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O-LevelAdditional MathematicsLogarithmic and exponential functions4037/21 · May/June 2014 · Q118 Marks

Solve 2^(x²-5x) = 1/64.

  1. (a)Solve 2^(x²-5x) = 1/64.[4]
  2. (b)By changing the base of log₂ₐ4, express (log₂ₐ4)(1 + log₂ₐ2) as a single logarithm to base a.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.

  1. [M1] 2^(x^2-5x) = 2^-6 Or (x^2-5x)ln2 = ln(1/64) = -6ln2
  2. [M1] x²- 5x + 6 = 0 their "6"
  3. [M1] Correct method of solution of their 3 term quadratic
  4. [A1] x = 2 or x = 3
  5. [B1] Correct change of base to log_a 4 / log_a 2a base a only at this stage but can recover at end
  6. [M1] for log 2a = log 2 + log a
  7. [M1] log_a a = 1 used soi
  8. [A1] simplification to log_a 4

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About this question

Topic
Logarithmic and exponential functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, May/June 2014 Paper 2 Variant 1, question 11.

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