IGCSE · Additional Mathematics 0606 · Geometry & trigonometry

Circular measure: IGCSE Additional Mathematics questions with answers

Free Circular measure questions for IGCSE Additional Mathematics (0606), part of Geometry & trigonometry. Each question has the answer and the marking points an examiner would look for.

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Circular measure practice questions

Question 1Structured · 4 marksA* challenge

The diagram shows a sector of radius 9 cm and angle π3 radians.

Find the exact perimeter and the exact area of the sector.

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
18 + 3π cm; 13.5π cm²
arc = rθ M1
18 + 3π A1
½r2θ M1
13.5π A1
4
Question 2Structured · 4 marks
(a)

A sector has radius 4 cm and angle π6 radians. Find the arc length, in terms of π.

[2]
(b)

Find the area of the sector, in terms of π.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)23π cm
s = rθ M1
23π A1
2
(b)43π cm²
A = ½r2θ M1
43π A1
2
Question 3Structured · 5 marks

A sector OAB of a circle has radius 5 cm and angle AOB = 2 radians.

(a)

Find the perimeter of the sector.

[2]
(b)

Find the area of the segment cut off by the chord AB.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)20 cm
rθ M1
20 A1
2
(b)13.6 cm²
½r2θ M1
½r2 sin θ M1
13.6 A1
3
Question 4Structured · 4 marksA* challenge

The diagram shows a sector of radius 6 cm and angle π3 radians.

Find the exact perimeter and the exact area of the sector.

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
12 + 2π cm; 6π cm²
arc = rθ M1
12 + 2π A1
½r2θ M1
6π A1
4
Question 5Structured · 4 marks
(a)

A sector has radius 8 cm and angle π6 radians. Find the arc length, in terms of π.

[2]
(b)

Find the area of the sector, in terms of π.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)43π cm
s = rθ M1
43π A1
2
(b)163π cm²
A = ½r2θ M1
163π A1
2
Question 6Structured · 5 marks

A sector OAB of a circle has radius 6 cm and angle AOB = 0.8 radians.

(a)

Find the perimeter of the sector.

[2]
(b)

Find the area of the segment cut off by the chord AB.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)16.8 cm
rθ M1
16.8 A1
2
(b)1.49 cm²
½r2θ M1
½r2 sin θ M1
1.49 A1
3

More Geometry & trigonometry questions

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Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in