# Exam-Style Questions.

## Problems adapted from questions set for previous Mathematics exams.

### 1.

IB Standard

Find the value of $$a$$ if $$\pi \lt a \lt 2\pi$$ and:

$$\int_\pi^a sin3x dx = -\frac13$$

### 2.

IB Standard

This graph represents the function $$f:x\to a \cos x, a\in \mathbf N$$

(a) Find the value of $$a$$.

(b) Find the area of the shaded region.

### 3.

IB Standard

Find $$f(x)$$ if $$f'(x)=6 \sin2x$$ and the graph of $$f(x)$$ passes through the point $$(\frac{\pi}{3},11)$$.

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