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A-LevelMathematicsQuadratics9709/12 · Feb/Mar 2021 · Q24 Marks

By using a suitable substitution, solve the equation 4 (2x-3)2 - - 3 = 0.

  1. By using a suitable substitution, solve the equation 4 (2x-3)2 - - 3 = 0.[4]

Mark scheme

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

  1. [1] u = 2x-3 leading to u² - 3u² - 4 [= 0] (Or u = (2x-3)² leading to u² - 3u – 4 [= 0])
  2. [1] (u²-4)(u²+1) [= 0] (Or (u-4)(u+1) [= 0])
  3. [1] 2x-3=[±]2
  4. [1] x=1/2, 5/2 only

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About this question

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

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