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O-LevelAdditional MathematicsQuadratic functions4037/21 · Oct/Nov 2011 · Q24 Marks

Given that the straight line y = 3x + c is a tangent to the curve y = x² + 9x + k, express k in terms of c.

  1. Given that the straight line y = 3x + c is a tangent to the curve y = x² + 9x + k, express k in terms of c.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.

  1. [1] Eliminates y
  2. [1] x² + 6x + k − c (= 0)
  3. [1] Uses b² = 4ac or completes square
  4. [1] k=c+9
  5. [1] dy/dx = 2x + 9
  6. [1] Equate to 3 and solve for x (x = −3)
  7. [1] Substitute in both equations and equate
  8. [1] k=c+9

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About this question

Topic
Quadratic functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 4 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2011 Paper 2 Variant 1, question 2.

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