IB Maths AA HL 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.

Question 1

Paper 1, no calculatorMedium6 marks

A survey team uses two points, AA and BB on level ground to locate the base PP of a vertical signal mast. Bearings are measured clockwise from north. Figure 1 is not to scale.

Plan view(not to scale)ABP300 mBearing of P from A: 060°Bearing of P from B: 300°Elevation view(not to scale)30°APT
(a)

Use the plan view in Figure 1 to determine APAP Give your answer in exact form.

[4]
(b)

Hence, or otherwise, determine the height PTPT of the mast. Give your answer in exact form.

[2]

Question 2

Paper 1, no calculatorMedium6 marks

In triangle ABCABC the sides aa bb and cc are opposite the angles AA BB and CC respectively. Angles are measured in radians.

It is given that A=π6A=\frac{\pi}{6} a=6a=6 and b=63b=6\sqrt{3}

(a)

Determine all possible values of BB

[2]
(b)

Hence determine the corresponding values of CC

[2]
(c)

For the obtuse value of BB determine the exact value of tan⁡B\tan B

[2]

Question 3

Paper 1, no calculatorHard6 marks

A circuit model represents the normalized voltage at phase ϕ\phi by v(ϕ)=sin⁡ϕv(\phi)=\sin\phi A controller operates at phase θ\theta where 0<θ<π20<\theta<\frac{\pi}{2} During calibration, the normalized voltage at phase 2θ2\theta is 12\frac12

(a)

Starting from the compound-angle identities, derive the double-angle identities for sin⁡2x\sin 2x cos⁡2x\cos 2x and tan⁡2x\tan 2x

[3]
(b)

Determine all possible exact values of tan⁡θ\tan\theta

[3]

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