O-LevelAdditional MathematicsTrigonometry4037/12 · Oct/Nov 2014 · Q119 Marks

Solve 2 cos 3x = cot 3x for 0° ≤ x ≤ 90°.

Mark scheme

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

[1] M1 for use of cot 3x = cos 3x / sin 3x, may be implied
[1] DM1 for attempt to solve cos 3x = 0 correctly from correct factorisation to obtain x
[2] A1 A1 for both, no excess solutions in the range (x = 30°, 90°)
[1] DM1 for attempt to solve sin 3x = 1/2 correctly to obtain x
[2] A1 A1 for both, condone excess solutions (x = 10°, 50°)
[1] M1 for dealing with sec (y + π/2) correctly
[1] DM1 for correct order of operations, must not mix degrees and radians
[2] A1, A1 so y = π/6, 5π/6 (0.524, 2.62)

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Topic: Trigonometry, O-Level Additional Mathematics (syllabus 4037). Structured question, 9 marks.
Source: O-Level Additional Mathematics, Oct/Nov 2014 Paper 1 Variant 2, question 11.

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