Knowledge Organiser: Inverse Proportion
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?
Explain what it means for y to be inversely proportional to x. Your answer should refer to the equation and the graph.
Quick Recall Flashcards
15 questions on Inverse Proportion — practise free
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