Maths questions
Don't forget to take a ruler and calculator into the exam.
Maths questions often start with the 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's wise to show your working so you can check your answer
- marks are given for working, including substitution and rearrangement
- errors carried forward are taken into account
Errors carried forward is to do with what happens if a later answer depends on an earlier answer, and you get the earlier one wrong. You could still get full marks in the later answer 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.
Some 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.
You may be given a grid with axes 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
- make sensible scales so that the plotted points cover at least 50% of the area of the graph
- label the axes with their quantity and unit, eg time (s)
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.
Sample question 1 - Foundation
Question
A wave has an amplitude of 1.8 m, a frequency of 2 Hz and a wavelength of 1.5 m.
How many seconds will it take this wave to travel 12 m?
Show your working. [3 marks]
OCR Gateway Science, GCE Physics, Paper J249, 2016.
speed = frequency × wavelength = 2 × 1.5 = 3 m/s
time = distance/speed = 12 ÷ 3 = 4 s
Sample question 2 - Foundation
Question
Chantal experiments with converging lenses.
(a) Write down another name for a converging lens. [1 mark]
(b) Complete the path of the light ray after it goes through the converging lens. [1 mark]
OCR Gateway Science, GCE Physics, Paper B752, June 2015.
(a) convex / biconvex
(b) straight ray drawn from the original ray or lens to (or through) the focal point
Sample question 3 - Higher
Question
Infrared waves have different wavelengths.
They have a range of wavelengths from 0.74 × 10–6 m to 300 × 10–6 m.
The speed of infrared waves in a vacuum is 3 × 108 m/s.
Show that the frequency range of these waves is 4.04 × 1014 Hz. [4 marks]
OCR Gateway Science, GCE Physics, Paper B751, June 2014 - Higher.
(3.00 × 108) ÷ wavelength
(3.00 × 108) ÷ 0.74 × 10-6 = 4.05 × 1014 Hz
(3.00 × 108) ÷ 300 × 10-6 = 0.01 × 1014 Hz
(4.05 × 1014) - (0.01 × 1014) = 4.04 × 1014 Hz
Sample question 4 - Higher
Question
Some infrared waves have a wavelength of 1 mm.
The speed of electromagnetic waves is 3 × 108 m/s.
Show, using a calculation, that the frequency of the infrared waves is 3 × 1011 Hz. [2 marks]
OCR Gateway Science, GCE Physics, Paper B751, May 2012 - Higher.
rearrange speed = frequency × wavelength: frequency = speed/wavelength
frequency = (3 × 108) ÷ (1 × 10-3)
