IB Maths AA SL Topic 3: Geometry and trigonometry questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

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Question 1

Paper 1, no calculatorMedium6 marks

A square-based right pyramid models a roof structure. The side length of its horizontal base is $4\text{ m}$ The apex $S$ is vertically above the centre $O$ of the base, and $SO=2\sqrt{2}\text{ m}$ Let $A$ be a vertex of the base.

(a)

Determine the distance $OA$

[2]

(b)

Hence determine the distance $SA$

[2]

(c)

Determine the angle between $SA$ and the plane of the base. Give your answer in degrees.

[2]

Question 2

Paper 1, no calculatorMedium6 marks

Figure 1 shows a point $P$ on the unit circle. The angle $\theta$ is measured anticlockwise from the positive $x$ -axis to $OP$ and $\theta$ lies in quadrant II.

(a)

Determine $\cos\theta$ and $\tan\theta$

[3]

(b)

Hence, determine the exact values of $\sin 2\theta$ and $\cos 2\theta$

[3]

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