0580/22 May/Jun 2024, Question 19: Proportion to Powers of x
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 4 marks
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The question, in short
Two proportion problems: use given values to find a constant and then a new value, and describe how one variable changes when another is scaled.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 3 marks
Given y proportional to (x − 1)² with x = 4 giving y = 3, find y when x = 7.
- 1y = k(x − 1)²
- 23 = k(4 − 1)² → 9k = 3 → k = 1/3
- 3y = 1/3 × (7 − 1)² = 1/3 × 36 = 12
Answer12
Part (b) · 1 mark
Given m inversely proportional to √p, state the effect on m when p is multiplied by 9.
- 1m = k/√p
- 2√(9p) = 3√p, so m becomes k/(3√p)
- 3m is divided by 3
Answerdivided by 3
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Also searched as: 0580/22/M/J/24 · 0580_s24_qp_22 · 0580 s24 22 · question 19.
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