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+\documentclass{article}
+\usepackage[fleqn]{amsmath}
+\usepackage[pointsonleft,nototals,
+ forcolorpaper,useforms,
+% choose to compile with exactly one of the next 4 options
+%-------------------
+ nosolutions, % compile with no solutions to get the exam document
+% answerkey, % get answer key
+% vspacewithsolns,% put solutions at end of document
+% solutionsonly, % compile with vspacewithsolns several times, then compile with solutionsonly
+%-------------------
+% coverpage,coverpagesumry=bypages
+ showgrayletters]{eqexam}
+\usepackage{graphicx}
+
+\forceNoColor
+\vspacewithkeyOn
+
+\university
+{%
+ NORTHWEST FLORIDA STATE COLLEGE\\
+ Department of Mathematics
+}
+\email{storyd@nwfsc.edu}
+
+\examSIDLabel{Class: MAC 1105, \vA{12:30 pm, L-134}\vB{12:30 am, L-105}}
+\coverpageSubjectFmt{\bfseries\LARGE}
+\coverpageTitleFmt{\bfseries\LARGE}
+\examNum{3}\numVersions{2}\forVersion{a}
+\subject[MAC1105]{College Algebra}
+\longTitleText
+ {Test~\nExam}
+ {Test~\nExam}
+\endlongTitleText
+\shortTitleText
+ {T\nExam}
+ {T\nExam}
+\endshortTitleText
+\altTitle{\vA{12:30 pm, L-134}\vB{12:30 pm, L-105}}
+\title[\sExam]{\Exam}
+\author{Dr.\ D. P. Story}
+\date{\thisterm, \the\year}
+\duedate{04/05/11}
+\keywords{MAC 1105, Exam \nExam, {\thisterm} semester, \theduedate, at NWFSC}
+\renewcommand{\fillInFormatDefault}{}
+\DoNotFitItIn
+\eqpartsitemsep{3pt}
+\solAtEndFormatting{\eqequesitemsep{3pt}}
+
+
+\everymath{\displaystyle}
+%\renameSolnAfterTo{}
+%\resetSolnAfterToDefault
+
+
+\eqCommentsColor{gray}
+\eqCommentsColorBody{gray}
+\newcommand{\cs}[1]{\texttt{\char`\\#1}}
+\def\qt#1{&&\qquad\text{#1}}
+
+
+\encloseProblemsWith{theseproblems}
+
+\begin{document}
+
+\maketitle
+
+
+\begin{exam}{Test\nExam}
+
+\ifsolutionsonly\NoPoints
+\begin{instructions}[Solutions:]
+The solutions to the test.
+\end{instructions}
+\else
+\begin{instructions}[Instructions:]
+This exam has {\nQuesInExam} questions distributed over {\nPagesOnExam} pages.
+Solve each of the problem and box in your final $\boxed{\text{answer}}$, where applicable.
+\end{instructions}
+\fi
+
+\begin{theseproblems}
+
+\renameSolnAfterTo{}
+
+\begin{problem*}[2ea]\label{shortAns}
+Answer each of the following, none of the problems shown below requires any
+calculations. Respond to True/False questions with \texttt{T} (for True) or \texttt{F} (for
+False).
+\begin{parts}
+ \item When viewing the graph of a function, we may use the
+ \fillin[u]{1.5in}{Horizontal Line} Test to determine if it is a
+ one-to-one function.
+\begin{solution}[]\ifvspacewithsolns
+When viewing the graph of a function, we may use the
+\fillin[u]{1.5in}{Horizontal Line} Test to determine if it is a
+one-to-one function.\fi
+\end{solution}
+
+ \item \TF{F} (\texttt{T} or \texttt{F}) The graph of the function $ f(x) =
+ 2-4x-3x^2$ is a parabola that opens up.
