IB Maths AA SL 2 Functions Questions

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

Exam points

Construct and interpret function graphs using intercepts, extrema, asymptotes, intersections, ranges and other labelled key features.
Evaluate, compose and invert functions while checking domain, range, one-to-one restrictions and the symmetry of a function and its inverse.
Solve equations and inequalities analytically or graphically, including parameter, branch and real-context restrictions.
Apply ordered translations, reflections and horizontal or vertical stretches to derive, sketch or evaluate a transformed graph.

Covered syllabus points

2.1 Functions - SL content

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Study 2 Functions conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[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.

(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 ]

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

[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

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