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4PM1/02 Nov 2021, Question 3: Rational Functions and Asymptotes

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 7 marks

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The question, in short

Curve y = (a − bx)/(cx − d) with a, c, d prime and b integer; vertical asymptote x = 3/2 and x-intercept (5/4, 0). Find constants, y-intercept p and horizontal asymptote.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 2 marks

Use the vertical asymptote x = 3/2 to determine the prime values of c and d.

  1. 1Vertical asymptote where cx − d = 0: x = d/c = 3/2
  2. 2c and d prime, so c = 2, d = 3

Answerc = 2, d = 3

Part (b) · 2 marks

Use the x-intercept (5/4, 0) to find the prime a and integer b.

  1. 1y = 0 when a − bx = 0, x = a/b
  2. 2a/b = 5/4 with a prime, so a = 5, b = 4

Answera = 5, b = 4

Part (c) · 2 marks

Find the rational y-intercept p of the curve.

  1. 1x = 0: y = (5 − 0)/(0 − 3)
  2. 2p = −5/3

Answerp = −5/3

Part (d) · 1 mark

Find the equation of the horizontal asymptote.

  1. 1As x → ∞, y → −b/c = −4/2 = −2

Answery = −2

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