Maths Skills in Biology

Approximately 10% of the total marks in Edexcel GCSE Biology require mathematical skills. That means around 20 marks across both papers are maths-based. These are often straightforward calculations, but students regularly lose marks by not showing working, forgetting units, or making conversion errors.

This lesson covers every type of mathematical skill you need for the exam.

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Calculating Means

The mean (average) is the most commonly required calculation.

Formula: Mean = sum of all values ÷ number of values

Example: A student measured the height of seedlings (in cm): 4.2, 3.8, 4.5, 4.1, 3.9

Mean = (4.2 + 3.8 + 4.5 + 4.1 + 3.9) ÷ 5 = 20.5 ÷ 5 = 4.1 cm

Exam tip: If there is an anomalous result (a value that does not fit the pattern), you should exclude it from the mean calculation and state that you have done so.

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Percentages

Calculating a Percentage

Formula: Percentage = (part ÷ total) × 100

Example: Out of 250 students, 45 have brown eyes. What percentage have brown eyes?

(45 ÷ 250) × 100 = 18%

Calculating a Percentage of an Amount

Example: 60% of 1500 bacteria survived treatment. How many survived?

(60 ÷ 100) × 1500 = 900 bacteria

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Percentage Change

This is one of the most frequently examined calculations in biology.

Formula: Percentage change = (change ÷ original value) × 100

Important: The denominator is always the original value, not the final value.

Example: A potato cylinder had a mass of 2.5 g before being placed in solution. After 30 minutes its mass was 2.8 g. Calculate the percentage change in mass.

Change = 2.8 − 2.5 = 0.3 g Percentage change = (0.3 ÷ 2.5) × 100 = 12%

Since the mass increased, this is a +12% change (positive).

Example with decrease: A population of 800 organisms drops to 600.

Change = 800 − 600 = 200 Percentage change = (200 ÷ 800) × 100 = −25% (negative, because it decreased)

Exam tip: Always state whether the change is positive (increase) or negative (decrease). And always divide by the original value — this is the most common error.

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Magnification Calculations

These relate to Core Practical 1 (microscopy) and can appear on either paper.

The Magnification Formula Triangle

To find...	Formula
Magnification	M = I ÷ A
Image size	I = M × A
Actual size	A = I ÷ M

Where:

• M = magnification (no units — it is a ratio)
• I = image size (the size of the drawing or photograph)
• A = actual size (the real size of the object)

Worked Example

A cell in a micrograph measures 30 mm. The actual size of the cell is 0.03 mm. Calculate the magnification.

M = I ÷ A = 30 ÷ 0.03 = ×1000

Worked Example — Finding Actual Size

An image of a cell is 45 mm long. The magnification is ×500. Calculate the actual size.

A = I ÷ M = 45 ÷ 500 = 0.09 mm = 90 μm

Exam tip: Before calculating, make sure both the image size and actual size are in the same units. Convert if necessary.

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Unit Conversions

Biology uses very small units. You must be able to convert between them.

From	To	Multiply or Divide	Factor
metres (m)	millimetres (mm)	× 1000	1 m = 1000 mm
millimetres (mm)	micrometres (μm)	× 1000	1 mm = 1000 μm
micrometres (μm)	nanometres (nm)	× 1000	1 μm = 1000 nm

And in reverse:

From	To	Factor
nm → μm	÷ 1000
μm → mm	÷ 1000
mm → m	÷ 1000

Example: Convert 0.05 mm to micrometres. 0.05 × 1000 = 50 μm

Example: Convert 7500 nm to micrometres. 7500 ÷ 1000 = 7.5 μm

Exam tip: A common error is converting in the wrong direction. Remember: going to smaller units = multiply; going to larger units = divide. Each step is × or ÷ 1000.

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Standard Form

Standard form is used for very large or very small numbers.

Format: A × 10ⁿ where 1 ≤ A < 10

Examples:

• 150,000 = 1.5 × 10⁵
• 0.00032 = 3.2 × 10⁻⁴
• The diameter of a red blood cell is about 7 μm = 0.007 mm = 7 × 10⁻³ mm

Calculations in Standard Form

Multiplying: Multiply the A values and add the powers. (3 × 10⁴) × (2 × 10³) = 6 × 10⁷

Dividing: Divide the A values and subtract the powers. (8 × 10⁶) ÷ (4 × 10²) = 2 × 10⁴

Exam tip: You are allowed to use a calculator, so practise entering standard form on your calculator before the exam. Know where the × 10ⁿ button (often labelled "EXP" or "×10ˣ") is.

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Surface Area to Volume Ratio

This concept is important for understanding diffusion, heat loss, and why organisms have adaptations for exchange.

Calculating SA:V for a cube:

Cube side length	Surface Area (6 × side²)	Volume (side³)	SA:V Ratio
1 cm	6 cm²	1 cm³	6:1
2 cm	24 cm²	8 cm³	3:1
3 cm	54 cm²	27 cm³	2:1
4 cm	96 cm²	64 cm³	1.5:1

Key principle: As an organism gets larger, its surface area to volume ratio decreases. This means:

• It becomes harder to exchange substances (gases, nutrients) by simple diffusion
• Larger organisms need specialised exchange surfaces (lungs, villi, gills) and transport systems (circulatory system)
• Smaller organisms lose heat faster than larger organisms

Exam tip: You do not need to memorise the formula for SA:V of complex shapes, but you must understand the relationship: as size increases, SA:V decreases, and you must be able to calculate it for simple cubes.

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Ratios in Genetics

Genetic crosses produce offspring in predictable ratios.

Common Ratios