Percentages, ratio and proportion
Pearson Edexcel International GCSE Mathematics · 4MA1
Paper 1F | Whole paper: Number, Algebra, Geometry, Statistics
Percentage change, reverse percentages, compound interest and ratio — the topics that appear on almost every paper and are answered wrongly on almost every paper.
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.