Inverse operations

Inverse operations undo each other. WJEC tests this from Foundation Unit 1 (basic checking) to Higher Unit 1 (rearranging formulae).

The four pairs of inverses

• Add ↔ Subtract: 7 + 5 = 12, so 12 − 5 = 7.
• Multiply ↔ Divide: 6 × 4 = 24, so 24 ÷ 4 = 6.
• Square ↔ Square root: 9^2 = 81, so √81 = 9 (positive root).
• Cube ↔ Cube root: 4^3 = 64, so ∛64 = 4.

Function machines (Foundation)

WJEC presents simple function machines: input → operation → operation → output.

To work backwards from output to input, apply inverse operations in reverse order.

Example: x → ×3 → +5 → 26. To find x, work back: 26 − 5 = 21, then 21 ÷ 3 = 7. So x = 7.

Solving linear equations

Solving 4x + 3 = 23 uses inverses:

• Subtract 3: 4x = 20.
• Divide by 4: x = 5.

Checking answers

Always check by substitution. If x = 5, then 4(5) + 3 = 23 ✓.

Rearranging formulae (Intermediate / Higher)

The "subject" of a formula is the variable on its own. To change the subject, use inverses.

Example: make r the subject of A = πr^2.

• Divide by π: r^2 = A/π.
• Square root: r = √(A/π).

WJEC exam tip

When asked to "use inverses to check" an answer, you must show the reverse calculation. Just re-checking the same operation forwards is not "using inverses" and scores zero of the C1.