Substitution into formulae and rearranging

WJEC Unit 1 always tests rearrangement; Unit 2 tests substitution into common formulae such as area, volume, speed and the cost-of-living ones.

Substitution

Just plug the values in. Use brackets to avoid sign errors:

• F = ma. If m = 4.5, a = 2, then F = 4.5 × 2 = 9 N.
• v = u + at. If u = -3, a = 2, t = 5, then v = -3 + 2 × 5 = -3 + 10 = 7.

Always show the substituted line, then the calculation, then the answer with units. WJEC awards M1 for clear substitution.

Changing the subject — the rule

Whatever you do to one side, do to the other. Inverse operations:

• Add → subtract
• Multiply → divide
• Square → square root
• Squared → take ± square root (for higher)

Linear example: make x the subject of y = 3x + 5

• y − 5 = 3x (subtract 5)
• (y − 5) ÷ 3 = x (divide by 3)
• x = (y − 5) / 3

Two-step with brackets: make r the subject of A = π r^2

• A / π = r^2 (divide by π)
• r = √(A / π) (square root, take positive root)

Subject appears twice (Higher)

Make x the subject of y = (x + 3) / (x − 1):

• y(x − 1) = x + 3 (multiply both sides by x − 1)
• xy − y = x + 3
• xy − x = y + 3 (collect x terms)
• x(y − 1) = y + 3 (factorise)
• x = (y + 3) / (y − 1)

This factorise step is the WJEC Higher A1.

Common formulae

• Area of triangle: A = (1/2) b h
• Volume of cuboid: V = l w h
• Speed: s = d / t (so d = st, t = d/s)
• Cost: C = nP + F (n items at price P plus a fixed cost F)
• Pythagoras: c^2 = a^2 + b^2

WJEC exam tip

After rearranging, check by substituting test values into both forms — if you don't get the same answer, you made an error. This catches sign mistakes and saves the A1.