+\begin{solution}[]\ifvspacewithsolns
+\TF{F} (\texttt{T} or \texttt{F}) The graph of the function $ f(x) =
+2-4x-3x^2$ is a parabola that opens up.\fi
+\end{solution}
+
+ \item \TF{F} (\texttt{T} or \texttt{F}) For a quadratic function of the form
+ $f(x)=ax^2+bx+c$, if $a>0$, then the function has a \emph{maximum
+ value}.
+\begin{solution}[]\ifvspacewithsolns
+\TF{F} (\texttt{T} or \texttt{F}) For a quadratic function of the form
+ $f(x)=ax^2+bx+c$, if $a>0$, then the function has a \emph{maximum
+ value}.\fi
+\end{solution}
+
+\pushProblem
+
+\begin{eqComments}[Comments:]
+Questions like the three above (fill-in and True/False) often have no
+solution; hence, normally, the \texttt{solution} environment is not used. When
+using the \texttt{vspacewithsolns} or the \texttt{solutionsonly} options
+you would like the ``answers'' to appear on the solutions pages. To
+rectify this, we simply copy and past the item into a solutions
+environment, like so, in the case of the last question above.
+\begin{verbatim}
+\begin{solution}[]\ifvspacewithsolns
+\TF{F} (\texttt{T} or \texttt{F}) For a quadratic function of the form
+ $f(x)=ax^2+bx+c$, if $a>0$, then the function has a \emph{maximum
+ value}.\fi
+\end{solution}
+\end{verbatim}
+The optional argument is empty (important). We don't want the student or instructor to
+see this solution when the document is compiled using the \texttt{answerkey}
+option, so we wrap this solution in a conditional
+\verb~\ifvspacewithsolns...\fi~ This switch will be true if either the
+options \texttt{vspacewithsolns} or \texttt{solutionsonly} options are
+taken
+\end{eqComments}
+
+\popProblem
+
+ \item\label{whichRatFunc} Which rational function below has a horizontal asymptote of
+ $y=-2$, and has vertical asymptotes of $x=1$ (odd) and $ x=2 $ (even)?
+ \begin{answers}{3}\rowsep{6pt}
+ \bChoices[label=whichRat]
+ \Ans0 $ y = \frac{(x+2) (1-2x)}{(1-x)(x-2)^2} $\eAns
+ \Ans0 $ y = \frac{(x+2)^2 (2x-1)}{(x-1)(x-2)^2} $\eAns
+ \Ans1 $ y = \frac{(x+2)^2 (1-2x)}{(x-1)(x-2)^2} $\eAns
+ \Ans0 $ y = \frac{(x+2)^2 (2x-1)}{(x-1)^2(x-2)} $\eAns
+ \Ans0 $ y = \frac{(x+2) (1-2x)^2}{(x-1)^2(x-2)} $\eAns
+ \Ans0 none of these\eAns
+ \eChoices
+ \end{answers}
+\begin{solution}[]\ifvspacewithsolns
+We can access the ``answers'' to a multiple choice question in several
+ways:
+\begin{itemize}
+\item The correct alternative is part~\useSavedAlts{whichRat},
+\useSavedAns{whichRat}.
+\begin{verbatim}
+The correct alternative is part~\useSavedAlts{whichRat},
+\useSavedAns{whichRat}.
+\end{verbatim}
+The command \verb!\useSavedAlts{whichRat}! expands to the letter alternative of the
+correct response, \useSavedAlts{whichRat}, in this case. Similarly,
+\verb!\useSavedAns{whichRat}! expands to the correct answer, here, the
+correct answer is \useSavedAns{whichRat}.
+
+\item The correct answer is \useSavedAltsAns{whichRat}.
+\begin{verbatim}
+The correct answer is \useSavedAltsAns{whichRat}.
+\end{verbatim}
+The command \verb!\useSavedAltsAns{whichRat}! expands to the correct
+letter followed by the correct answer.
+\item You can now copy and paste the \texttt{answers} (or \texttt{manswers})
+ environment into the \texttt{solutions} environment, like so.
