4MA1/2HR Jun 2020, Question 20: Inverse Proportion: y = k/x
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 4 marks
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The question, in short
Given T varies inversely as m squared, with T = 30 at m = 0.5, derive the equation linking T and m, then evaluate T at m = 0.1.
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Part (a) · 3 marks
Use the inverse-square relationship and the given pair of values to work out the constant, then state the equation for T in terms of m.
- 1T = k / m²
- 230 = k / (0.5)²
- 330 = k / 0.25
- 4k = 30 × 0.25
- 5k = 7.5
- 6T = 7.5 / m²
AnswerT = 7.5 / m²
Part (b) · 1 mark
Substitute m = 0.1 into the inverse-square relationship to calculate the resulting value of T.
- 1T = 7.5 / (0.1)²
- 2T = 7.5 / 0.01
- 3T = 750
Answer750
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