IB Maths AA SL 2.1 Functions Sl Content Questions

Practise IB Mathematics AA SL 2.1 by analysing function notation, domains, transformations, inverses, composite functions and graph behaviour.

Exam points

Construct and interpret function graphs by labelling intercepts, extrema, asymptotes, intersections and other stated key features.
Evaluate functions, compositions and inverses, checking domain, range, one-to-one restrictions and the symmetry of f and fâ»Â¹.
Solve quadratic, rational, exponential or logarithmic equations and inequalities, using algebraic or graphical methods and rejecting invalid branches.
Apply translations, reflections and horizontal or vertical stretches in the correct order, then derive or sketch the transformed graph.

Covered syllabus points

SL 2.1—Straight lines SL 2.2—Functions and inverses SL 2.3—Graphing functions SL 2.4—Key graph features SL 2.5—Composite and inverse functions SL 2.6—Quadratic functions SL 2.7—Quadratic equations and inequalities SL 2.8—Reciprocal and rational functions SL 2.9—Exponential and logarithmic functions SL 2.10—Solving equations SL 2.11—Graph transformations

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Study 2.1 Functions - SL content 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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