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O-LevelAdditional MathematicsTrigonometry4037/12 · Oct/Nov 2011 · Q1010 Marks

Solve 2 sec² x = 5 tan x + 5, for 0° < x < 360°.

(i)Solve 2 sec² x = 5 tan x + 5, for 0° < x < 360°.[5]
(ii)Solve √2 sin( (y/2) + (π/3) ) = 1, for 0 < y < 4π radians.[5]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.

[M1] M1 for use of correct identity
[M1] M1 for solution of 3 term quadratic equation
[M1] M1 for attempt to solve tanx = k from a 3 term quadratic equation
[A1, A1] A1 for any pair
[M1] M1 for dealing with √2 correctly
[M1] M1 for correct order of operations
[M1] M1 for correct order of operations and attempt to get a solution in the range
[A1, A1] Allow decimal equivalents 2.62 and 12.0

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About this question

Topic: Trigonometry, O-Level Additional Mathematics (syllabus 4037). Structured question, 10 marks.
Source: O-Level Additional Mathematics, Oct/Nov 2011 Paper 1 Variant 2, question 10.

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