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 a 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)

Questions courtesy of Eduqas.

Sample question 1 - Foundation

Side view of water waves produced in a pool. Distance between A and B, labelled as well as distance between the ground and trough/crest labelled.

a) Use information from the diagram to answer the following questions.

i) Write down the number of complete waves between A and B. [1 mark]

ii) Calculate the wavelength of the water waves. [1 mark]

iii) Calculate the amplitude of the waves. [2 marks]

b) The wavelength of the waves is affected by the frequency of the wave machine.

i) Using your answer from a) ii), calculate, using an equation you can recall, the wave speed given that the frequency is 0.3 Hz. [2 marks]

ii) State how the wavelength is affected when the frequency of the wave machine is increased. [1 mark]

Question courtesy of Eduqas.

a) i) Use the data in the table below to plot a graph on the grid below. [3 marks]

ii) 2.5 m [1]

iii) 1.9 - 1.5 = 0.4 [1]

0.4 ÷ 2 = 0.2 m [1]

b) i) v  = f  \times  \lambda [1]

v  =  0.3  \times  2.5  =  0.75~m/s [1]

ii) Wavelength decreases as speed is unchanged [1]

Sample question 2 - Higher


The data below shows how the speed of water waves changes with the depth of the water.

a) Use the data in the table below to plot a graph on the grid below. [3 marks]

Graph showing wave speed against depth of water

b) Describe how the wave speed changes with the depth of the water. [2 marks]

a) Scale on x-axis from 0 — 4.0 present with intervals of 0.5 and scale on y-axis from 0 — 6.0 present with intervals of 1.0 [1]

Points plotted within +/- ½ small square division [1]

Smooth curve of best fit from origin +/- 1 small square division on each point [1]

b) As the depth increases the wave speed increases [1]

ii) At a decreasing rate [1]