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
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.
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
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.