IB Maths AI HL 2.1 Functions Sl Content Questions

Practise IB Mathematics AI HL 2.1 by analysing advanced function models, transformations, inverse and regression evidence with technology.

Exam points

Represent functions with correct notation, domain, range and inverse relationships, evaluating and composing them in context.
Construct, sketch and transform function graphs, identifying intercepts, extrema, symmetry, asymptotes and intersections.
Select and use function models, interpret parameters and use technology to fit, solve or predict within a valid domain.
Use graph and model features to answer thresholds, optimisation and applied questions with appropriate units.
Check a function or model using substitution, graph behaviour, data fit, assumptions and contextual reasonableness.

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—Modelling with functions SL 2.6—Modelling process

[Maximum number: 3]

The Voronoi diagram below shows four supermarkets represented by points with coordinates A(0,0), B(6,0), C(0,6) and D(2,2). The vertices X, Y, Z are also shown. All distances are measured in kilometres.

The equation of (XY) is y=2-x and the equation of (YZ) is y=0.5x+3.5.
Find the coordinates of X.

identifying the correct equations to use:

y=2-x \text { and } y=2 x-7

evidence of solving their correct equations or finding points of intersection graphically

(3,-1)

Note: Accept an answer expressed as " x=3, y=-1 ".

[Maximum number: 2]

The function f is defined by $f(x)=4 \ln (2 x-3)$ , where $x>\frac{3}{2}$ .
The graph of y=f(x) is obtained from the graph of $y=\ln x$ by a sequence of three transformations.

The graph of y=g(x) is shown.
The graph passes through the points (-2,-2),(-1,0),(0,2),(1,3),(2,5) and (3,6).

Find $(f \circ g)(2)$ .

$\quad g(2)=5$ $f(5)=7.78 \quad(=7.78364 \ldots, 4 \ln 7)$

[Maximum number: 3]

A student investigating the relationship between chemical reactions and temperature finds the Arrhenius equation on the internet.

k=A \mathrm{e}^{-\frac{c}{T}}

This equation links a variable k with the temperature T, where A and c are positive constants and T>0.

Given that $\lim_{T\to\infty}k=A$ and $\lim_{T\to0}k=0$ , sketch the graph of k against T.

All question bank results loaded

Covered syllabus points

Question 1

Question 2

Question 3