Mathematical Skills Across All Three Sciences

At least 20% of the marks across all six AQA GCSE Combined Science: Trilogy (8464) papers require mathematical skills. This means around 84 marks out of 420 will involve calculations, data handling, unit conversions, or graph work. This lesson covers the key mathematical skills you need, with worked examples and common pitfalls.

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Overview of Mathematical Requirements

The AQA specification lists the following mathematical skills across all three sciences:

Category	Skills	Where they appear
Arithmetic and numerical computation	Percentages, ratios, fractions, decimals, standard form, significant figures	All six papers
Handling data	Mean, median, mode, range, identifying anomalies	All six papers
Algebra	Rearranging equations, substituting values, understanding proportionality	Mainly Physics and Chemistry
Graphs	Plotting, reading values, calculating gradients, area under a curve, lines of best fit	All six papers
Geometry and measurement	Unit conversions, scale, surface area to volume ratios	All six papers

Exam Tip: The maths skills are not confined to Physics. Biology papers include percentage change, ratios (genetics), and graph interpretation. Chemistry papers include moles calculations, concentration, and rates from graphs.

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Key Skill 1: Rearranging Equations

Many students lose marks not because they cannot do the maths, but because they cannot rearrange the equation. Use the formula triangle method or algebraic rearrangement.

Example: speed = distance ÷ time

To find distance: distance = speed × time To find time: time = distance ÷ speed

The Three-Step Approach for Any Calculation

1. Write the equation (from memory or the equation sheet).
2. Substitute the values (with correct units).
3. Calculate and give the answer with the correct unit.

Exam Tip: Even if your final numerical answer is wrong, you can still earn marks for writing the correct equation and substituting correctly. Always show your working.

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Key Skill 2: Unit Conversions

Questions often give values in non-standard units. You must convert before substituting.

Conversion	How
cm → m	÷ 100
mm → m	÷ 1000
km → m	× 1000
g → kg	÷ 1000
mg → g	÷ 1000
mA → A	÷ 1000
kJ → J	× 1000
cm³ → dm³	÷ 1000
dm³ → cm³	× 1000
minutes → seconds	× 60
hours → seconds	× 3600

Exam Tip: If the question gives you a length in centimetres and the equation uses metres, you must convert. Failure to convert units is one of the most common reasons for losing calculation marks.

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Key Skill 3: Standard Form

Standard form expresses very large or very small numbers as a number between 1 and 10 multiplied by a power of 10.

Number	Standard form
6700	6.7 × 10³
0.0045	4.5 × 10⁻³
300 000 000 (speed of light)	3.0 × 10⁸ m/s
0.000 000 001 (1 nanometre)	1.0 × 10⁻⁹ m

How to Convert to Standard Form

1. Move the decimal point so you have a number between 1 and 10.
2. Count how many places you moved the point — this is the power.
3. If you moved the point to the left, the power is positive; to the right, it is negative.

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Key Skill 4: Significant Figures

If a question does not specify how many significant figures to use, give your answer to 3 significant figures (or the same number as the data in the question).

Number	Significant figures	Rounded to 3 s.f.
0.004562	4	0.00456
1234	4	1230
45.678	5	45.7

Exam Tip: Only round at the final step. If you round intermediate values, errors accumulate and your final answer may be wrong.

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Key Skill 5: Percentage Change

Percentage change appears in Biology (osmosis, population changes), Chemistry (percentage yield, atom economy) and Physics (efficiency).

Formula:

percentage change = (change ÷ original) × 100

Worked Example (Osmosis)

A potato chip starts with a mass of 2.50 g and ends with a mass of 2.80 g.

• Change = 2.80 − 2.50 = 0.30 g
• Percentage change = (0.30 ÷ 2.50) × 100 = 12.0%

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Key Skill 6: Ratios

Ratios appear most prominently in Biology (genetic crosses — 3:1 ratios, 1:1 ratios) but also in Chemistry (mole ratios from balanced equations).

Example: Genetic Cross

If a genetic cross predicts a 3:1 ratio of tall to short plants, and there are 120 offspring:

• Expected tall = (3/4) × 120 = 90
• Expected short = (1/4) × 120 = 30

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Key Skill 7: Using the Equation Sheet (Higher Tier Only for Some)

On Higher tier Physics papers, some equations must be recalled from memory while others are provided on the equation sheet. On Foundation tier, all required equations are given.

Higher Tier Recall Equations (Physics)

You must memorise these (not on the equation sheet):

• speed = distance ÷ time
• acceleration = change in velocity ÷ time
• weight = mass × gravitational field strength
• kinetic energy = ½ × mass × velocity²
• gravitational potential energy = mass × g × height
• power = energy transferred ÷ time
• efficiency = useful output ÷ total input
• charge = current × time
• potential difference = current × resistance
• power = potential difference × current
• power = current² × resistance
• energy transferred = power × time
• energy transferred = charge × potential difference
• density = mass ÷ volume
• wave speed = frequency × wavelength

Exam Tip: If the question says "use the Physics Equations Sheet", you must select the equation from the sheet. If it does not say this, you are expected to recall it from memory.

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Maths Across the Three Sciences

flowchart LR
    A["Mathematical Skills"] --> B["Biology"]
    A --> C["Chemistry"]
    A --> D["Physics"]
    B --> B1["% change, ratios,<br/>magnification, means,<br/>graphs"]
    C --> C1["Moles, concentration,<br/>% yield, atom economy,<br/>rates from graphs"]
    D --> D1["Equations, rearranging,<br/>standard form, gradients,<br/>area under curves"]

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Common Mathematical Mistakes