EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Sectors of Circles
Sectors of circles · Area and volume · Lesson 5 of 7 · 20 marks · 30 minutes
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Instructions
• Answer all the questions.
• Write your answers in the spaces provided.
• The marks for each question are shown in brackets - use this as a guide to how much to write.
• The answers are on separate pages at the back. Attempt every question before you look at them.
• Answer all questions. Show your working.
Question 1 CALCULATOR (3 marks)
The diagram shows a sector of a circle of radius 9 cm. The angle at the centre is 40°. Work out the length of the arc. Give your answer correct to 3 significant figures.
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(Total for Question 1 = 3 marks)
Question 2 CALCULATOR (3 marks)
A sector of a circle has radius 10 cm and angle 72°. Work out the area of the sector. Give your answer correct to 3 significant figures.
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(Total for Question 2 = 3 marks)
Question 3 CALCULATOR (4 marks)
A sector of a circle has radius 5 cm and angle 90°. Work out the perimeter of the sector. Give your answer correct to 3 significant figures.
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(Total for Question 3 = 4 marks)
Question 4 NON-CALCULATOR (3 marks)
A sector of a circle has radius 12 cm and angle 150°. Work out the length of the arc. Give your answer in terms of π.
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(Total for Question 4 = 3 marks)
Question 5 NON-CALCULATOR (3 marks)
A sector of a circle has radius 12 cm. The arc length of the sector is 8π cm. Work out the angle at the centre of the sector.
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(Total for Question 5 = 3 marks)
Question 6 CALCULATOR (4 marks)
A sector of a circle has radius 8 cm and angle 90°. Work out the area of the segment formed by the chord joining the ends of the two radii. Give your answer correct to 3 significant figures.
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(Total for Question 6 = 4 marks)
TOTAL FOR PAPER = 20 MARKS
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Answers and mark scheme
Check your answer only once you have written one.
Question 1 (3 marks)
40/360 × 2π × 9 = 2π= 6.28 cm.
• 40/360 M1
• 40/360 × 2 × π × 9 M1
• 6.28 A1
Question 2 (3 marks)
72/360 × π × 10² = 20π= 62.8 cm².
• 72/360 M1
• 72/360 × π × 10² M1
• 62.8 A1
Question 3 (4 marks)
The arc is 90/360 × 2π × 5 = 7.854 cm. The perimeter is 7.854 + 5 + 5 = 17.9 cm.
• Arc length method M1
• 7.854 A1
• Adding two radii M1
• 17.9 A1
Question 4 (3 marks)
150/360 × 2 × π × 12 = 5/12 × 24π= 10π cm.
• 150/360 or 5/12 M1
• 5/12 × 24π M1
• 10π A1
Question 5 (3 marks)
θ/360 × 24π= 8π, so θ/360 = ⅓ and θ= 120°.
• θ/360 × 2π × 12 = 8π M1
• θ/360 = ⅓ M1
• 120 A1
Question 6 (4 marks)
Sector = 16π= 50.27 cm². Triangle = ½ × 8 × 8 = 32 cm². Segment = 50.27 − 32 = 18.3 cm².
• Sector area 50.27 M1
• Triangle area 32 M1
• 50.27 − 32 M1
• 18.3 A1