Direct and inverse proportion
Higher-tier territory on Edexcel 1MA1, although Foundation sees the direct case in real-life context. Tested on Paper 2H or 3H most commonly.
Direct proportion
y is directly proportional to x: y ∝ x. Equation: y = kx for some constant k.
If y is directly proportional to x², then y = kx². If y ∝ √x, then y = k√x.
Inverse proportion
y is inversely proportional to x: y ∝ 1/x. Equation: y = k/x.
For inverse-square: y ∝ 1/x², so y = k/x².
Method (every question)
- Write the proportionality statement (y ∝ x, etc.).
- Convert to an equation with constant k: y = k × (expression).
- Substitute the given pair to find k.
- Re-write the equation with k filled in.
- Substitute the new value to find the requested quantity.
✦Worked example
y is inversely proportional to x². When x = 4, y = 5. Find y when x = 10.
- y ∝ 1/x²
- y = k/x²
- 5 = k/16 ⇒ k = 80
- y = 80/x²
- y = 80/100 = 0.8
Common Edexcel mark-scheme phrasing
- M1 for the correct proportionality / equation form.
- M1 for substituting to find k.
- A1 for the value of k.
- M1 for substituting the new value.
- A1 for the final answer.
⚠Common mistakes— Common errors
- Confusing "inversely proportional to x²" with "inversely proportional to x".
- Skipping step 3 (finding k) and trying to set up a single equation directly.
- Forgetting to write the final equation with k substituted before computing.
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