O-LevelAdditional MathematicsLogarithmic and exponential functions4037/22 · Oct/Nov 2015 · Q59 Marks

Solve the following equations to find p and q. 8^(q-1) × 2^(2p+1) = 4⁷ 9^(p-4) × 3^q = 81

(a)Solve the following equations to find p and q. 8^(q-1) × 2^(2p+1) = 4⁷ 9^(p-4) × 3^q = 81[4]
(b)Solve the equation 1g(3x - 2) + 1g(x + 1) = 2 - lg2.[5]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2015). The mark or mark type is shown in brackets.

[B1] (a) 2^(3(q-1)) x 2^(2p+1) = 2^14 Correct powers of 2 allow unsimplified isw
[B1] (a) 3^(2(p-4)) x3q = 3^4 Correct powers of 3 allow unsimplified isw
[M1] (a) Solve 3q+2p = 16 ; q+2p = 12 Attempt to solve their linear equations by eliminating one variable
[A1] (a) p=5, q=2 Both correct
[M1] (b) (3x-2)(x+1) = 50 LHS oe isw
[A1] (b) 50 from correct processing of 2-lg2
[M1] (b) 3x² + x − 52 = 0 → (3x+13)(x-4) Solution of their three term quadratic Roots must be obtained from correct quadratic
[A1] (b) x = 4
[A1] (b) x = -13/3 discarded

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Topic: Logarithmic and exponential functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 9 marks.
Source: O-Level Additional Mathematics, Oct/Nov 2015 Paper 2 Variant 2, question 5.

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