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4PM1/01 Jun 2019, Question 4: 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

Sector OAB has radius 15 cm and angle θ; C and D divide OA and OB in ratio 2:1; shaded region ABDC has area 100 cm². Find θ and the perimeter of ABDC.

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Part (a) · 3 marks

Find the value of θ in radians using the shaded region's area of 100 cm².

  1. 1OC = OD = 10 cm
  2. 2½ × 15²θ − ½ × 10²θ = 100
  3. 362.5θ = 100
  4. 4θ = 8/5 = 1.6

Answerθ = 8/5 (1.6)

Part (b) · 3 marks

Find the perimeter of the shaded region ABDC.

  1. 1Arc CD = 10 × 1.6 = 16
  2. 2Arc AB = 15 × 1.6 = 24
  3. 3AC = BD = 5
  4. 4Perimeter = 16 + 24 + 5 + 5 = 50 cm

Answer50 cm

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