide, CuO, and carbon dioxide.

CuCO3 → CuO + CO2

When 100 g of copper carbonate is decomposed completely in this way, it is found that the total mass of products is 100 g.

Give a reason why the starting mass of copper carbonate is always the same as the mass of the products formed. [1 mark]

Edexcel question courtesy of Pearson Education Ltd.

All the original atoms have simply been rearranged in the products/mass and conserved during chemical reactions. [1]

Sample question 2 - Foundation

Question

It takes 46.8 MJ of energy to extract 1 kg of aluminium from its ore. It only takes 5% of this to recycle 1 kg of aluminium.

Calculate the amount of energy used when recycling 1 kg of aluminium. [1 mark]

This question has been written by a Bitesize consultant as a suggestion to the type of question that may appear in an exam paper.

Amount of energy used = 46.8 × (5 ÷ 100) = 2.34 MJ. [1]

Sample question 3 - Higher

Question

It takes 46.80 MJ of energy to extract 1 kg of aluminium from its ore. It only takes 5% of this to recycle 1 kg of aluminium.

Calculate the amount of energy saved by recycling 20 kg of aluminium instead of extracting it from its ore. Give your answer to 3 significant figures. [3 marks]

This question has been written by a Bitesize consultant as a suggestion to the type of question that may appear in an exam paper.

  • percentage of energy saved = (100 - 5) = 95% [1]
  • amount of energy saved for 1 kg = 46.80 × (95 ÷ 100) = 44.46 MJ [1]
  • amount of energy saved for 5 kg = 44.46 × 5 = 222.3 MJ = 222 MJ [1]

Sample question 4 - Higher

Question

Iron ore contains iron[III] oxide, Fe2O3.

Calculate the mass of iron atoms in 320 g of Fe2O3. [3 marks]

This question has been written by a Bitesize consultant as a suggestion to the type of question that may appear in an exam paper.

  • Mr of Fe2O3 = (2 × 56) + (3 × 16) = 160 [1]
  • total Ar of Fe = (2 × 56) = 112 [1]
  • mass of iron in 320 g = 112 × (320 ÷ 160) = 224 g [1]