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O-LevelAdditional MathematicsDifferentiation and integration4037/22 · Oct/Nov 2018 · Q109 Marks

Two lines are tangents to the curve y = 12-4x-x². The equation of each tangent is of the form y = 2k+1-kx, where k is a constant.

  1. (i)Find the two possible values of k.[5]
  2. (ii)Find the coordinates of the point of intersection of the two tangents.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

  1. [M1*] 2k+1-kx = 12-4x-x²
  2. [M1 Dep*] x²+4x-kx+2k-11=0
  3. [M1 Dep*] (4-k)²-4(2k-11)
  4. [A1] k²-16k+60
  5. [M1] (k-6)(k-10)
  6. [A1] k = 6 or 10
  7. [B1 FT] k=6 → [y]=13-6x
  8. [B1 FT] k=10 → [y]=21-10x
  9. [M1] solve
  10. [A1] x = 2, y = 1. cao

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 9 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2018 Paper 2 Variant 2, question 10.

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