Ratio, Proportion & Rates of Change

Ratio and proportion connects arithmetic to real contexts, and it appears in exam questions far more often than its size suggests. The unit covers simplifying and sharing in a ratio, direct and inverse proportion, scale factors, compound measures such as speed and density, percentage change, growth and decay, and best-value problems.

The key skill is recognising which structure a worded problem has. Direct proportion means one quantity multiplied by a constant; inverse means their product is constant. Confusing the two is the single most common error. Students also lose marks by treating a ratio as a fraction of the whole rather than of the parts, and by forgetting units in compound measure questions. Write down what one part is worth before doing anything else, and the rest usually follows.