IB Mathematics Analysis and Approaches Topic AHL 2.16—graphing Modulus Equations and Inequalities Questionbank (HL)

IB Mathematics Analysis and Approaches Topic AHL 2.16—graphing Modulus Equations and Inequalities Questionbank (HL) | RevisionDojo

Practice IB Mathematics Analysis and Approaches (AA) Topic AHL 2.16—graphing Modulus Equations and Inequalities with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 2.16—graphing Modulus Equations and Inequalities and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

HLPaper 2

Let $f (x) = \frac{2 x + 1}{x - 3}, x \in R </span> {3}, and g (x) = arctan (∣ x - 1∣), x \in R . The inverse of f restricted to x > 3 is f^{- 1} .$

Find the equations of the vertical and horizontal asymptotes of $y = f (x)$ .

[2]

On the axes below, sketch the graph of $y = f (x)$ for $- 2 \leq x \leq 6$ . Label the asymptotes, intercepts, and any local minima or maxima. ![](A set of coordinate axes suitable for sketching $y = \frac{2 x + 1}{x - 3}$ on $- 2 \leq x \leq 6$ , with $y$ -values shown up to at least $5$ , and with the vertical line $x = 3$ visible.)

[4]

Show that $f^{- 1} (x) = \frac{3 x + 1}{x - 2}$ for $x > 2$ .

[4]

Solve the inequality $f (x) \leq 1$ . Give your answer in interval notation.

[3]

Question 2

HLPaper 2

The function $f$ is defined by $f (x) = x^{2} - 4 x$ for $x \in R$ .

Find the $x$ -intercepts and the coordinates of the vertex of $y = f (x)$ .

[3]

On the same set of axes, sketch the graphs of $y = f (x)$ and $y = [f (x)]^{2}$ , indicating clearly the $x$ -intercepts and the $y$ -coordinate of the local maximum of $y = [f (x)]^{2}$ .

[4]

State the coordinates of the local minima of $y = [f (x)]^{2}$ and explain why these points coincide with the $x$ -intercepts of $f$ .

[3]

Solve the equation $[f (x)]^{2} = 4 f (x)$ algebraically.

[3]

On a separate set of axes, sketch the graph of $y = f (∣ x ∣)$ , indicating all $x$ -intercepts, the $y$ -intercept and any turning points.

[3]

Question 3

HLPaper 1

The figure displays the graph of $y = f (x)$ , with $f (x) = x + 3$ . It cuts the $x$ -axis at $x = - 3$ and the $y$ -axis at $y = 3$ .

On the same coordinate axes, sketch the graph of $y = ∣ f (x) ∣$ , labelling the coordinates of any intercepts and vertices.

[3]

Solve the inequality $∣ f (x) ∣ \leq 3$ , giving your answer in interval notation.

[2]

Question 4

HLPaper 1

Solve the inequality $∣2 x - 1∣ > x + 3$ for $x \in R$ .

[7]

Question 5

HLPaper 1

The function $f$ is defined by $f (x) = x^{3} - 3 x$ for $x \in R$ .

Find the $x$ -intercepts and the coordinates of the stationary points of $y = f (x)$ .

[3]

Sketch the graph of $y = ∣ f (x) ∣$ , clearly showing the $x$ -intercepts and the coordinates of all turning points.

[4]

IB Mathematics Analysis and Approaches AHL 2.16—graphing Modulus Equations and Inequalities Questionbank

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IB Mathematics Analysis and Approaches AHL 2.16—graphing Modulus Equations and Inequalities Questionbank

IB Mathematics Analysis and Approaches (AA) Topic AHL 2.16—graphing Modulus Equations and Inequalities Questionbank

Unlock all 18 questions with a free account