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O-LevelAdditional MathematicsDifferentiation and integration4037/12 · May/June 2021 · Q117 Marks

The normal to the curve y = ln(x²+2)/(2x-3) at the point where x = 2 meets the y-axis at the point P. Find the coordinates of P.

  1. (a)The normal to the curve y = ln(x²+2)/(2x-3) at the point where x = 2 meets the y-axis at the point P. Find the coordinates of P.[7]

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

  1. [1] B1 for (2x)/(x²+2) or 2/(2x-3)
  2. [1] M1 for differentiation of a quotient
  3. [1] M1 For 1/their dy/dx
  4. [1] B1 When x = 2, y = ln 6 or 1.79(176)
  5. [1] M1 Dep for equation of normal using their dy/dx and their y with x = 2.
  6. [1] A1 Must be evaluated.

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 7 marks.
Source
O-Level Additional Mathematics, May/June 2021 Paper 1 Variant 2, question 11.

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