+
+\item[] Which rational function below has a horizontal asymptote of
+ $y=-2$, and has vertical asymptotes of $x=1$ (odd) and $ x=2 $ (even)?
+ \begin{answers}{3}\rowsep{6pt}
+ \bChoices[label=whichRat]
+ \Ans0 $ y = \frac{(x+2) (1-2x)}{(1-x)(x-2)^2} $\eAns
+ \Ans0 $ y = \frac{(x+2)^2 (2x-1)}{(x-1)(x-2)^2} $\eAns
+ \Ans1 $ y = \frac{(x+2)^2 (1-2x)}{(x-1)(x-2)^2} $\eAns
+ \Ans0 $ y = \frac{(x+2)^2 (2x-1)}{(x-1)^2(x-2)} $\eAns
+ \Ans0 $ y = \frac{(x+2) (1-2x)^2}{(x-1)^2(x-2)} $\eAns
+ \Ans0 none of these\eAns
+ \eChoices
+ \end{answers}
+\end{itemize}\fi
+\end{solution}
+
+\pushProblem
+\begin{eqComments}[Comments:]
+Multiple choice and multiple selection questions were an especially
+difficult problem to solve; the \texttt{answers} and \texttt{manswers}
+environments are undefined outside of an \texttt{exam} environment so one
+cannot simply copy and paste the choices into the \texttt{solution} environment.
+
+To resolve this issue, I added a key-value pair to the \cs{bChoices} command,
+the key is \texttt{label}. The source code for the above question reads
+\verb!\bChoices[label=whichRat]! The value of the label key is used to
+build a series of macros that record the labels and text for the choices
+that are marked correct by \cs{Ans1}. The information gathered by these
+macros are accessible through \cs{useSavedAlts}, \cs{useSavedAns},
+\cs{useSavedAltsAns}, and \cs{useSavedNumAns}, as described in the \textsf{eqexam}
+manual. See the solutions pages to see the answers to these multiple
+choice questions and details on the use of these commands.
+\end{eqComments}
+\popProblem
+
+ \item How many times can a quadratic equation cross the $x$-axis?
+ Check as many of the alternatives that are possibly correct for a
+ quadratic function.
+ \begin{manswers}{4}
+ \bChoices[label=nCrossings]
+ \Ans1 0\eAns
+ \Ans1 2\eAns
+ \Ans1 3\eAns
+ \Ans0 4\eAns
+ \Ans0 5\eAns
+ \Ans0 6\eAns
+ \Ans0 infinitely many\eAns
+ \Ans0 none of these\eAns
+ \eChoices
+ \end{manswers}
+\begin{solution}[]\ifvspacewithsolns
+Here is how these same macros expand for multiple selection problems.
+\begin{itemize}
+\item The correct alternatives are parts~\useSavedAlts{nCrossings}.
+\begin{verbatim}
+The correct alternatives are parts~\useSavedAlts{nCrossings}.
+\end{verbatim}
+\item The correct answers are \useSavedAns{nCrossings}.
+\begin{verbatim}
+The correct answers are \useSavedAns{nCrossings}.
+\end{verbatim}
+\item The correct responses are \useSavedAltsAns{nCrossings}.
+\begin{verbatim}
+The correct responses are \useSavedAltsAns{nCrossings}.
+\end{verbatim}
+\item[] End each case, the command expands to a comma-delimited list of correct
+answers.
+\end{itemize}
+You can also access the answers individually, for example the second
+correct response is part~\useSavedAlts[2]{nCrossings}, the answer for
+part~\useSavedAlts[2]{nCrossings} is \useSavedAns[2]{nCrossings}. Or,
+we can say, \useSavedAltsAns[2]{nCrossings} to get a combined listing of
+the second correct response.
+\begin{verbatim}
+You can also access the answers individually, for example the second
+correct response is part~\useSavedAlts[2]{nCrossings}, the answer for
+part~\useSavedAlts[2]{nCrossings} is \useSavedAns[2]{nCrossings}. Or,
+we can say, \useSavedAltsAns[2]{nCrossings} to get a combined listing of
+the second correct response.
