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O-LevelAdditional MathematicsDifferentiation and integration4037/22 · May/June 2017 · Q46 Marks

The point P lies on the curve y = 3x² – 7x + 11. The normal to the curve at P has equation 5y + x = k. Find the coordinates of P and the value of k.

  1. The point P lies on the curve y = 3x² – 7x + 11. The normal to the curve at P has equation 5y + x = k. Find the coordinates of P and the value of k.[6]

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

  1. [B1] dy/dx = 6x-7 soi
  2. [B1] m_normal = -1/5 soi
  3. [M1] m_tangent = 5 soi or (6x-7)(-1/5) = -1 oe uses m₁m₂ = -1 with numerical gradients
  4. [A1] 6x-7 = 5 oe => x = 2
  5. [A1] y=9
  6. [A1] k=47

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source
O-Level Additional Mathematics, May/June 2017 Paper 2 Variant 2, question 4.

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