IB Mathematics Analysis and Approaches Topic SL 3.4—circle, Radians, Arcs, Sectors Questionbank (SL/HL)

IB Mathematics Analysis and Approaches Topic SL 3.4—circle, Radians, Arcs, Sectors Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Analysis and Approaches (AA) Topic SL 3.4—circle, Radians, Arcs, Sectors with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 3.4—circle, Radians, Arcs, Sectors and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

SLPaper 2

The given diagram shows a circle with center O and radius

r

. The angle AOB is

θ

radians.

Find the value of $θ$ , in each of the following three cases :

Given that the area of the triangle OAB is equal to the shaded area.

[3]

Given that the ratio of the lengths of two arcs (minor AB to major AB ) is $1 : 5$ .

[3]

Given that the ratio of the shaded area to the non-shaded area is $1 : 5$

[5]

Question 2

SLPaper 1

The diagram shows a sector of a circle with centre $O$ and radius $r$ cm. The area of the sector is $16 π$ cm $^{2}$ and the length of the arc is $4 π$ cm.

Find the value of $r$ .

[3]

Find the angle of the sector in radians.

[3]

Question 3

SLPaper 1

Points $A$ and $B$ lie on a circle with centre $O$ and radius $r$ cm, where $∠ A O B = 0.75$ radians. This is shown on the following diagram.

The area of sector $O A B$ is $24$ cm $^{2}$ .

Determine the value of $r$ .

[3]

Hence, calculate the perimeter of sector $O A B$ .

[2]

Question 4

SLPaper 1

Points $A$ and $B$ lie on a circle with centre $O$ and radius $r$ cm, where $∠ A O B = 0.5$ radians. This is shown on the following diagram.

The area of sector $O A B$ is $16$ cm $^{2}$ .

Determine the value of $r$ .

[3]

Hence, calculate the perimeter of sector $O A B$ .

[2]

Question 5

SLPaper 2

A hot-air balloon $P$ is anchored by two ropes to points $A$ and $B$ on level ground. The distance $A B$ is 75 m. The balloon is vertically above $P_{0}$ , and $∠ A P_{0} B = 6 0^{\circ}$ in the horizontal triangle $A B P_{0}$ .

The angles of elevation of the balloon are $2 8^{\circ}$ from $A$ and $3 7^{\circ}$ from $B$ .

Draw a fully-labelled 3-D diagram showing $A, B, P_{0}, P$ and all the given angles.

[2]

Let $A P_{0} = x$ m and $B P_{0} = y$ m. Show that $x tan 2 8^{\circ} = y tan 3 7^{\circ}$ .

[2]

Using the cosine rule in triangle $A B P_{0}$ , write an equation relating $x$ and $y$ .

[2]

Find the height $h$ of the balloon, to the nearest metre.

[2]

Now suppose instead that $P_{0}$ moves horizontally on a circle of radius $75 m$ centered at $A$ . Find the central angle (radians) and the length of the arc (metres) when the bearing of $P_{0}$ from $A$ changes from $04 5^{\circ}$ to $11 5^{\circ}$ .

[3]

If $T_{A} = k ∣ A P ∣$ and $T_{B} = k ∣ B P ∣$ , find $\frac{T _{A}}{T _{B}}$ .

[3]

IB Mathematics Analysis and Approaches SL 3.4—circle, Radians, Arcs, Sectors Questionbank

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IB Mathematics Analysis and Approaches SL 3.4—circle, Radians, Arcs, Sectors Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 3.4—circle, Radians, Arcs, Sectors Questionbank

Unlock all 29 questions with a free account