+\end{verbatim}
+\fi
+\end{solution}
+\end{parts}
+\end{problem*}
+
+\begin{eqComments}[Comments:]
+The above question is a multiple selection question. The student must
+select all the correct choices. See the solutions pages to see the answers
+to these multiple choice questions and details on the use of these
+commands.
+\end{eqComments}
+
+\begin{problem}[5]
+Which rational function below has a horizontal asymptote of
+ $y=-2$, and has vertical asymptotes of $x=1$ (odd) and $ x=2 $ (even)?
+ \begin{answers}{3}\rowsep{6pt}
+ \bChoices[label=whichRat1]
+ \Ans0 $ y = \frac{(x+2) (1-2x)}{(1-x)(x-2)^2} $\eAns
+ \Ans0 $ y = \frac{(x+2)^2 (2x-1)}{(x-1)(x-2)^2} $\eAns
+ \Ans1 $ y = \frac{(x+2)^2 (1-2x)}{(x-1)(x-2)^2} $\eAns
+ \Ans0 $ y = \frac{(x+2)^2 (2x-1)}{(x-1)^2(x-2)} $\eAns
+ \Ans0 $ y = \frac{(x+2) (1-2x)^2}{(x-1)^2(x-2)} $\eAns
+ \Ans0 none of these\eAns
+ \eChoices
+ \end{answers}
+\begin{solution}[]\ifvspacewithsolns
+We can access the ``answers'' to a multiple choice question in several
+ways:
+\begin{itemize}
+\item The correct alternative is part~\useSavedAlts{whichRat1},
+\useSavedAns{whichRat1}.
+\begin{verbatim}
+The correct alternative is part~\useSavedAlts{whichRat1},
+\useSavedAns{whichRat1}.
+\end{verbatim}
+The command \verb!\useSavedAlts{whichRat1}! expands to the letter alternative of the
+correct response, \useSavedAlts{whichRat1}, in this case. Similarly,
+\verb!\useSavedAns{whichRat1}! expands to the correct answer, here, the
+correct answer is \useSavedAns{whichRat1}.
+
+\item The correct answer is \useSavedAltsAns{whichRat1}.
+\begin{verbatim}
+The correct answer is \useSavedAltsAns{whichRat1}.
+\end{verbatim}
+The command \verb!\useSavedAltsAns{whichRat1}! expands to the correct
+letter followed by the correct answer.
+\end{itemize}\fi
+\end{solution}
+\end{problem}
+
+\begin{eqComments}[Comments:]
+This is the same question as Problem~\ref{shortAns} (\ref{whichRatFunc}),
+but this one is a stand alone question. The lettering of the label can
+change depending on the options you take, so, if you compile this document
+without the \texttt{useforms} options, the choices listed in~\ref{shortAns} (\ref{whichRatFunc})
+will be numbers, (A), (B),\dots, and the choices of this question will be
+letters, (a), (b),\dots. Check the solutions page, the references should
+change to reflect the change in options, let's hope.
+\end{eqComments}
+
+\resetSolnAfterToDefault
+
+\begin{problem*}[\auto]
+Let $f(x) = 4x+3$ and $ g(x) = 2x^2 - 5 $. Compute each of the following,
+simplify were appropriate.
