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WMA11/01 Jun 2024, Question 5: Radians, Arcs and Sectors

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

The question, in short

For a garden made of triangle ABE, right triangle BCD and sector BDE (radius 6 m, angle 1.3 rad), with AB = 10.8 m and AE = 12.2 m, find sector area, angle ABE, and total garden area.

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

Part (a) · 2 marks

Calculate the area of sector BDE in m², using radius 6 m and angle EBD = 1.3 radians.

  1. 1Sector area = ½r²θ
  2. 2= ½ × 6² × 1.3
  3. 3= 23.4 m²

Answer23.4 m²

Part (b) · 2 marks

Find angle ABE in radians to 2 decimal places, using triangle ABE with AB = 10.8 m and AE = 12.2 m.

  1. 1Cosine rule: 12.2² = 6² + 10.8² − 2 × 6 × 10.8 × cos ABE
  2. 2cos ABE = (36 + 116.64 − 148.84)/129.6 = 3.8/129.6 = 19/648
  3. 3ABE = 1.54 rad (2 d.p.)

AnswerAngle ABE = 1.54 rad

Part (c) · 3 marks

Find the total area of the garden in m² to 3 significant figures, combining the triangle and sector areas.

  1. 1Area ABE = ½ × 10.8 × 6 × sin(1.5415) = 32.38
  2. 2Angle DBC = π − 1.3 − 1.5415 = 0.3001 rad
  3. 3BC = 6 cos 0.3001 = 5.732, CD = 6 sin 0.3001 = 1.774
  4. 4Area BCD = ½ × 5.732 × 1.774 = 5.08
  5. 5Total = 32.38 + 23.4 + 5.08 = 60.9 m² (3 s.f.)

Answer60.9 m²

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Also searched as: WMA11 June 2024 · WMA11/01 · wma11 jun24 · IAS Maths Pure Mathematics 1 June 2024 · question 5.
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