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O-LevelAdditional MathematicsDifferentiation and integration4037/11 · May/June 2014 · Q78 Marks

A curve is such that dy/dx = 4x + 1/(x+1)² for x > 0. The curve passes through the point (1/2, 5/6).

  1. (i)Find the equation of the curve.[4]
  2. (ii)Find the equation of the normal to the curve at the point where x = 1.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.

  1. [B1] B1 for 2x²
  2. [B1] B1 for -1/(x+1)
  3. [M1] M1 for attempt to find +c, must have at least 1 of the previous B marks
  4. [A1] A1 Allow A1 for c = 1
  5. [M1] M1 for using x = 1 in their (i) to find y
  6. [B1] B1 for gradient of normal
  7. [DM1] DM1 for attempt at normal equation
  8. [A1] A1 - allow unsimplified (fractions must not contain decimals)

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, May/June 2014 Paper 1 Variant 1, question 7.

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