+\begin{multicols}{2}
+\begin{parts}
+\item \PTs{2} $ (fg)(-2) = \fillin[boxed,boxsize=LARGE,align=l]{1in}{-15} $
+
+\begin{solution}[.65in]
+We have \[ (fg)(-2)=f(-2)g(-2)=(-5)(3)=\boxed{-15}\]
+\end{solution}
+
+\item \PTs{2} $\left(\frac{g}{f}\right)(x)= \fillin[boxed,boxsize=LARGE]{\ifNoSolutions{1in}{}}{\frac{2x^2-5}{4x+3}} $
+
+\begin{solution}[\sameVspace]
+$ \left(\frac{g}{f}\right)(x)=\frac{g(x)}{f(x)}=\boxed{\frac{2x^2 - 5}{4x+3}}$
+\end{solution}
+
+\item \PTs{2} $ (f\circ f )(x) = \fillin[boxed,boxsize=LARGE]{\ifNoSolutions{1in}{}}{16x+15} $
+
+\begin{solution}[\sameVspace]
+Composing, $(f\circ f )(x)=f(f(x))=f(4x+3)=4(4x+3)+3=\boxed{16x+15}$
+\end{solution}
+
+\item \PTs{4} $ (f\circ g )(x) = \fillin[boxed,boxsize=LARGE]{1in}{8x^2-17} $
+
+\begin{solution}[\sameVspace]
+Composing, $(f\circ g )(x)=f(g(x))=f(2x^2 - 5)=4(2x^2 -5)+3=\boxed{8x^2-17}$
+\end{solution}
+\end{parts}
+\end{multicols}
+\end{problem*}
+
+\begin{eqComments}[Comments:]
+Nothing new about the above problem, each has a solution, no special
+attention is needed. In some of the answer boxes, \cs{ifNoSolutions} is
+used to set the width then \texttt{nosolutions} is in effect, and to et the box to
+its natural width otherwise.
+\end{eqComments}
+
+
+\begingroup
+
+\setlength{\columnsep}{30pt}
+
+\begin{multicols}{2}
+\begin{problem}[5]
+Use the \textbf{vertex formula} to find the $x$-coordinate, $h$, and the
+$y$-coordinate, $k$, of the quadratic function $ f(x) = 2x^2 - 8x + 5 $.
+\begin{equation*}
+ \fillin[boxed,boxsize=LARGE,align=l,boxpretext={h=}]{1in}{2}\quad
+ \fillin[boxed,boxsize=LARGE,align=l,boxpretext={k=}]{1in}{-3}
+\end{equation*}
+\begin{solution}[.5in]
+We use the vertex formula, $ h = -b/(2a) = - (-8)/4 = 2 $, and
+so $h=f(2) = 8 - 16 + 5 = -3$.
+\end{solution}
+\end{problem}
+
+\columnbreak
+
+\begin{problem}[] %
+\PTs{3}\addtocounter{eqpointvalue}{3} The function $ f(x) = x^2 - x + 1 $ has a
+\fillin[u]{.75in}{minimum} (max/min) at $x = \fillin[u]{.5in}{1/2}$.
+\begin{solution}[\sameVspace]
+We use the vertex formula, $ h = -b/(2a) = - (-1)/2 =
+1/2 $. A \textbf{minimum} occurs since the leading coefficient is
+positive, which means the parabola opens up, the vertex is a minimum.
+\end{solution}
+\end{problem}
+\end{multicols}
+
+\endgroup
+
+\begin{eqComments}[Comments:]
+I include this problem in this file, because it is a construct that
+appeared in a test of mine. I wanted to conserve vertical space so I put
+to problems into two column format. The problem is the points appear to
+the left. So, for the problem on the left, the points appear as usual, for
+the problem on the right, the points appear in-line, I had to explicitly
+increment the points counter, like so
+\verb~\addtocounter{eqpointvalue}{3}~. Some adjustment of the space
+between the columns was necessary \verb~\setlength{\columnsep}{30pt}~.
+\end{eqComments}
+
+\renameSolnAfterTo{}
+
+\begin{problem}[5]
+For a polynomial of degree $12$, according to theory, the maximum number
+of zeros is \fillin[u]{.5in}{12}, and the maximum number of turning points
+is \fillin[u]{.5in}{11}.
+\begin{solution}[]\ifvspacewithsolns
+For a polynomial of degree $12$, according to theory, the maximum number
+of zeros is \fillin[u]{.5in}{12}, and the maximum number of turning points
+is \fillin[u]{.5in}{11}.\fi
+\end{solution}
+\end{problem}
+
+\begin{eqComments}[Comments:]
+A fill-in the blank problem, just copy and paste it into the solution
+environment, protected by \verb~\ifvspacewithsolns...\fi~.
