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WMA11/01 Jan 2019, Question 10: Radians, Arcs and Sectors

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 7 marks

The question, in short

Sector AOB has radius r cm and angle θ radians, area 6 cm² and perimeter 10 cm; derive the given quadratic in θ and find r and θ.

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Part (a) · 4 marks

Using area 6 and perimeter 10 for the sector, show that 3θ² − 13θ + 12 = 0.

  1. 1Area: ½r²θ = 6; perimeter: 2r + rθ = 10
  2. 2From the perimeter, r = 10/(2 + θ)
  3. 3Substitute: ½ × 100θ/(2 + θ)² = 6, so 50θ = 6(4 + 4θ + θ²)
  4. 424θ + 6θ² + 24 − 50θ = 0 gives 6θ² − 26θ + 24 = 0, so 3θ² − 13θ + 12 = 0

AnswerShown: eliminating r gives 50θ = 6(2 + θ)², so 3θ² − 13θ + 12 = 0

Part (b) · 3 marks

Solve the quadratic to find the possible values of r and θ.

  1. 1Factorise: (3θ − 4)(θ − 3) = 0, so θ = 4/3 or θ = 3
  2. 2θ = 4/3: r = 10/(2 + 4/3) = 3
  3. 3θ = 3: r = 10/(2 + 3) = 2

Answerθ = 4/3, r = 3 or θ = 3, r = 2

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Also searched as: WMA11 January 2019 · WMA11/01 · wma11 jan19 · IAS Maths Pure Mathematics 1 January 2019 · question 10.
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