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O-LevelAdditional MathematicsDifferentiation and integration4037/11 · May/June 2015 · Q79 Marks

The point A, where x = 0, lies on the curve y = ln(4x² + 3)/(x – 1). The normal to the curve at A meets the x-axis at the point B.

  1. (i)Find the equation of this normal.[7]
  2. (ii)Find the area of the triangle AOB, where O is the origin.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.

  1. [M1] differentiation of a quotient (or product)
  2. [B1] correct differentiation of ln(4x² + 3)
  3. [A1] all else correct
  4. [B1] for y value
  5. [M1] valid attempt to obtain gradient of the normal
  6. [M1] attempt at normal equation must be using a perpendicular
  7. [A1] cao (Allow y = 0.91x-1.1)
  8. [M1] valid attempt at area
  9. [A1] Area = ±0.66 or ±0.67 or awrt these or (1/2)(ln3)²

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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, May/June 2015 Paper 1 Variant 1, question 7.

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