+\end{eqComments}
+
+
+\begin{problem}[5]
+In the boxes provided, list the laws of the exponents and the laws of
+logarithms.
+ \begin{equation*}\def\bwidth{2.75in}\def\bheight{1.5in}
+ \begin{tabular}{cc}
+ \textbf{Laws of the Exponents} & \textbf{Laws of Logarithms}\\
+ \multicolumn{1}{p{\bwidth}}{%
+ \fillin[boxed,enclosesoln,parbox={[c][\bheight][t]}]{\linewidth}{%
+%
+ \begin{enumerate}
+ \item $a^x a^y = a^{x+y}$
+ \item $a^x/a^y = a^{x-y}$
+ \item $ (a^x)^y = a^{xy}$
+ \end{enumerate}
+%
+ }}&
+ \multicolumn{1}{p{\bwidth}}{%
+ \fillin[boxed,enclosesoln,parbox={[c][\bheight][t]}]{\linewidth}{%
+%
+ \begin{enumerate}
+ \item $\log_a(xy) = \log_a(x)+\log_a(y)$
+ \item $\log_a(x/y) = \log_a(x)-\log_a(y)$
+ \item $\log_a(x^r) = r\log_a(x)$
+ \end{enumerate}
+%
+ }}
+ \end{tabular}
+ \end{equation*}
+\begin{solution}[]\ifvspacewithsolns
+Write sentences, in the provided boxes, describing, in laymen's terms, Type I
+ and Type II errors for this test of hypothesis.
+ \begin{equation*}\def\bwidth{2.75in}\def\bheight{1.5in}
+ \begin{tabular}{cc}
+ \textbf{Laws of the Exponents} & \textbf{Laws of Logarithms}\\
+ \multicolumn{1}{p{\bwidth}}{%
+ \fillin[boxed,enclosesoln,parbox={[c][\bheight][t]}]{\linewidth}{%
+%
+ \begin{enumerate}
+ \item $a^x a^y = a^{x+y}$
+ \item $a^x/a^y = a^{x-y}$
+ \item $ (a^x)^y = a^{xy}$
+ \end{enumerate}
+%
+ }}&
+ \multicolumn{1}{p{\bwidth}}{%
+ \fillin[boxed,enclosesoln,parbox={[c][\bheight][t]}]{\linewidth}{%
+%
+ \begin{enumerate}
+ \item $\log_a(xy) = \log_a(x)+\log_a(y)$
+ \item $\log_a(x/y) = \log_a(x)-\log_a(y)$
+ \item $\log_a(x^r) = r\log_a(x)$
+ \end{enumerate}
+%
+ }}
+ \end{tabular}
+ \end{equation*}\fi
+\end{solution}
+\end{problem}
+
+\begin{eqComments}[Comments:]
+The above pair of boxes use the \texttt{enclosesoln} key. When this key is
+used, the vertical size of the box is adjusted to the vertical size the
+solution uses when either \texttt{nosolutions} or \texttt{vspacewithsolns}
+option are used. Note the dimensions of the \cs{parbox} are adjusted so
+that the width and height are correct. The \cs{boxed} command adds
+\texttt{2\cs{fboxesp}+2\cs{fboxrule}}, so we reduce the \cs{parbox} by
+that amount so the boxes are the correct size.
+\end{eqComments}
+
+\begin{problem}[12]
+Define $ f(x) = -2x^2(x+1) $. Make a good sketch of the graph in the
+coordinate plane below, taking into consideration the end-behavior of the
+polynomial, and its intercepts.
+\begin{solution}[3in]
+The graph of $ f(x) = -2x^2(x+1) $ is seen below.
