Answering a maths question

Laura Armstrong & Joe Wolfensohn

Teachers

Laura Armstrong Joe Wolfensohn

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 102.71

  • 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.

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)

  • Radius = 0.5 mm

  • Volume = πr²h = 3.14 × (0.5)² × 6.4 = 5.02 mm³

  • Time = 10 mins = 1/6 hour

  • 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!