IB Mathematics Analysis and Approaches Topic SL 2.9—exponential and Logarithmic Functions Questionbank (SL/HL)

IB Mathematics Analysis and Approaches Topic SL 2.9—exponential and Logarithmic Functions Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Analysis and Approaches (AA) Topic SL 2.9—exponential and Logarithmic Functions with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 2.9—exponential and Logarithmic Functions and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

SLPaper 2

Let $f(x)=e^{kx},\quad g(x)=\ln(x+2),\quad x>-2,\ k>0.$ It is given that $(f \circ g) (3) = 4$ .

Determine $k$ correct to 3 significant figures.

[3]

Find the composites and their maximal domains.

[4]

Solve $(x + 2)^{k} = ln (2 + e^{k x})$ for $x \geq 0$ (3 d.p.) and justify uniqueness.

[7]

Find $(f \circ g)^{- 1} (y)$ with domain and range.

[4]

Question 2

SLPaper 1

The function $f$ is defined by $f (x) = ln (4 x)$ , where $x > 0$ .

Calculate the exact value of $f (\frac{e ^{4}}{4})$ .

[2]

Calculate the exact value of $f (\frac{1}{4})$ .

[1]

Determine an expression for the inverse function $f^{- 1} (x)$ .

[4]

Using your result from part 3, or otherwise, calculate the value of $f^{- 1} (- 2)$ .

[1]

The graph of $y = f (\frac{e ^{3}}{4} x^{5})$ can be generated through a sequence of a vertical stretch and a vertical translation of the graph of $y = ln x$ . Describe these two transformations, clearly stating the order in which they should be performed.

[6]

Question 3

SLPaper 2

Consider the function $f (x) = 7 - 3 e^{- 0.4 x}$ .

Write down the domain of $f$ .

[1]

Find the y-intercept of the graph of $f$ .

[2]

Find $f (4)$ , correct to three significant figures.

[2]

Find the smallest integer $x$ such that $f (x) > 6.8$ .

[2]

Sketch the graph of $f$ . Indicate the y-intercept and the horizontal asymptote.

[2]

Question 4

SLPaper 2

Consider the function $f (x) = 4 e^{0.2 x} - 2$ .

Write down the domain of $f$ .

[1]

Find the y-intercept of the graph of $f$ .

[2]

Find $f (3)$ , correct to three significant figures.

[2]

Find the smallest integer $x$ such that $f (x) > 10$ .

[2]

Sketch the graph of $f$ . Indicate the y-intercept and the horizontal asymptote.

[2]

Question 5

SLPaper 1

The function $g$ is defined by $g (x) = lo g_{3} (27 x)$ , where $x > 0$ . Calculate the exact value of:

$g (3)$ .

[2]

$g (\frac{1}{27})$ .

[1]

Determine an expression for the inverse function $g^{- 1} (x)$ .

[4]

Using your result from part 3, or otherwise, calculate the value of $g^{- 1} (0)$ .

[1]

The graph of $y = g (9 x^{3})$ can be generated through a sequence of a vertical stretch and a vertical translation of the graph of $y = lo g_{3} x$ . Describe these two transformations, clearly stating the order in which they should be performed.

[6]

IB Mathematics Analysis and Approaches SL 2.9—exponential and Logarithmic Functions Questionbank

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IB Mathematics Analysis and Approaches SL 2.9—exponential and Logarithmic Functions Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 2.9—exponential and Logarithmic Functions Questionbank

Unlock all 15 questions with a free account