Advanced: Complex Proportions

Part of Proportion · Section 12 of 16

Deep DiveUnit: NumberGCSE

This deep dive covers Advanced: Complex Proportions 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 12 of 16 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

Advanced: Complex Proportions

More complex relationships include:

  • Square relationships: y ∝ x² (area problems)
  • Cube relationships: y ∝ x³ (volume problems)
  • Square root: y ∝ √x (some physics laws)
  • Combined: z ∝ xy (z proportional to product of x and y)

Key insight: The constant k gives the relationship its "strength"

If y ∝ x² and k = 3, then doubling x makes y four times bigger (×4), but also three times that due to k

Practice questions for Proportion

y is directly proportional to x. Which equation could represent this relationship?

  • A. y = k/x
  • B. y = kx
  • C. y = k − x
  • D. y = x²
1 markfoundation

Explain how you can tell from a graph whether two quantities are in direct or inverse proportion.

2 marksstandard

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)

12 questions on Proportion — practise free

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