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Edexcel IGCSE Maths (4MA1) · Unit 5: Geometry

Edexcel IGCSE 4MA1 Circles, Arcs and Sectors: Exam Questions and Answers

Circles, Arcs and Sectors questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 2 worked examples first, then try the 8 exam-style questions yourself and check your working against the mark scheme.

2 worked examples
8 questions with mark schemes
Higher tier · calculator allowed
Free, no sign-in

Practise circles, arcs and sectors in Unit 5 →Circles, Arcs and Sectors revision notes

What this topic covers

Circles 1: Circumference & Area: Circumference and area of circles, including working backwards to the radius.
Arcs, Sectors & Segments: Arc lengths, sector areas and segment areas of circles.

Circles, Arcs and Sectors worked examples

Worked example 1: Area of a circle

Find the area of a circle of radius 4.2 cm.

Solution

$A = π r^{2} = π \times 17.64$ .
$= 55.4$ cm² (3 s.f.).

3 steps

Tip: Square the radius, not the diameter.

Worked example 2: Arc length and sector area

A sector has radius 12 cm and angle $75^{\circ}$ . Find its arc length and area.

Sector of radius 12 cm and angle 75 degrees

Solution

Arc $= \frac{75}{360} \times 2 π \times 12 = 15.7$ cm.
Area $= \frac{75}{360} \times π \times 144 = 94.2$ cm².

3 steps

Tip: The fraction of the circle is angle/360.

Circles, Arcs and Sectors exam-style questions

Try each question before you open the answer (one has its full worked solution open). The mark schemes use Edexcel-style marks: M for method, A for accuracy (after the method mark), B for an independent result.

Question 1 · easy · 2 marks

A circle has radius 6.5 cm. Work out its circumference. Give your answer to 3 significant figures.

Show the answer and mark scheme

M1 2 × π × 6.5 or π × 13
A1 40.8 (40.84…)

Answer: 40.8 cm

Question 2 · easy · 2 marks

A circle has diameter 14 cm. Work out its area. Give your answer to 3 significant figures.

Show the answer and mark scheme

M1 π × 7²
A1 154 (153.9…)

Answer: 154 cm²

Question 3 · easy · 1 mark

A circle has radius 5 cm. Write down its area, in cm², in terms of π.

Show the answer and mark scheme

B1 25π

Answer: $25 π$ cm²

Question 4 · medium · 2 marks

A circle has an area of 80 cm². Work out its radius. Give your answer to 3 significant figures.

Full worked solution Free, no sign-in

M1 πr² = 80 or r = √(80 ÷ π)
A1 5.05 (5.046…)

Answer: 5.05 cm

Every question here has a full worked solution. See them all →

Question 5 · medium · 3 marks

The circumference of a circle is 60 cm. Work out the area of the circle. Give your answer to 3 significant figures.

Show the answer and mark scheme

M1 r = 60 ÷ (2π) (= 9.549…)
M1 π × their r²
A1 286 (286.4…)

Answer: 286 cm²

Question 6 · medium · 3 marks

A semicircle has diameter 12 cm. Work out the perimeter of the semicircle. Give your answer to 3 significant figures.

Show the answer and mark scheme

M1 ½ × π × 12 (= 18.84…)
M1 their 18.84… + 12
A1 30.8 (30.84…)

Answer: 30.8 cm

Question 7 · hard · 3 marks

A bicycle wheel has diameter 65 cm. How many complete turns does the wheel make when the bicycle travels 1 km?

Show the answer and mark scheme

M1 circumference π × 65 (= 204.2… cm)
M1 100 000 ÷ their 204.2 (consistent units)
A1 489

Answer: 489 complete turns

Question 8 · hard · 3 marks

A flat ring is the region between two circles with the same centre. The outer radius is 9 cm and the inner radius is 6 cm. Work out the area of the ring. Give your answer to 3 significant figures.

Show the answer and mark scheme

M1 π × 9² − π × 6²
A1 45π
A1 141 (141.3…)

Answer: 141 cm² ( $45 π$ )

Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.

Revise circles, arcs and sectors for the exam

Unit 5 practice: Geometry in the student hub (more questions with mark schemes)
IGCSE Maths revision notes for this topic and the IGCSE Maths formula sheet
Edexcel IGCSE Maths 4MA1 past papers to practise under exam conditions
IGCSE Maths 4MA1 examiner report summary: where students lose marks

Questions students ask

Which Edexcel IGCSE Maths papers test circles, arcs and sectors?

Either Higher tier paper, 1H or 2H, can test circles, arcs and sectors: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.

Where can I practise more circles, arcs and sectors questions?

In the IGCSE student hub: Unit 5 (Geometry) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.

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Edexcel IGCSE 4MA1 Circles, Arcs and Sectors: Exam Questions and Answers

Try it first

What this topic covers

Circles, Arcs and Sectors worked examples

Worked example 1: Area of a circle

Solution

Worked example 2: Arc length and sector area

Solution

Circles, Arcs and Sectors exam-style questions

Question 1 · easy · 2 marks

Question 2 · easy · 2 marks

Question 3 · easy · 1 mark

Question 4 · medium · 2 marks

Full worked solution Free, no sign-in

Question 5 · medium · 3 marks

Question 6 · medium · 3 marks

Question 7 · hard · 3 marks

Question 8 · hard · 3 marks

Revise circles, arcs and sectors for the exam

Questions students ask

Practise circles, arcs and sectors with your progress saved

More Unit 5 topics: Geometry