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O-LevelAdditional MathematicsQuadratic functions4037/22 · May/June 2020 · Q36 Marks

Find the values of k for which the line y=x-3 intersects the curve y = k²x² +5kx+1 at two distinct points.

  1. (a)Find the values of k for which the line y=x-3 intersects the curve y = k²x² +5kx+1 at two distinct points.[6]

Mark scheme

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

  1. [1] x-3=k²x²+5kx+1
  2. [1] k²x²+(5k-1)x+4=0 soi
  3. [1] (5k-1)² - 4(k²)(4)
  4. [1] 9k²-10k+1*0
  5. [1] Critical values: 1/9 and 1 soi
  6. [1] k<1/9 or k>1

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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 2020 Paper 2 Variant 2, question 3.

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