Maths questions
Maths questions will appear throughout both exams 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 大象传媒 Sounds.
Brush up on the maths you need for your exam - percentages, averages and converting units.
Sample question 1 - Foundation
The image below shows a wave.
Question
a) Use data from the diagram above to calculate the amplitude and the wavelength of the wave. Show your working. [3 marks]
b) Five waves pass in 10 seconds. Calculate the frequency of the wave. [2 marks]
c) Using your answers to parts a) and b), calculate the speed of the wave using the equation:
wave speed = frequency 脳 wavelength [2 marks]
OCR 21st Century Science, GCE Physics, Paper J259, 2016.
a) Amplitude: 0.6 梅 2 = 0.3 m
Wavelength: 0.25 m
The amplitude is the height of the wave taken from the taken from the zero line. The entire height of the wave is shown on the diagram as 0.6 m. You need to half this number to get the amplitude.
The wavelength can be seen in the diagram as distance between peaks. This is 0.25 m.
b) Frequency: 5 梅 10 = 0.5 Hz
The frequency is the number of waves that pass each second so to calculate the frequency you simply divide the number of waves by the time.
c) Wave speed = 0.5 脳 0.25
Wave speed = 0.125 m/s
In this question, the equation is given so it is simply a task of putting the correct numbers into the equation and doing the calculation. If you have made errors in previous questions, you will not lose marks here. Error carried forward is allowed.
Sample question 2 - Higher
Question
The frequency of a sound wave is 100 kHz.
Calculate the wavelength of these waves given that their speed is 330 m/s. [4 marks]
OCR 21st Century Science, GCE Physics, Paper J259, 2016 - Higher.
\(\text{v} = \text{f}\times \lambda\)
Rearrange to give:
\(\lambda = \frac{\text{v}}{\text{f}}\)
Convert kHz to Hz: 100 kHz = 100,000 Hz
330 m/s 梅 100,000 Hz = 3.3 脳 10-3 (m)
In this question the first thing you need to do is recall the equation. If you are not given the equation, it is best practice to first right down the equation you are going to use.
Next rearrange the equation to give wavelength.
Then, and with any maths question, it is important to look at the units in the question. In this example the frequency is given in kHz so this will need to be converted to Hz by multiplying by 1,000.
The final step is to just to put the numbers into the equation and do the calculation.