CAIE A-Level Mathematics AS 2.5.2 Trig Integration Questions

Practise applying statistical inference methods within the AS mathematics syllabus.

Exam points

use vector notation and operations
solve geometric problems with vectors
interpret vector relationships

[Maximum number: 2]

The expression $\mathrm{f}(\theta)$ is defined by $\mathrm{f}(\theta)=12 \sin \theta \cos \theta+16 \cos ^{2} \theta$ .

Find $\int f(\theta) d \theta$ .

Integrate trigonometry term from part (a) to obtain $k_{1} \sin (2 \theta$ -their 0.6435)
any non-zero constant $k_{1}$ .

Obtain $5 \sin (2 \theta-0.6435)+8 \theta$
condone absence of ... +c.

Alternative method for question 8(c)

Integrate to obtain at least form $k_{2} \cos 2 \theta+k_{3} \sin 2 \theta$
any non-zero constants $k_{2}, k_{3}$ .

Obtain $-3 \cos 2 \theta+4 \sin 2 \theta+8 \theta$
condone absence of ... +c.

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CAIE A-Level Mathematics AS 2.5.2 Trig Integration Questions question 1