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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.
Insights pulled from Cambridge IGCSE (0580) examiner reports — the exact mistakes candidates make every year.
For train-crossing-bridge problems: (1) Total distance = train length + bridge length, (2) Convert all units to be consistent (all metres + seconds, or all km + hours) BEFORE calculating.
“This was the most challenging question on the paper with less than half of the candidates scoring full marks... Weaker candidates did not attempt a conversion of one or both the units between km and m or hours and seconds. Many combinations of multiplications and divisions of the given values were seen among the weaker candidates.”
Source: CIE 0580 · June 2024 · Paper 2 · Q14
If 5/13 are sold, then 8/13 remain. Set the remainder (96) equal to the remaining fraction (8/13 of total), not the sold fraction. A decimal answer in a whole-number context should alert you to an err
“most candidates not realising that they had to relate the 96 biscuits left to the fraction 8/13 and not to the sold fraction, 5/13. The decimal answers resulting from this error perhaps should have made candidates realise that it had to be incorrect.”
Source: CIE 0580 · June 2021 · Paper 1 · Q13
Percentage profit = (profit / COST PRICE) × 100 — divide by COST, not selling price. Profit = selling − cost. This is the most-missed type of percentage question.
“Calculating the percentage profit proved to be challenging for many candidates. Very few fully correct solutions or part solutions were seen. This was because the majority of candidates divided by the selling price of $24 instead of the cost of $12.80.”
Source: CIE 0580 · November 2021 · Paper 3 · Q1f(i)
Based on 3of 510+ insights extracted from CIE 0580 examiner reports (2018–2024).
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