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A-LevelMathematicsLogarithmic and exponential functions9709/32 · Oct/Nov 2018 · Q45 Marks

Showing all necessary working, solve the equation (eˣ + e⁻ˣ)/(eˣ + 1) = 4, giving your answer correct to 3 decimal places.

  1. Showing all necessary working, solve the equation ex + e-x ex + 1 = 4, giving your answer correct to 3 decimal places.[5]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

  1. [B1] Substitute and obtain 3-term quadratic 3u² + 4u - 1 = 0, or equivalent
  2. [M1] Solve a 3 term quadratic for u
  3. [A1] Obtain root (√7-2)/3, or decimal in [0.21, 0.22]
  4. [M1] Use correct method for finding x from a positive value of eˣ
  5. [A1] Obtain answer x = -1.536 only

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About this question

Topic
Logarithmic and exponential functions, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Oct/Nov 2018 Paper 3 Variant 2, question 4.

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