sample_exam.tex
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\begin{document}
\begin{large}Math 110 - College Algebra\end{large} \hfill Tuesday, November 13, 2001\\*[5mm]
Name: \blank\blank\blank\blank \hfill Exam 1 \\[5mm]
\centerline{Show all your work to receive full credit.}
\begin{enumerate}
% Question 1 -- Note that this remark does not set the page number, but makes
% it easier to see which question is which while editing the document
\item (2 points each) Consider the numbers $-9.8,3\frac{1}{5},\sqrt[3]{4},0.38,0,\sqrt{13},\frac{8}{5},-4$.
\begin{enumerate} % This starts a numbered list
\item Which are whole numbers? \smallspace
\item Which are rational numbers? \smallspace
\end{enumerate}
% Question 2
\item (2 points) Write interval notation for $\{x|-10< x\leq 4\}$. \smallspace
% Question 3
\item (2 points) Compute and write scientific notation for
$\displaystyle\frac{3.9\times10^{-2}}{5.2\times10^7}$. \smallspace
% Question 4
\item (3 points each) Simplify. \begin{enumerate}
\item $(-6a^2b^-5)(3a^4b^7)$ \smallspace
\item $\displaystyle\frac{2+\frac{2}{y}}{y-\frac{2}{y}}$ \smallspace\smallspace
\end{enumerate}
% Question 5
\item (3 points each) Factor. \begin{enumerate}
\item $4x^2+3x-10$ \smallspace
\item $n^3-27$ \smallspace
\end{enumerate}
\newpage
% Question 6
\item (4 points) Subtract and simplify $\frac{x}{x^2-49}-\frac{5}{x^2-6x-7}$ \mediumspace
% Question 7
\item (3 points) Solve $x^2-2x-15=0$ algebraically for $x$. \smallspace
% Question 8
\item (3 points) Solve $A=\frac{1}{2}h(b_1+b_2)$ for $b_1$. \smallspace
% Question 9
\item (3 points) A guy wire is extended from the top of a 9-ft pole to a place on the ground 4 ft
from the base of the pole. How long is the guy wire? Round your answer to the nearest tenth
of a foot. \smallspace
% Question 10
\item (2 points each) Consider the relation $\{(-1,0),(3,-1),(4,6),(-4,2)\}$ \begin{enumerate}
\item Is this a function? \smallspace
\item What is the range of the relation? \smallspace
\end{enumerate}
% Question 11
\item (2 points each) Consider the function $f(x)=\sqrt{x^2-16}$ \begin{enumerate}
\item Use your grapher to graph the function. Raise your hand to have the instructor check
your answer.
\item Visually estimate the domain of $f(x)$. \smallspace
\end{enumerate}
\newpage % this forces a page break
% Question 12
\item (3 points) Write the equation for the line that passes through $(5,0)$ and $(-3,-6)$. \smallspace\smallspace
% Question 13
\item (3 points) Determine whether the lines $$\left\{\begin{array}{l}
y+2x=6 \\
2x-y=4 \
\end{array}\right.$$ are parallel, perpendicular, or neither. \smallspace\smallspace
% Question 14
\item The table below shows the amount of waste generated in pounds per person, per day,
in the United States over several years.
\begin{center} % Centers the table between the left and right margins
\begin{tabular}{|c|c|} % Starts a table and specifies the number of columns
\hline
Year, $x$ & Average local monthly bill \\ \hline
1980, 0 & 3.7 \\ \hline
1985, 5 & 3.8 \\ \hline
1990, 10 & 4.3 \\ \hline
1995, 15 & 4.3 \\ \hline
\end{tabular}
\end{center}
\begin{enumerate}
\item (4 points) Use a grapher to fit a regression line to the data. Write the equation of
the line. \smallspace
\item (2 points) Use the regression line to predict the amount of waste generated per
person, per day, in 2003. \smallspace
\end{enumerate}
% Question 15
\item (3 points) Write an equation for a function that has the shape of $y=x^3$ but shifted left
3 units and up 2 units. \smallspace
\newpage
% Question 16
\item (4 points) The graph of the function $y=f(x)$ is shown on the left. On the right, make
a graph of $y=f(-x)$.
