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

An espresso machine is an electrical appliance. The espresso machine has an electrical heater connected to a 440 V mains supply. The power of the electrical heater is 3.5 kW. Before the espresso machine can be used, its heater must raise the temperature of some cold water.

The specific heat capacity of water is 4,200 J/kg K.

Show that it takes the heater about 90 s to raise the temperature of 1 kg of water from 18°C to 95°C. [3 marks]

\Delta Q = mc \Delta \theta

\Delta Q = 1 \times 4,200 \times (95 - 18) = 323,400~J [1]

t = \frac{E}{P} [1]

t = \frac{323,400}{3,500} = 92~s [1]

Use the formula sheet to find an equation which links energy, mass, specific heat capacity and temperature change. Find the energy required. Recall an equation which links power, energy and time. Use this to find the time. You must give the time to at least 2 sf. Note that the question asks you to show that the time is about 90 s - you must not use 90 in your calculation - you should calculate a number close to 90 as the answer.

Sample question 2 - Foundation and Higher

Question

A horseshoe from a furnace is plunged into a tank of water.

The horseshoe has a mass of 400 g.

Iron (horseshoe) has a specific heat capacity of 450 J/kg K.

Water has a specific heat capacity of 4200 J/kg K.

The mass of water in the tank is 2.5 kg.

The temperature of the water rose from 10 °C to 32 °C.

Find the initial temperature of the horseshoe. [4 marks]

Heat energy lost by the horseshoe = heat energy gained by the water [1]

Energy gained by water = m \times c \times \Delta \theta = 2.5 \times 4200 \times 22 = 231,000~J

\Delta \theta = 2.5 \times 4,200 \times 22 = 231,000~J

Energy lost by iron horseshoe = 231,000 J [1]

Temperature loss of horseshoe, \Delta \theta = \frac{energy}{(m × c)} = \frac{231,000}{(0.4 × 450)} = 1283 °C [1]

Since the final temperature of the horseshoe is that of the water at 32 °C then the initial temperature of the horseshoe has to be 1,283 + 32 = 1,315 °C [1]