IB Mathematics Applications & Interpretation Topic SL 2.2—functions, Domains, Range, Graphs Questionbank (SL/HL)

IB Mathematics Applications & Interpretation Topic SL 2.2—functions, Domains, Range, Graphs Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Applications & Interpretation (AI) Topic SL 2.2—functions, Domains, Range, Graphs with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 2.2—functions, Domains, Range, Graphs and mirrors Paper 1, 2, 3 style where relevant.

Get instant solutions, detailed explanations, and build confidence with questions aligned to IB examiner expectations.

Paper

Level

Question 1

SLPaper 2

The time taken for a chemical reaction to complete, $t (T)$ (in seconds), depending on temperature $T$ (in degrees Celsius), is modeled by: $t (T) = \frac{1000}{T - 5} for T > 5$

Find the range of the function $t (T)$ , giving your answer with units.

[2]

Describe the behaviour of $t (T)$ as $T \to \infty$ , giving your answer with units.

[2]

Question 2

SLPaper 1

An engineer models the cross-section of a reflector by $r (x) = \frac{3}{2} (x - 6)^{2} + 7$ , where $x$ and $r (x)$ are measured in centimetres.

Calculate the derivative $r^{'} (x)$ .

[2]

Find the slope of the tangent line at $x = 8$ .

[2]

Find the equation of the normal line to the function at $x = 8$ .

[2]

Determine the value of $x$ for which the slope of the tangent is $0$ .

[2]

State the domain and range of the function $r (x)$ .

[2]

Question 3

SLPaper 1

Consider the function $y = ln (x^{2} - 2 x - 3)$ .

Draw a sketch, clearly indicating its domain, the equations of any asymptotes and any points where the graph intersects the coordinate axes.

[4]

Utilizing your graph or an analytical method, find the solution to the inequality $∣ y ∣ \leq ln 3$ .

[5]

Question 4

HLPaper 1

The function $f$ is defined by $f (x) = 2 x^{3} + 5$ , $- 2 \leq x \leq 2$ .

Write down the range of $f$ .

[2]

Find an expression for $f^{- 1} (x)$ .

[2]

Write down the domain and range of $f^{- 1}$ .

[2]

Question 5

HLPaper 1

Let $f (x) = x^{2} + 2 x + 1$ and $g (x) = x - 5$ , for $x \in R$ .

Expand and simplify $f (x) - 5$ .

[2]

Find $f (8)$ .

[2]

Solve $x^{2} + 2 x - 4 = 0$ .

[3]

IB Mathematics Applications & Interpretation SL 2.2—functions, Domains, Range, Graphs Questionbank

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IB Mathematics Applications & Interpretation SL 2.2—functions, Domains, Range, Graphs Questionbank

IB Mathematics Applications & Interpretation (AI) Topic SL 2.2—functions, Domains, Range, Graphs Questionbank

Unlock all 23 questions with a free account