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Units and standard form, magnification, averages, percentages, ratios and probability, body calculations such as BMI and cardiac output, and reading graphs.
Specification references this topic covers: Edexcel B1.5, B1.11, B3.16, B7.17, B8.12.
Biology uses maths in every topic: sizes of cells, rates of reactions, probabilities in genetics and measurements of the body. About one in ten of the marks in a biology paper are for maths skills.
The skills are the same few over and over: units, standard form, averages, percentages, ratios and graphs. Practise them once and you will gain marks in every topic.
By the end you will be able to do each of these with biology examples, and to show your working clearly.
Cells are very small, so we use small units. 1 millimetre (mm) = 1000 micrometres (µm). 1 micrometre = 1000 nanometres (nm). To change to a smaller unit multiply. To change to a bigger unit divide. So 0.2 mm = 0.2 × 1000 = 200 µm.
Standard form writes a number as A × 10ⁿ, where A is between 1 and 10. A bacterium that is 0.000 002 m long is 2 × 10⁻⁶ m. A number such as 4 500 000 is 4.5 × 10⁶.
Prefixes: milli (m) is 10⁻³, micro (µ) is 10⁻⁶, nano (n) is 10⁻⁹ and pico (p) is 10⁻¹². Check the units before you calculate and write the unit in the answer.
Magnification = image size ÷ real size. You can rearrange this: image size = real size × magnification, and real size = image size ÷ magnification. A formula triangle helps.
Use the same units for the image and the real object before you divide. If a drawing of a cell is 30 mm long and the magnification is ×100, the real length is 30 ÷ 100 = 0.3 mm, which is 300 µm.
Magnification has no unit. A scale bar tells you the real length. Measure the bar and the cell on the picture with a ruler, then divide the cell length by the bar length and multiply by the length the bar stands for.
The mean is the total divided by the number of values. The median is the middle value when the numbers are in order. The mode is the most common value. The range is the largest minus the smallest.
For 3, 5, 5, 6, 9: the total is 28, so the mean is 28 ÷ 5 = 5.6. The median is 5. The mode is 5. The range is 9 − 3 = 6.
Leave out anomalous results before finding a mean. A frequency table shows how many times each value occurs. A bar chart is used for categories, and a histogram or line graph for continuous data. Round your answer sensibly, to the same number of significant figures as the data.
Percentage = part ÷ whole × 100. Percentage change = (new − old) ÷ old × 100. Percentage cover is the percentage of a quadrat covered by one plant. Always divide by the original value for a change.
A ratio compares amounts. In a genetic cross between two heterozygous parents (Cc × Cc) the offspring are CC, Cc, Cc and cc. The ratio of dominant to recessive offspring is 3 : 1. To share an amount in a ratio, add the parts, divide, and multiply.
Probability = number of ways it can happen ÷ total number of outcomes. The chance that an offspring of Cc × Cc is cc is 1 out of 4, which is 1/4, 0.25 or 25%. Probabilities are chances for each offspring. They do not say what will happen exactly in a small family.
Body mass index (BMI) = mass (kg) ÷ height² (m²). For a mass of 70 kg and a height of 1.75 m the BMI is 70 ÷ 1.75² = 70 ÷ 3.0625 = 22.9. A BMI between 18.5 and 24.9 is usually described as healthy, 25 to 29.9 as overweight and 30 or more as obese, but the question will usually give you the ranges.
Waist-to-hip ratio = waist measurement ÷ hip measurement. A waist of 85 cm and hips of 100 cm give 85 ÷ 100 = 0.85. A high ratio shows more fat stored around the middle of the body, which is linked to a higher risk of type 2 diabetes and heart disease.
Heart rate is the number of beats each minute. Stroke volume is the volume of blood pumped out of the heart in one beat. Cardiac output = stroke volume × heart rate. A stroke volume of 70 cm³ and a heart rate of 72 beats per minute give 70 × 72 = 5040 cm³ per minute.
Plot the independent variable on the x-axis and the dependent variable on the y-axis. Label both axes with the quantity and the unit, choose a scale that uses more than half of the grid, plot the points carefully and join them with a line of best fit or a smooth curve.
The gradient of a straight line is the change in y ÷ change in x. On a graph of oxygen volume against time, a gradient is a rate. If the volume rises from 0 to 30 cm³ in 60 s, the rate is 30 ÷ 60 = 0.5 cm³/s. For a curve, draw a tangent at the point and find its gradient.
A correlation is a link between two variables. A scatter graph with the points going up to the right shows a positive correlation. A correlation shows a link but does not prove that one variable causes the other, because a third factor could be responsible.
1 mm = 1000 µm = 1 000 000 nm. Standard form: A × 10ⁿ. Magnification = image size ÷ real size.
Mean = total ÷ number. Percentage change = (new − old) ÷ old × 100. Probability = ways ÷ total outcomes.
BMI = mass ÷ height². Cardiac output = stroke volume × heart rate. Gradient = change in y ÷ change in x. A correlation does not prove cause.
Write 0.000 045 m in standard form.
Answer: 4.5 × 10⁻⁵ m
A person has a mass of 80 kg and a height of 1.60 m. Calculate the BMI to 1 decimal place.
Answer: 31.3
Two parents are both heterozygous (Cc) for a recessive condition. Give the ratio of unaffected to affected children and the percentage chance that a child is affected.
Answer: 3 : 1 and 25%
Maths skills for biology practice questions for GCSE Combined Science Biology. Try each one, then open the answer. Easy questions come first.
How many micrometres are there in 1 mm?
Answer: 1000
What is the mean of 4, 6 and 8?
Answer: 6
What is the median of 2, 9, 4, 7 and 5?
Answer: 5
What is the mode of 3, 5, 5, 6, 9?
Answer: 5
Write 4 500 000 in standard form.
Answer: 4.5 × 10⁶
A cell drawing is 45 mm long at a magnification of ×150. What is the real length in mm?
Answer: 0.3 mm
Convert 0.5 mm to micrometres (µm).
Answer: 500 µm
A plant is 5.0 cm tall at the start and 8.0 cm tall at the end. Calculate the percentage increase in height.
Answer: 60%
Longer questions in the style of a written paper, with the marking points. These are Yumio practice questions.
(a) A cell is 0.05 mm long. Give this length in micrometres. [1 mark] (b) A student draws the cell 40 mm long. Calculate the magnification. [3 marks]
Answer: (a) 50 µm (b) ×800
(a) A person has a mass of 90 kg and a height of 1.80 m. Calculate the BMI. [2 marks] (b) A heart has a stroke volume of 75 cm³ and a heart rate of 80 beats per minute. Calculate the cardiac output in cm³ per minute. [2 marks]
Answer: (a) 27.8 (b) 6000 cm³ per minute
Not squaring the height in a BMI calculation
BMI = mass ÷ height². Square the height first.
Adding stroke volume and heart rate
Cardiac output = stroke volume × heart rate.
Dividing by the new value in a percentage change
Divide the change by the original value.
Using a mean that includes an anomalous result
Leave anomalies out first.
Saying a correlation proves cause
A correlation shows a link only. Another factor may cause both.
Maths skills for biology is on both Foundation and Higher papers for GCSE Combined Science Biology, aimed at around grade 4.
Not squaring the height in a BMI calculation. BMI = mass ÷ height². Square the height first.
Open Show answer under each question on this page. The questions are Yumio practice questions, not past exam questions.
See how the papers are set: AQA Combined Science papers and Edexcel Combined Science papers.
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