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\begin{center}
Math 101 - Final

Autumn 1997
\end{center}

Name \rule{5in}{.2pt}

\vspace{.1in}

Code Name \rule{5in}{.2pt}

\vspace{.1in}

Section Number \rule{5in}{.2pt}

\vspace{.1in}

\begin{enumerate}

\item  Sketch the graph of the equation 
and find its intersection with the $x$--axis.
\[
3x-2y+3=0
\]
\vspace{3.1in}

\item Factor the polynomial $p(x)= 2x^2+12x-14$, and
solve the equation $p(x)=0$.
%\vspace{2.6in}
\newpage

\item  Compute and simplify
\[
\frac{16-x}{x^2-2x-8}+\frac{4}{x+2}-\frac{2}{x-4}
\]
\vspace{2.6in}

\item  Find the solutions of the equation
\[
4z^2+12z+25=0
\]
\vspace{2.6in}

\item   We have to build a rectangular patio such that
its width is 5 ft less than its length, and its total area is 150
square feet. What should be its length and width?
%\vspace{2.6in}
\newpage

\item  Find the equation of the line that goes through
the points $(0,4)$ and $(2,-1)$. Find the intersection of this
line with the horizontal line $y=1$.
\vspace{2.6in}

\item  Solve the system
\[
\left\{ 
\begin{array}{cccc}
 x & -2y & +3z & =0 \\
-x &  -y &  +z & =2 \\
2x &     & -3z & =1 
\end{array}
\right.
\]
\vspace{2.6in}

\item  If $g(x)=x(3-x)$ evaluate and simplify:
$g(5)$, $g(-2)$, $g(t+2)$.
\vspace{2.6in}

\item  Find the equation of the line through (2,-4) and (-10,1),
and find the distance between these points.
\vspace{2.6in}

\item  Simplify and factor:
\[
3y^2-(y-3(y^2-5))
\]
\vspace{2.6in}

\item  Simplify:
\[
\frac
{ \left( \frac{1}{x}-\frac{1}{y} \right) }
{ \left( \frac{1}{x^2}-\frac{1}{y^2} \right) }
\]
\vspace{2.6in}

\item Divide:
\[
\frac{x^4+3x^2-35}{x+2}
\]
\vspace{2.6in}

\item  Solve:
\[
\frac{7}{x+3}-\frac{6}{x-2}=6
\]
\vspace{2.6in}

\item  Rewrite using only positive exponents and simplify:
\[
(3x^2y^{-1})^2(4x^4y^{-3})^{-\frac{1}{2}}
\]
\vspace{2.6in}

\item  Rationalize the denominator and simplify:
\[
\frac{\sqrt{12}}{\sqrt{6}-3}
\]
\vspace{2.6in}

\item  Write the complex number in standard form $(a+bi)$:
\[
\frac{2-\sqrt{-9}}{1+2i}
\]
\vspace{2.6in}

\item  Solve and graph the inequality.
\[ -3 < \frac{2x-3}{2} \leq 3 \]
\vspace{2.6in}

\item  Solve the equation:
\[ |x+2|=|3x-1| \]
\vspace{2.6in}

\item  Factor the polynomial.  (Hint: $(x-2)$ is a factor)
\[
x^3-4x^2+x+6
\]
\vspace{2.6in}

\item  You take a 15 mile hike.  
For the first 10 miles you travel at one speed.  
Then you pick up the pace and finish the next 5 miles 
3 miles per hour faster then the first 10 miles.  
The trip takes 6 hours.
How fast did you go in each part of the hike?











\end{enumerate}

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