%% This document created by Scientific Word (R) Version 2.5


\documentclass[12pt,thmsa]{article}
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\usepackage{sw20jart}

%TCIDATA{TCIstyle=article/art4.lat,jart,sw20jart}

%TCIDATA{<META NAME="ViewSettings" CONTENT="17">}
%TCIDATA{<META NAME="GraphicsSave" CONTENT="32">}
%TCIDATA{Created=Sat Nov 16 20:56:01 1996}
%TCIDATA{LastRevised=Thu Feb 13 15:33:43 1997}
%TCIDATA{CSTFile=Exam.cst}

\input{tcilatex}
\begin{document}


\section{Exam}

\subsection{Text}

\section{SAT Questions}

This exam is a set of problems similar to those you'd find in the
mathematics sections of the SAT%
\CustomNote[$^{\ast }$]{Note}{%
SAT and Scholastic Assessment Test are registered trademarks of the College
Entrance Examination Board.} test.\bigskip

Your Name: 
%TCIMACRO{\HTML{<Input TYPE="Text" NAME="STUDENTNAME" VALUE=" " SIZE=0>}}
%BeginExpansion
%%
%EndExpansion

\vspace{1pt}

\subsection{Comment}

In no way is this test comprehensive. \ As time permits, we will add more
variety and possibly include a complete SAT practice test.

Other approaches to SAT test preparation can be found on the World Wide Web (%
\hyperref{WebWare}{}{}{http://www.testprep.com/satmenu.html}, \hyperref{%
BRAINCHILD}{}{}{http://www.thejournal.com/bc/sat.html})\ .

\subsubsection{Setup}

Choice Space: 2

Question Space: 1

Choices: No Break, Radio buttons, Permute

Title:Sample SAT Questions

\section{Question}

\section{Variant}

\subsection{Setup}

$t:=\func{rand}(20,50)$

$r:=\func{rand}(20,50)$

Condition: $\left( t\neq r\right) \wedge \left( \gcd (t,r)\neq 1\right) $

\subsection{Statement}

Joe drives to work at an average speed of $%
%TCIMACRO{\FORMULA{t}{t}{evaluate}}
%BeginExpansion
t%
%EndExpansion
$ miles per hour and returns along the same route at $%
%TCIMACRO{\FORMULA{r}{r}{evaluate}}
%BeginExpansion
r%
%EndExpansion
$ miles per hour. If his total traveling time is 1 hour, what is the total
number of miles of his round trip?

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{t}{t}{evaluate}}
%BeginExpansion
t%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{\frac{t+r}{2}}{\frac{1}{2}t+\frac{1}{2}r}{evaluate}}
%BeginExpansion
\frac{1}{2}t+\frac{1}{2}r%
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{\frac{1}{\frac{1}{t}+\frac{1}{r}}}{\frac{1}{\frac{1}{t}+\frac{1}{r}}}{evaluate}}
%BeginExpansion
\frac{1}{\frac{1}{t}+\frac{1}{r}}%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{r}{r}{evaluate}}
%BeginExpansion
r%
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{\frac{1}{\frac{1}{t}+\frac{1}{r}}+1}{\frac{1}{\frac{1}{t}+\frac{1}{r}}+1}{evaluate}}
%BeginExpansion
\frac{1}{\frac{1}{t}+\frac{1}{r}}+1%
%EndExpansion
$
\end{itemize}

\subsection{Comment}

(This is really the solution.)

\begin{enumerate}
\item  Let $d$ be the one--way distance. Recall the formula \textit{distance}
$=$ \textit{rate}$\cdot $\textit{time}.

\item  Then, solving for time $\frac{d}{%
%TCIMACRO{\FORMULA{\FORMULA{t}{t}{expand}}{t}{evaluate}}
%BeginExpansion
t%
%EndExpansion
}+\frac{d}{%
%TCIMACRO{\FORMULA{\FORMULA{r}{r}{expand}}{r}{evaluate}}
%BeginExpansion
r%
%EndExpansion
}=1$.

\item  Hence $d\left( \frac{1}{%
%TCIMACRO{\FORMULA{t}{t}{evaluate}}
%BeginExpansion
t%
%EndExpansion
}+\frac{1}{%
%TCIMACRO{\FORMULA{r}{r}{evaluate}}
%BeginExpansion
r%
%EndExpansion
}\right) =1$.

\item  This is $d\left( 
%TCIMACRO{
%\FORMULA{\frac{1}{t}+\frac{1}{r}}{\frac{1}{t}+\frac{1}{r}}{evaluate}}
%BeginExpansion
\frac{1}{t}+\frac{1}{r}%
%EndExpansion
\right) =1$.

\item  We get $d=\frac{1}{%
%TCIMACRO{
%\FORMULA{\frac{1}{t}+\frac{1}{r}}{\frac{1}{t}+\frac{1}{r}}{evaluate}}
%BeginExpansion
\frac{1}{t}+\frac{1}{r}%
%EndExpansion
}=%
%TCIMACRO{
%\FORMULA{\frac{1}{\frac{1}{t}+\frac{1}{r}}}{\frac{1}{\frac{1}{t}+\frac{1}{r}}}{evaluate}}
%BeginExpansion
\frac{1}{\frac{1}{t}+\frac{1}{r}}%
%EndExpansion
$.

\item  The round trip distance is twice $d$.
\end{enumerate}

\section{Variant}

\subsection{Setup}

$d:=\func{rand}(5,20)$

$s:=\func{rand}(5,10)$

$a:=\func{rand}(5,10)$

Conditions: $\left( a<s\right) $

Conditions: $\left( \frac{60d}{s}=\left\lfloor \frac{60d}{s}\right\rfloor
\right) $ [Total time is an integral number of minutes.]

