Maths questions

Maths questions will appear throughout both exam papers (Breadth and Depth) and at both Foundation Tier and Higher Tier.

Don't forget to take a ruler and a calculator into the exams.

Maths questions often start with the command word 'calculate', followed by a blank space for 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 wrong.

Always include the correct units for your answer unless they are already given on the answer line. This may earn you an additional mark.

Check carefully to see if the question tells you to round your answer to a particular number of significant figures or decimal places. And don't forget to check your rounding.

If the question does not tell you to round your answer but it has lots of decimal places, you should give your answer to the same number of significant figures as the data in the question. For example, if two significant figures are used in the question, then usually your answer should also be given to two significant figures.

Other command words you might see in maths question include:

  • 'predict' (look at some data and suggest an outcome - don't just guess, look at trends in the data and use your scientific knowledge and understanding to make a sensible suggestion)
  • 'estimate' (suggest a rough value without doing a calculation - don't just guess, use your scientific knowledge and understanding to make a sensible suggestion)
  • 'show' (write down the details, steps or calculations to prove that an answer is correct)

Maths questions might include tables and graphs as well as calculations. When drawing a graph, make sure you:

  • put the independent variable (the factor you changed) on the x-axis
  • put the dependent variable (the factor you measured) on the y-axis
  • construct regular scales for the axes
  • label each axis with the quantity and units, eg time (s)
  • plot each point accurately
  • decide whether the origin (0,0) should be used as a data point
  • draw a straight or curved line of best fit if appropriate

Sample question 1 - Foundation


This question is about energy transfers in electrical appliances.

The plates on the back of three electrical appliances are shown below.

Plate APlate BPlate C
Power2.0 kWN/A800 W
Frequency50 Hz50 Hz50 Hz
Voltage230 V230 - 240 V230 V
CurrentN/A1.2 A3.5 A

Calculate the number of kWh of energy transferred by appliance A if it is on for 195 minutes. [3 marks]

In your answer use the equation:

energy transferred = power × time

OCR 21st Century Science, GCE Physics, Paper J259, 2016.

Convert 195 minutes into hours = 3.25 h [1]

2.0 (kW) × 3.25 (h) [1]

= 6.5 (kWh) [1]

The important thing when answering maths questions is to look at the units because you may have to convert between units. In this instance, the first step is to convert from minutes to hours. Once you have done that, simply put the numbers into the given equation and complete the calculation.

Sample question 2 - Foundation


More and more homes are having solar panels fitted to reduce household electricity bills.

The graph shows how the power output from a solar panel varies during a typical summer day.

Graph plotting time of day against power in kW. A rough bell shapped curve which peaks between 12:00 and 14:00.

With the help of the graph, estimate the mean power output between 11:00 and 15:00 hours. [1 mark]

OCR 21st Century Science, GCE Physics, Paper J259, 2016.

2.7 (kW) [1]

This question requires you to use the graph to see mean power output between a certain time scale. An answer between 2.6 and 2.8 would be allowed. For most of the time, the graph is between 2.6 and 2.8, hence 2.7 is the estimate.

Sample question 3 - Higher


A kettle is 90% efficient.

To boil the water 420 kJ is needed.

Calculate how much electrical energy is used by the kettle. [2 marks]

OCR 21st Century Science, GCE Physics, Paper A181, January 2012.

420 ÷ 0.9 [1]

= 467 kJ [1]

In this question you are being asked to calculate the total energy inputted. As efficiency = useful energy transferred ÷ total energy transferred, you need to divide the useful energy by the efficiency to get the total energy.