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. Calculation errors carried forward are worked through to give credit for later working.

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. Take extra care when converting between units.

Maths questions might include graphs and tables as well as calculations. Don't forget to take a ruler and scientific calculator into the exam.

If drawing graphs, make sure you:

  1. put the independent variable on the x-axis and the dependent variable on the y-axis
  2. construct regular scales for the axes
  3. label the axes appropriately
  4. plot each point accurately
  5. 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.

This page contains AQA material which is reproduced by permission of AQA.

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 = power ÷ potential difference [1]

= 10,690 W ÷ 230 V [1]

= 46.478 A [1]

Rounding to two significant figures gives 47 A [1]

Sample question 2 - Foundation

Question

A car demister passes 0.4 A of current for two minutes to demist the rear window of the car.

The equation that links charge, current and time is:

charge = current × time

Calculate how much charge flows during this time and show your working.

Give the correct unit. [2 marks]

OCR Gateway, GCE Physics, P2 2009 - Higher

Time in two minutes = 120 seconds charge × potential difference [1]

Charge = 0.4 × 120 = 48 [1]

Unit = Coulombs [1]

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]

Current = charge ÷ time

=18,000 C ÷ 300 s [1]

=60 A [1]

Power = current2 × resistance

Resistance = power ÷ current2 [1]

= 13,800 W ÷ (60 A)2 [1]

= 13,800 ÷ 3,600

Resistance = 3.83 Ω [1]

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 figure below shows the recommended maximum power input to wires of different cross-sectional areas:

A graph showing the maximum power input against the cross sectional area.

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]

A graph showing the maximum power input against the cross sectional area. Two dotted lines are joined to show that 13.8 kilowatts on the y axis meets 9.6 millimetres squared on the x axis.

The graph shows that a power of 13.8 kW requires a cross sectional area of 9.6 mm2. [1]

Therefore:

diameter = \sqrt{\frac{4 \times 9.6}{\pi}}

Minimum diameter = 3.50 mm [1]