O-LevelAdditional MathematicsTrigonometry4037/12 · May/June 2023 · Q67 Marks

Given that cot²θ = 1/(y+2) and sec θ = x-4, find y in terms of x.

(a)Given that cot²θ = 1/(y+2) and sec θ = x-4, find y in terms of x.[2]
(b)Solve the equation √3 cosec (2φ + 3π/4) = 2, for -π < φ < π, giving your answers in terms of π.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

[B1] No inverse trig functions A correct equation in terms of x and y only
[B1] y=(x-4)²-3 or y = x² - 8x + 13
[B1] May be implied by one correct solution sin (2φ + 3π/4) = √3/2 soi
[M1] for explicitly correct order of operations from their 2φ + 3π/4 = k, or may be implied by one correct solution
[A1] for two correct solutions
[A1] for a third correct solution
[A1] for a further solution with no extra solutions in the range (5π/24, -π/24, -19π/24, -23π/24)

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Topic: Trigonometry, O-Level Additional Mathematics (syllabus 4037). Structured question, 7 marks.
Source: O-Level Additional Mathematics, May/June 2023 Paper 1 Variant 2, question 6.

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