Conditions: $\left( \frac{60d}{a}=\left\lfloor \frac{60d}{a}\right\rfloor
\right) $ [Total time is an integral number of minutes.]

\subsection{Statement}

Simon ran a $%
%TCIMACRO{\FORMULA{d}{d}{evaluate}}
%BeginExpansion
d%
%EndExpansion
$ mile race at an average speed of $%
%TCIMACRO{\FORMULA{s}{s}{evaluate}}
%BeginExpansion
s%
%EndExpansion
$ miles per hour. Allan ran the same race at an average speed of $%
%TCIMACRO{\FORMULA{a}{a}{evaluate}}
%BeginExpansion
a%
%EndExpansion
$ miles per hour. How many minutes longer than Simon did Allan take to
complete the race?

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{
%\FORMULA{20\left( \frac{d}{a}-\frac{d}{s}\right) }{20\frac{d}{a}-20\frac{d}{s}}{evaluate}}
%BeginExpansion
20\frac{d}{a}-20\frac{d}{s}%
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{30\left( \frac{d}{a}-\frac{d}{s}\right) }{30\frac{d}{a}-30\frac{d}{s}}{evaluate}}
%BeginExpansion
30\frac{d}{a}-30\frac{d}{s}%
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{60\left( \frac{d}{a}-\frac{d}{s}\right) }{60\frac{d}{a}-60\frac{d}{s}}{evaluate}}
%BeginExpansion
60\frac{d}{a}-60\frac{d}{s}%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{60\frac{d}{a}}{60\frac{d}{a}}{evaluate}}
%BeginExpansion
60\frac{d}{a}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{60\frac{d}{s}}{60\frac{d}{s}}{evaluate}}
%BeginExpansion
60\frac{d}{s}%
%EndExpansion
$
\end{itemize}

\section{Question}

\subsection{Setup}

$p:=\func{rand}(50,100)$

$d:=\func{rand}(\{10,20,30,40\})$

Condition: $\left( \frac{p}{1-\frac{d}{100}}=\left\lfloor \frac{p}{1-\frac{d%
}{100}}\right\rfloor \right) $

\subsection{Statement}

A pair of shoes is selling for \$$%
%TCIMACRO{\FORMULA{p}{p}{evaluate}}
%BeginExpansion
p%
%EndExpansion
$ after a $%
%TCIMACRO{\FORMULA{d}{d}{evaluate}}
%BeginExpansion
d%
%EndExpansion
$ percent discount. What was the original selling price?

\subsection{Choices}

\begin{itemize}
\item  \$$%
%TCIMACRO{
%\FORMULA{p(1-\frac{d}{100})}{p\left( 1.0-.0\,\allowbreak 1d\right) }{evaluatenum}}
%BeginExpansion
p\left( 1.0-.0\,\allowbreak 1d\right) %
%EndExpansion
$

\item  \$$%
%TCIMACRO{
%\FORMULA{p\left( 1-\frac{d}{50}\right) }{p\left( 1.0-.0\,\allowbreak 2d\right) }{evaluatenum}}
%BeginExpansion
p\left( 1.0-.0\,\allowbreak 2d\right) %
%EndExpansion
$

\item  \$$%
%TCIMACRO{
%\FORMULA{p\left( 1+\frac{d}{100}\right) }{p\left( 1.0+.0\,\allowbreak 1d\right) }{evaluatenum}}
%BeginExpansion
p\left( 1.0+.0\,\allowbreak 1d\right) %
%EndExpansion
$

\item  \$$%
%TCIMACRO{
%\FORMULA{p(1+\frac{d}{50})}{p\left( 1.0+.0\,\allowbreak 2d\right) }{evaluatenum}}
%BeginExpansion
p\left( 1.0+.0\,\allowbreak 2d\right) %
%EndExpansion
$

\item  \$$%
%TCIMACRO{
%\FORMULA{\frac{p}{1-\frac{d}{100}}}{\frac{p}{1.0-.0\,\allowbreak 1d}}{evaluatenum}}
%BeginExpansion
\frac{p}{1.0-.0\,\allowbreak 1d}%
%EndExpansion
\correctchoice{}$
\end{itemize}

\subsection{Comment}

(This is really the solution.)

\begin{enumerate}
\item  Let $P$ be the original price.

\item  Then, $P-\frac{%
%TCIMACRO{\FORMULA{d}{d}{evaluate}}
%BeginExpansion
d%
%EndExpansion
}{100}P=%
%TCIMACRO{\FORMULA{p}{p}{evaluate}}
%BeginExpansion
p%
%EndExpansion
$.

\item  Hence $P\left( 1-\frac{%
%TCIMACRO{\FORMULA{d}{d}{evaluate}}
%BeginExpansion
d%
%EndExpansion
}{100}\right) =%
%TCIMACRO{\FORMULA{p}{p}{evaluate}}
%BeginExpansion
p%
%EndExpansion
$.

\item  This is $P\left( 
%TCIMACRO{
%\FORMULA{1-\frac{\FORMULA{d}{d}{evaluate}}{100}}{1-\frac{1}{100}d}{evaluate}}
%BeginExpansion
1-\frac{1}{100}d%
%EndExpansion
\right) =%
%TCIMACRO{\FORMULA{p}{p}{evaluate}}
%BeginExpansion
p%
%EndExpansion
$.

