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 - Higher

Question

Figure 1 shows a piece of apparatus called a current balance.

Figure 1

Wire being suspended in a magnet with a insulating bar and a metal support, which itself is attached to a circuit of a battery, switch, ammeter and a variable resistor.

When the switch is closed, the part of the wire labelled X experiences a force and moves downwards.

Figure 2 shows how a small weight placed on the insulating bar makes the wire X go back and balance in its original position.

Figure 2

Side view of a current balance, wire being suspended in a magnet with a metal support, and insulating bar and a small weight in support.

The wire X is 5 cm long and carries a current of 1.5 A.

The small weight causes a clockwise moment of 4.8 × 10-4 Nm.

Calculate the magnetic flux density where the wire X is positioned.

Give the unit. [5 marks]

This question must be answered in two parts. Use the clockwise moment and distance from the pivot to find the force acting on wire X due to the motor effect. Then use F = B x I × L to find the strength of the magnetic field.

clockwise movement = anticlockwise movement

4.8 × 10-4 = F × 8 × 10-2 [1]

F = 6 × 10-3 N [1]

F = B × I × L

6 × 10-3 = B × 1.5 × (5 × 10-2) [1]

B = \frac{{6} \times {10^{-3}}}{{7.5} \times {10^{-2}}} [1]

B = 0.08 T [1]

Sample question 2 - Higher

Question

A teacher used the equipment shown in the figure below to demonstrate the motor effect:

Copper rod attached to a circuit containing an open switch, battery and a variable resistor; suspended in the middle of a horseshoe magnet.

The copper rod in the figure above has a length of 7 cm and a mass of 4 ×10-4 kg.

When there is a current of 1.12 A the resultant force on the copper rod is 0 N.

Calculate the magnetic flux density.

Gravitational field strength = 9.8 N / kg [5 marks]

This question must be answered in two parts. Calculate the weight of the rod to find the force acting upwards due to the motor effect. Then use F = B x I x L to find the strength of the magnetic field.

Weight = mass x gravitational field strength

W = 9.8 × 4 × 10-4 [1]

= 3.92 × 10-3 [1]

7cm = 0.07m

F = B x I x L

3.92 × 10-3 = B × 1.12 × 0.07 [1]

B = \frac{3.92 \times 10^{-3}}{0.0784} [1]

B = 0.05T [1]