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Direct and Inverse Proportion

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The symbol y∝xy \propto xy∝x means yyy is proportional to xxx. In GCSE questions, you usually replace ∝\propto∝ with an equation using a constant kkk.

For direct proportion, y=kxy = kxy=kx, so both variables scale by the same factor. For inverse proportion, y=kxy = \frac{k}{x}y=xk​, so when one variable gets bigger, the other gets smaller.

Watch the wording carefully. If AAA is directly proportional to the square of BBB, write A=kB2A = kB^2A=kB2, but if PPP is inversely proportional to the cube of QQQ, write P=kQ3P = \frac{k}{Q^3}P=Q3k​.

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A machine fills 1000 bottles in 5 hours.

Work out how many hours it would take the machine to fill 1200 bottles.

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What does the symbol ∝\propto∝ represent in a formula?

Direct and Inverse Proportion Revision Guide

  1. GCSE
  2. /Maths
  3. /Direct and Inverse Proportion

Revision notes for Edexcel GCSE Maths Direct and Inverse Proportion. Open the guide for explanations and worked examples. Written against the Edexcel GCSE Maths (1MA1) specification, so the content matches what's examinable rather than general Maths background.

Revision guides

SurdsBoundsDirect and Inverse ProportionQuadratic FormulaFactorising Harder QuadraticsAlgebraic FractionsRearranging Harder FormulaeTrigonometric and Exponential GraphsInverse and Composite FunctionsIterationFinding the Area of Any TriangleThe Sine RuleThe Cosine RuleCongruent Triangles3d Pythagoras and TrigonometryHistogramsConditional Probability

Practise questions

1 of 5

ppp is directly proportional to qqq. When p=15p=15p=15 and q=5q=5q=5, find ppp when q=12q=12q=12.