IB Maths AA SL 2.1 Functions SL content Question Bank

Practise forming and transforming functions, reading key graph features, composing or inverting mappings, solving quadratics and applying exponential or logarithmic models.

Exam points

form straight-line equations from coordinates or gradients and describe translations, stretches or reflections
sketch functions with intercepts, extrema and asymptotes, then use intersections to solve equations or inequalities
compose functions in the correct order and find inverses with valid domain and range restrictions
complete the square or use the discriminant to solve quadratics and classify roots or parameter ranges
solve exponential or logarithmic equations and use fitted functions to predict values in context

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)