\item  We get $P=\frac{%
%TCIMACRO{\FORMULA{p}{p}{evaluate}}
%BeginExpansion
p%
%EndExpansion
}{%
%TCIMACRO{\FORMULA{1-\frac{d}{100}}{1-\frac{1}{100}d}{evaluate}}
%BeginExpansion
1-\frac{1}{100}d%
%EndExpansion
}=%
%TCIMACRO{
%\FORMULA{\frac{p}{1-\frac{d}{100}}}{\frac{p}{1-\frac{1}{100}d}}{evaluate}}
%BeginExpansion
\frac{p}{1-\frac{1}{100}d}%
%EndExpansion
$.
\end{enumerate}

\section{Question}

\section{Variant}

\subsection{Setup}

$x:=\func{rand}(1,100)$

$y:=\func{rand}(1,100)$

$z:=\func{rand}(1,100)$

$a:=10\func{rand}(1,10)$

$d=\frac{x+y+a}{3}-\frac{y+z+a}{3}$

Condition: $\left( x-z>0\right) \wedge \left( d=\left\lfloor d\right\rfloor
\right) $

\subsection{Statement}

If the average of $x$, $y$, and $%
%TCIMACRO{\FORMULA{a}{a}{evaluate}}
%BeginExpansion
a%
%EndExpansion
$ is $%
%TCIMACRO{\FORMULA{d}{d}{evaluate}}
%BeginExpansion
d%
%EndExpansion
$ more than the average of $y$, $z$, and $%
%TCIMACRO{\FORMULA{a}{a}{evaluate}}
%BeginExpansion
a%
%EndExpansion
$, what is the value of $x-z$?

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{2\left( x-z\right) }{2x-2z}{evaluate}}
%BeginExpansion
2x-2z%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{x-z}{x-z}{evaluate}}
%BeginExpansion
x-z%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{x-y}{x-y}{evaluate}}
%BeginExpansion
x-y%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{d}{d}{evaluate}}
%BeginExpansion
d%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  Cannot be determined from the information given.
\end{description}

\section{Variant}

\subsection{Setup}

$P:=1000\func{rand}(40,100)$

Condition: $\left( \gcd \left( \frac{P}{1000},2\right) >1\right) \wedge
\left( \gcd \left( \frac{P}{1000},3\right) >1\right) $

$p:=\func{rand}(12,50)$

$t:=\func{rand}(12,50)$

Condition: $p>t$

Condition: $\left( \gcd \left( p,2\right) >1\right) \wedge $ $\left( \gcd
\left( t,2\right) >1\right) $

Condition: $\left( \frac{tP}{p}=\left\lfloor \frac{tP}{p}\right\rfloor
\right) $

\subsection{Statement}

OurTown, USA has a population of $%
%TCIMACRO{\FORMULA{P}{P}{evaluate}}
%BeginExpansion
P%
%EndExpansion
$. It was found that OurTown has a mean of $%
%TCIMACRO{\FORMULA{\frac{p}{10}}{.\,\allowbreak 1p}{evaluatenum}}
%BeginExpansion
.\,\allowbreak 1p%
%EndExpansion
$ persons per household and a mean of $%
%TCIMACRO{\FORMULA{\frac{t}{10}}{.\,\allowbreak 1t}{evaluatenum}}
%BeginExpansion
.\,\allowbreak 1t%
%EndExpansion
$ televisions per household. How many televisions are in OurTown?

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{
%\FORMULA{\frac{p-t}{10}P}{\frac{1}{10}\left( p-t\right) P}{evaluate}}
%BeginExpansion
\frac{1}{10}\left( p-t\right) P%
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{\frac{t}{10}\left( \frac{P}{p/10}\right) }{t\frac{P}{p}}{evaluate}}
%BeginExpansion
t\frac{P}{p}%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{
%\FORMULA{\frac{t}{20}\left( \frac{P}{p/10}\right) }{\frac{1}{2}t\frac{P}{p}}{evaluate}}
%BeginExpansion
\frac{1}{2}t\frac{P}{p}%
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{\frac{t}{50}\left( \frac{P}{p/10}\right) }{\frac{1}{5}t\frac{P}{p}}{evaluate}}
%BeginExpansion
\frac{1}{5}t\frac{P}{p}%
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{\frac{p-t}{5}P}{\frac{1}{5}\left( p-t\right) P}{evaluate}}
%BeginExpansion
\frac{1}{5}\left( p-t\right) P%
%EndExpansion
$
\end{itemize}

\section{Question}

\section{Variant}

\subsection{Setup}

$t:=\func{rand}(8,16)$

$f:=\frac{3}{t-1}$ [to make the formula in answers simpler]

\subsection{Statement}

A student bought $%
%TCIMACRO{\FORMULA{t}{t}{evaluate}}
%BeginExpansion
t%
%EndExpansion
$ books for the semester. If the cost of her engineering textbook was three
times the mean cost of the other $%
%TCIMACRO{\FORMULA{t-1}{t-1}{evaluate}}
%BeginExpansion
t-1%
%EndExpansion
$ books, then the cost of the engineering book was what fraction of the
total amount paid for the $%
%TCIMACRO{\FORMULA{t}{t}{evaluate}}
%BeginExpansion
t%
%EndExpansion
$ books?

