IB Mathematics AA SL 2.1 Functions Question Bank

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

Exam points

SL syllabus concepts and methods

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

[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 2.1 Functions - SL content 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 ]

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

[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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Covered syllabus points

2.1 Functions - SL content question 1

Question (a)

Question (b)

2.1 Functions - SL content question 2

Question (a)

Question (b)

2.1 Functions - SL content question 3

Question (a)

Question (b)