4MA1/1HR Jun 2025, Question 18: Inverse Proportion: y = k/x
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 5 marks
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The question, in short
F varies inversely as the cube of r, with F = 6 when r = 2. Find a formula linking F and r, then find r when F = 3072.
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Part (a) · 3 marks
Use the inverse cube relationship and the given pair of values to derive an equation expressing F in terms of r.
- 1F = k/r³
- 26 = k/2³
- 3k = 6 × 8 = 48
- 4F = 48/r³
AnswerF = 48/r³
Part (b) · 2 marks
Substitute F = 3072 into your formula and solve to find the corresponding value of r.
- 13072 = 48/r³
- 2r³ = 48/3072 = 1/64
- 3r = ∛(1/64) = 1/4
Answer1/4
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