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{\frac{f}{f+1}}{\frac{f}{f+1}}{evaluate}}
%BeginExpansion
\frac{f}{f+1}%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{\frac{f}{1-f}}{\frac{f}{1-f}}{evaluate}}
%BeginExpansion
\frac{f}{1-f}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{\frac{1-f}{f+1}}{\frac{1-f}{f+1}}{evaluate}}
%BeginExpansion
\frac{1-f}{f+1}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{\frac{1-f}{f}}{\frac{1-f}{f}}{evaluate}}
%BeginExpansion
\frac{1-f}{f}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{f}{f}{evaluate}}
%BeginExpansion
f%
%EndExpansion
$
\end{itemize}

\section{Variant}

\subsection{Setup}

$p:=\func{rand}(2,3)$

$t:=\func{rand}(4,6)$

$c:=\func{rand}(20,100)$

Condition: $\left( \gcd (p,c)\neq 1\right) $

\subsection{Statement}

If $%
%TCIMACRO{\FORMULA{p}{p}{evaluate}}
%BeginExpansion
p%
%EndExpansion
$ packages contain a total of $%
%TCIMACRO{\FORMULA{c}{c}{evaluate}}
%BeginExpansion
c%
%EndExpansion
$ cookies, how many cookies are there in $%
%TCIMACRO{\FORMULA{t}{t}{evaluate}}
%BeginExpansion
t%
%EndExpansion
$ packages?

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{\frac{tc}{p}}{t\frac{c}{p}}{evaluate}}
%BeginExpansion
t\frac{c}{p}%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{tc}{tc}{evaluate}}
%BeginExpansion
tc%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{\frac{c}{p}}{\frac{c}{p}}{evaluate}}
%BeginExpansion
\frac{c}{p}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{tp}{tp}{evaluate}}
%BeginExpansion
tp%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{cp}{cp}{evaluate}}
%BeginExpansion
cp%
%EndExpansion
$
\end{itemize}

\section{Variant}

\subsection{Setup}

$t:=\func{rand}(50,150)$

$n:=\func{rand}(\left\{ 2,3,5,7\right\} )$

Condition: $\gcd (n,t)\neq 1$

\subsection{Statement}

If $%
%TCIMACRO{\FORMULA{t}{t}{evaluate}}
%BeginExpansion
t%
%EndExpansion
$ equally priced tickets cost a total of $d$ dollars, $%
%TCIMACRO{\FORMULA{n}{n}{evaluate}}
%BeginExpansion
n%
%EndExpansion
$ of these tickets cost how many dollars?

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{nd}{nd}{evaluate}}
%BeginExpansion
nd%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{\frac{d}{n}}{\frac{d}{n}}{evaluate}}
%BeginExpansion
\frac{d}{n}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{n\cdot \frac{d}{t}}{n\frac{d}{t}}{evaluate}}
%BeginExpansion
n\frac{d}{t}%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{\frac{n}{d}}{\frac{n}{d}}{evaluate}}
%BeginExpansion
\frac{n}{d}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{\frac{t}{nd}}{\frac{t}{nd}}{evaluate}}
%BeginExpansion
\frac{t}{nd}%
%EndExpansion
$
\end{itemize}

\section{Question}

\section{Variant}

\subsection{Setup}

$r:=100\func{rand}(2,5)$

$j:=\func{rand}(\left\{ 5,10,15\right\} )$

\subsection{Statement}

Your school paid \$$%
%TCIMACRO{\FORMULA{r}{r}{evaluate}}
%BeginExpansion
r%
%EndExpansion
$ to rent a piece of office equipment for one year. The rent was then
increased by $%
%TCIMACRO{\FORMULA{j}{j}{evaluate}}
%BeginExpansion
j%
%EndExpansion
$ percent each year thereafter. How much will your school pay for the first
three years it rents the equipment?

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{3r+3j}{3.0r+3.0j}{evaluatenum}}
%BeginExpansion
3.0r+3.0j%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{3r+j}{3.0r+j}{evaluatenum}}
%BeginExpansion
3.0r+j%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{3r+2j}{3.0r+2.0j}{evaluatenum}}
%BeginExpansion
3.0r+2.0j%
%EndExpansion
$

\item  $%
%TCIMACRO{
%\FORMULA{3r+3\frac{j}{100}r+\left( \frac{j}{100}\right) ^{2}r}{3.0r+.0\,\allowbreak 3jr+.000\,\allowbreak 1j^{2}r}{evaluatenum}}
%BeginExpansion
3.0r+.0\,\allowbreak 3jr+.000\,\allowbreak 1j^{2}r%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{
%\FORMULA{3r+2\frac{jr}{100}}{3.0r+.0\,\allowbreak 2jr}{evaluatenum}}
%BeginExpansion
3.0r+.0\,\allowbreak 2jr%
%EndExpansion
$
\end{itemize}

\section{Variant}

\subsection{Setup}

$p:=\func{rand}(5,25)$

$n:=\func{rand}(4,6)$

\subsection{Statement}

Cheryl made $%
%TCIMACRO{\FORMULA{n}{n}{evaluate}}
%BeginExpansion
n%
%EndExpansion
$ payments on a loan with each payment being twice the amount of the
preceding one. If the total of all $%
%TCIMACRO{\FORMULA{n}{n}{evaluate}}
%BeginExpansion
n%
%EndExpansion
$ payments was \$$%
%TCIMACRO{
%\FORMULA{p\sum_{i=1}^{n}2^{i-1}}{p\left( \frac{1}{2}2^{n+1}-1\right) }{evaluate}}
%BeginExpansion
p\left( \frac{1}{2}2^{n+1}-1\right) %
%EndExpansion
$, how much was the first payment?

