Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed

Multipliers & Percentage Change

In one sentence. The multiplier method — one number that does the whole job — for increases, decreases, repeated change and 'what was the overall change?'

Percentages — one of 3 modules in this strand, and one of 53 in Pearson Edexcel International GCSE Mathematics. Both tiers.

This module ends with Simon Stevin. Learn Multipliers & Percentage Change, teach it, then defend it against Simon Stevin.

Where this sits in the specification

Specification 4MA1, 1.6 Percentages — percentage change, repeated change. Incandio is aligned to this specification; it is not published by, endorsed by or affiliated with Pearson, and the sub-topic numbers are given so you can check every module against your own copy.

  • 1.6 — Percentages — percentage change, repeated change

1 · Understand it

What it is

Every percentage change is captured by one multiplier: +15% is ×1.15, −24% is ×0.76. Percentage change is measured against the ORIGINAL: change ÷ original × 100. Repeated change multiplies multipliers: 3% growth for 4 years is ×1.03⁴, not ×1.12.

Why it works

A 15% rise leaves you with 100% + 15% = 115% of what you had — one multiplication. Repeated changes compound because each year's 3% is charged on the NEW total, including previous growth: growth grows. That's why 1.03⁴ = 1.1255…, slightly more than four separate 3%s.

When a question is asking for it

'Increase/decrease … by …%' → build the multiplier. 'By what percentage did … change?' → change ÷ original. 'Each year for n years' → multiplier to the power n. Two successive changes → multiply the two multipliers, and read the overall change off the result.

How to hold it in your head

The multiplier IS the story: 0.85 × 0.92 = 0.782 says 'after both falls you keep 78.2% — so you lost 21.8%'. Never add or subtract percentages of different-sized wholes; let the multipliers carry the sizes for you.

2 · The mistakes that cost marks

  • Measuring change against the NEW value. Percentage change always divides by the ORIGINAL.
  • Adding successive percentages: −15% then −8% is not −23%. Multipliers: 0.85 × 0.92 = 0.782, a 21.8% fall.
  • Doing compound growth as simple growth: 3% for 4 years is ×1.03⁴ (≈ +12.55%), not +12%.
  • Building the wrong multiplier for a decrease: −24% is ×0.76 (keep 76%), not ×0.24 (which keeps only 24%).

3 · Worked examples

Laid out the way an examiner wants working shown — every step is a mark.

A population of 5000 grows by 3% per year. What is it after 4 years?

  1. Yearly multiplier: 1.03.
  2. Four years: 5000 × 1.03⁴.
  3. 1.03⁴ = 1.12550881, so 5000 × 1.12550881 = 5627.5…

Answer: 5628 (nearest whole)

A car loses 15% of its value, then 8% of its new value. What is the overall percentage fall?

  1. Multipliers: 0.85 then 0.92.
  2. Overall: 0.85 × 0.92 = 0.782 — the car keeps 78.2%.
  3. Fall: 100% − 78.2% = 21.8%.

Answer: 21.8%

4 · Prove it — the five questions

The five questions climb Grade 6 → 9+ and are marked inside Incandio on your own device, against authored accepted forms, with a diagnosis of the wrong answer you actually gave. The answers stay in the app so that the practice is worth doing; the questions themselves are here.

  1. Grade 6 — A price rises from £80 to £92. Work out the percentage increase. (answer in %)
  2. Grade 7 — Decrease 340 by 24%.
  3. Grade 8 — A town's population of 5000 grows by 3% each year. What is the population after 4 years? Give your answer to the nearest whole number.
  4. Grade 9 — A car's value falls by 12% in its first year. In its second year it falls by a further x% of its new value. Over the two years its value falls by 23.44% in total. Work out x. (answer in %)
  5. 9+ — A value is increased by 20%, and then decreased by x% so that it returns exactly to its original value. Find x, correct to 3 significant figures. (answer in %)

Think you understand it?

Reading is the start. On Incandio a topic counts as mastered only once you have taught it and defended it — the two things a revision guide cannot ask of you.

Incandio this topic → Prove it. Teach it. Defend it. What does “Incandio it” mean?

  1. Prove it — five questions on Multipliers & Percentage Change, marked on the spot, that tell you what was missing rather than just what was wrong.
  2. Teach it — Explain how Multipliers & Percentage Change works — and why — to Ember, an AI pupil who does not have it yet. The method matters more than the vocabulary.
  3. Defend it — Argue Multipliers & Percentage Change against Simon Stevin — three rounds, marked against descriptors you can read before you begin.
  4. Then the exam — read all 10 authored exam-style questions on this unit, each with its command word and its tariff, then have them marked on Incandio with the mistake you actually made named.

Completely free. No subscriptions, no paywalls, no account needed to start.

Carry on through the course