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O-LevelAdditional MathematicsQuadratic functions4037/21 · May/June 2021 · Q76 Marks

Find the exact values of the constant k for which the line y=2x+1 is a tangent to the curve y = 4x² +kx+k-2.

  1. Find the exact values of the constant k for which the line y=2x+1 is a tangent to the curve y = 4x² +kx+k-2.[6]

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

  1. [M1] 4x²+kx+k-2 = 2x+1
  2. [A1] 4x² + (k-2)x + k-3 [*0] soi (* can be <, >, =, ≤, ≥)
  3. [M1] (k-2)² - 4(4)(k-3)
  4. [A1] k² - 20k + 52 * 0
  5. [M1] k = (-(-20)±√(-20)²-4(1)(52))/2
  6. [A1] k = 10±√48 oe isw
  7. [M1] (Alternative) 2 = 8x + k oe
  8. [M1] (Alternative) y = 4x² + (2-8x) x + 2-8x-2 or y = -4x²-6x
  9. [A1] (Alternative) 0 = 4x² + 8x + 1
  10. [M1] (Alternative) x = (-8±√8²-4(4)(1))/8
  11. [A1] (Alternative) x = -1±√48/8 oe
  12. [A1] (Alternative) for k = 10±√48 oe

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About this question

Topic
Quadratic functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source
O-Level Additional Mathematics, May/June 2021 Paper 2 Variant 1, question 7.

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