+\par\nobreak\medskip\vskip-1.5\baselineskip
+\begin{minipage}[t]{3.5in}\vskip\baselineskip\kern0pt
+\includegraphics[width=3.5in]{graph}
+\end{minipage}\hfill
+\begin{minipage}[t]{\linewidth-3.5in-30pt}\vskip\baselineskip\kern0pt
+\noindent\makebox[\linewidth][c]{\textbf{Work Area}}
+\begin{itemize}
+\item The end-behavior is like $y=-x^3$
+\item $x$-int: $x=0$ (even); $ x=-1 $ (odd)
+\item $y$-int: $y=0$ (passes through origin)
+\end{itemize}
+\end{minipage}
+\end{solution}
+\begin{workarea}{\sameVspace}%
+\begin{minipage}[t]{3.5in}\kern0pt
+\includegraphics[width=3.5in]{coorplane}
+\end{minipage}\hfill
+\begin{minipage}[t]{\linewidth-3.5in-30pt}\kern0pt
+\makebox[\linewidth][c]{\textbf{Work Area}}
+\end{minipage}
+\end{workarea}
+\end{problem}
+
+\begin{eqComments}[Comments:]
+Finally, we have the above problem. It uses the \texttt{workarea}
+environment. Previously, \texttt{workarea} appeared with the \texttt{nosolutions}
+option. Now it appears with the \texttt{vspacewithsolns} option as well.
+On the actual test, I used \textsf{PSTricks} for the graphics, for this
+demo file, I replace the \textsf{pstricks} code this a figure depicting what the
+\textsf{pstricks} produced, that way users of pdflatex can compile this
+file! \texttt{:-)}
+\end{eqComments}
+
+\newpage
+
+\begin{eqComments}%
+On this page, we more clearly demonstrate the new feature of preserving
+the vertical space even when the \texttt{answerkey} option is used. In the
+preamble, we have \cs{vspacewithkeyOn}.
+\end{eqComments}
+
+
+\resetSolnAfterToDefault
+% try changing \vspacewithkeyOn to \vspacewithkeyOff and recompile,
+% the 4 inches of vertical space are not preserved when you compile
+% with the answerkey option.
+\vspacewithkeyOn
+
+\begin{problem}[10]
+Solve the equation $2x^2 - 5x + 10 = 0 $ using the quadratic formula.
+\begin{solution}[4in]
+Applying the quadratic formula with $a=2$, $ b = -5 $, and $ c = 10 $,
+\begin{alignat*}{2}
+ x & = \frac{-b \pm \sqrt{b^2 -4ac}}{2a} \qt{The Quad.\ Formula}\\&
+ = \frac{5 \pm \sqrt{25 -4(2)(10)}}{2(2)} \qt{substitute}\\&
+ = \frac{5 \pm \sqrt{25 -80}}{4} \qt{arithmetic}\\&
+ = \frac{5 \pm \sqrt{-45}}{4} \qt{ditto}\\&
+ = \frac{5 \pm 3\sqrt{5}\,\imath}{4} \qt{simplify}
+\end{alignat*}
+The solution is $\boxed{x=\frac{5 \pm 3\sqrt{5}\,\imath}{4}}$
+\end{solution}
+\end{problem}
+
+\begin{problem}[5]
+Write the equation, in standard form, for the circle with center at
+$C(1,-3)$ and radius of $2$
+\begin{solution}[1in]
+We have $(x-1)^2 + (y+2)^2 = 4 $. Expanding and combining the equation, we
+have\dots \[\boxed{x^2+y^2-2x+4y+1=0}\]
+\end{solution}
+\end{problem}
+
+\begin{eqComments}[Comments:]
+The \texttt{solution} environments in the above problems declared 4 inches
+and 1 inch of vertical space, respectively. With \cs{vspacewithkeyOn} we
+should have about 4 inches (resp., 1 inch) of vertical space even with the
+\texttt{answerkey} option. Try compiling the file with
+\cs{vspacewithkeyOff}.
+\end{eqComments}
+
+\end{theseproblems}
+
+\end{exam}
+
+\end{document}