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A-LevelFurther MathematicsRational functions and graphs9231/12 · Oct/Nov 2017 · Q912 Marks

The curve C has equation y = (3x - 9) / ((x - 2)(x + 1)).

  1. (i)Find the equations of the asymptotes of C.[2]
  2. (ii)Show that there is no point on C for which 1/3 < y < 3.[4]
  3. (iii)Find the coordinates of the turning points of C.[3]
  4. (iv)Sketch C.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

  1. [1] B1
  2. [1] B1
  3. [1] M1
  4. [1] M1
  5. [1] A1
  6. [1] A1 AG
  7. [1] B1
  8. [1] B1
  9. [1] B1
  10. [1] B1 Axes, asymptotes and points on axes (0, 4.5) (3,0).
  11. [2] B1B1 RH branch; Other two branches

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About this question

Topic
Rational functions and graphs, A-Level Further Mathematics (syllabus 9231). Structured question, 12 marks.
Source
A-Level Further Mathematics, Oct/Nov 2017 Paper 1 Variant 2, question 9.

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