IB · Mathematics: Analysis & Approaches SL & HL · Geometry & trigonometry

Radians, arcs & sectors: IB Mathematics: Analysis & Approaches questions with answers

Free Radians, arcs & sectors questions for IB Mathematics: Analysis & Approaches (SL & HL), part of Geometry & trigonometry. Each question has the answer and the marking points an examiner would look for.

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Radians, arcs & sectors practice questions

Question 1Structured · 8 marks

A circle has centre O and radius 6 cm. Points A and B lie on the circle and AÔB = π2.

(a)

Find the length of the minor arc AB.

[2]
(b)

Find the exact area of the minor segment bounded by the chord AB and the arc AB.

[4]
(c)

Find the exact perimeter of the minor segment.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)3π cm
l = rθ = 6 × π2 (M1)
3π cm A1
2
(b)9π − 18 cm2
sector area 12(6)2(π2) = 9π A1
triangle area 12(6)2sin π2 (M1)
sin π2 = 1 (A1)
9π − 18 A1
4
(c)3π + 6√2 cm
AB = 6√2 (A1)
3π + 6√2 A1
2
Question 2Structured · 5 marks

A sector of a circle has arc length 8.40 cm and area 16.8 cm2.

Find the radius of the circle and the angle of the sector in radians.

[5]
Show answers and mark scheme
PartAnswer and marking pointsMarks
r = 4.00 cm, θ = 2.10
rθ = 8.40 A1
12r2θ = 16.8 A1
attempt to eliminate θ: 12r(8.40) = 16.8 (M1)
r = 4.00 A1
θ = 2.10 A1
5
Question 3Structured · 5 marks

A sector has radius 10 cm and perimeter 40 cm.

(a)

Find the angle of the sector in radians.

[2]
(b)

Find the area of the segment formed by the chord joining the ends of the arc.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)2.00
2(10) + 10θ = 40 (M1)
2.00 A1
2
(b)54.5 cm2
sector area (M1)
minus triangle area (M1)
54.5 A1
3
Question 4Structured · 8 marks

A circle has centre O and radius 8 cm. Points A and B lie on the circle and AÔB = π2.

(a)

Find the length of the minor arc AB.

[2]
(b)

Find the exact area of the minor segment bounded by the chord AB and the arc AB.

[4]
(c)

Find the exact perimeter of the minor segment.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)4π cm
l = rθ = 8 × π2 (M1)
4π cm A1
2
(b)16π − 32 cm2
sector area 12(8)2(π2) = 16π A1
triangle area 12(8)2sin π2 (M1)
sin π2 = 1 (A1)
16π − 32 A1
4
(c)4π + 8√2 cm
AB = 8√2 (A1)
4π + 8√2 A1
2
Question 5Structured · 5 marks

A sector of a circle has arc length 9.60 cm and area 19.2 cm2.

Find the radius of the circle and the angle of the sector in radians.

[5]
Show answers and mark scheme
PartAnswer and marking pointsMarks
r = 4.00 cm, θ = 2.40
rθ = 9.60 A1
12r2θ = 19.2 A1
attempt to eliminate θ: 12r(9.60) = 19.2 (M1)
r = 4.00 A1
θ = 2.40 A1
5
Question 6Structured · 4 marks

A sector of a circle has radius 6 cm and angle π3.

(a)

Find the arc length, giving your answer in terms of π.

[2]
(b)

Find the area of the sector, giving your answer in terms of π.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)2π cm
rθ (M1)
2π A1
2
(b)6π cm2
½r2θ (M1)
6π A1
2

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Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in