IB Mathematics Applications & Interpretation Topic SL 3.4—the Circle, Arc and Area of Sector, Degrees Only Questionbank (SL/HL)

IB Mathematics Applications & Interpretation Topic SL 3.4—the Circle, Arc and Area of Sector, Degrees Only Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Applications & Interpretation (AI) Topic SL 3.4—the Circle, Arc and Area of Sector, Degrees Only with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 3.4—the Circle, Arc and Area of Sector, Degrees Only and mirrors Paper 1, 2, 3 style where relevant.

Get instant solutions, detailed explanations, and build confidence with questions aligned to IB examiner expectations.

Paper

Level

Question 1

SLPaper 1

Consider the figure provided.

In the coordinate plane,

D (- 4, 0)

E (4, 0)

and

F (0, 8)

N

is the midpoint of

[D E]

. A circular arc

D E

is drawn with

O

, the midpoint of

[F N]

, as its centre.

Calculate the length of $D O$ .

[3]

Determine the area of the shaded segment.

[3]

Question 2

HLPaper 2

A circular mirror of radius

8 cm

is centred at

O

. The vertices

A

B

and

C

of an equilateral triangular frame lie on the mirror, so the three regions between the frame and the mirror are shaded.

Let

M

represent the mass of silver coating, in grams, applied to the mirror after

t

minutes. The application rate is given by

\frac{d M}{d t} = 0.8 t e^{- t /4}

Determine the magnitude of angle $A \hat{O} B$ .

[3]

Calculate the area of one shaded segment.

[5]

Calculate the length of minor arc $A B$ .

[2]

Calculate the total area of the shaded regions.

[3]

Find the time $t$ when the rate of coating is at its maximum.

[2]

Question 3

HLPaper 1

A circle has a radius of 5 cm.

Express an angle of $24 0^{\circ}$ in radians.

[2]

Find the area of the sector subtended by the angle $24 0^{\circ}$ .

[4]

Determine the length of the arc subtended by the angle $24 0^{\circ}$ .

[3]

Question 4

SL & HLPaper 1

A clock has a circular face of radius

15

cm. The minute hand of the clock has length

11

cm and is attached at the centre of the clock face.

Calculate the area swept by the minute hand in $10$ minutes.

[3]

Calculate the length of the arc traced by the tip of the minute hand in $10$ minutes.

[3]

Question 5

HLPaper 2

A sprinkler is fixed at the centre

O

of a square lawn of side length

12 m

. It sprays water in all directions to a distance of

43 m

. The spray circle meets one side of the lawn at

A

and

B

, forming the shaded segment shown.

Let

W

represent the volume of water, in

m^{3}

, delivered by the sprinkler after

t

hours. The delivery rate is given by

\frac{d W}{d t} = 0.6 t e^{- 2 t}

Determine the magnitude of angle $A \hat{O} B$ .

[3]

Calculate the area of the shaded segment.

[5]

Calculate the total surface area of a circle with a $43 m$ radius.

[2]

Calculate the area of the lawn watered by the sprinkler.

[3]

Find the time $t$ when the rate of water delivery is at its maximum.

[2]

IB Mathematics Applications & Interpretation SL 3.4—the Circle, Arc and Area of Sector, Degrees Only Questionbank

Unlock all 21 questions with a free account

IB Mathematics Applications & Interpretation SL 3.4—the Circle, Arc and Area of Sector, Degrees Only Questionbank

IB Mathematics Applications & Interpretation (AI) Topic SL 3.4—the Circle, Arc and Area of Sector, Degrees Only Questionbank

Unlock all 21 questions with a free account