IGCSEMathsCambridge (CIE)ExtendedExam QuestionsLengths, Areas & VolumesCircles, Arcs & Sectors

Circles, Arcs & Sectors (Cambridge (CIE) IGCSE Maths: Extended): Exam Questions

Exam code: 0580 & 0980

4 hours45 questions

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Circles, Arcs & Sectors

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1
Sme Calculator3 marks
q8-paper2-spec2025-cie-igcse-further-maths

The diagram shows a semicircle with diameter 9cm.

Calculate the total perimeter of this semicircle.

Give your answer in exact form.

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2
Sme Calculator2 marks
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 as a simplified expression in terms of straight pi.

How did you do?

3
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 as a simplified expression in terms of straight pi.

How did you do?

4
Sme Calculator3 marks

The region, shown shaded in the diagram, is a path.

q8-4ma1-1h-qp-jan21-paper1-igcse-maths

The boundary of the path is formed by two semicircles, with the same centre O, and two straight lines.

The inner semicircle has a radius of 7 metres.

The path has a width of 2 metres.

Work out the perimeter of the path.

Give your answer as a simplified expression in terms of straight pi.

...................................................... m

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5
Sme Calculator4 marks

A circle centre O has radius 9 cm.

q11-4ma1-2hr-qp-jan21-paper2-igcse-maths

Calculate the perimeter of the shaded sector of the circle.

Give your answer as a simplified expression in terms of straight pi.

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

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1
Sme Calculator3 marks
cie-igcse-2019-oct-nov-p2-tz1-q17

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

Give your answer in terms of straight pi.

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

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2
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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3
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 in terms of straight pi.

How did you do?

4
Sme Calculator5 marks
~35-_5Zr_q9-4-6-medium-edexcel-gcse-maths

O A C is a sector of a circle, centre O, radius 10 m.

B A is the tangent to the circle at point A.

B C is the tangent to the circle at point C.

Angle A O C equals space 120 degree

Calculate the area of the shaded region. Give your answer as an exact value in terms of straight pi.

How did you do?

1a
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.

Give your answer as an exact value.  

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

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1b
Sme Calculator3 marks

Work out the area of the shaded region APB. Give your answer as an exact value in terms of straight pi.  

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

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2
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= ..............................................

How did you do?

3
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.

Give your answer as an exact value in terms of straight pi.  

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

How did you do?

4a
Sme Calculator2 marks
cie-igcse-2018-march-p4-q2

The vertices of a square ABCD lie on the circumference of a circle, radius 8 cm.   Calculate the area of the square.  

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

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4b
Sme Calculator7 marks

i) Calculate the area of the shaded segment. Give your answer as a simplified expression in terms of straight pi.  

 ......................................... cm2 [3]

ii) Calculate the perimeter of the shaded segment. Give your answer as a simplified expression in terms of straight pi.  

 .......................................... cm [4]

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5
Sme Calculator6 marks
Diagram with sector and circle. Sector marked "A" has angles and lengths, 60 degrees, 3x+1 cm radius, 2x cm arc. Circle "B", diameter 2x+1 cm.

The diagram above shows two shaded shapes, Aand B.

Shape Ais formed by removing a sector with radius open parentheses 3 x plus 1 close parentheses space cm form a sector with radius open parentheses 5 x plus 1 close parentheses space cm.

Shape B is a circle with diameter open parentheses 2 x plus 1 close parentheses space cm.

The two shaded sections have equal areas.

Find the value of x.

How did you do?