IB Mathematics Analysis and Approaches Topic SL 5.2—increasing and Decreasing Functions Questionbank (SL/HL)

IB Mathematics Analysis and Approaches Topic SL 5.2—increasing and Decreasing Functions Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Analysis and Approaches (AA) Topic SL 5.2—increasing and Decreasing Functions with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 5.2—increasing and Decreasing Functions and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

SLPaper 1

Consider the function $f (x) = (x - 1)^{2} (3 - x) + 2$ .

Write down the $y$ -intercept of the graph.

[1]

Expand the expression for $f (x)$ .

[2]

Find $f^{'} (x)$ .

[3]

Find the $x$ -coordinates of the points on the graph where the tangent is horizontal.

[3]

Determine the interval where the graph of $y = f (x)$ is increasing.

[2]

Find the range of $f (x)$ for $x \in [0, 3]$ .

[3]

Question 2

SLPaper 1

Given $h^{'} (x) = e^{x} - 2$ , determine the intervals where the function $h (x)$ is increasing or decreasing.

[3]

Question 3

SLPaper 1

Consider the function $f (x) = x^{3} - 3 x^{2} - 9 x + 7$ .

Write down the $y$ -intercept of the graph.

[1]

Find $f^{'} (x)$ .

[2]

Find the $x$ -coordinates of the points where the tangent is horizontal.

[3]

Determine the interval where the graph of $y = f (x)$ is decreasing.

[2]

Find the coordinates of the local minimum point.

[3]

Find the set of values of $k$ for which the equation $f (x) = k$ has three distinct real roots.

[3]

Question 4

SLPaper 1

Consider the function $f (x) = 2 x^{3} - 9 x^{2} + 12 x - 3$ .

Write down the $y$ -intercept of the graph.

[1]

Find $f^{'} (x)$ .

[2]

Find the $x$ -coordinates of the points where the tangent to the graph is horizontal.

[3]

Determine the intervals where the graph of $y = f (x)$ is decreasing.

[2]

Find the value of $f (1)$ and state whether this point is a local maximum or minimum.

[3]

Question 5

SLPaper 1

Consider the function $f (x) = x^{3} - 6 x^{2} + 12 x - 4$ .

Write down the $y$ -intercept of the graph.

[1]

Find $f^{'} (x)$ .

[2]

Show that the point at $x = 2$ is a stationary point and determine its nature.

[3]

Determine the interval where the graph of $y = f (x)$ is increasing.

[2]

Find the range of $f (x)$ for $x \in [0, 4]$ .

[3]

Consider the function $g (x) = f (x) + k$ . Find the value of $k$ such that the stationary point of the graph of $y = g (x)$ lies on the $x$ -axis.

[3]

IB Mathematics Analysis and Approaches SL 5.2—increasing and Decreasing Functions Questionbank

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IB Mathematics Analysis and Approaches SL 5.2—increasing and Decreasing Functions Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 5.2—increasing and Decreasing Functions Questionbank

Unlock all 16 questions with a free account