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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.
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Students make these errors again and again. Knowing them in advance gives you a head start.
Dividing by the wrong total number of parts when sharing in a ratio
Confusing ratio (part to part) with fraction (part to whole)
Not converting units before comparing ratios
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.
Source: CIE 0580 · Feb/March 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
Source: CIE 0580 · Feb/March 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.
Source: CIE 0580 · May/June 2021 · Paper 3 · Q1f(i)
Based on 3of 500+ insights extracted from CIE 0580 examiner reports (2018–2024).
This topic appears in the Cambridge IGCSE past papers. Our AI tutor can help with it on any question.
Useful for this topic:
Direct proportion describes relationships where one quantity increases at the same rate as another. 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.
Online Maths Olympiad preparation opens doors to advanced problem-solving skills and mathematical thinking. This guide explores effective resources and strategi
Exam PreparationCambridge publishes a free examiner report for each IGCSE maths series, showing where students lost marks. Here is how to use them for targeted revision.
Take our free diagnostic quiz to find out exactly where you stand, then practise ratio, proportion & rates of change with our AI tutor.
Ratio, proportion, and percentage formulae