Substituting into formulae
Substitution underpins every WJEC topic from area to compound interest. The key habits are brackets around inputs and following BIDMAS in the resulting numerical expression.
The substitution recipe
- Copy the formula exactly.
- Replace each variable with its value, surrounding negatives with brackets.
- Apply BIDMAS: Brackets, Indices, Division/Multiplication (left-right), Addition/Subtraction (left-right).
- Show one operation per line.
✦Worked example— Example 1 — linear formula
The cost C of hiring a kayak in Pembrokeshire is C = 15 + 8n, where n is the number of hours.
For n = 4: C = 15 + 8(4) = 15 + 32 = £47.
✦Worked example— Example 2 — formula with a power
The area A of a circle is A = πr^2.
For r = 6 cm: A = π(6)^2 = π × 36 = 113.097… ≈ 113 cm^2 (3 s.f.).
WJEC trap: students compute (π × 6)^2 by mistake. Indices first, then multiplication.
✦Worked example— Example 3 — negative substitution
If v = u + at and u = 4, a = -3, t = 2:
v = 4 + (-3)(2) = 4 + (-6) = 4 − 6 = -2.
✦Worked example— Example 4 — formula with a fraction or root
Pythagoras: c = √(a^2 + b^2). For a = 5, b = 12:
c = √(5^2 + 12^2) = √(25 + 144) = √169 = 13.
WJEC exam tip
Each line of working should change exactly one thing. The first M1 is for "values correctly substituted", the second M1 is for "BIDMAS applied correctly". A1 is the final value with units. Skipping lines often costs marks.
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