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O-LevelAdditional MathematicsLogarithmic and exponential functions4037/12 · May/June 2014 · Q57 Marks

Given that 2⁵ˣ × 4ʸ = 1/8, show that 5x + 2y = -3.

  1. (i)Given that 2⁵ˣ × 4ʸ = 1/8, show that 5x + 2y = -3.[3]
  2. (ii)Solve the simultaneous equations 2⁵ˣ × 4ʸ = 1/8 and 7ˣ × 49²ʸ = 1.[4]

Mark scheme

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

  1. [B1] (i) B1 for 2^{2y}
  2. [B1] (i) B1 for 2^{-3}
  3. [B1] (i) B1 for dealing with indices correctly to obtain given answer
  4. [B1] (ii) B1 for either 7^{4y} or 7^0 seen
  5. [B1] (ii) B1 for x + 4y = 0
  6. [M1] (ii) M1 for solution of their simultaneous equations, must both be linear
  7. [A1] (ii) Al for both, allow equivalent fractions only

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About this question

Topic
Logarithmic and exponential functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 7 marks.
Source
O-Level Additional Mathematics, May/June 2014 Paper 1 Variant 2, question 5.

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