IB Mathematics Analysis and Approaches Topic Functions Questionbank (SL/HL)

IB Mathematics Analysis and Approaches Topic Functions Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Analysis and Approaches (AA) Topic Functions with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for Functions 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

HLPaper 2

Consider the function $f (x) = ln (2 x - 1) - sin (x)$ , where $x > \frac{1}{2}$ .

Sketch the graph of $y = f (x)$ for $0.5 < x \leq 4$ , showing the intercepts and the behavior at $x = \frac{1}{2}$ .

[3]

Solve the inequality $ln (2 x - 1) < sin (x)$ .

[4]

Question 2

SLPaper 1

A line through $A (- 4, 3)$ with gradient $m$ intersects $C:\ y=x^2+8x$ at points $P$ and $Q$ . The distance $P Q = 11$ .

Show the $x$ -coordinates satisfy $x^2+(8-m)x+(-4m-3)=0.$

[4]

Determine the condition on $m$ for two distinct intersections.

[2]

Show $(x_{P} - x_{Q})^{2} = m^{2} + 76$ .

[3]

Solve for $m$ using $P Q = 11$ .

[4]

Question 3

SLPaper 1

The graph of

y = f (x)

is shown below. The points

(- 1, 0)

and

(3, 0)

lie on the graph, with a minimum at

(1, - 2)

Sketch the graph of

y = \frac{1}{2} f (x)

on the diagram below.

[3]

The point $B (- 1, 0)$ is on the graph of $f$ . Find the coordinates of the corresponding point on the graph of $y = f (x + 3)$ .

[2]

Question 4

HLPaper 2

Consider the rational function $f (x) = \frac{6 x ^{2} - 5 x - 4}{2 x ^{2} - 8}$ , where $x \in R, x \neq = \pm 2$ . The graph of $y = f (x)$ has a local minimum at point P and a local maximum at point Q.

Express $f (x)$ in the form $\frac{a ( x - b ) ( x - c )}{( x - d ) ( x - e )}$ , where $a, b, c, d, e \in R$ .

[3]

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

[2]

Find the coordinates of the points where the graph of $y = f (x)$ intersects the $x$ -axis and $y$ -axis.

[2]

Using a graphical calculator, find the coordinates of the local minimum at P and the local maximum at Q, and hence state the range of $f (x)$ .

[3]

Solve the inequality $\frac{6∣ x ∣ ^{2} - 5∣ x ∣ - 4}{2∣ x ∣ ^{2} - 8} \geq \frac{3}{2}$ , for $x \in R, x \neq = \pm 2$ .

[4]

Question 5

SLPaper 1

The points $A (3, 2), B (7, 2)$ , and $C (3, 8)$ are shown in the diagram below.

Find the equation of the perpendicular bisector of the line segment $[A B]$ .

[2]

Find the equation of the perpendicular bisector of the line segment $[A C]$ .

[2]

Write down the coordinates of the point of intersection $P$ of the two bisectors, and show that $P$ is the midpoint of the line segment $[B C]$ .

[3]

Find the equation of the perpendicular bisector $L$ of the line segment $[B C]$ , in the form $a x + b y + d = 0$ , where $a, b, d \in Z$ .

[3]

Show that the line $L$ does not pass through point $A$ .

[2]

IB Mathematics Analysis and Approaches Functions Questionbank

Unlock all 189 questions with a free account

IB Mathematics Analysis and Approaches Functions Questionbank

IB Mathematics Analysis and Approaches (AA) Topic Functions Questionbank

Unlock all 189 questions with a free account