IGCSEMaths: CoreCIETopic QuestionsLengths, Areas & VolumesCircles, Arcs & Sectors

Syllabus Edition

First teaching 2023

First exams 2025

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Circles, Arcs & Sectors (CIE IGCSE Maths: Core)

Topic Questions

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1
Sme Calculator3 marks

A circle has diameter 6 cm.

Calculate the area of the circle.
Give the units of your answer.

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2
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Calculate the area of a circle with radius 12cm.

............................................. cm2 

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3
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Henry buys a circular mirror for the room.
The diameter of the mirror is 80 cm.

Calculate the circumference of the mirror.

.............................................. cm

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4
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Calculate the circumference of a circle with radius 4.5cm.

.............................................. cm 

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5
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A circle has diameter 7 cm.

Show that the circumference of the circle is 21.99cm, correct to 2 decimal places.

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1a
Sme Calculator1 mark

qp6-0580-31-paper-3-may-2020-cie-igcse-maths

The diagram shows a circle, centre O, radius 11 cm.
C comma space F comma space G and H are points on the circumference of the circle.
The line A D touches the circle at C and is parallel to the line E G.
B is a point on A D and angle A B O = 140°.

Write down the mathematical name of the straight linespace A D.

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1b
Sme Calculator6 marks
i)
Find, in terms of pi, the circumference of the circle.

[2]

ii)
Work out angle F O H.

Angle F O H = ................................................. [2]

iii)
Calculate the length of the minor arc F H.
............................................ cm [2]

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2
Sme Calculator5 marks

qp7d-0580-32-paper-3-may-2020-cie-igcse-maths

The diagram shows a square with vertices on the circumference of a circle, centre O.
The radius of the circle is 6 cm.

Work out the shaded area.

.......................................... cm2 

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3
Sme Calculator5 marks

q8b-058031-mayjune2019-cie-igcse-maths-core

Points P comma space Q and R are on the circumference of a semicircle, centre O and radius 8 cm.
Angle P O Q = 90°.

Calculate the shaded area.

.........................................cm2 

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4
Sme Calculator8 marks

The diagram shows a rectangle and two semicircles with diameters A C and B D.
This diagram is a scale drawing of a running track.
A C space equals space B D space equals space 60 straight m space A B space equals space C D space equals space 120 straight m

q9-058032-march2019-cie-igcse-maths-core

i)
Complete the statement.

1 centimetre represents ............................ metres.

[2]

ii)
Work out the total length of the running track in metres.
............................. m [3]
iii)
Shreva walks at 1.4m/s.

Work out how long it will take her to walk once around the track.
Give your answer in minutes and seconds, correct to the nearest second.

.................... minutes .................... seconds [3]

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5
Sme Calculator3 marks

q10e-058032-march2019-cie-igcse-maths-core

This shape is drawn using two semicircles that have the same centre.
The large semicircle has radius 7 cm.
The small semicircle has radius 3 cm.

Calculate the area of the shape.

.............................. cm2 

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1
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A circle has a circumference of 56mm.

Work out the radius of this circle.

.............................mm 

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2
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Rachel has a pond in her garden in the shape of a circle.
The circumference of the pond is 4.25m.

Calculate the diameter of the pond.
Give your answer in centimetres.

............................................ cm

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3
Sme Calculator2 marks

qp28-0580-01-paper-1-specimen-2020-cie-igcse-maths

O A B is a sector of a circle with radius 9 cm and centre O.
The angle at O is 30°.

Calculate the area of this sector.
Give your answer in terms of pi.

......................................... cm2 

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4
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q21-058012-mayjune2019-cie-igcse-maths-core

The diagram shows a semicircle with diameter 9 cm.

Calculate the total perimeter of this semicircle.

......................................... cm 

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5
Sme Calculator4 marks

There is a circular pool in the play area at a park.
The pool has a diameter of 8m.

Calculate

i)
the circumference of the pool,

..........................m [2]

ii)
the area of the pool.

........................... m2 [2]

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