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O-LevelAdditional MathematicsSimultaneous equations4037/21 · May/June 2020 · Q66 Marks

Find the values of k for which the line y = kx-7 and the curve y = 3x² +8x+5 do not intersect.

  1. Find the values of k for which the line y = kx-7 and the curve y = 3x² +8x+5 do not intersect.[6]

Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

  1. [M1] 3x²+8x+5= kx-7
  2. [A1] 3x² + (8-k) x + 12 [= 0] soi
  3. [M1] (8-k)²-4 (3) (12)
  4. [M1] k²-16k-80 < 0
  5. [A1] Critical values: -4 and 20 soi
  6. [A1] -4 < k < 20
  7. Alternative method: [M1] for k = 6x + 8 oe
  8. [M1] for y = (6x + 8)x-7
  9. [M1] for 3x² + 8x + 5 = (6x + 8)x−7
  10. [A1] for x = ±2
  11. [A1] for k=-4, k = 20
  12. [A1] for -4<k<20

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About this question

Topic
Simultaneous equations, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source
O-Level Additional Mathematics, May/June 2020 Paper 2 Variant 1, question 6.

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