IB Mathematics Analysis and Approaches Topic SL 2.10—solving Equations Graphically and Analytically Questionbank (SL/HL)

IB Mathematics Analysis and Approaches Topic SL 2.10—solving Equations Graphically and Analytically Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Analysis and Approaches (AA) Topic SL 2.10—solving Equations Graphically and Analytically with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 2.10—solving Equations Graphically and Analytically 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 $f (x) = 3 sin (\frac{π}{5} (x - 2)) + k, 0 \leq x \leq 10, k \in R$ , and $g (x) = p cos (\frac{π}{8} (x + 1)) + q, 0 \leq x \leq 10, p, q \in R$ . The function $f$ has a local maximum at $(4.5, 8)$ and a local minimum at $(9.5, 2)$ . The function $g$ passes through the points $(1, 4)$ and $(5, 2)$ .

Find the period of $f$ .

[2]

Find the value of $k$ .

[2]

Find the values of $p$ and $q$ .

[4]

Find the values of $x$ where $f (x) = g (x)$ in the interval $0 \leq x \leq 10$ .

[3]

Question 4

SLPaper 2

A particle moves along a straight line with velocity given by $v (t) = 2 t cos (\frac{π}{4} t), 0 \leq t \leq 8$ , where $t$ is measured in seconds and $v$ in meters per second.

Find the times when the particle is stationary.

[2]

Find the acceleration of the particle at $t = 4$ .

[3]

Find the time when the particle's speed is maximized in the interval $0 \leq t \leq 8$ .

[3]

Question 5

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]

IB Mathematics Analysis and Approaches SL 2.10—solving Equations Graphically and Analytically Questionbank

Unlock all 36 questions with a free account

IB Mathematics Analysis and Approaches SL 2.10—solving Equations Graphically and Analytically Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 2.10—solving Equations Graphically and Analytically Questionbank

Unlock all 36 questions with a free account