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O-LevelAdditional MathematicsDifferentiation and integration4037/11 · May/June 2012 · Q57 Marks

Find the equation of the tangent to the curve y = x³ + 2x² – 3x + 4 at the point where the curve crosses the y-axis.

  1. (i)Find the equation of the tangent to the curve y = x³ + 2x² – 3x + 4 at the point where the curve crosses the y-axis.[4]
  2. (ii)Find the coordinates of the point where this tangent meets the curve again.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2012). The mark or mark type is shown in brackets.

  1. [B1] (i) (0,4) (point where curve crosses y-axis)
  2. [M1] (i) for differentiation (dy/dx = 3x² + 4x – 3)
  3. [M1] (i) for attempt at line equation (When x = 0, dy/dx = -3)
  4. [A1] (i) y - 4 = -3x (or y = -3x + 4)
  5. [M1] (ii) for equating line and curve (-3x + 4 = x³ + 2x² – 3x + 4)
  6. [M1] (ii) for solution of cubic (leading to 0 = x³ + 2x²)
  7. [A1] (ii) x = -2
  8. [A1] (ii) y = 10

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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 2012 Paper 1 Variant 1, question 5.

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