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
Learn maths skills with Dr Alex Lathbridge
Listen to the full series on ±«Óătv Sounds.
Brush up on the maths you need for your exam - percentages, averages and converting units.
Sample question 1 - Foundation
Question
A volume of air measuring 3 m3 has a mass of 3.9 kg.
Calculate its density. [2 marks]
OCR 21st Century Science, GCE Physics, Paper J259, 2016.
Using the equation: density = mass Ă· volume [1]
3.9 Ă· 3.0 = 1.3 kg/m3 [1]
This is a simple maths question. There are no units that need converting so all you need to do is put the numbers into the given equation and calculate the answer.
Sample question 2 - Foundation
Question
A bike contains a front wheel suspension fork. Each time the rider pushes down on the pedal, a spring in the suspension is compressed.
When the bike hits a tree stump, a force of 510 N compresses the spring by 15 cm. Calculate the spring constant of the spring. [4 marks]
OCR 21st Century Science, GCE Physics, Paper J260, 2016.
Recall: Force = spring constant Ă— extension [1]
F = k x
Rearrange to give k = F Ă· x [1]
Convert 15 cm into 0.15 m. [1]
k = 510 Ă· 0.15
k = 3,400 N/m [1]
This is a four mark question so it's important to look carefully at the units in the question because, for this many marks, it is likely that you will need to convert units. In this case it's cm to m. Next recall the equation and rearrange to make the spring constant the subject of the equation. Lastly put the numbers into the equation and calculate the answer.
Sample question 3 - Higher
Question
A kettle heats 1 kg of water from 20°C to 100°C and continues heating until half of the water has turned to steam.
Calculate the total increase in internal energy of the water and state the units. [5 marks]
Specific heat capacity of water = 4,200 J/kg°C
Specific latent heat of water vaporisation = 2,260 kJ/kg
OCR 21st Century Science, GCE Physics, Paper J260, 2016 - Higher.
Select and apply:
change in internal energy = mass Ă— specific heat capacity Ă— change in temperature
ΔE = m x c × ΔT [1]
ΔE = 1 × 4,200 × 80
ΔE = 336,000 J or 336 kJ [1]
Select and apply:
energy to cause a change of state = mass Ă— specific latent heat
ΔE = m × L [1]
Boiling half water turns to steam, therefore: m = 0.5 Ă— 1 kg
m = 0.5 Ă— 2,260,000
m = 1,130,000 J or 1,130 kJ [1]
Total energy change = 336,000 + 1,130,000
Total energy change = 1,466,000 J or 1,466 kJ [1]
This question is worth five marks and involves multiple steps. Read the question carefully and work out the equations you need to use. In this case it involves using the equation for specific heat capacity and specific latent heat. Once you have calculated the energy in heating the water by 80°C and the energy in changing state, you simply add the two values together to get the total increase in internal energy.