AP Precalculus Hard practice

Solve $\ln (x+2)-\ln (x)=\ln (3)$ for $x>0$.

A polynomial $f(x)$ has degree $3$, real coefficients, and zeros at $x=-2$, $x=1$, and $x=4$. If $f(0)=16$, what is $f(x)$?

Simplify $\frac{\sin (2\theta )}{\sin (\theta )}$ for $\sin (\theta )\ne 0$.

A radioactive substance decays according to $A(t)=A_0\cdot (1/2{)}^{t/H}$ where $H$ is the half-life. If $A_0=80$ grams and $H=5$ days, how many grams remain after $15$ days?

Solve the system using matrix methods: $2x+y=5$ and $x-y=1$.

Let $f(x)=\frac{2x^2+3x+1}{x^2-1}$. Identify all asymptotes and any holes.

The parametric curve $x(t)=\cos (t)$, $y(t)=\sin (2t)$ has what behavior at $t=0$?

Which best describes the behavior of $f(x)=\frac{x^2-1}{x-1}$ at $x=1$?

An investment of \2000$growscontinuouslyatanannualrateof$6%$.Accordingto$A(t) = 2000 \cdot e^{0.06 t}$,approximatelyhowlonguntilitdoubles?(Use$\ln 2 \approx 0.693$.)

Find all $\theta \in [0,2\pi )$ that satisfy $2{\cos }^2(\theta )-\cos (\theta )-1=0$.

A Ferris wheel of radius $10$ m has its center $12$ m above the ground and completes one revolution every $30$ seconds. Starting from the bottom at $t=0$, which function models the rider's height $h(t)$ in meters?

Find the inverse of the matrix $A=\left[\begin{array}{cc}2& 1\\ 1& 1\end{array}\right]$.

A projectile is launched with initial velocity ${\mathbf{v}}_0=⟨20,30⟩$ m/s. Ignoring gravity, what is its position vector at $t=4$ seconds, starting from the origin?