IB Mathematics Analysis and Approaches Topic SL…

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

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

Write $f(x)$ in vertex form $f (x$ . Hence the vertex and the range of for . Give to 3 d.p.

Let $f(x)=e^{kx},\quad g(x)=\ln(x+2),\quad x>-2,\ k>0.$ It is given that .

Let $f(x)=3 \sin \left(\frac{\pi}{5}(x-2)\right)+k, 0 \leq x \leq 10, k \in \mathbb{R}$ , and . The function has a local maximum at and a local minimum at . The function passes through the points and .

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

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

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

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

$k$ correct to 3 significant figures.

Find the composites and their maximal domains.

Solve $(x+2)^k=\ln(2+e^{kx})$ for $x\ge0$ (3 d.p.) and uniqueness.

Find $(f\circ g)^{-1}(y)$ with domain and range.

Find the period of $f$ .

Find the value of $k$ .

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

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

Find the times when the particle is stationary.

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

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

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

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

Solve $q(x)=g(x)$ for $x\ge0$ , giving solutions correct to $3$ d.p., and the number of solutions.

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

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

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

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