\setlength{\unitlength}{4mm} % Specifies the size of a unit in the following picture environment
\begin{center}\begin{tabular}{ccc}
% Here we have a table with 1 row, 3 columns. The first box has a picture environment, the second
% has some space (\hspace) and the third has another picture environment.
\begin{picture}(11,11)(-5.5,-5.5) % Starts a picture 11 x 11 units, the bottom corner at (-5.5,-5.5)
% Draw axes
\put(0,-5.5){\line(0,1){11}} \put(-5.5,0){\line(1,0){11}}
% Draw little hash marks at each unit
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\put(4,-.25){\line(0,1){.5}} \put(5,-.25){\line(0,1){.5}}
% Draw the function
\put(-3,-2){\line(1,2){2}} \put(-1,2){\line(1,0){3}} \put(2,2){\line(2,1){2}}
\end{picture} & \hspace*{1cm} & \begin{picture}(11,11)(-5.5,-5.5) % This has the end of the first picture, the middle column of space, and the beginning of the third column's picture
% Draw axes
\put(0,-5.5){\line(0,1){11}} \put(-5.5,0){\line(1,0){11}}
% Draw little has marks at each unit
\put(-.25,-5){\line(1,0){.5}} \put(-.25,-4){\line(1,0){.5}} \put(-.25,-3){\line(1,0){.5}}
\put(-.25,-2){\line(1,0){.5}} \put(-.25,-1){\line(1,0){.5}} \put(-.25,1){\line(1,0){.5}}
\put(-.25,2){\line(1,0){.5}} \put(-.25,3){\line(1,0){.5}} \put(-.25,4){\line(1,0){.5}}
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\put(-3,-.25){\line(0,1){.5}} \put(-2,-.25){\line(0,1){.5}} \put(-1,-.25){\line(0,1){.5}}
\put(1,-.25){\line(0,1){.5}} \put(2,-.25){\line(0,1){.5}} \put(3,-.25){\line(0,1){.5}}
\put(4,-.25){\line(0,1){.5}} \put(5,-.25){\line(0,1){.5}}
\end{picture}
\end{tabular} % Remember: everything starting with \begin needs to end with \end.
\end{center} \smallspace\smallspace\smallspace
% Question 17
\item For $f(x)=-2x-5$ and $g(x)=x^2-4$, find
\begin{enumerate}
\item (1 point) the domain of $f$ \smallspace
\item (1 point) the domain of $g$ \smallspace
\item (3 points) $(f-g)(x)$ \smallspace
\item (3 points) $(fg)(x)$ \smallspace
\item (2 points) the domain of $(f/g)(x)$ \smallspace
\end{enumerate}
\newpage
% Question 18
\item Solve. Find exact solutions.
\begin{enumerate}
\item (4 points) $x+3\sqrt{x}-40=0$ \mediumspace
\item (3 points) $\displaystyle\frac{40}{2x-3}+\frac{30}{4x+5}=-11$ \mediumspace
\item (4 points) $|x-3|\leq7$ \mediumspace
\end{enumerate}
% Question 19
\item Simplify.
\begin{enumerate}
\item (3 points) $(6+4i)(7-3i)$ \smallspace
\item (2 points) $i^{16}$ \smallspace
\end{enumerate}
\newpage
% Question 20
\item Consider the function $f(x)=-x^2-4x+2$.
\begin{enumerate}
\item (3 points) Find the vertex. \smallspace
\item (3 points) Find the line of symmetry \smallspace
\item (2 points) Is there a maximum? If so, what is it? \smallspace
\item (2 points) Is there a minimum? If so, what is it? \smallspace
\end{enumerate}
% Question 21
\item (4 points) The sum of the base and the height of a triangle is 60 in. Find the
dimensions for which the area is maximum.
\end{enumerate}
\end{document}