Ratio & ProportionTopic Summary

Knowledge Organiser: Inverse Proportion

Part of Inverse Proportion · GCSE GCSE Mathematics revision

This topic summary covers Knowledge Organiser: Inverse Proportion within Inverse Proportion for GCSE Mathematics. Revise Inverse Proportion in Ratio & Proportion for GCSE Mathematics with 15 exam-style questions and 10 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 6 of 6 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 6 of 6

Practice

15 questions

Recall

10 flashcards

Knowledge Organiser: Inverse Proportion

Key Terms
  • Inverse proportion: When one quantity increases, the other decreases at the same rate
  • y ∝ 1/x: Symbol meaning "y is inversely proportional to x"
  • Constant k: The product x × y, which stays constant throughout
  • Hyperbola: The curved shape of an inverse proportion graph
Must-Know Facts
  • y ∝ 1/x means y = k/x, where k = x × y (constant)
  • When x doubles, y halves; when x triples, y becomes a third
  • Graph is a CURVE (hyperbola) — never touches either axis
  • Find k by multiplying any pair of corresponding x and y values
  • Direct proportion: more → more. Inverse: more → less
Key Formulas
  • y = k ÷ x (inverse proportion equation)
  • k = x × y (find the constant from a pair of values)
  • New y = k ÷ new x
  • Higher: y ∝ 1/x² means y = k/x²
Common Mistakes
  • Confusing with direct proportion: Inverse means as x increases, y decreases — check the relationship first
  • Finding k: For y = k/x, find k = x × y (multiply, not divide)
  • Graph shape: Inverse proportion gives a hyperbola curve, never a straight line
  • y ∝ 1/x²: Use y = k/x², not y = k/x — substitute correctly to find k

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Practice Questions for Inverse Proportion

Which of the following correctly reads the mathematical statement y ∝ 1/x?

  • A. y is directly proportional to x
  • B. y is inversely proportional to x
  • C. y equals 1 divided by x
  • D. y is greater than x
1 markfoundation

Explain what it means for y to be inversely proportional to x. Your answer should refer to the equation and the graph.

2 marksstandard

Quick Recall Flashcards

What is the formula for inverse proportion?
y = k/x, where k is the constant of proportionality. The product xy is always constant.
What shape is the graph of y = k/x?
A hyperbola — a curved line that never touches either axis. For k > 0, the curve is in the 1st and 3rd quadrants.

15 questions on Inverse Proportion — practise free

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