Ratio, Proportion and Rates of Change
This domain tests comparing quantities multiplicatively and handling compound measures. Expect ratio sharing, direct and inverse proportion, percentages, speed, density, pressure and growth/decay, often in a real-world context.
Core rules
- Simplify a ratio by dividing by the HCF; ratios have no units. To share an amount in the ratio a:b, total parts = a+b.
- Direct proportion: y = kx. Inverse proportion: y = k/x. Find k from the given pair, then substitute.
- Percentage change = (change ÷ original) × 100. A 20% increase is ×1.20; a 15% decrease is ×0.85.
- Compound interest: amount = P(1 + r/100)^n.
- Speed = distance ÷ time; density = mass ÷ volume; pressure = force ÷ area. Convert units before calculating.
Worked example
y is inversely proportional to x. When x = 5, y = 12. Find y when x = 15. Write y = k/x. Substitute: 12 = k/5, so k = 60. Hence y = 60/x. When x = 15, y = 60/15 = 4. A common wrong step is to assume y falls by the same amount as x rises; inverse proportion means the product xy stays constant (5×12 = 15×4 = 60).
Traps
Adding successive percentage changes (a 20% rise then a 20% fall is not back to the original); using the new value as the denominator; confusing direct and inverse proportion; forgetting to convert minutes to hours; writing a ratio in the wrong order.