Answering a maths question

Laura Armstrong & Joe Wolfensohn

Teachers

Essential Maths Skills in Biology

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Key Equations to Know

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Logarithms and Standard Form

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Ratio, Proportions & Percentages

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Laura Armstrong

Head of Biology

Joe Wolfensohn

Assistant Head of Biology

Recall Questions

You can test your knowledge on some basic maths skills below.

0.0125 moles of a particular substance were dissolved in 2.5 dm³ of water. What is the concentration of this substance in mol dm^-3?

0.0125/2.5 = 0.005 = 5x10^-3

Convert 5,000,000 mm³ to m³.

5,000,000 / 1x10⁹ = 5x10^-3

What is the formula to calculate rate in biology?

Rate = Change ÷ Time

Topic Explainer Video

Check out this @JoeDoesBiology video that explains answering a maths question or read the full notes below. Once you've gone through the whole note, try out the practice questions!

If you want another explainer of answering a maths question, check out this video from @JoeDoesBiology and once you've gone through the whole note, try out the practice questions!

Essential Maths Skills in Biology

Standard Form & Significant Figures

Know how to convert to/from standard form:
e.g., 0.00021 → 2.1 × 10⁻⁴
Give answers to appropriate significant figures. Give your answer to the minimum number of significant figures used in the question if you are not told.

Unit Conversions

Master converting between:

Length: mm → µm → nm
Area & Volume: cm² ↔ m²; mm³ ↔ cm³ ↔ m³

1 mm = 1000 µm
1 m² = 1,000,000 mm²
1 m³ = 1,000,000,000 mm³

Key Equations to Know

Equation	Possible Use
Rate = change ÷ time	Enzyme activity, uptake rates
Magnification = image size ÷ actual size	Microscopy
Pulmonary ventilation = tidal volume × breathing rate	Lung volume and time graphs
Cardiac output = stroke volume x heart rate	Cardiac output
Density = mass ÷ volume	Cell contents, blood
Percentage change = (difference ÷ original) × 100	Osmosis practical, growth
Population = (number in sample 1 x number in sample 2) / marked number in sample 2	Estimating population using mark-release recapture
Efficiency = (energy transferred ÷ energy intake) × 100	Food chains and energy transfer
Net Primary Production = NPP = GPP – R	Energy in producers
Net production = I – (F + R)	Energy in consumers
p + q = 1 and p² + 2pq + q² = 1	Allele and genotype frequencies - Hardy Weinberg

You will be given the equations for statistical tests in the exam but not how to determine the number of degrees of freedom.

Graph-Based Calculations

Identify values from axes carefully.
Determine gradients using a tangent and average rate.
Use standard deviation bars to determine the variability and significance of any difference
Express rates in correct units (e.g., cm³ hour^-1 or mm³ min^-1).

Logarithms and Standard Form

Know how to convert from log₁₀ values and to log10 values using the 10x function and log10x function.

Example

Convert 512 into a log₁₀ value:

log₁₀(512) = 2.71 to 3 sig.fig, so 10^2.71

Identify values from logarithmic scales

Graph showing enzyme activity over time, where product formation increases rapidly at first and then levels off as the reaction rate decreases.

The log scale could also be represented as 1, 10¹, 10², 10³ etc. or if the y axis label says log₁₀ scale it may be represented as 0, 1, 2, 3, 4 etc.

No answer provided.

Ratio, Proportions & Percentages

Use ratios to compare biological quantities (e.g., lung volume/body mass).
Percentages are commonly used to:

Calculate error
Determine decrease/increase from graphs
Analyse experimental results

Example

% decrease = ((initial – final) ÷ initial) × 100

No answer provided.

Exam Tips

1. Understand the Question First

Read all the information provided before jumping into calculations.
Identify what you’re being asked to find (e.g., a rate, a percentage change, a concentration).
Look at units – they often indicate what type of calculation is required (e.g., mol dm⁻³ = moles ÷ volume).

2. Context, Units and Estimation

Check the units of the final answer and the format required (e.g., standard form).
Identify and list the data needed – this might involve calculating intermediate steps first.
Make a rough estimate to spot major errors later.

3. Data Collection & Execution

Gather data from tables, graphs or questions.
Check units are compatible – convert if necessary.
Perform the calculation, show all working, and add units to your answer.

4. Final Check

Compare your answer to your earlier estimate.
Check for silly calculator errors or unit mismatches.
Ensure your answer has the correct number of significant figures and is in the right format (e.g., standard form).

No answer provided.

Common Mistakes

Using wrong units or forgetting to convert.
Incorrect rounding or ignoring significant figures.
Writing the final answer in the wrong format (e.g., not in standard form).
Not showing full working – even if using a calculator.

No answer provided.

A student used a potometer. An air bubble moved 6.4 mm in 10 minutes. The capillary tube has a diameter of 1 mm. Calculate the rate of water uptake in mm³ per hour. Show your working. (2 marks)