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WMA11/01 Oct 2024, Question 5: The Cosine Rule

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 9 marks

The question, in short

Sector OAB has radius 5 km and angle 1.2 radians; find its perimeter, then use a point P on OB splitting the sector so R₁ is three times R₂ to show R₂'s area and find AP.

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

Part (a) · 2 marks

Calculate the perimeter of the sector OAB using radius 5 km and angle 1.2 radians.

  1. 1Arc AB = rθ = 5 × 1.2 = 6 km
  2. 2Perimeter = 5 + 5 + 6 = 16 km

Answer16 km

Part (b) · 3 marks

Using area of R₁ equal to 3 times area of R₂, show that the area of R₂ is 3.75 km².

  1. 1Sector area = ½r²θ = ½ × 25 × 1.2 = 15 km²
  2. 2R₁ + R₂ = 15 and R₁ = 3R₂, so 4R₂ = 15
  3. 3R₂ = 15/4 = 3.75 km²

AnswerShown: sector area = ½ × 5² × 1.2 = 15 km², R₂ = ¼ × 15 = 3.75 km²

Part (c) · 4 marks

Find the length of AP, giving the answer to the nearest 100 m.

  1. 1Triangle OAP: ½ × 5 × OP × sin 1.2 = 3.75
  2. 2OP = 7.5/(5 sin 1.2) = 1.609… km
  3. 3AP² = 5² + 1.609…² − 2 × 5 × 1.609… × cos 1.2 = 21.76…
  4. 4AP = 4.66… ≈ 4.7 km = 4700 m (nearest 100 m)

AnswerAP = 4.7 km (4700 m)

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Also searched as: WMA11 October 2024 · WMA11/01 · wma11 oct24 · IAS Maths Pure Mathematics 1 October 2024 · question 5.
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