IB Maths AA SL AA 3.2 Radians and circular functions 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 calculatorPaper 2, calculator
Difficulty
EasyMediumHard

Question 1

Paper 2, calculatorMedium6 marks

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

(a)

Show that sin⁡B=0.75\sin B=0.75

[2]
(b)

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

[4]

Question 2

Paper 1, no calculatorHard6 marks

A Ferris-wheel passenger’s height above the ground, hh metres, tt minutes after the ride begins is modelled by

h(t)=asin⁡(b(t+c))+d,h(t)=a\sin\bigl(b(t+c)\bigr)+d,

where a,b>0a,b>0 and 0≤c<2πb0\leq c<\frac{2\pi}{b}

The passenger’s lowest and highest heights are 33 m and 1515 m respectively. The wheel reaches its highest point at t=2t=2 its lowest point at t=8t=8 and its next highest point at t=14t=14

(a)

Write down the amplitude of hh

[1]
(b)

Use the model and observations above.

(i)

Show that

h(t)=6sin⁡(π6(t+1))+9.h(t)=6\sin\left(\frac{\pi}{6}(t+1)\right)+9.
[3]
(ii)

Hence determine all values of tt where 0≤t≤280\leq t\leq 28 for which the passenger’s height is 1212 m.

[2]

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