CIE IGCSE Maths: Extended

Topic Questions

IGCSEMaths: ExtendedCIETopic Questions3. Geometry3.6 Circles, Arcs & Sectors

Syllabus Edition

First teaching 2021

Last exams 2024

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3.6 Circles, Arcs & Sectors

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1
Sme Calculator3 marks

Calculate the area of the sector of a circle with radius 65 mm and sector angle 42°.
Give your answer in square centimetres.
 

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

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2
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cie-igcse-2019-oct-nov-p2-tz1-q17

The diagram shows two sectors of circles with the same centre.

Calculate the shaded area.

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

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3
Sme Calculator3 marks

cie-igcse-2018-oct-nov-p2-tz3-q19

The diagram shows a sector of a circle with radius 6 cm and sector angle 72°.
The perimeter of this sector is  left parenthesis p plus q straight pi right parenthesis cm.

Find the value of p and the value of q.

p = ................................................     
q = ................................................     

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4
Sme Calculator5 marks

q9-4-6-medium-edexcel-gcse-maths

O N Q is a sector of a circle with centre O and radius 11 cm.

A is the point on O N and B is the point on O Q such that A O B is an equilateral triangle of side 7 cm.

Calculate the area of the shaded region as a percentage of the area of the sector O N Q.
Give your answer correct to 1 decimal place.

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5
Sme Calculator4 marks

The diagram shows a square A B C D inside a circle.

q10-4-6-medium-edexcel-gcse-maths

The points A comma space B comma space C and D lie on the circle.

The radius of the circle is 6 cm.

Work out the total area of the shaded regions.
Give your answer correct to 3 significant figures.

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6
Sme Calculator3 marks

q12-4-6-medium-edexcel-gcse-maths

The arc A B C is a quarter of a circle with centre O and radius 4.8 cm.
A C is a chord of the circle.

Work out the area of the shaded segment.
Give your answer correct to 3 significant figures.

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7
Sme Calculator3 marks

q13-4-6-medium-edexcel-gcse-maths

O A B is a sector of a circle, centre O.
O C D is a sector of a circle, centre O.
O C A and O D B are straight lines.

Angle A O B space equals space 75 degree
O D space equals space 6 space cm space D B space equals space 4 space cm

Calculate the perimeter of the shaded region.
Give your answer correct to 3 significant figures.

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8
Sme Calculator5 marks

The diagram shows a shaded shape space A B C D spacemade from a semicircle space A B C spaceand a right-angled triangle A C D.

q11-4ma1-2h-qp-jan20-paper2-igcse-maths

A C spaceis the diameter of the semicircle A B C.

Work out the perimeter of the shaded shape.
Give your answer correct to 3 significant figures.

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

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1
Sme Calculator2 marks

cie-igcse-2020-oct-nov-p2-tz2-q15

Calculate the area of this sector of a circle.


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

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2
Sme Calculator2 marks

cie-igcse-2019-may-jun-p2-tz3-q12

The diagram shows a sector of a circle with radius 6.2 cm and sector angle 217°.

Calculate the area of this sector.
 

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

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3
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Calculate the area of a circle with radius 5.1 cm.

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

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4
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q3-4-6-easy-edexcel-gcse-maths

O A B is a sector of a circle, centre O.
The radius of the circle is 15 cm.
The angle of the sector is 30 degree.

Calculate the area of sector O A B.
Give your answer correct to 3 significant figures.

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5
Sme Calculator2 marks

The diagram shows a sector of a circle of radius 7 cm.

q4-4-6-easy-edexcel-gcse-maths

Work out the length of arc A B.
Give your answer correct to 3 significant figures.

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6
Sme Calculator2 marks

The diagram shows a sector of a circle of radius 4 cm.

q5-4-6-easy-edexcel-gcse-maths

Work out the length of the arc A B C.
Give your answer correct to 3 significant figures.

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7
Sme Calculator2 marks

The diagram shows sector space O P Q spaceof a circle, centre O

q11-4ma1-1hr-qp-jan22-paper1-igcse-maths-1

O P space equals space O Q space equals space 7.1 space cm
Angle P O Q space equals space 110 degree

Calculate the area of sector O P Q
Give your answer correct to one decimal place.

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1
Sme Calculator4 marks

cie-igcse-2020-mary-jun-p2-tz2-q24

The diagram shows a sector of a circle of radius 8 cm.
The length of the arc P Q is 6.4 cm.
 
Find the area of the sector.
 

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

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2
Sme Calculator3 marks

The total perimeter of a semicircle is 19.02 cm.
 
Calculate the radius of the semicircle.
 

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

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3
Sme Calculator3 marks

A B is an arc of a circle, centre O, radius 9 cm. 

cie-igcse-q23-arc-sector

The length of the arc A B is 6 straight pi cm.
The area of sector A O B is k straight pi cm2.

Find the value of k.

k space= ..............................................

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4
Sme Calculator4 marks

cie-igcse-2018-oct-nov-p2-tz2-q21

The diagram shows an equilateral triangle ABC with sides of length 10 cm.
AMN is a sector of a circle, centre A.
M is the mid-point of AC.

Work out the area of the shaded region.
 

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

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5a
Sme Calculator3 marks

cie-igcse-2020-oct-nov-p2-tz3-q21

OAB is the sector of a circle, centre O.
OB = 8 cm and angle AOB = 30°.
BP is perpendicular to OA.

Calculate AP.
 

AP =  ........................................... cm

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5b
Sme Calculator3 marks

Work out the area of the shaded region APB.
 

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

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