Direct Proportion
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.
Tier
Exam Board
No questions match the current filters for Direct Proportion.
What You'll Learn
- Recognising directly proportional relationships
- Setting up and using y = kx to solve problems
- Working with proportion to powers (y proportional to x squared, x cubed)
- Interpreting direct proportion graphs (straight line through the origin)
Watch Out For These Mistakes
Students make these errors again and again. Knowing them in advance gives you a head start.
Confusing direct and inverse proportion
Forgetting to find the constant of proportionality k before solving
Not squaring or cubing x when the proportion is to a power of x
What Examiners Say About Direct Proportion
Insights pulled from Cambridge IGCSE (0580) examiner reports — the exact mistakes candidates make every year.
- Common Mistake●●●●●
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
- Common Mistake●●●●●
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
- Misconception●●●●●
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).
Exam Coverage
This topic appears in the Cambridge IGCSE past papers. Our AI tutor can help with it on any question.
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Related Topics
Ratio and Proportion
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.
Inverse Proportion
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.
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Straight-line graphs form the basis for understanding gradients, intercepts and real-world modelling. Students need to plot lines from equations, find gradients and interpret y = mx + c.
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Ratio, proportion, and percentage formulae