Lemmara logoLemmaraWorked solution

WMA11/01 Jan 2020, Question 4: Radians, Arcs and Sectors

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

The question, in short

Using a rectangle ABCD with AB = 16 m and a sector APCOA of radius 12 m centred at O on DC, find angle AOD, then the lawn's area and perimeter.

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

Part (a) · 2 marks

Show that angle AOD equals 1.231 radians, correct to 3 decimal places.

  1. 1OC = 12 (radius), so OD = 16 − 12 = 4
  2. 2Triangle AOD is right-angled at D: cos AOD = 4/12 = 1/3
  3. 3Angle AOD = cos⁻¹(1/3) = 1.23095… = 1.231 radians

AnswerShown: OD = 16 − 12 = 4 and OA = 12, so cos AOD = 4/12 giving AOD = 1.231 radians

Part (b) · 4 marks

Calculate the area of the shaded lawn APCDA in m², to one decimal place.

  1. 1Reflex angle AOC = π + 1.231 = 4.373 radians
  2. 2Major sector area = ½ × 12² × 4.373 = 314.8
  3. 3AD = √(12² − 4²) = √128; triangle AOD = ½ × 4 × √128 = 22.6
  4. 4Lawn = 314.8 − 22.6 = 292.2 m²

Answer292.2 m²

Part (c) · 3 marks

Calculate the perimeter of the lawn APCDA in metres, to one decimal place.

  1. 1Major arc APC = 12 × (π + 1.231) = 52.47
  2. 2AD = √128 = 11.31 and DC = AB = 16
  3. 3Perimeter = 52.47 + 16 + 11.31 = 79.8 m

Answer79.8 m

Stuck on a step? Read the free lesson: Radians, Arcs and Sectors

Practise more radians, arcs and sectors 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 radians, arcs and sectors

Also searched as: WMA11 January 2020 · WMA11/01 · wma11 jan20 · IAS Maths Pure Mathematics 1 January 2020 · question 4.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.