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O-LevelAdditional MathematicsTrigonometry4037/12 · Oct/Nov 2025 · Q134 Marks

For –1 ≤ x ≤ 1 it is given that x = 2−3sinθ and y = 3cot²θ. Find y in terms of x.

  1. For –1 ≤ x ≤ 1 it is given that x = 2−3sinθ and y = 3cot²θ. Find y in terms of x.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

  1. [4] B1 sinθ = (2-x)/3
  2. B1 y = 3(cos²θ / sin²θ) soi
  3. B1 Dep on both previous B marks for Use of sin²θ + cos²θ = 1 to obtain y = 3( (1 - ((2-x)/3)²) / ((2-x)/3)² )
  4. B1 Dep on all previous B marks. No fractions within fractions. y = 3(9/(2-x)² - 1) oe

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About this question

Topic
Trigonometry, O-Level Additional Mathematics (syllabus 4037). Structured question, 4 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2025 Paper 1 Variant 2, question 13.

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