Calculation Techniques

At least 20% of the marks across all six Edexcel GCSE Combined Science papers (1SC0) require mathematical skills. This lesson covers the key techniques you need to maximise your marks on every calculation question.

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The Golden Rule: Show Your Working

If you write the correct final answer with no working, you get full marks. But if your final answer is wrong and you showed no working, you get zero. If you showed correct working but made a small arithmetic error, you can still earn most of the marks.

The Four-Step Method

Every calculation should follow this pattern:

Step	What to do	Example
1. Write the equation	From memory or the equation sheet	v = f × λ
2. Substitute	Plug in the values with units	v = 500 Hz × 0.68 m
3. Calculate	Do the arithmetic	v = 340
4. Unit and answer	State the final answer with the correct unit	v = 340 m/s

Exam Tip: Even on a 2-mark calculation, following all four steps ensures you pick up method marks if your arithmetic goes wrong.

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Rearranging Equations

Many questions give you values that require the equation to be rearranged before substituting. The triangle method is useful for equations with three variables.

Example: v = f × λ

flowchart TD
    A["v"] --- B["f × λ"]

• To find v: v = f × λ (multiply the bottom two).
• To find f: f = v ÷ λ (cover f; v is above λ).
• To find λ: λ = v ÷ f (cover λ; v is above f).

Practice: The Formula Triangle

Draw the triangle on your exam paper for any three-variable equation. It takes 5 seconds and prevents rearrangement errors.

Equation	Triangle top	Triangle bottom-left	Triangle bottom-right
v = f × λ	v	f	λ
E = m × c × ΔT	E	m × c	ΔT
P = I × V	P	I	V
Q = I × t	Q	I	t

Exam Tip: If you are unsure of your rearrangement, check by substituting simple numbers. For example, if v = 10, f = 2, λ = 5 — does your rearranged equation give the right answer?

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Units and Unit Conversion

Getting the unit wrong costs you the final mark on almost every calculation question. Common conversions you must know:

Conversion	Multiply by	Example
km → m	× 1000	2.5 km = 2500 m
cm → m	÷ 100	45 cm = 0.45 m
mm → m	÷ 1000	750 mm = 0.75 m
g → kg	÷ 1000	250 g = 0.25 kg
mg → g	÷ 1000	500 mg = 0.5 g
minutes → seconds	× 60	3 min = 180 s
hours → seconds	× 3600	2 h = 7200 s
kJ → J	× 1000	4.5 kJ = 4500 J
cm³ → m³	÷ 1 000 000	50 cm³ = 0.00005 m³

Exam Tip: Before substituting into an equation, check that all your values are in SI units (metres, kilograms, seconds, joules, etc.). If the question gives values in non-SI units, convert first.

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Significant Figures

The mark scheme often states: "Give your answer to 2 (or 3) significant figures." If the question does not specify, give your answer to 3 significant figures or to the same number of significant figures as the data in the question.

Counting Significant Figures

Number	Significant figures	Count
340	3, 4	2 s.f. (trailing zero may or may not be significant — context dependent)
340.	3, 4, 0	3 s.f. (the decimal point indicates the zero is significant)
0.0045	4, 5	2 s.f. (leading zeros are never significant)
6.02 × 10²³	6, 0, 2	3 s.f.
1500	depends on context	2 s.f. unless told otherwise

Rounding Rules

1. Look at the digit after the last significant figure you want to keep.
2. If it is 5 or more, round up.
3. If it is less than 5, round down.

Exam Tip: Do not round intermediate steps. Only round your final answer. Rounding too early (sometimes called "premature rounding") can lead to an incorrect final value.

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Standard Form

Very large or very small numbers should be written in standard form: a × 10ⁿ where 1 ≤ a < 10.

Number	Standard form
300 000 000	3.0 × 10⁸
0.00025	2.5 × 10⁻⁴
6 700	6.7 × 10³
0.08	8.0 × 10⁻²

Calculating with Standard Form

When multiplying or dividing numbers in standard form:

• Multiply: multiply the coefficients, add the powers. (2 × 10³) × (3 × 10⁴) = 6 × 10⁷
• Divide: divide the coefficients, subtract the powers. (6 × 10⁸) ÷ (2 × 10³) = 3 × 10⁵

Exam Tip: On your calculator, use the × 10ˣ button (sometimes labelled EXP or EE) to enter standard form. Practise this before the exam so you are confident.

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Common Calculation Errors