IB Mathematics Analysis and Approaches Topic…

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

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

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

The graph of $y=f(x)$ is shown below. The points $(-1,0)$ and lie on the graph, with a minimum at .

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

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

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

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

the condition on $m$ for two distinct intersections.

Show $(x_P-x_Q)^2=m^2+76$ .

Solve for $m$ using $PQ=11$ .

the graph of $y=\frac{1}{2}f(x)$ on the diagram below.

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

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

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

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

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

Solve the inequality $\frac{6|x|^{2}-5|x|-4}{2|x|^{2}-8} \geq \frac{3}{2}$ , for .

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

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

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 $[B C]$ .

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

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

IB Mathematics Analysis and Approaches Functions Questionbank

IB Mathematics Analysis and Approaches Functions Questionbank

IB Mathematics Analysis and Approaches Functions Questionbank

IB Mathematics Analysis and Approaches Functions Questionbank

IB Mathematics Analysis and Approaches (AA) Topic Functions Questionbank