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 appropriate
  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.

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

The World Health Organisation (WHO) collects data on the disease tuberculosis (TB), which is caused by a bacterium. The WHO used the data shown in the table below to estimate:

  • the total number of people with the disease in each region
  • the number of deaths from TB in each region.
RegionNumber of people with TB per 100 000Number of deaths from TB per 100 000
Africa34578
USA436
Eastern Mediterranean12228
Europe508
South East Asia19038
Western Pacific11219

(i) Give one reason why it is necessary to express the number of people as 'per 100 000'. [1 mark]

(ii) Calculate the percentage of those with TB in Europe who survive the disease. Show your working. [2 marks]

(i) This is so that countries can be fairly compared as some regions have higher populations than others.

(ii) In Europe there were 50 people per 100,000 who contracted TB and of those 8 died. This means that 50 - 8 = 42 survived. This first calculation is worth 1 mark.

The percentage who survived can be calculated as:

\frac{42}{50} \times 100 = 84%. This gets the second mark.

Sample question 2 - Foundation

A scientist investigated the growth of the bacterium E. coli at different temperatures.

Their results are shown in the tables below.

Time (h)Number of bacteria per mm3 at 37°C
0100
10130
20200
30340
40475
50550
60600
Temperature bacteria are incubated at (°C)Number of bacteria per mm3 after 25 hours.
28230
38250
48195
Question

Describe the relationship between time and the number of bacteria per mm3 at 37°C. [1 mark]

As the time increases the number of bacteria per mm3 also increases.

Hint - when asked to describe a relationship it will usually follow the format:

As ________a________ increases/decreases then _________b_________ increases/decreases. Where a = the independent variable in the experiment and b = the dependent variable in the experiment.

Question

Calculate the difference in numbers of bacteria between 28°C and 38°C at 25 hours. Show your working. [2 marks]

280 – 230 = 50 per mm3 [1]

The number of bacteria at 380°C was 280 and at 280°C it was 230. To calculate the difference, take the smallest number from the largest. [1]

Sample question 3 - Higher

Question

The bacterium E. coli often infects humans and can cause blood poisoning. Doctors recorded 18,000 cases in the year 2000 but in 2008 the number rose to 23,000 because the bacterium became more difficult to kill with antibiotics.

Calculate the percentage increase in cases of E.coli infection from the year 2000 to 2008.

In 2000 there were 18,000 cases and in 2008 there were 23,000 cases. This is an increase of 23,000 - 18,000 = 5000 cases.

5000 as a percentage of the original 18,000 cases is \frac{5000}{18000} \times 100 = 27.8% increase in cases.