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4PM1/01 Jun 2025, Question 3: Radians, Arcs and Sectors

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 6 marks

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The question, in short

Two equal circles of radius 7 cm intersect at A and B, with angle AOB = θ radians; the shaded common region R has perimeter 28π/9 cm. Find θ and the area of R.

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

Part (a) · 2 marks

Find the exact value of θ, in radians, using the given perimeter of the shaded region R.

  1. 1The perimeter of R is two equal arcs of radius 7 subtending θ
  2. 22 × 7 × θ = 28π/9
  3. 3θ = 2π/9

Answerθ = 2π/9

Part (b) · 4 marks

Find the area of the shaded region R in cm², giving the answer to 3 significant figures.

  1. 1Sector area = ½ × 7² × 2π/9
  2. 2Triangle area = ½ × 7² × sin(2π/9) = 15.7…
  3. 3Segment = sector − triangle
  4. 4R = 2 × segment = 2.71

Answer2.71 cm²

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