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Understand ratio, direct and inverse proportion, compound interest, and speed-distance-time problems.
Ratio and proportion underpin many real-world problems from recipes to map scales. Students must simplify ratios, share amounts in a given ratio, and solve proportion problems using the unitary method or scale factors.
Direct proportion describes relationships where one quantity increases at the same rate as another. Higher-tier students work with algebraic representations including y is proportional to x squared or x cubed.
Inverse proportion describes situations where one quantity decreases as the other increases. Students must recognise this relationship, use the formula y = k/x, and solve problems involving inverse square and inverse cube relationships.
Finding percentages of amounts is one of the most practical maths skills students learn. This includes calculating discounts, tax, tips, pay rises, and other real-world percentage applications that appear heavily in exam contexts.
Compound interest builds on percentage multiplier methods to model growth and decay over time. Students apply repeated percentage change to financial contexts, population growth, and depreciation problems.
Speed-distance-time problems appear in both numerical and graphical form. Students must convert between units, interpret distance-time and speed-time graphs, and solve multi-step journey problems.
Density problems link ratio work with geometry through the relationship density = mass / volume. Students must rearrange this formula, convert units, and often combine it with volume calculations for 3D shapes.
Take our free diagnostic quiz to find out which ratio, proportion & rates of change topics need the most work, then practise with our AI tutor.