IB Mathematics Applications & Interpretation Topic AHL 3.7—radians Questionbank (HL)

IB Mathematics Applications & Interpretation Topic AHL 3.7—radians Questionbank (HL) | RevisionDojo

Practice IB Mathematics Applications & Interpretation (AI) Topic AHL 3.7—radians with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 3.7—radians 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

A fan-shaped garden forms a sector of a circle of radius 8 m and angle $21 0^{\circ}$ .

Express the angle in radians.

[2]

Find the area of the sector.

[4]

Determine the length of the arc forming the curved edge.

[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 an angle of $24 0^{\circ}$ .

[4]

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

[3]

Question 4

HLPaper 1

A sector-shaped park has radius $x$ m, where $x > 0$ , and subtends an angle of $2$ radians at its centre in its design. Let $A$ m $^{2}$ denote the area of this sector and $P$ m denote its total perimeter.

Determine the value of $x$ if $A = P$ .

[3]

Question 5

HLPaper 2

A computer-controlled laser engraver is calibrated to perform a sequence of coordinate transformations on a design positioned in the $x$ - $y$ plane relative to the origin $O$ . The following three operations are applied to every point on the design:

an anticlockwise rotation about $O$ through $\frac{2 π}{3}$ radians
a mirror reflection across the line $y = - x$
a clockwise rotation about $O$ through $\frac{π}{6}$ radians. The computer executes the transformations in the order they are listed.

Determine the matrix for an anticlockwise rotation about $O$ through $\frac{2 π}{3}$ radians.

[1]

Determine the matrix for a mirror reflection across the line $y = - x$ .

[1]

Determine the matrix for a clockwise rotation about $O$ through $\frac{π}{6}$ radians.

[1]

Determine the composite matrix $T$ that represents the resulting mapping by finding the product of these three matrices in the appropriate order.

[2]

Calculate $T^{2}$ .

[2]

Hence state what the value of $T^{2}$ indicates about the final position of the design if the complete sequence of operations is performed twice.

[1]

Consider three points $U, V$ , and $W$ on the original design. After the laser engraver applies the transformations, these points move to $U^{'}, V^{'}$ , and $W^{'}$ respectively.

Show that the area of triangle $U V W$ is equal to the area of triangle $U^{'} V^{'} W^{'}$ .

[3]

Describe the specific geometric transformation that corresponds to matrix $T$ .

[1]

IB Mathematics Applications & Interpretation AHL 3.7—radians Questionbank

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IB Mathematics Applications & Interpretation AHL 3.7—radians Questionbank

IB Mathematics Applications & Interpretation (AI) Topic AHL 3.7—radians Questionbank

Unlock all 21 questions with a free account