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{p-5}{p-5}{evaluate}}
%BeginExpansion
p-5%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{2p}{2p}{evaluate}}
%BeginExpansion
2p%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{p-1}{p-1}{evaluate}}
%BeginExpansion
p-1%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{p+2}{p+2}{evaluate}}
%BeginExpansion
p+2%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{p}{p}{evaluate}}
%BeginExpansion
p%
%EndExpansion
\correctchoice{}$
\end{itemize}

\section{Variant}

\subsection{Setup}

$t:=\func{rand}(120,199)$

$d:=\func{rand}(20,60)$

Condition: $\gcd (2,t+d)>1$

\subsection{Statement}

Out of $%
%TCIMACRO{\FORMULA{t}{t}{evaluate}}
%BeginExpansion
t%
%EndExpansion
$ total games played, a softball team won $%
%TCIMACRO{\FORMULA{d}{d}{evaluate}}
%BeginExpansion
d%
%EndExpansion
$ more games than it lost. If there were no ties, how many games did the
team win?

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{\frac{t+d}{2}}{\frac{1}{2}t+\frac{1}{2}d}{evaluate}}
%BeginExpansion
\frac{1}{2}t+\frac{1}{2}d%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{t-d}{t-d}{evaluate}}
%BeginExpansion
t-d%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{t-2d}{t-2d}{evaluate}}
%BeginExpansion
t-2d%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{\frac{t+d}{2}+1}{\frac{1}{2}t+\frac{1}{2}d+1}{evaluate}}
%BeginExpansion
\frac{1}{2}t+\frac{1}{2}d+1%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{2d}{2d}{evaluate}}
%BeginExpansion
2d%
%EndExpansion
$
\end{itemize}

\subsection{Comment}

(This is really the solution.)

\begin{enumerate}
\item  Let $w$ be the number of games won.

\item  Then, $%
%TCIMACRO{\FORMULA{t}{t}{evaluate}}
%BeginExpansion
t%
%EndExpansion
-w$ games were lost.

\item  Hence $w-\left( 
%TCIMACRO{\FORMULA{t}{t}{evaluate}}
%BeginExpansion
t%
%EndExpansion
-w\right) =%
%TCIMACRO{\FORMULA{d}{d}{evaluate}}
%BeginExpansion
d%
%EndExpansion
$.

\item  This is $2w=%
%TCIMACRO{\FORMULA{t}{t}{evaluate}}
%BeginExpansion
t%
%EndExpansion
+%
%TCIMACRO{\FORMULA{d}{d}{evaluate}}
%BeginExpansion
d%
%EndExpansion
=%
%TCIMACRO{\FORMULA{t+d}{t+d}{evaluate}}
%BeginExpansion
t+d%
%EndExpansion
$.

\item  We get $w=\frac{%
%TCIMACRO{\FORMULA{t+d}{t+d}{evaluate} }
%BeginExpansion
t+d%
%EndExpansion
}{2}$.
\end{enumerate}

\section{Question}

\subsection{Setup}

$a:=\func{rand}(-5,-1)$

$b:=\func{rand}(1,9)$

$c:=\func{rand}(10,30)$

Condition: $\frac{c-b}{a}=\left\lfloor \frac{c-b}{a}\right\rfloor $

\subsection{Statement}

If $%
%TCIMACRO{\FORMULA{ax}{ax}{evaluate}}
%BeginExpansion
ax%
%EndExpansion
+%
%TCIMACRO{\FORMULA{b}{b}{evaluate}}
%BeginExpansion
b%
%EndExpansion
\leq 
%TCIMACRO{\FORMULA{c}{c}{evaluate}}
%BeginExpansion
c%
%EndExpansion
$, which of the following must be true?

\subsection{Choices}

\begin{itemize}
\item  $x\geq 
%TCIMACRO{\FORMULA{\frac{b}{a}}{\frac{b}{a}}{evaluate}}
%BeginExpansion
\frac{b}{a}%
%EndExpansion
$

\item  $x\leq 
%TCIMACRO{\FORMULA{\frac{c-b}{a}}{\frac{c-b}{a}}{evaluate}}
%BeginExpansion
\frac{c-b}{a}%
%EndExpansion
$

\item  $x\geq 
%TCIMACRO{\FORMULA{\frac{c}{a}}{\frac{c}{a}}{evaluate}}
%BeginExpansion
\frac{c}{a}%
%EndExpansion
$

\item  $x\geq 
%TCIMACRO{\FORMULA{\frac{c-b}{a}}{\frac{c-b}{a}}{evaluate}}
%BeginExpansion
\frac{c-b}{a}%
%EndExpansion
\correctchoice{}$

\item  $x\leq 
%TCIMACRO{\FORMULA{c-b}{c-b}{evaluate}}
%BeginExpansion
c-b%
%EndExpansion
$
\end{itemize}

\section{Question}

\section{Variant}

\subsection{Setup}

$b:=\func{rand}(2,5)$

$c:=\func{rand}(20,30)$

\subsection{Statement}

$%
%TCIMACRO{\FORMULA{b}{b}{evaluate}}
%BeginExpansion
b%
%EndExpansion
^{%
%TCIMACRO{\FORMULA{c+1}{c+1}{evaluate} }
%BeginExpansion
c+1%
%EndExpansion
}-%
%TCIMACRO{\FORMULA{b}{b}{evaluate}}
%BeginExpansion
b%
%EndExpansion
^{%
%TCIMACRO{\FORMULA{c}{c}{evaluate} }
%BeginExpansion
c%
%EndExpansion
}=$

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{b}{b}{evaluate}}
%BeginExpansion
b%
%EndExpansion
^{\frac{%
%TCIMACRO{\FORMULA{c+1}{c+1}{evaluate} }
%BeginExpansion
c+1%
%EndExpansion
}{%
%TCIMACRO{\FORMULA{c}{c}{evaluate} }
%BeginExpansion
c%
%EndExpansion
}}$

