Answering a maths question
Laura Armstrong & Joe Wolfensohn
Teachers


Contents
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
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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:
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Length: mm → µm → nm
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Area & Volume: cm² ↔ m²; mm³ ↔ cm³ ↔ m³
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1 mm = 1000 µm
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1 m2 = 1,000,000 mm²
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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
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Identify values from axes carefully.
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Determine gradients using a tangent and average rate.
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Use standard deviation bars to determine the variability and significance of any difference
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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 102.71
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Identify values from logarithmic scales
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.
Ratio, Proportions & Percentages
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Use ratios to compare biological quantities (e.g., lung volume/body mass).
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Percentages are commonly used to:
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Calculate error
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Determine decrease/increase from graphs
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Analyse experimental results
Example
% decrease = ((initial – final) ÷ initial) × 100
Exam Tips
1. Understand the Question First
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Read all the information provided before jumping into calculations.
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Identify what you’re being asked to find (e.g., a rate, a percentage change, a concentration).
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Look at units – they often indicate what type of calculation is required (e.g., mol dm⁻³ = moles ÷ volume).
2. Context, Units and Estimation
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Check the units of the final answer and the format required (e.g., standard form).
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Identify and list the data needed – this might involve calculating intermediate steps first.
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Make a rough estimate to spot major errors later.
3. Data Collection & Execution
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Gather data from tables, graphs or questions.
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Check units are compatible – convert if necessary.
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Perform the calculation, show all working, and add units to your answer.
4. Final Check
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Compare your answer to your earlier estimate.
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Check for silly calculator errors or unit mismatches.
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Ensure your answer has the correct number of significant figures and is in the right format (e.g., standard form).
Common Mistakes
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Using wrong units or forgetting to convert.
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Incorrect rounding or ignoring significant figures.
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Writing the final answer in the wrong format (e.g., not in standard form).
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Not showing full working – even if using a calculator.
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)
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Radius = 0.5 mm
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Volume = πr²h = 3.14 × (0.5)² × 6.4 = 5.02 mm³
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Time = 10 mins = 1/6 hour
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Rate = 5.02 × 6 = 30.1 mm³ hour-1
Practice Question
Try to answer the practice question from the TikTok on your own, then watch the video to see how well you did!