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A-LevelMathematicsQuadratics9709/12 · May/June 2021 · Q14 Marks

Express 16x² – 24x + 10 in the form (4x + a)² + b.

  1. (a)Express 16x² – 24x + 10 in the form (4x + a)² + b.[2]
  2. (b)It is given that the equation 16x² – 24x + 10 = k, where k is a constant, has exactly one root. Find the value of this root.[2]

Mark scheme

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

  1. [B1] (4x – 3)² or (4x +(-3))² or a = -3
  2. [B1] + 1 or b = 1
  3. [B1 FT] [For one root] k = 1 or 'their b'
  4. [B1] [Root or x =] 3/4 or 0.75

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About this question

Topic
Quadratics, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source
A-Level Mathematics, May/June 2021 Paper 1 Variant 2, question 1.

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