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O-LevelAdditional MathematicsDifferentiation and integration4037/12 · May/June 2025 · Q45 Marks

Find ∫₀^(π/2) sin θ dθ.

  1. (a)Find ∫₀^(π/2) sin θ dθ.[2]
  2. (b)Given that 0 < α < π/2, show that sec α / (cot α + tan α) can be written as sin α.[3]

Mark scheme

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

  1. [B1] [-cosθ] (May be implied by (−cosπ)-(−cos0))
  2. [B1] 2
  3. [B1] 1/cosα / (cosα/sinα + sinα/cosα) (For ratios in terms of sine and cosine)
  4. [B1] 1/cosα / ((cos²α + sin²α)/(sinαcosα)) (For simplifying the denominator to one term)
  5. [B1] 1/cosα / (1/(sinαcosα)) (= sinα) (Must show sufficient correct detail)

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source
O-Level Additional Mathematics, May/June 2025 Paper 1 Variant 2, question 4.

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