O-LevelAdditional MathematicsTrigonometry4037/12 · May/June 2015 · Q1012 Marks

Solve 2cos3x = sec 3x for 0° ≤ x ≤ 120°.

Mark scheme

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

[3] (a) M1 complete correct method, dealing with sec and 3, correctly
[3] (a) A1,A1 A1 for each correct pair
[5] (b) M1 use of a correct identity to get an equation in terms of one trig ratio only
[5] (b) M1 for cot y = 1/tan y to obtain either a quadratic equation in tan y or solutions in terms of tan y; allow where appropriate
[5] (b) M1 for solution of a quadratic equation in terms of either tan y or cot y
[5] (b) A1,A1 A1 for each correct 'pair'
[4] (c) M1 completely correct method of solution
[4] (c) A1 one correct solution in range
[4] (c) M1 correct attempt to obtain a second solution within the range
[4] (c) A1 second correct solution (and no other)

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Topic: Trigonometry, O-Level Additional Mathematics (syllabus 4037). Structured question, 12 marks.
Source: O-Level Additional Mathematics, May/June 2015 Paper 1 Variant 2, question 10.

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