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A-LevelFurther MathematicsRational functions and graphs9231/12 · Oct/Nov 2019 · Q47 Marks

The line y = 2x + 1 is an asymptote of the curve C with equation y = (x² + 1)/(ax + b)

  1. (i)Find the values of the constants a and b.[3]
  2. (ii)State the equation of the other asymptote of C.[1]
  3. (iii)Sketch C. [Your sketch should indicate the coordinates of any points of intersection with the y-axis. You do not need to find the coordinates of any stationary points.][3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

  1. [M1] Uses that 2x+1 is the quotient.
  2. [A1 A1]
  3. [B1 FT]
  4. [B1] Intersection (0,-4) given and asymptotes drawn.
  5. [B1] Left branch correct.
  6. [B1 FT] Right branch correct.
  7. Deduct at most one mark for poor forms at infinity.

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About this question

Topic
Rational functions and graphs, A-Level Further Mathematics (syllabus 9231). Structured question, 7 marks.
Source
A-Level Further Mathematics, Oct/Nov 2019 Paper 1 Variant 2, question 4.

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