\item  $%
%TCIMACRO{\FORMULA{b}{b}{evaluate}}
%BeginExpansion
b%
%EndExpansion
^{1}$

\item  $%
%TCIMACRO{\FORMULA{b-1}{b-1}{evaluate}}
%BeginExpansion
b-1%
%EndExpansion
\cdot 
%TCIMACRO{\FORMULA{b}{b}{evaluate}}
%BeginExpansion
b%
%EndExpansion
^{%
%TCIMACRO{\FORMULA{c}{c}{evaluate} }
%BeginExpansion
c%
%EndExpansion
}\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{b}{b}{evaluate}}
%BeginExpansion
b%
%EndExpansion
^{%
%TCIMACRO{\FORMULA{c+1}{c+1}{evaluate} }
%BeginExpansion
c+1%
%EndExpansion
}$

\item  $%
%TCIMACRO{\FORMULA{b}{b}{evaluate}}
%BeginExpansion
b%
%EndExpansion
^{%
%TCIMACRO{\FORMULA{2c+1}{2c+1}{evaluate} }
%BeginExpansion
2c+1%
%EndExpansion
}$
\end{itemize}

\section{Variant}

\subsection{Setup}

$b:=\func{rand}\left( 1,5\right) $

$c:=\func{rand}(1,5)$

Condition: $b<c$

\subsection{Statement}

$\frac{4^{%
%TCIMACRO{\FORMULA{b}{b}{evaluate} }
%BeginExpansion
b%
%EndExpansion
}}{2^{%
%TCIMACRO{\FORMULA{c}{c}{evaluate} }
%BeginExpansion
c%
%EndExpansion
}}+\frac{2^{%
%TCIMACRO{\FORMULA{c}{c}{evaluate} }
%BeginExpansion
c%
%EndExpansion
}}{4^{%
%TCIMACRO{\FORMULA{b}{b}{evaluate} }
%BeginExpansion
b%
%EndExpansion
}}=$

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{2^{2b-c}+2^{c-2b}}{2^{2b-c}+2^{c-2b}}{evaluate}}
%BeginExpansion
2^{2b-c}+2^{c-2b}%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{2^{b-c}+2^{c-b}}{2^{b-c}+2^{c-b}}{evaluate}}
%BeginExpansion
2^{b-c}+2^{c-b}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{2^{2b}+2^{-2b}}{2^{2b}+2^{-2b}}{evaluate}}
%BeginExpansion
2^{2b}+2^{-2b}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{2^{2b-c}+2^{c}}{2^{2b-c}+2^{c}}{evaluate}}
%BeginExpansion
2^{2b-c}+2^{c}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{2^{-c}+2^{c-2b}-1}{2^{-c}+2^{c-2b}-1}{evaluate}}
%BeginExpansion
2^{-c}+2^{c-2b}-1%
%EndExpansion
$
\end{itemize}

\section{Question}

\section{Variant}

\subsection{Setup}

$a:=\func{rand}(1,20)$

$b:=\func{rand}(1,10)$

$c:=\func{rand}(1,9)$

$d:=\func{rand}(1,9)$

Condition: $c\neq d$

Choices: No Permute

\subsection{Statement}

Try and find a relationship between $A$ and $B$.

\begin{center}
\begin{tabular}{|c|c|}
\hline
$A$ & $B$ \\ \hline
$%
%TCIMACRO{\FORMULA{a}{a}{evaluate} }
%BeginExpansion
a%
%EndExpansion
-%
%TCIMACRO{\FORMULA{b}{b}{evaluate} }
%BeginExpansion
b%
%EndExpansion
-\left( 
%TCIMACRO{\FORMULA{c}{c}{evaluate} }
%BeginExpansion
c%
%EndExpansion
-%
%TCIMACRO{\FORMULA{d}{d}{evaluate} }
%BeginExpansion
d%
%EndExpansion
\right) $ & $%
%TCIMACRO{\FORMULA{a}{a}{evaluate} }
%BeginExpansion
a%
%EndExpansion
-\left( 
%TCIMACRO{\FORMULA{b}{b}{evaluate} }
%BeginExpansion
b%
%EndExpansion
-%
%TCIMACRO{\FORMULA{c}{c}{evaluate} }
%BeginExpansion
c%
%EndExpansion
-%
%TCIMACRO{\FORMULA{d}{d}{evaluate} }
%BeginExpansion
d%
%EndExpansion
\right) $ \\ \hline
\end{tabular}
\end{center}

\subsection{Choices}

\begin{itemize}
\item  $A<B\correctchoice{}$

\item  $A=B$

\item  $A>B$
\end{itemize}

\begin{description}
\item[Fixed]  the relationship cannot be determined from the information
given
\end{description}

\section{Variant}

\subsection{Setup}

$a:=\func{rand}(2,20)$

$b:=\func{rand}(1,10)$

$c:=\func{rand}(1,9)$

$d:=\func{rand}(1,9)$

Condition: $\left( c\neq d\right) \wedge \left( c+d<9\right) \wedge \left(
a\neq b\right) \wedge \left( d>c\right) $

Choices: No Permute

\subsection{Statement}

Try and find a relationship between $A$ and $B$.

