4PM1/02R Jun 2019, Question 2: Rational Functions and Asymptotes
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 4 marks
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The question, in short
Use the asymptotes y = −2 and x = −3 plus the x-intercept (4, 0) of y = (ax + b)/(x + c) to find a, b, c and the y-intercept p.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1Horizontal asymptote y = a/1 = −2 ⇒ a = −2
- 2Curve passes through (4, 0): −2 × 4 + b = 0 ⇒ b = 8
- 3Vertical asymptote x = −c = −3 ⇒ c = 3
- 4y = (8 − 2x)/(x + 3); at x = 0, y = 8/3 ⇒ p = 8/3
Answera = −2, b = 8, c = 3, p = 8/3
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