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LearnAQA8300First teaching 2015Papers 1–3 · Foundation tierRatio, proportion and rates of change

Papers 1–3 · Module

Ratio, proportion and rates of change

3 subtopics≈ 95 min in total

Start the module: Ratio, proportion and rates Open graphing calculator

Ratio, proportion and rates
A ratio compares parts: add the parts, find one part, then multiply. Direct proportion keeps the ratio fixed; inverse proportion keeps the product fixed. A rate is one quantity per unit of another: speed is distance per hour, density is mass per cm³, unit price is cost per item.
≈ 30 min
Percentages, interest, growth and decay
Turn every percentage change into a multiplier: a $15\%$ increase is $\times1.15$ , a $12\%$ decrease is $\times0.88$ . Repeated changes multiply, so compound interest and depreciation use powers of the multiplier. To undo a change (reverse percentage), divide by the multiplier.
≈ 35 min
Direct and inverse proportion
Proportion links two quantities by one constant $k$ . Direct: $y=kx^n$ , so $y$ grows with $x$ . Inverse: $y=\dfrac k{x^n}$ , so $y$ shrinks as $x$ grows. Write the equation, find $k$ from the given pair, then use it.
≈ 30 min