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%TCIDATA{Created=Tuesday, August 22, 2006 00:04:17}
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%TCIDATA{<META NAME="Title" CONTENT="Sample Problems 1 - Solutions - Math 99">}
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\lhead{}
\chead{\LARGE Integers}
\rhead{\large page   \ \thepage\\ \LARGE \color{red}Answers}
\lfoot{\small   \copyright $\;$ copyright  Hidegkuti,  Powell,  2007}
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\begin{document}


\begin{center}
{\LARGE Part 1 - Sample Problems}\bigskip
\end{center}

\begin{enumerate}
\item Perform each of the indicated operations.

\begin{enumerate}
\item $21-2\left( -5\right) =~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
31$%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion

\item $\sqrt{60\div 4\div 5+1}=~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
2$%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion

\item $20-\left\vert 32\div \left( -2\right) \right\vert =~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
4$%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion

\item $\dfrac{-3^{2}+30\div \left( -2\right) }{-4}=~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
6$%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion

\item $\left( 9-6\right) ^{2}=~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
9$%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion

\item $9^{2}-6^{2}=~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
45$%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion

\item $16-\sqrt{2^{3}-2^{2}}-5=~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
9$%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion

\item $\sqrt{25}\cdot \dfrac{-3^{5}+\left( -1\right) ^{3}}{\left\vert \left(
-5\right) ^{3}-\left\vert 6+\left( -5\right) ^{3}\right\vert \right\vert }=~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
-5%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion
\allowbreak $

\item $\dfrac{3+\left( 6^{2}-3^{2}\right) +\left( 3^{3}-2^{3}\right) -9}{%
4^{2}+\left( 5-3\right) ^{2}}=~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
2$%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion
$\allowbreak $

\item $\sqrt{\sqrt{3^{6}}-2\left( 3^{2}+3^{3}\right) +2\left( 4\left(
17-2^{3}\right) -3^{2}\right) }=~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
3$%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion
$\allowbreak $

\item $2\cdot 3^{2}-\left( 6-4+\left( 6\cdot 4-3\left( 2^{4}-12\right)
\right) \right) =~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
4$%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion
$\allowbreak $
\end{enumerate}

\item Let $a=-4$, $\ b=2$, and $x=-3$. Evaluate each of the following
expressions.

\begin{enumerate}
\item $a^{2}-b^{2}=~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
12$%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion
$\allowbreak $

\item $\left( a-b\right) ^{2}=~~%
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%BeginExpansion
\color{red}%
%EndExpansion
36$%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion
$\allowbreak $

\item $a^{b}-2bx+x-\left\vert 2x\right\vert =~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
19$%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion
$\allowbreak $

\item $\dfrac{-x^{2}+\left( x+2\right) ^{2}}{\left( x-1\right) }=~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
2$%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion
$\allowbreak $

\item $\dfrac{x-1}{x+3}=~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
\func{undefined}$%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion
\end{enumerate}

\item Consider the equation $x^{2}-10x+x^{3}-4=4\left( x+5\right) $. \ In
each case, determine whether the number given is a solution of the equation
or not.

\begin{enumerate}
\item $x=0~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
-4\not=20~~~$%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
no%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion

\item $x=-2~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
12=12~~~$%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
yes%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion

\item $x=-3~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
8=8~~~$%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
yes%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion
\pagebreak
\end{enumerate}
\end{enumerate}

\begin{center}
{\LARGE Part 2 - Practice Problems}
\end{center}

\bigskip

\begin{enumerate}
\item Simplify each of the following expressions.

\begin{enumerate}
\item $\left\vert \left\vert -20-3\left( -4\right) \right\vert
-10\right\vert =~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
2$%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion

\item $15-3\left( -2\right) =~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
21$%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion

\item $\left( \left( \left( 1-2\right) ^{2}-2\right) ^{2}-2\right) ^{2}-2=~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
-1$%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion

\item $\sqrt{-7^{2}+15\left( 2\right) ^{2}-18\div 3\div 3}=~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
3$%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion

\item $\dfrac{-6^{2}\div 2\cdot 3+\left\vert 2^{2}\cdot 12-11\right\vert
+2\left( -1\right) ^{3}-\left( -1\right) ^{2}}{\left( -2\right) ^{2}+\left(
-2\right) ^{3}}=~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
5$%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion

\item $\sqrt{36}-\sqrt{81}+2\sqrt{25}=~~%
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%BeginExpansion
\color{red}%
%EndExpansion
7$%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion
\end{enumerate}

\item Evaluate $\dfrac{8x+x^{2}-33}{x+11}=~~%
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%BeginExpansion
\color{red}%
%EndExpansion
x-3$%
%TCIMACRO{\TeXButton{black}{\color{black}} }%
%BeginExpansion
\color{black}
%EndExpansion
\ \ ~if \ \ \ \ \ \ \ \ \ 

\begin{enumerate}
\item $x=0~~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
-3$%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion

\item $x=-11~~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
\func{undefined}$%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion
\end{enumerate}

\item Evaluate $\dfrac{x-2}{2-x}$ \ if

\begin{enumerate}
\item $x=0~~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
-1$%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion

\item $x=2~~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
\func{undefined}$%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion
\end{enumerate}

\item Consider the equation $-x+x^{3}+6=3\left( -x^{2}+x+2\right) $. \ In
each case, determine whether the number given is a solution of the equation
or not.

\begin{enumerate}
\item $x=0~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
6=6~~~$%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
yes%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion

\item $x=1~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
6=6~~~$%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
yes%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion

\item $x=-1~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
6\not=0~~~$%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
no%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion

\item $x=2~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
12\not=0~~~$%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
no%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion

\item $x=-2~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
0\not=-12~~~$%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
no%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion

\item $x=3~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
30\not=-12~~~$%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
no%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion

\item $x=-3~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
-18\not=-30~~~$%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
no%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion

\item $x=4~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
66\not=-30~~~$%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
no%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion

\item $x=-4~~%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
-54=-54~~~$%
%TCIMACRO{\TeXButton{red}{\color{red}}}%
%BeginExpansion
\color{red}%
%EndExpansion
yes%
%TCIMACRO{\TeXButton{black}{\color{black}}}%
%BeginExpansion
\color{black}%
%EndExpansion
\end{enumerate}
\end{enumerate}

\end{document}