Maths questions
Maths questions often start with the command words ‘C²¹±ô³¦³Ü±ô²¹³Ù±ð...’ or ‘D±ð³Ù±ð°ù³¾¾±²Ô±ð...’. They will then have a blank space for you to show your working. It is important that you show your working, don’t just write the answer down. You might earn marks for your working even if you get the answer incorrect.
In some maths questions you will be required to give the units. This may earn you an additional mark. Don’t forget to check whether you need to do this.
Maths questions might include graphs and tables as well as calculations. Don’t forget to take a ruler and calculator.
If drawing graphs, make sure you:
- put the independent variable on the x-axis and the dependent variable on the y-axis
- construct regular scales for the axes
- label the axes appropriately
- plot each point accurately
- draw a straight or curved line of best fit
If you are asked to calculate an answer and it has lots of significant figures, you should try to round it to the same number of significant figures you were given in the data in the question. Don’t forget to check your rounding.
This page contains AQA material which is reproduced by permission of AQA.
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Sample question 1 - Foundation
Question
The table below gives data for five different satellites orbiting the Earth.
| Satellite | Average height above Earth's surface in kilometres | Time taken to orbit Earth once in minutes | Mass of satellite in kilograms |
| A | 370 | 93 | 419,000 |
| B | 697 | 99 | 280 |
| C | 827 | 103 | 630 |
| D | 5,900 | 228 | 400 |
| E | 35,800 | 1,440 | 2,030 |
| A | |
|---|---|
| Average height above Earth's surface in kilometres | 370 |
| Time taken to orbit Earth once in minutes | 93 |
| Mass of satellite in kilograms | 419,000 |
| B | |
|---|---|
| Average height above Earth's surface in kilometres | 697 |
| Time taken to orbit Earth once in minutes | 99 |
| Mass of satellite in kilograms | 280 |
| C | |
|---|---|
| Average height above Earth's surface in kilometres | 827 |
| Time taken to orbit Earth once in minutes | 103 |
| Mass of satellite in kilograms | 630 |
| D | |
|---|---|
| Average height above Earth's surface in kilometres | 5,900 |
| Time taken to orbit Earth once in minutes | 228 |
| Mass of satellite in kilograms | 400 |
| E | |
|---|---|
| Average height above Earth's surface in kilometres | 35,800 |
| Time taken to orbit Earth once in minutes | 1,440 |
| Mass of satellite in kilograms | 2,030 |
(a)State the relationship, if any, between the height of the satellite above the Earth’s surface and the time taken for the satellite to orbit the Earth once. [1 mark]
(b)State the relationship, if any, between the time taken for the satellite to orbit the Earth once and the satellite’s mass. [1 mark]
(a) Increasing the height above the Earth’s surface increases the time taken for one orbit. [1 mark]
(b) There is no relationship between the time taken for the satellite to orbit the Earth once and the satellite’s mass. [1 mark]
Sample question 2 - Higher
Question
Electromagnetic waves travel through space at a speed of 3.0 x 108 m/s.
The radio waves emitted from a distant galaxy have a wavelength of 25 metres.
Calculate the frequency of the radio waves emitted from the galaxy and give the unit. [3 marks]
1.2 × 107 Hz
Wave speed = frequency x wavelength
Frequency = 3 × 108 / 25
Frequency = 3 × 108 / 25
= 12,000,000 Hz or 1.2 × 107 Hz
Write out the equation in full and show all stages of the calculation. Include units in the answer.
Sample question 3 - Higher
Question
From data collected, a graph can be drawn that links the speed of a galaxy with the distance of the galaxy from the Earth.
A third galaxy, C, seems to be travelling away from the Earth at about 60,000 km/s.
Estimate how far galaxy C might be from the Earth, showing how you use the graph to do this. [2 marks]
3,600 million light years [1 mark]
The line should be extended up to 60,000 km/s and the distance in millions of light year read from the x-axis. [1 mark]
This technique is called extrapolation and can be used to make predictions or estimates based on known data.