Using and rearranging formulae

Foundation Edexcel uses substitution into standard formulae. Higher requires changing the subject — sometimes when the new subject appears more than once.

Substitution into standard formulae

See A2. Brief reminders:

• Speed = distance / time.
• Density = mass / volume.
• Pythagoras: c² = a² + b².
• Area of trapezium: A = ½(a + b)h.

Changing the subject

Same principle as solving equations: do the same to both sides until the desired letter is alone on one side.

Single-occurrence rearrangement

Rearrange v = u + at to make a the subject. v − u = at (subtract u from both sides). (v − u)/t = a (divide both sides by t). So a = (v − u)/t.

Rearrange A = πr² to make r the subject. A/π = r² (divide). r = √(A/π) (square root, taking positive value).

Multi-occurrence rearrangement (Higher)

When the new subject appears more than once, factorise to combine.

Example: rearrange ax + b = c − dx to make x the subject. ax + dx = c − b (collect x-terms). x(a + d) = c − b (factorise). x = (c − b)/(a + d).

Example: rearrange (x + 2)/y = 3x − 1 to make x the subject. x + 2 = y(3x − 1) (multiply both sides by y). x + 2 = 3xy − y. x − 3xy = −y − 2. x(1 − 3y) = −y − 2. x = (−y − 2)/(1 − 3y) = (y + 2)/(3y − 1) (multiplying top and bottom by −1).

Edexcel exam tip

For "show that the subject is …", every step must be shown. Skipping algebra loses C1.

For Higher 4-mark questions involving fractions or roots, M1 is awarded for clearing fractions/roots, M1 for collecting subject terms, M1 for factorising, A1 for the final answer.