Maths questions
Maths questions often start with the command words 'calculate' or 'determine'. They will then have a blank space for you to show 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 incorrect.
In some maths questions you will be required to give the units. This may earn you an additional mark. Don't forget to check whether you need to do this.
Maths questions might include graphs and tables as well as calculations. Don't forget to take a ruler and calculator.
If drawing graphs, make sure you:
- put the independent variable on the x-axis and the dependent variable on the y-axis
- construct regular scales for the axes
- label the axes appropriately
- plot each point accurately
- draw a straight or curved line of best fit
If you are asked to calculate an answer and it has lots of significant figures, you should try to round it to the same number of significant figures you were given in the data in the question. Don’t forget to check your rounding.
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Sample question 1 - Foundation
Question
A new shower has a power output of 10,690 W when it is connected to the 230 V mains electricity supply.
The equation which links current, potential difference and power is:
current = power ÷ potential difference
Calculate the current passing through the new shower.
Give your answer to two significant figures. [4 marks]
Current = 47 A
current = power ÷ potential difference
= 10,690 W ÷ 230 V
= 46.478 A
Rounding to two significant figures gives 46 A.
Sample question 2 - Foundation
Question
When the potential difference between a Van de Graaff generator and an earthed sphere is 60 kV, a spark jumps between the metal dome and the earthed sphere.
The spark transfers 0.000025 coulombs of charge to the earthed sphere.
The equation that links charge, energy and potential difference is:
energy transferred = charge × potential difference
Calculate the energy transferred by the spark. [2 marks]
Energy transferred = 1.5 J
energy transferred = charge × potential difference
= 0.00025 C x 60 kV
= 0.00025 C x 60,000 V
= 1.5 J
Write out the equation in full and show all stages of the calculation. Include units in the answer.
Sample question 3 - Higher
Question
The charge that flows through a new shower in 300 seconds is 18,000 C.
The new electric shower has a power of 13.8 kW.
Calculate the resistance of the heating element in the new shower.
Write down any equations you use. [5 marks]
Resistance = 3.83 Ω
Current = charge ÷ time
= 18,000 C ÷ 300 s
= 60 A
Power = current2 × resistance
Resistance = power ÷ current2
= 13,800 W ÷ (60 A)2
= 13,800 ÷ 3,600
= 3.83 \(\Omega\)
Write out the equation in full and show all stages of the calculation. Include units in the answer.
Sample question 4 - Higher
Question
Different electrical wires need to have a cross sectional area that is suitable for the power output.
The graph below shows the recommended maximum power input to wires of different cross sectional areas:
A new electric shower has a power input of 13.8 kW.
Determine the minimum diameter of wire that should be used for the new shower.
The diameter, d, can be calculated using the equation:
\(d=\sqrt{\frac{4A}{\pi}}\)
A is the cross sectional area of the wire. [2 marks]
Minimum diameter = 3.50 mm
The graph shows that a power of 13.8 kW requires a cross sectional area of 9.6 mm2.
Therefore, diameter = \(\sqrt{\frac{4 \times 9.6}{\pi}}\)
= 3.50 mm
