Science calculations

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.

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 dependant variable on the y-axis
  2. construct regular scales for the axes
  3. label the axes appropriately
  4. plot each point accurately
  5. decide whether the origin should be used as a data point
  6. 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 use the same number of significant figures as the data in the question. For example, if two significant figures are used in the question, then usually your answer would also be to two significant figures. Don't forget to check your rounding.

Sample question 1 - Foundation

Question

A student measured the change in mass of potato cylinders placed in different concentrations of salt solution ranging from 0.0 to 0.4 mol dm-3.

Their results are shown below.

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

Plot these points on graph paper and draw a line of best fit. [4 marks]

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

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]
  • all points plotted correctly [2] - one mark available for 2 to 3 points plotted correctly
  • appropriate line of best fit [1]

Concentration should be on the x-axis and change on the y-axis. The y-axis has a positive and negative scale. Divisions on the scales should be regular and axes should be labelled and include units

You should have drawn an appropriate line of best fit. In this case, it is a curve.

Sample question 2 - Foundation

Question

Assuming that a xylem vessel is a cylinder, calculate the cross sectional area of a xylem vessel with a diameter of 0.025mm using the formula \text{\pi}r2.

Give your answer to two significant figures. Use \text{\pi} = 3.142 [2 marks]

Question courtesy of Eduqas.

radius = diameter ÷ 2 = 0.025 ÷ 2

= 0.0125

area = \text{\pi} × 0.01252 [1]

= 0.000490 = 0.00049 mm2 [1]

Sample question 3 - Higher

Question

Siân grows tomato plants. She decides to use a fertiliser called InstantGrow. The label from a bottle of InstantGrow is shown below.

Concentrated nutrient solution
Dilution1 part InstantGrow: 200 parts water
Contents of bottle500 cm3

Using the instructions for use shown on the label, calculate the volume of diluted InstantGrow that can be made from the contents of one bottle. [2 marks]

Question courtesy of Eduqas.

For every 1 cm3, 200 cm3 of water will be added. The contents of the bottle is 500 cm3, so 500 × 200 gives in total 100,000 cm3 of diluted InstantGrow. [1]

There are 1000 cm3 in a litre so 100,000 ÷ 1000 = 100 litres or 100 dm3 [1]

Alternatively, you could calculate that 1 cm3 and an additional 200 cm3 results in 201 cm3 of InstantGrow solution for every cm3 in the 500 cm3 bottle.

201 × 500 = 100,500 cm3 or 100.5 litres