\documentclass[11pt]{article}

\usepackage{precalc}
\usepackage{enumitem}

\begin{document}

\assigntitle{7}{Algebra/Geometry Review}

This week we'll spend some time reviewing some material from algebra
and geometry.  Of course, it would be impossible---not to mention
silly---to review \emph{everything} you learned in algebra and
geometry.  It would take far too long, and some of it is not all that
important anyway.  Instead, we'll just review some of the pieces that
will be an important foundation throughout the rest of the year.

The format is simple---there are a number of problems, each
of which you should (theoretically) know how to solve.  It's fine if
you don't remember how to solve some of them---that's the point of a
review, after all---but you're responsible for refreshing your memory
on the things you've forgotten.  In order to refresh your memory, you
are welcome to ask me for help, read an old textbook, consult
Wikipedia, send a letter to Santa Claus, or whatever you like.  

All answers must be exact.  For example, write $\sqrt{17}$ instead of
$4.123\dots$, or $3\pi$ instead of $9.425\dots$.  Show your work.  The
\verb|align*| environment may be useful.  For example, if asked to
solve the equation $3x + 4x = 9 + 5$, you could write
\begin{verbatim}
  \begin{align*}
    3x + 4x &= 9 + 5 \\
    7x &= 14 \\
     x &= 2
  \end{align*}
\end{verbatim}
which would produce output like this:
  \begin{align*}
    3x + 4x &= 9 + 5 \\
    7x &= 14 \\
     x &= 2
  \end{align*}
Do not just write ``$x = z$''; you must show the steps you used to
obtain that solution for $x$.

\textbf{Problems \ref{prob:eq1}--\ref{prob:eqn}.} Solve each equation
for $x$.  

\begin{enumerate}
\item $4x - 13 = 31$ \label{prob:eq1}

\item $\sqrt{x + 3} = 7$

\item $x^{-5} = 2$

\item $x + \frac{2}{x} = -3$

\item $17x - x(4 + x) = 29$

\item $\frac{x}{3} + \frac{4x}{7} = \frac{3}{12}$

\item $x^{2/3} = 25$

\item $\frac{3/7}{x/14} = \frac{8}{4/3}$

  \label{prob:eqn}

\end{enumerate}

For \textbf{problems \ref{prob:a}--\ref{prob:b}}, follow the
instructions given.

\begin{enumerate}[resume]

\item Expand: \label{prob:a}
  \begin{enumerate}
  \item $(x + 2)(3x - 1)$
  \item $(y + 5)^3$
  \item $(z^3 + 2z + 1)(z + 6)$
  \end{enumerate}

\item Factor:
  \begin{enumerate}
  \item $x^2 - 2x - 8$
  \item $9h^2 - 16$
  \end{enumerate}

\item Let $f(x) = x^2 - 3$.  Evaluate:
  \begin{enumerate}
  \item $f(5)$
  \item $f(f(0))$
  \item $f(y+2)$
  \end{enumerate}

\item Solve for $y$: $-3y - 5 \leq (y+1)^2$.

\item Solve for $x$ and $y$:
  \begin{align*}
    2x + 3y &= 9 \\
    5x - y &= 3 + x
  \end{align*}


\item A right triangle has a hypotenuse of length $20$ and a leg of
  length $12$.  What is the length of the other leg?

\item What is the area of a square whose diagonal has length $7$?

\item A cylindrical container full of whipped cream has circumference
  $12\pi$ inches.  When spread evenly on a basketball court with a
  depth of $1/4$ inch, the whipped cream covers $63$ square feet.  How
  tall was the container?

  \label{prob:b}
\end{enumerate}

\end{document}