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4PM1/02R Jan 2023, Question 4: Rational Functions and Asymptotes

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 6 marks

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The question, in short

Curve C has equation y = (2x + q)/(x + r) with vertical asymptote x = −4 and horizontal asymptote y = p; use the y-intercept (0, 3/2) and x-intercept (s, 0) to find p, r, q and s.

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Part (a) · 2 marks

Write down the value of p from the horizontal asymptote and the value of r from the vertical asymptote x = −4.

  1. 1Horizontal asymptote: y = 2x/x = 2, so p = 2
  2. 2Vertical asymptote where x + r = 0: x = −4 so r = 4

Answer(i) p = 2 (ii) r = 4

Part (b) · 2 marks

Using the y-intercept (0, 3/2), find the integer q.

  1. 1At (0, 3/2): 3/2 = (2(0) + q)/(0 + 4)
  2. 2q = 6

Answerq = 6

Part (c) · 2 marks

Using the x-intercept (s, 0), find the value of s.

  1. 10 = (2s + 6)/(s + 4)
  2. 22s + 6 = 0 → s = −3

Answers = −3

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