Pearson Edexcel International GCSE Mathematics · specification 4MA1 · Paper 1F | Whole paper: Number, Algebra, Geometry, Statistics · Free · no account needed
Percentages, ratio and proportion (4MA1 specification)
Percentage change, reverse percentages, compound interest and ratio — the topics that appear on almost every paper and are answered wrongly on almost every paper.
Learn it on Incandio
The 7 Incandio pages that teach this — each explained in full, then proved in marked questions, taught back to an AI pupil and defended in a debate. Completely free.
- Standard Form — Writing enormous and tiny numbers as a×10ⁿ, and calculating with them confidently — the physicist's notation, on both papers.
- Rounding, Estimation & Bounds — Significant figures, one-significant-figure estimates that sanity-check everything, and the upper and lower bounds of a rounded measurement.
- Percentage Basics — What 'per cent' actually means, finding a percentage of an amount, and writing one number as a percentage of another.
- Multipliers & Percentage Change — The multiplier method — one number that does the whole job — for increases, decreases, repeated change and 'what was the overall change?'
- Reverse Percentages & Compound Interest — Finding the original price before a change (the question everyone gets backwards), and money growing multiplier-on-multiplier.
- Ratio — Sharing in a ratio, finding totals from parts, and combining two ratios into one — all powered by the value of ONE part.
- Direct & Inverse Proportion — Quantities that scale together, quantities that trade off, and the algebraic y = kx² machinery of Higher Tier proportion.
The teaching routes these belong to: Number · Percentages · Ratio & Proportion — the lessons in order, with every gate.
Specification coverage
1 Numbers and the number system — statements 1.6–1.9 (Foundation and Higher Tier)
Assessment objectives: AO1. Suggested learning time: 90 minutes.
Required knowledge
- Understand that 'percentage' means 'number of parts per hundred'
- Express one number as a percentage of another
- Calculate percentage increase and decrease, including repeated (compound) change
- Solve reverse percentage problems
- Divide a quantity in a given ratio and solve proportion problems
Required skills
- Use a multiplier rather than finding the percentage and adding it
- Recognise a reverse percentage question from its wording
- Set up and simplify ratios, including three-part ratios
How it is examined
- Structured questions building from a routine start to a multi-step finish
- Problem-solving questions with no method given
- 'Show that' and reasoning questions where the working IS the answer
Common mistakes
- Answering a reverse percentage by taking 15% off the sale price. That gives the wrong answer every time — the percentage was applied to the ORIGINAL, not the sale price.
- Doing compound interest by multiplying the first year's interest by the number of years. Use a multiplier raised to a power.
- Confusing a ratio with a fraction: in 4 : 5, the first share is 4/9 of the total, not 4/5.
This page maps the specification. The pages above teach it, and the Mathematics modules hold the whole course — completely free.