Practice IB Mathematics Applications & Interpretation (AI) Topic SL 3.2—2d and 3d Trig with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 3.2—2d and 3d Trig and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

SLPaper 1

In the figure, $W X Y Z$ is a quadrilateral.

$W X = 10 cm, W Z = 14 cm, X \hat{W} Z = 7 5^{\circ}, Y \hat{X} Z = 5 4^{\circ}, and X \hat{Y} Z = 7 1^{\circ}$

Calculate the length of the diagonal $X Z$ .

[3]

Calculate the length of side $Y Z$ .

[3]

Question 2

SLPaper 1

A glass ornament is a tetrahedron with vertices $A (0, 0, 0)$ , $B (8, 0, 0)$ , $C (0, 6, 0)$ and $D (0, 0, 9)$ , where coordinates are in cm. $M$ is the midpoint of $B C$ .

Calculate the volume of the tetrahedron.

[3]

Determine the angle between $D M$ and plane $A B C$ .

[3]

Question 3

SLPaper 1

Consider the triangle

P QR

represented in the diagram below.

Side lengths are given by

P R = 18 cm

and

QR = 12 cm

, where

P \hat{Q} R = θ

. Additionally, it is known that

sin (Q \hat{P} R) = \frac{1}{2}

Calculate $sin θ$ , given that $θ$ is an acute angle.

[3]

Determine the value of $cos (2 Q \hat{P} R)$ .

[3]

Question 4

SLPaper 1

One triangular face $△ U V W$ of a glass pyramid has side lengths $V W = 14$ m, $U W = 15$ m, and angle $V = 4 9^{\circ}$ opposite side $U W$ . The face is acute-angled.