Data response questions

Do not forget to take a ruler and calculator into the exam.

Maths questions often start with the command words like 'calculate', 'determine', 'estimate' and 'measure'. They will then include blank space for you to show your working.

When an answer to a maths question is marked:

  • full marks are given for the right answer (but it is wise to show your working so you can check your answer)
  • marks are given for working, including substitution and rearrangement
  • errors carried forward are taken into account

Errors carried forward are related to what happens if a later answer depends on an earlier answer, and you get the earlier one wrong. You could still get full marks in the later answer if your working is correct but you use the incorrect earlier answer.

If your answer has many decimal places or figures, make sure you give it to an appropriate number of decimal places or significant figures. You may be asked to give units. This may earn you an additional mark, so do not forget to check whether you need to do this.

Some maths questions might ask you to plot or complete a graph or table. When you draw a graph, make sure you:

  • plot each point accurately
  • draw a best-fit straight line or curve

You may be given a grid with axes and scales already given. Sometimes you may be given an empty grid for you to supply your own axes. When you do this:

  • put the independent variable on the x-axis and the dependent variable on the y-axis
  • make sensible scales so that the plotted points cover at least 50% of the area of the graph
  • label the axes with their quantity and unit, eg time (s)

Sample question 1 - Foundation

Question

A householder installs underfloor heating in the kitchen that uses a heated wire in the form of a grid. The power produced by the wire grid depends on its area as shown in the table below:

Area of wire grid (m²)Power from wire grid (W)
0.00
1.0150
2.0300
4.0600
6.0900
8.01,200

a) Describe the relationship between the power and the area of the wire grid. [2 marks]

b) Use the data to find the power produced by a grid of area 12 m2. [1 mark]

Question courtesy of Eduqas.

a) They're proportional/the area doubles, the power doubles/as the area increases [1], the power increases at a constant rate/power = area × 150 [1].

b) Each 1 m2 has a power of 150 W so 12 m2 will have a power of 12 × 150 = 1,800 W. [1]

Sample question 2 - Foundation

Question

Some power companies produce electricity by using gas.

Not all the energy stored in the gas is converted into electrical energy.

The diagram below shows the energy flow in the process of producing electricity from gas:

Flow chart showing the energy trasnfer process from gas to electrical energy. Some figures are missing.

a) i) Complete the flow diagram above. [2 marks]

ii) State the amount of useful energy output from an input of 2,000 J. [1 mark]

b) Give two reasons, one of which must refer to an environmental effect, why power companies should look for other methods of producing electricity instead of using gas. [2 marks]

Question courtesy of Eduqas.

a) i) 1,000 J in rotating turbine [1], 300 J heats the air [1].

ii) 700 J [1]

b)

  • burning gas adds to greenhouse emissions/global warming/release of CO2 [1]
  • limited resource/non-renewable/finite source [1]

Sample question 3 - Higher

Question

In Britain, the demand for electricity in a day changes in the way shown on the graph below:

Graph plotting time of day against power in MW, time plot graph with the peak coming later in the day.

a) At what time was the demand for electricity smallest? [1 mark]

b) Write down the maximum power used in Britain during the day. [1 mark]

c) In the early hours of the morning, demand for electricity is low. Name one type of power station that is not supplying electricity to the distribution system at this time. [1 mark]

d) At 20:00, Britain transferred in 400 MW of electricity from Ireland, 1,000 MW from France and 1,000 MW from the Netherlands to cope with demand. Calculate how much electrical power was being produced in Britain at this time. Give the correct unit. [3 marks]

Question courtesy of Eduqas.

a) 06:00 (or 6 am) [1]

b) 45,000 MW [1]

c) Pumped storage hydroelectric/solar [1]

d) 45,000 - 2,400 [1]

= 42,600 MW [1]

Unit - MW not mW [1]

Sample question 4 - Higher

Question

An electrical immersion heater supplies heat at a steady rate to 2 kg of water at 30°C in a container. In 8 minutes the temperature of the water rose to 100°C.

a) Calculate, by choosing the correct formula from the list, the heat energy needed to change the temperature of the water. (Specific heat capacity of water is 4,200 J/kg°C) [2 marks]

b) If 372,000 J of energy is also absorbed by the container during this time, calculate the total energy supplied by the heater. [1 mark]

c) Calculate, by recalling an equation, the power of the immersion heater. [2 marks]

d) In a further 1 hour, with the heater left on, all the water turns into steam. Use a formula you can recall to calculate the energy needed to do this. [2 marks]

e) Choose an equation from the list to calculate a value for the latent heat of vaporisation for the water in this experiment. [2 marks]

f) Comment on this calculated value when compared with the actual value for water of 2,300,000 J/kg. [1 mark]

This question has been written by a Bitesize consultant as a suggestion to the type of question that may appear in an exam paper.

a) \Delta Q = m \: c \: \Delta \theta

\Delta Q = 2 \times 4,200 \times 70 [1]

= 588,000 J [1]

b) Total energy supplied = 588,000 J + 372,000 J = 960,000 J [1]

c) Power = energy supplied ÷ time in seconds [1]

= 960,000 ÷ (8 × 60) = 2,000 W [1]

d) Energy to turn all water into steam = power × time in seconds [1]

= 2,000 × (60 × 60) = 7,200,000 J [1]

e) Q = m L

L = \frac{Q}{m} [1]

L = \frac{7,200,000}{2}

= 3,600,000 J/kg [1]

f) No account was taken of heat energy lost to the surroundings during the vaporisation, so this answer is higher than the true value. [1]