4PM1/02R Jun 2025, Question 3: Radians, Arcs and Sectors
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 6 marks
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The question, in short
Sector OABC has radius 6 cm and angle θ radians, with perimeter 12 + π cm. Find the exact area S of the shaded region between arc ABC and chord AC.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 6 marks
- 1Arc length = 6θ
- 26 + 6 + 6θ = 12 + π, so θ = π/6
- 3Sector area = (1/2)(6²)(π/6) = 3π
- 4Triangle area = (1/2)(6²)sin(π/6) = 9
- 5S = 3π − 9
AnswerS = 3π − 9
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