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


An atom of phosphorus has the symbol _{15}^{31}\textrm{P}.

Give the number of protons, neutrons and electrons in this atom of phosphorus. [3 marks]

Number of protons ______

Number of neutrons ______

Number of electrons ______

Number of protons = 15 [1]

Number of neutrons = 31 - 15 = 16 [1]

Number of electrons = number of protons = 15 [1]

Sample question 2 - Foundation


The radius of an atom is 1 × 10-10 m.

The radius of the nucleus of this atom is 1 × 10-14 m.

Calculate how many times smaller the radius of the nucleus is than the radius of the atom. [2 marks]

(1 × 10-10 m) ÷ (1 × 10-14 m) [1]

Nucleus is 10,000 times smaller [1]

Sample question 3 - Higher


Magnesium exists naturally as three isotopes.

Table 1 shows the relative abundance of each isotope.

Table 1

Relative mass of isotopePercentage abundance of isotope

Calculate the relative atomic mass, Ar, of magnesium.

Give your answer to two decimal places. [2 marks]

A_{r} =\frac{(79 \times 24)+ (10 \times 25) + (11 \times 26)}{100} [1]

= 24.32 [1]

Sample question 4 - Higher


Plot the data in table 2 on a bar chart. [4 marks]

Table 2

Group 1 elementBoiling point in °C
A blank graph.

Marks will be given for the following:

x-axis labelled 'Element'. [1]

y-axis labelled 'Boiling point in °C'. [1]

Even scale on y-axis, taking up most of the height of the grid. [1]

Bars correctly drawn. [1]