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A-LevelMathematicsQuadratics9709/12 · Oct/Nov 2016 · Q36 Marks

A curve has equation y = 2x² – 6x + 5.

  1. (i)Find the set of values of x for which y > 13.[3]
  2. (ii)Find the value of the constant k for which the line y = 2x + k is a tangent to the curve.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2016). The mark or mark type is shown in brackets.

  1. [M1] Sets to 0 + attempts to solve
  2. [A1] Both values required
  3. [A1] Allow all recognisable notation.
  4. [M1*] Equates and sets to 0.
  5. [DM1] Use of discriminant
  6. [A1] → -3
  7. [M1*] Sets (their dy/dx) = 2
  8. [DM1] Uses their x = 2 and their y = 1
  9. [A1] → k = -3

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About this question

Topic
Quadratics, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, Oct/Nov 2016 Paper 1 Variant 2, question 3.

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