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.

Some maths questions might ask you to 'show that' something is true. These questions often require you to prove something mathematically. For example, you might have to calculate two values and then compare them.

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:

  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 (you can use a special best fit line ruler to help with this)

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.

Edexcel questions courtesy of Pearson Education Ltd.

Sample question 1 - Foundation and Higher

Question

The mass of a car is 580 kg. The car gains 39,000 J of gravitational potential energy as it climbs a height, \Delta h. Calculate \Delta h. (gravitational field strength, g = 10 N/kg.) [3 marks]

\Delta h = \frac{\Delta GPE}{mg} [1]

= \frac{39,000}{580 \times 10} [1]

= 6.72 m [1]

Sample question 2 - Foundation and Higher

Question

The efficiency of an electric motor is investigated as shown in Figure 1.

The motor lifts a mass at a constant speed.

A motor rests at the edge of a bench and hangs a weighted mass by a string.

The results are shown in the table below:

Current in motor1.9 A
Voltage across motor10.0 V
Time taken to lift mass9.0 s

Electrical power = current × potential difference ( P = I~V).

a) Show that the total energy supplied to the motor in the 9 s is about 170 J. [2 marks]

During the 9 s the efficiency of the motor is 70%.

b) Calculate the amount of useful energy transferred in the 9 s. [3 marks]

a) P = I~V

= 1.9 \times 10 = 19 W [1]

Then calculate E = P~t = 19 \times 9 [1]

= 171 J

Recall the equation linking current, voltage and power to find the power. Then recall the equation linking energy, power and time to find the energy. Remember that in a 'show that' question you can't use the number you are asked to show in your calculation anywhere. You should finish with a statement that you have shown what was asked (eg '171 J is approximately 170 J').

b) Calculate: e = \frac{\text{useful energy transferred}}{\text{total energy supplied}}

so \text{useful energy transferred} = e \times \text{total energy supplied} [1]

= 0.7 x 171 [1]

= 120 J [1]

Recall the equation for efficiency and rearrange it to make 'useful energy transferred' the subject.

Sample question 3 - Foundation and Higher

Question

Fuel weighing 230,000 N is pumped into an aircraft. This fuel moves upwards through a vertical height of 4.7 m. The power developed by the pump is 1,600 W.

Calculate the time needed to refuel the aircraft. [3 marks]

Calculate: E = F~d

= 230,000 x 4.7

= 1,081,000 J [1]

t = \frac{E}{P}

t = \frac{1,081,000}{1,600} [1]

Time = 676 s [1]

Recall the equation linking work done, force and distance. Use this to calculate the work done. Then recall the equation linking energy, power and time. Rearrange it to make time the subject and use this to calculate the time taken.