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.

Paper

Paper 1, no calculator Paper 2, calculator

Difficulty

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Question 1

Paper 2, calculatorEasy5 marks

During map-making, a survey team records three landmarks, $P$ $A$ and $B$ The distances $PA$ and $PB$ are $8.0\text{ km}$ and $11.0\text{ km}$ respectively, and $\angle APB=60.0^\circ$

Give your answers to three significant figures.

(a)

Using the cosine rule, determine the distance $AB$

[3]

(b)

Calculate the area of triangle $PAB$

[2]

Question 2

Paper 2, calculatorMedium6 marks

In triangle $ABC$ angles $A,B,C$ are measured in degrees. Using the usual notation for sides opposite the corresponding angles, $A=30^\circ$ $a=6\text{ cm}$ and $b=9\text{ cm}$

(a)

Show that $\sin B=0.75$

[2]

(b)

Hence determine all possible values of $B$ and the corresponding values of $C$ correct to the nearest $0.1^\circ$ Explain why the sine rule permits two possibilities here.

[4]

Question 3

Paper 2, calculatorMedium6 marks

For $0\leq x<2\pi$ let $f(x)=2\sin^2x+3\cos x-1$

(a)

Solve $f(x)=0$ analytically. Give all solutions in the interval to 3 significant figures.

[4]

(b)

Hence, use a GDC to check graphically that these are the only solutions in the stated interval.

[2]

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