IB Maths AA SL 2 Functions

Practise IB Maths AA SL functions through graphs, transformations, equations, inverses and models, explaining structure and selecting exact methods.

[Maximum number: 3]

Consider the function $f(x)=\frac{2}{\pi} \sin (3 \pi x)+2$ , where $0 \leq x \leq 2$ . The following diagram shows the graph of f.

Figure for Question 2 Functions question 1 — IB Maths AA SL

(a)

Write down the gradient of the line $L_{1}$ .

The line $L_{1}$ is normal to the graph of f at point A(1,2).
The line $L_{2}$ is tangent to the graph of f at A .

[ 1 ]

$\quad\left(m_{L_{1}}=\right) 0.167\left(=\frac{1}{6}\right)$

(b)

Find the coordinates of B.

The shaded region is enclosed by the graph of f and the line $L_{1}$ between A and B .

[ 2 ]

equating $L_{1}$ and f

[Maximum number: 4]

Let $f(x)=\cos 2 x$ and $g(x)=2 x^{2}-1$ .

(a)

Find $f\left(\frac{\pi}{2}\right)$ .

[ 2 ]

$\quad f\left(\frac{\pi}{2}\right)=\cos \pi$

=-1

(b)

Find $(g \circ f)\left(\frac{\pi}{2}\right)$ .

[ 2 ]

$\quad(g \circ f)\left(\frac{\pi}{2}\right)=g(-1)\left(=2(-1)^{2}-1\right)$

=1

[Maximum number: 4]

The velocity of a particle in $\mathrm{ms}^{-1}$ is given by $v=\mathrm{e}^{\sin t}-1$ , for $0 \leq t \leq 5$ .

(a)

On the grid below, sketch the graph of v.

Figure for Question (a) — IB Maths AA SL

[ 3 ]

(b)

Write down the positive t-intercept.

[ 1 ]

$\quad t=\pi$ (exact), 3.14

All question bank results loaded

Covered syllabus points

2 Functions question 1

Question (a)

Question (b)

2 Functions question 2

Question (a)

Question (b)

2 Functions question 3

Question (a)

Question (b)