0580/22 May/Jun 2022, Question 18: Proportion to Powers of x
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 4 marks
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The question, in short
Proportionality question: use the cube root relationship with x = 7, y = 1 to find y at x = 124, and describe the effect on F when d is halved.
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Part (a) · 3 marks
Given y proportional to cube root of (x + 1), with x = 7 giving y = 1, find y when x = 124.
- 1y = k × ∛(x + 1)
- 21 = k × ∛8 = 2k, so k = 1/2
- 3y = 1/2 × ∛(124 + 1) = 1/2 × 5
- 4y = 2.5
Answer2.5
Part (b) · 1 mark
F is inversely proportional to d squared; state how F changes when d is halved.
- 1F = k/d²; if d is halved, d² is divided by 4
- 2So F is multiplied by 4
Answermultiplied by 4
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Also searched as: 0580/22/M/J/22 · 0580_s22_qp_22 · 0580 s22 22 · question 18.
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