Fractions and percentages as operators
Edexcel 1MA1 tests this throughout Paper 1F and 1H. The big idea: a fraction or percentage is a multiplier. "25% of 80" means "0.25 × 80".
Fraction as multiplier
3/4 of 60 = 3/4 × 60 = 45.
For non-calculator: divide first to keep numbers small. 60 ÷ 4 = 15, then × 3 = 45.
Percentage as multiplier
15% of 240 = 0.15 × 240 = 36.
For non-calculator: 10% = 24, 5% = 12, total 15% = 36.
Increase / decrease as a single multiplier
- Increase by 12% → multiplier 1.12.
- Decrease by 12% → multiplier 0.88.
- Increase by 7.5% → multiplier 1.075.
Reverse percentages (Higher and top-end Foundation)
If a price after a 20% increase is £108, original = 108 ÷ 1.20 = £90.
If a sale price after 30% off is £42, original = 42 ÷ 0.70 = £60.
Compound multiplier
A 5% rise each year for 3 years multiplies by 1.05³ = 1.157625, so a 15.7625% overall rise.
Common Edexcel mark-scheme phrasing
- M1 for a correct multiplier (e.g. 1.20 for "increase by 20%").
- M1 for setting up the correct equation (especially in reverse-% problems).
- A1 for the correct final value.
- B1 for stating the original / final amount with units.
⚠Common mistakes— Common errors
- Adding 20% as "+20" (treating % as a count, not a multiplier).
- Forgetting to apply the multiplier and instead computing the increase only.
- On reverse-%: dividing by 1.2 vs subtracting 20% — the latter is wrong.
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