Direct and inverse proportion
Edexcel tests proportion across both tiers. Foundation handles informal direct proportion ("if 5 books cost £15, find the cost of 8"). Higher introduces algebraic proportionality including powers, square roots and inverse proportion.
Direct proportion
y is directly proportional to x means y = kx for some constant k > 0. Notation: y ∝ x.
Higher tier extends this to powers: y ∝ x², y ∝ √x, y ∝ x³ etc.
- y ∝ x²: y = kx²
- y ∝ √x: y = k√x
Inverse proportion
y is inversely proportional to x means y = k/x. Notation: y ∝ 1/x.
Extensions: y ∝ 1/x², y ∝ 1/√x.
Method (Edexcel mark scheme template)
- Write the proportionality M1: "y = kx²" or "y = k/x" etc.
- Substitute the given pair to find k M1.
- Write the explicit equation linking y and x A1.
- Substitute the new x to find y M1A1.
✦Worked example— Worked example (Higher Paper 2H)
y is inversely proportional to the square of x. When x = 4, y = 5.
- y = k/x²
- 5 = k/16, so k = 80.
- Equation: y = 80/x².
- When x = 10: y = 80/100 = 0.8.
Direct vs inverse — quick check
- Direct: as x doubles, y doubles. Graph through the origin (linear or curve depending on power).
- Inverse: as x doubles, y halves. Graph is a hyperbola — never touches the axes.
Common Edexcel exam tip
Always state the equation y = kx (or whatever form) explicitly before substituting. Mark schemes give M1 just for that line.
⚠Common mistakes— Common errors
- Confusing y ∝ x with y ∝ 1/x.
- Forgetting to find k first.
- Using y/x = constant for inverse proportion (it should be xy = constant).
AI-generated · claude-opus-4-7 · v3-edexcel-maths-leaves