Proportion as equality of ratios
Edexcel 1MA1 frames "direct proportion" as equal ratios: a : b = c : d, equivalently a/b = c/d. Foundation tests this as map scales, recipes and currency. Higher tests it as algebraic direct proportion (R10) and inverse proportion.
Direct proportion (basic)
Two quantities are in direct proportion if their ratio is constant — when one doubles, the other doubles.
Example: 5 apples cost £1.20. How much for 8 apples?
Set up equal ratios: 5/1.20 = 8/x, equivalent to 5x = 1.20 × 8.
x = 9.60 / 5 = £1.92.
Unitary method
Find one unit, then scale up.
Example: 4 hours of work pays £52. How much for 7 hours?
- Per hour: £52 ÷ 4 = £13.
- For 7 hours: £13 × 7 = £91.
Recipe (most-asked Edexcel context)
A recipe for 6 people uses 300 g flour. How much flour for 10 people?
- Per person: 300 ÷ 6 = 50 g.
- For 10 people: 50 × 10 = 500 g.
Or by ratio: 6/300 = 10/x → x = 500.
Map scales
A map has scale 1 : 25,000. A road on the map measures 8 cm. Real distance:
8 × 25,000 cm = 200,000 cm = 2,000 m = 2 km.
Currency conversion
£1 = €1.18. Convert £75 to euros: 75 × 1.18 = €88.50.
For the reverse, divide: €100 ÷ 1.18 = £84.75 (to 2 d.p.).
Inverse proportion (Foundation introduction)
Two quantities are in inverse proportion if their product is constant — when one doubles, the other halves.
Example: 4 builders take 12 days to build a wall. How long would 6 builders take?
Total person-days = 4 × 12 = 48. Time for 6 = 48 ÷ 6 = 8 days.
Common Edexcel exam tip
For "best buy" questions, find unit price for both options, then compare.
Pack A: 6 yoghurts for £2.10 → 35p each. Pack B: 10 yoghurts for £3.20 → 32p each. Pack B is better value.
⚠Common mistakes— Common errors
- Forgetting unit conversion in map scale problems (cm to km).
- Using direct proportion when the situation is inverse (e.g. "more workers = less time").
- Treating "one increases by 50%" as direct proportion — always double-check the relationship.
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