IB Mathematics Analysis and Approaches Topic SL 2.3—graphing Questionbank (SL/HL)

IB Mathematics Analysis and Approaches Topic SL 2.3—graphing Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Analysis and Approaches (AA) Topic SL 2.3—graphing with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 2.3—graphing 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

A quadratic model $f (x) = a x^{2} + b x + c$ is fitted to three measured points $P (1, ln 5)$ , $Q (4, 1.5 + ln 10)$ , $R (7, 1 + ln 4)$ .

Determine $a, b, c$ (numerically). Give your values correct to 3 significant figures.

[5]

Write $f (x)$ in vertex form $f (x) = a (x - h)^{2} + k$ . Hence state the vertex and the range of $f$ for $x \in R$ . Give $h, k$ to 3 d.p.

[4]

Let $g (x) = ln (x + 2) + 1$ . Solve $f (x) = g (x)$ for $x \geq 0$ , giving $x$ correct to 3 d.p., and justify the number of solutions.

[6]

Solve $f (x) \geq g (x)$ for $x \geq 0$ .

[3]

Question 2

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 3

SLPaper 2

Let $p \in R$ and $q_{p} (x) = x^{2} - (p + 8) x + (2 p + 8)$ .

Find all real values of $p$ for which $q_{p}$ has two distinct real roots and both roots are greater than $1$ .

[6]

Let $p = 3$ (not necessarily satisfying the condition in the previous part) so that $q (x) = x^{2} - 11 x + 14$ , and $g (x) = ln (x + 2) + 1$ . Find the exact roots of $q (x) = 0$ .

[3]

Solve $q (x) = g (x)$ for $x \geq 0$ , giving solutions correct to $3$ d.p., and justify the number of solutions.

[6]

Question 4

HLPaper 2

Consider the function $f (x) = sin (x) + \frac{x}{2}$ , for $0 < x < 2 π$ .

Find the coordinates of the local maximum of the graph of $y = f (x)$ , giving the coordinates to three decimal places.

[4]

Sketch the graph of $y = f (x)$ for $0 < x < 2 π$ , indicating the local maximum, any axis intercepts, and the behavior as $x \to 0^{+}$ and $x \to 2 π^{-}$ .

[4]

Hence, or otherwise, solve the inequality $f (x) > 1$ for $0 < x < 2 π$ .

[3]

Question 5

SLPaper 2

Consider the function $f (x) = cos (x) + \frac{3}{2} x$ , for $0 < x < 2 π$ .

Find the coordinates of the local maximum of the graph of $y = f (x)$ , giving the coordinates to three decimal places.

[4]

Sketch the graph of $y = f (x)$ for $0 < x < 2 π$ , indicating the local maximum, any axis intercepts, and the behavior as $x \to 0^{+}$ and $x \to 2 π^{-}$ .

[4]

Hence, or otherwise, solve the inequality $f (x) > 1.2$ for $0 < x < 2 π$ .

[3]

IB Mathematics Analysis and Approaches SL 2.3—graphing Questionbank

Unlock all 29 questions with a free account

IB Mathematics Analysis and Approaches SL 2.3—graphing Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 2.3—graphing Questionbank

Unlock all 29 questions with a free account