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O-LevelAdditional MathematicsLogarithmic and exponential functions4037/12 · May/June 2012 · Q25 Marks

Using the substitution u = 2ˣ, find the values of x such that 2²ˣ⁺² = 5 (2ˣ) – 1 .

Mark scheme

Marking points from the official mark scheme (May/June 2012). The mark or mark type is shown in brackets.

[B1, M1] B1 for 2^(2x+2) = 4u² or 4 × 2^(2x) or 2² × 2^(2x) or 2²u². M1 for attempt to obtain a 3 term quadratic equation in terms of either or, equated to zero.
[DM1] DM1 for solution of quadratic equation
[A1] A1 for both
[A1] A1 for both
[A1] 2^x = 1/4, leading to x = -2
[A1] 2^x = 1, leading to x = 0

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About this question

Topic: Logarithmic and exponential functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source: O-Level Additional Mathematics, May/June 2012 Paper 1 Variant 2, question 2.

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