Ratio, proportion and rates of change — domain overview
This domain accounts for roughly 20% of marks in AQA GCSE Maths and spans 16 specific points (R1–R16). It is the most "applied" domain — virtually every word problem in the paper draws on ratio, proportion or rates.
The four strands
| Strand | Key spec points | Core skill |
|---|---|---|
| Ratio | R1–R4 | Simplify, share, unitary method, map scales |
| Percentages | R5–R9 | Calculate, increase/decrease, reverse %, compound growth/decay |
| Rates of change | R10–R12 | Speed/distance/time, density, pressure, unit conversion |
| Proportion | R13–R16 | Direct & inverse proportion, best value, exchange rates |
Key techniques
Ratio sharing
To share £240 in ratio 3:5:
- Total parts = 3 + 5 = 8
- One part = £240 ÷ 8 = £30
- Shares = £90 and £150
Percentage change
$$ ext{Percentage change} = dfrac{ ext{Change}}{ ext{Original}} imes 100$$
Reverse percentage (finding the original)
If price after 20% increase = £144:
- 120% = £144 → 1% = £1.20 → 100% = £120
Compound interest / exponential growth
$$A = Pleft(1 + dfrac{r}{100} ight)^n$$
- $P$ = principal, $r$ = % rate, $n$ = number of periods
Depreciation (decay)
$$A = Pleft(1 - dfrac{r}{100} ight)^n$$
Direct proportion
$y propto x$ means $y = kx$; find $k$ from a known pair, then use it.
Inverse proportion
$y propto dfrac{1}{x}$ means $y = dfrac{k}{x}$; find $k$ from a known pair.
Speed, distance, time
$$S = dfrac{D}{T}, quad D = S imes T, quad T = dfrac{D}{S}$$
Always check units — convert km/h ↔ m/s by multiplying/dividing by $dfrac{18}{5}$ (or ×1000/3600).
Common exam mistakes
- Ratio ≠ fraction — "Ratio of boys to girls is 2:3" means $dfrac{2}{5}$ of the total are boys, not $dfrac{2}{3}$
- Simple vs compound interest — always check whether the question says "compound"
- Reverse % — don't reverse the wrong way — dividing by 0.8 (not by 1.2) reverses a 20% decrease
- Units in rates — $60$ mph × $1.5$ h $= 90$ miles (not 90 km); be explicit with units at every step
- Best-value wrong direction — always compare same unit quantity (e.g. pence per 100g)
AI-generated · claude-opus-4-7 · v3-deep-ratio