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

Question

A company extracts iron from rock that contains 30% iron by mass.

Calculate the mass of iron in 200 kg of the rock. [2 marks]

Mass of iron = $$\frac{30}{100} \times 200 \\ kg$$ [1]

= 60 kg [1]

Sample question 2 - Foundation

Question

A student electrolysed copper sulfate solution for five minutes.

Table 1 shows his results.

Table 1

AnodeCathode
Mass of electrode before electrolysis1.16 g1.28 g
Mass of electrode after electrolysis0.85 g1.57 g

Calculate the mass of copper deposited on the cathode. [2 marks]

Mass deposited = 1.57 - 1.28 [1]

= 0.29 g [1]

Sample question 3 - Higher

Question

Use the formulae in table 2 to deduce the formulae of the salts named in table 3.

Table 2

Name of ionChemical formula
AluminiumAl3+
CarbonateCO32-
MagnesiumMg2+
NitrateNO3-
PhosphatePO43-
SodiumNa+
SulfateSO42-

Use the formulae in table 1 to deduce the formulae of the salts named in table 2. [5 marks]

Table 3

Name of saltChemical formula of salt
Sodium carbonate
Magnesium nitrate
Aluminium phosphate
Aluminium sulfate
Magnesium phosphate
Name of saltChemical formula of salt
Sodium carbonateNa2CO3
Magnesium nitrate Mg(NO3)2
Aluminium phosphate AlPO4
Aluminium sulfate Al2(SO4)3
Magnesium phosphateMg3(PO4)2

Sample question 4 - Higher

Question

A student adds water to a sample of dilute hydrochloric acid.

The concentration of hydrogen ions decreases by a factor of 100.

Predict the effect on the pH. [2 marks]

The pH increases. [1]

It increases by 2. [1]