\begin{center}
\begin{tabular}{|c|c|}
\hline
$A$ & $B$ \\ \hline
$\frac{1}{%
%TCIMACRO{\FORMULA{a}{a}{evaluate} }
%BeginExpansion
a%
%EndExpansion
}+\frac{1}{%
%TCIMACRO{\FORMULA{b}{b}{evaluate} }
%BeginExpansion
b%
%EndExpansion
}+\frac{1}{%
%TCIMACRO{\FORMULA{c}{c}{evaluate} }
%BeginExpansion
c%
%EndExpansion
}$ & $\frac{1}{%
%TCIMACRO{\FORMULA{b}{b}{evaluate} }
%BeginExpansion
b%
%EndExpansion
}+\frac{1}{%
%TCIMACRO{\FORMULA{a}{a}{evaluate} }
%BeginExpansion
a%
%EndExpansion
}+\frac{1}{%
%TCIMACRO{\FORMULA{d}{d}{evaluate} }
%BeginExpansion
d%
%EndExpansion
}$ \\ \hline
\end{tabular}
\end{center}

\subsection{Choices}

\begin{itemize}
\item  $A<B$

\item  $A=B$

\item  $A>B\correctchoice{}$
\end{itemize}

\begin{description}
\item[Fixed]  the relationship cannot be determined from the information
given
\end{description}

\section{Variant}

\subsection{Setup}

$a:=\func{rand}(2,20)$

$b:=\func{rand}(1,10)$

Condition: $\left( a>b\right) $

Choices: No Permute

\subsection{Statement}

Try and find a relationship between $A$ and $B$.

\begin{center}
\begin{tabular}{|c|}
\hline
$%
%TCIMACRO{\FORMULA{a}{a}{evaluate} }
%BeginExpansion
a%
%EndExpansion
A<%
%TCIMACRO{\FORMULA{b}{b}{evaluate} }
%BeginExpansion
b%
%EndExpansion
B$ \\ \hline
\end{tabular}
\end{center}

\subsection{Choices}

\begin{itemize}
\item  $A<B\correctchoice{}$

\item  $A=B$

\item  $A>B$
\end{itemize}

\begin{description}
\item[Fixed]  the relationship cannot be determined from the information
given
\end{description}

\section{Variant}

\subsection{Setup}

$a:=\func{rand}(2,20)$

$b:=\func{rand}(1,10)$

Condition: $\left( a>b\right) $

Choices: No Permute

\subsection{Statement}

Try and find a relationship between $A$ and $B$.

\begin{center}
\begin{tabular}{|c|}
\hline
$%
%TCIMACRO{\FORMULA{a}{a}{evaluate} }
%BeginExpansion
a%
%EndExpansion
A>%
%TCIMACRO{\FORMULA{b}{b}{evaluate} }
%BeginExpansion
b%
%EndExpansion
B$ \\ \hline
\end{tabular}
\end{center}

\subsection{Choices}

\begin{itemize}
\item  $A<B$

\item  $A=B$

\item  $A>B$
\end{itemize}

\begin{description}
\item[Fixed]  the relationship cannot be determined from the information
given$\correctchoice{}$
\end{description}

\section{Variant}

\subsection{Setup}

$a:=\func{rand}(2,20)$

$b:=\func{rand}(1,10)$

Condition: $\left( a>b\right) \wedge \left( a+b<10\right) $

Choices: No Permute

\subsection{Statement}

Try and find a relationship between $A$ and $B$.

\begin{center}
\begin{tabular}{|c|c|}
\hline
$A$ & $B$ \\ \hline
$\frac{%
%TCIMACRO{\FORMULA{\frac{a}{b}}{\frac{a}{b}}{evaluate} }
%BeginExpansion
\frac{a}{b}%
%EndExpansion
}{\left( 
%TCIMACRO{\FORMULA{\frac{a}{b}}{\frac{a}{b}}{evaluate} }
%BeginExpansion
\frac{a}{b}%
%EndExpansion
\right) ^{2}}$ & $%
%TCIMACRO{\FORMULA{\frac{b}{a}}{\frac{b}{a}}{evaluate} }
%BeginExpansion
\frac{b}{a}%
%EndExpansion
$ \\ \hline
\end{tabular}
\end{center}

\subsection{Choices}

\begin{itemize}
\item  $A<B$

\item  $A=B\correctchoice{}$

\item  $A>B$
\end{itemize}

\begin{description}
\item[Fixed]  the relationship cannot be determined from the information
given
\end{description}

\section{Variant}

\subsection{Setup}

$b:=\func{rand}(-10,10)$

Choices: No Permute

\subsection{Statement}

Try and find a relationship between $A$ and $B$.

\begin{center}
\begin{tabular}{|c|c|}
\hline
$A$ & $B$ \\ \hline
$x^{2}$ & $\left( 
%TCIMACRO{\FORMULA{x-b}{x-b}{evaluate} }
%BeginExpansion
x-b%
%EndExpansion
\right) ^{2}$ \\ \hline
\end{tabular}
\end{center}

\subsection{Choices}

\begin{itemize}
\item  $A<B$

\item  $A=B$

\item  $A>B$
\end{itemize}

\begin{description}
\item[Fixed]  the relationship cannot be determined from the information
given$\correctchoice{}$
\end{description}

\section{Question}

\subsection{Setup}

Choices: No Permute

\subsection{Statement}

\FRAME{dtbpF}{3.0441in}{1.0326in}{0pt}{}{}{sat line figure.bmp}{\special%
{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "USEDEF";valid_file "F";width 3.0441in;height 1.0326in;depth
0pt;original-width 216.8125pt;original-height 72.25pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'SAT Line
Figure.bmp';file-properties "XNPEU";}}

If $AB>CD$ then which of the following is true?

\begin{center}
$
\begin{tabular}{|l|l|}
\hline
I & $AB<BD$ \\ \hline
II & $AC>BD$ \\ \hline
III & $BC<CD$ \\ \hline
\end{tabular}
$
\end{center}

