Lemmara logoLemmaraWorked solution

WMA11/01 Oct 2020, Question 3: The Cosine Rule

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 10 marks

The question, in short

A kite-shaped badge is made from two congruent triangles AOC and BOC plus sector AOB with AO = OB = 3 cm, OC = 5 cm and angle AOB = α. Sector area is 7.2 cm².

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

Part (a) · 2 marks

Show that α = 1.6 radians using the given sector area of 7.2 cm² and radius 3 cm.

  1. 1Sector area = (1/2)r²α
  2. 2(1/2) × 3² × α = 7.2
  3. 34.5α = 7.2, so α = 7.2/4.5 = 1.6 radians

AnswerShown: (1/2) × 3² × α = 7.2 gives α = 7.2/4.5 = 1.6

Part (bi) · 4 marks

Find the total area of the badge in cm², giving the answer to 2 significant figures.

  1. 1Angle COA = (2π − 1.6)/2 = 2.3416 radians
  2. 2Area of triangle COA = (1/2) × 5 × 3 × sin 2.3416 = 5.380
  3. 3Total area = 2 × 5.380 + 7.2 = 17.96
  4. 4Area ≈ 18 cm² (2 s.f.)

Answer18 cm²

Part (bii) · 4 marks

Find the perimeter of the badge in cm, giving the answer to one decimal place.

  1. 1Arc AB = 3 × 1.6 = 4.8 cm
  2. 2AC² = 5² + 3² − 2 × 5 × 3 cos 2.3416 = 54.91
  3. 3AC = 7.410 cm
  4. 4Perimeter = 2 × 7.410 + 4.8 = 19.6 cm

Answer19.6 cm

Stuck on a step? Read the free lesson: The Cosine Rule

Practise more the cosine rule questions

Real XMA01 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on the cosine rule

Also searched as: WMA11 October 2020 · WMA11/01 · wma11 oct20 · IAS Maths Pure Mathematics 1 October 2020 · question 3.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.