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A-LevelMathematicsAlgebra9709/22 · Feb/Mar 2017 · Q36 Marks

Solve the inequality |2x – 5| < |x + 3|.

  1. (i)Solve the inequality |2x – 5| < |x + 3|.[4]
  2. (ii)Hence find the largest integer y satisfying the inequality |2 ln y – 5| < | ln y + 3|.[2]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2017). The mark or mark type is shown in brackets.

  1. [B1] State or imply non-modulus inequality (2x−5)² < (x + 3)² or corresponding equation or pair of linear equations
  2. [M1] Attempt solution of 3-term quadratic inequality or equation or of 2 linear equations
  3. [A1] Obtain critical values ⅔ and 8
  4. [A1] State answer ⅔ < x < 8
  5. [M1] Attempt to find y from ln y = upper limit of answer to part (i)
  6. [A1] Obtain 2980

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About this question

Topic
Algebra, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, Feb/Mar 2017 Paper 2 Variant 2, question 3.

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