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. 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.

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 decimal places, don't forget to only use one more than the data in the question. For example, if whole numbers are given in the question, then your answer would be to one decimal place. Don't forget to check your rounding.

These questions have been written by Bitesize consultants as suggestions to the types of questions that may appear in an exam paper.

Sample question 1 - Foundation

Question

A student observed a cell with a microscope. The magnification of the eyepiece was x10. The magnification of the objective was x20.

What magnification was the student using?

[1 mark]

x200

Sample question 2 - Foundation

Question

The student measured a cell they were looking at as 0.5 mm.

Convert this into micrometres.

500 μm

(1 millimetre = 1000 μm)

Sample question 3 - Foundation

Question

A student measured the change in mass of potato cylinders placed in different concentrations of salt solution. Their results are shown below.

Concentration (mol dm-3)0.00.10.20.30.4
Average change in mass (%)+10+2-3-6-8

Plot these points on graph paper. Draw a line of best fit.

[4 marks]

Your graph should look like this:

Graph showing the change in mass of potato cylinders place in different concentrations of salt solution
  • axes and scales correct [1 mark]
  • all points plotted correctly [2 marks] or 2 to 3 points plotted correctly [1 mark]
  • appropriate line of best fit [1 mark]
  • You should have concentration on the x-axis and change on the y-axis
  • the y-axis has a positive and negative scale
  • your divisions on your scales should be regular
  • your axes should be labelled and include units
  • all points should be plotted accurately
  • you should have drawn an appropriate line of best fit - in this case, it is a curve

Sample question 4 - Higher

Question

(a) A student is calibrating an eyepiece graticule.

The student finds that 45 divisions on the eyepiece graticule correspond with 100 μm on the stage micrometer.

Calculate what one division of the eyepiece graticule at this magnification represents. Write your answer to two significant figures.

[2 marks]

  • 2.2 μm
  • 100 μm divided by 45 divisions on the eyepiece graticule equals 2.2 μm
  • \frac{100}{45} \mu m = 2.2 μm (to two significant figures)
Question

(b) The student then finds that the length of a protist they are examining measures 42 divisions on the eyepiece graticule.

What is the length of the protist? [2 marks]

  • 88 μm
  • 42 × 2.1 μm

Sample question 5 - Higher

Question

The diameter of a red blood cell is 7 μm.

The diameter of one species of Amoeba is 0.7 mm.

Calculate the difference in order of magnitude between the two.

[2 marks]

  • 2
  • The diameter of a red blood cell is 7 μm = 7 × 10-6 m
  • The diameter of one species of Amoeba is 0.7 mm = 7 × 10-4 m
  • The difference in order of magnitude is 6 - 4 = 2