This topic summary covers Knowledge Organiser: Proportion within Proportion for GCSE Mathematics. Revise Proportion in Number for GCSE Mathematics with 12 exam-style questions and 22 flashcards. Use this page as part of a wider topic revision path rather than treating it as an isolated fact. It is section 16 of 16 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Knowledge Organiser: Proportion
Key Terms
- Direct proportion: Both quantities increase/decrease together (y ∝ x)
- Inverse proportion: One increases as the other decreases (y ∝ 1/x)
- Constant of proportionality (k): The fixed multiplier connecting two proportional quantities
- ∝ symbol: Means "is proportional to"
Must-Know Facts
- Direct: graph is a straight line through the origin
- Inverse: graph is a curved hyperbola (never touches axes)
- To find k: substitute given values into the equation
- Direct proportion: if x doubles, y doubles
- Inverse proportion: if x doubles, y halves
- y ∝ x² means y = kx² (square proportionality)
Key Formulas
- Direct: y = kx; find k = y ÷ x
- Inverse: y = k/x; find k = xy
- Square direct: y = kx²; find k = y ÷ x²
- Method: (1) write equation, (2) substitute to find k, (3) use equation to find unknown
Common Mistakes
- Direct vs inverse: Confusing y = kx (direct) with y = k/x (inverse) — check: does y increase or decrease as x increases?
- Finding k: Substitute a given pair of values immediately — don't leave k as unknown
- y ∝ x² vs y ∝ x: Different equations — check what the question says carefully
- Inverse proportion graph: It is a curve (hyperbola), not a straight line
- Units: Keep units consistent when substituting into proportion equations
Practice questions for Proportion
y is directly proportional to x. Which equation could represent this relationship?
Explain how you can tell from a graph whether two quantities are in direct or inverse proportion.
Quick recall flashcards
Recipe Application
Recipe for 4 people uses 300g flour
How much for 10 people?
Flour ∝ People (direct)
F = kP
300 = k × 4, so k = 75
For 10 people: F = 75 × 10 = 750g
Proportion Symbol
∝ means 'proportional to'
Examples:
y ∝ x (y is proportional to x)
y ∝ 1/x (y is inversely proportional to x)