\subsection{Choices}

\begin{itemize}
\item  I

\item  II$\correctchoice{}$

\item  II and III

\item  I and II

\item  I, II, and III
\end{itemize}

\section{Question}

\subsection{Setup}

$b:=\func{rand}\left( 2,5\right) $

$c:=\func{rand}(2,5)$

$d:=\func{rand}(2,5)$

$q:=\func{rand}\left( 2,12\right) $

\subsection{Statement}

If $%
%TCIMACRO{\FORMULA{bc}{bc}{evaluate}}
%BeginExpansion
bc%
%EndExpansion
q=%
%TCIMACRO{\FORMULA{bcq}{bcq}{evaluate}}
%BeginExpansion
bcq%
%EndExpansion
$, then $%
%TCIMACRO{\FORMULA{d}{d}{evaluate}}
%BeginExpansion
d%
%EndExpansion
\times 
%TCIMACRO{\FORMULA{b}{b}{evaluate}}
%BeginExpansion
b%
%EndExpansion
q=$

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{dbq}{dbq}{evaluate}}
%BeginExpansion
dbq%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{bq}{bq}{evaluate}}
%BeginExpansion
bq%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{q}{q}{evaluate}}
%BeginExpansion
q%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{dbcq}{dbcq}{evaluate}}
%BeginExpansion
dbcq%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{dbq+2}{dbq+2}{evaluate}}
%BeginExpansion
dbq+2%
%EndExpansion
$
\end{itemize}

\section{Question}

\subsection{Setup}

$b:=\func{rand}\left( 2,20\right) $

$c:=\func{rand}(2,20)$

Condition: $\left( b\neq c\right) \wedge \left( \gcd (bc,3)>1\right) \wedge
\left( \gcd (bc,2)>1\right) $

\subsection{Statement}

If $%
%TCIMACRO{\FORMULA{b}{b}{evaluate}}
%BeginExpansion
b%
%EndExpansion
$ and $%
%TCIMACRO{\FORMULA{c}{c}{evaluate}}
%BeginExpansion
c%
%EndExpansion
$ each divide a number $N$ without remainder, what is the value of $N$?

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{\frac{bc}{6}}{\frac{1}{6}bc}{evaluate}}
%BeginExpansion
\frac{1}{6}bc%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{\frac{bc}{3}}{\frac{1}{3}bc}{evaluate}}
%BeginExpansion
\frac{1}{3}bc%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{\frac{bc}{2}}{\frac{1}{2}bc}{evaluate}}
%BeginExpansion
\frac{1}{2}bc%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{bc}{bc}{evaluate}}
%BeginExpansion
bc%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  $N$ cannot be determined from the information given.$%
\correctchoice{}$
\end{description}

\section{Question}

\subsection{Setup}

$c:=\func{rand}(1,20)$

\subsection{Statement}

What is the diameter of a circle with circumference $%
%TCIMACRO{\FORMULA{c}{c}{evaluate}}
%BeginExpansion
c%
%EndExpansion
$?

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{\frac{c}{\pi }}{\frac{c}{\pi }}{evaluate}}
%BeginExpansion
\frac{c}{\pi }%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{\frac{c}{2\pi }}{\frac{1}{2}\frac{c}{\pi }}{evaluate}}
%BeginExpansion
\frac{1}{2}\frac{c}{\pi }%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{c}{c}{evaluate}}
%BeginExpansion
c%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{c\pi }{c\pi }{evaluate}}
%BeginExpansion
c\pi %
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{2c\pi }{2c\pi }{evaluate}}
%BeginExpansion
2c\pi %
%EndExpansion
$
\end{itemize}

\section{Question}

\subsection{Statement}

How many numbers from $4$ to $99$ inclusive are equal to the square of an
integer?

\subsection{Choices}

\begin{itemize}
\item  nine

\item  ten

\item  eight$\correctchoice{}$

\item  seven

\item  six
\end{itemize}

\section{Question}

\subsection{Setup}

$m:=\func{rand}\left( -2,1\right) $

$n:=\func{rand}\left( 0,1\right) $

$p:=\func{rand}\left( 1,3\right) $

Condition: $\left( m\neq n\right) $

\subsection{Statement}

If $%
%TCIMACRO{\FORMULA{10^{m}}{10.0^{m}}{evaluatenum}}
%BeginExpansion
10.0^{m}%
%EndExpansion
$\% of $m$ is equal to $%
%TCIMACRO{\FORMULA{10^{n}}{10^{n}}{evaluate}}
%BeginExpansion
10^{n}%
%EndExpansion
$\% of $n$, then $m$ is what percent of $%
%TCIMACRO{\FORMULA{10^{p}}{10^{p}}{evaluate}}
%BeginExpansion
10^{p}%
%EndExpansion
n$?

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{10^{n-m-p}}{10^{n-m-p}}{evaluate}}
%BeginExpansion
10^{n-m-p}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{10^{n-m-p+1}}{10^{n-m-p+1}}{evaluate}}
%BeginExpansion
10^{n-m-p+1}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{10^{n-m-p+2}}{10^{n-m-p+2}}{evaluate}}
%BeginExpansion
10^{n-m-p+2}%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{10^{n-m-p+3}}{10^{n-m-p+3}}{evaluate}}
%BeginExpansion
10^{n-m-p+3}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{10^{n-m-p+5}}{10^{n-m-p+5}}{evaluate}}
%BeginExpansion
10^{n-m-p+5}%
%EndExpansion
$
\end{itemize}

\end{document}
