Maths questions
Don't forget to take a ruler and 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
- errors carried forward are worked through to give credit for later working
Learn maths skills with Dr Alex Lathbridge
Listen to the full series on BBC Sounds.
Brush up on the maths you need for your exam - percentages, averages and converting 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)
Sample question 1 - Foundation
Question
A coarse particle has a diameter of 1 × 10-6 m.
A nanoparticle has a diameter of 1.6 × 10-9 m.
Calculate how many times bigger the diameter of the coarse particle is than the diameter of the nanoparticle.
[2 marks]
This question is AQA material which is reproduced by permission of AQA.
1 ÷ 1.6 = 0.625
and use of indices 10-6 ÷ 10-9 = 103 = 1000 [1]
0.625 × 1000 = 625 times bigger. [1]
Sample question 2 - Foundation
Question
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]
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 tin \(\frac{15.0~g}{(15.0 + 22.5)~g}\) × 100 [1]
= 40.0% [1]
Sample question 3 - Higher
Question
Gold is mixed with other metals to make jewellery.
Figure 1 shows the composition of different carat values of gold.
Figure 1
An 18 carat gold ring has a mass of 5 g.
Calculate the masses of gold and copper in the ring.
[2 marks]
This question is AQA material which is reproduced by permission of AQA.
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
Question
A nanoparticle has a cubic shape. The length of its sides is 4 nm.
Calculate the surface area to volume ratio for the nanoparticle.
[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.
Surface area = 6 × 4 nm × 4 nm
= 96 nm2 [1]
Volume = (4 nm)3 = 64 nm3
Surface area : volume ratio = 96 : 64 [1]
= 1.5 [1]
