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

The table shows information about a substance, X.

Melting pointBoiling point
-39°C356°C

Predict the physical state of substance X at -10°C. [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.

Liquid. [1]

Sample question 2 - Foundation

Question

The table shows information about a substance, Y.

Melting pointBoiling point
-218°C-183°C

Predict the physical state of substance Y at 25°C. [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.

Gas. [1]

Sample question 3 - Higher

Question

Paper chromatography was carried out on a sample of ink. A red spot travelled 42 mm and the solvent front travelled 75 mm.

Calculate the Rf value of the substance in the red spot.

R_{f}~\textup{value} = \frac{\textup{distance~travelled~by~a~dye}}{\textup{distance~travelled~by~solvent~front}}

[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.

Rf = 42 ÷ 75 = 0.56 [1]

Sample question 4 - Higher

Question

Paper chromatography was carried out on a sample of ink. The solvent front travelled 153 mm and a blue spot travelled 145 mm.

Calculate the Rf value of the substance in the blue spot, giving your answer to 2 significant figures.

R_{f}~\textup{value} = \frac{\textup{distance~travelled~by~a~dye}}{\textup{distance~travelled~by~solvent~front}}

[2 marks]

Edexcel question courtesy of Pearson Education Ltd.

Rf = 145 ÷ 153 = 0.9477 [1]

= 0.95 (answer to 2 significant figures) [1]