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0606/13 May/Jun 2025, Question 7: Radians, Arcs and Sectors

Cambridge IGCSE Additional Mathematics 0606 · Paper 13 (Non-calculator) · Non-calculator · 6 marks

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The question, in short

Sector OAB has centre O and radius 6 with angle θ radians; using the triangle area and the shaded segment area, find sin θ and then the exact arc length AB.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 2 marks

Triangle AOB has area 9 cm²; find sin θ.

  1. 1Area = (1/2) × 6 × 6 × sin θ = 9
  2. 218 sin θ = 9
  3. 3sin θ = 1/2

Answersin θ = 1/2

Part (b) · 4 marks

Shaded segment area is (15π − 9) cm²; find the exact length of arc AB.

  1. 1Segment = sector − triangle: (1/2)(36)(θ − sin θ) = 15π − 9
  2. 218θ − 9 = 15π − 9
  3. 3θ = 5π/6
  4. 4Arc AB = 6 × 5π/6 = 5π

Answer5π cm

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Also searched as: 0606/13/M/J/25 · 0606_s25_qp_13 · 0606 s25 13 · question 7.
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