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 car takes 6 m to brake when moving at 8 m/s.
Look at the graph of a car travelling at 8 m/s, starting to brake and then stopping.
Calculate the acceleration of the car during braking.
Show your working and state the unit. [4 marks]
OCR Gateway Science, GCE Physics, Paper J249, 2016.
Using the graph we know that: final velocity = 0, and initial velocity = 8.
Time taken: t = (2.25 – 0.75) = 1.5 s
\(acceleration = \frac{change in velocity}{time \ taken}\)
\(a = \frac{0 - 8}{1.5}\)
\(a = \frac{-8}{1.5}\)
\(a = - 5.3~m/s^{2}\)
Sample question 2 - Foundation
Question
A car takes 6 m to brake when moving at 8 m/s. The car has a braking force of 5,000 N.
(a) Calculate the work done by the brakes on the car. [2 marks]
(b) If a driver is tired how will this affect the braking distance? Explain your answer. [2 marks]
OCR Gateway Science, GCE Physics, Paper J249, 2016.
(a) 5,000 × 6 = 30,000 J
(b) No effect
Braking distance is not effected by the driver/braking distance is only based on the car and road conditions.
Sample question 3 - Higher
Question
An artificial satellite is kept in a stable circular orbit around a planet by a centripetal force caused by gravity.
(a) Explain how the velocity of a satellite is constantly changing whilst its speed remains the same when it is in orbit. [2 marks]
(b) The satellite is remotely controlled from Earth. The scientists want the satellite to move slower. What effect will this change in speed have on the height of its orbit?
Explain your answer. [2 marks]
OCR Gateway Science, GCE Physics, Paper J249, 2016 - Higher.
(a) Velocity is speed in a given direction/known direction/straight line.
The direction is continuously changing.
(b) Higher orbit.
Less force of gravity/less acceleration.
Sample question 4 - Higher
Question
The formula to work out kinetic energy is kinetic energy = 0.5 × mass × (velocity)2
A car has 30,000 J of energy and a mass of 1 tonne (1 tonne = 1,000 kg).
Calculate the velocity of the car and show your working. [2 marks]
OCR Gateway Science, GCE Physics, Paper J249, 2016 - Higher.
Formula re-arranged and numbers substituted correctly velocity = √30,000/(0.5 × 1,000) = 7.75 m/s
