LaTeX Multiple Choice Exam Template (Precalculus)

latex_multiplechoice_exam.tex

\documentclass[legalpaper, 12pt, addpoints]{exam}
\usepackage[margin=1in]{geometry}
\usepackage[utf8]{inputenc}
\usepackage{graphics}
\usepackage{color}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{enumitem}
\usepackage{xcolor}
\usepackage{cancel}
\usepackage{ragged2e}
\usepackage{graphicx}
\usepackage{multicol}
\usepackage{color}
\usepackage{tikz}

\CorrectChoiceEmphasis{\itseries\color{red}}

\begin{document}
\begin{coverpages}

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%\begin{figure}[t]
%\includegraphics[width=1\textwidth,height=1.2\textheight,keepaspectratio]{%header-cufm.png}
%\end{figure}

\begin{center}
Spring 2018 \\
\textbf{Precalculus' Final Examination } \\
nth Semester \\
Section 000
\end{center}
\extraheadheight{-0.8in}

\vspace{0.25in}
\parbox{6in}{
\textbf{Objective:} Assess understanding of function behavior and calculus readiness. This exam also aims to provide a comprehensive assessment on concepts and definitions that are necessary to be successful in further Mathematics courses.)}
\vspace{0.15in}

\parbox{6in}{{\textbf{General Instructions:} Read carefully each exercise. Fill in your \textit{scantron} with a pencil and circle the correct answer on paper as well. Scratch paper is not allowed under any circumstances. All your work must be done in these pages.}
\vspace{0.15in}}

 \begin{center}
\fbox{\fbox{\parbox{6in}{
\begin{itemize}
    \item You have up to 120 minutes.
    
    \item Every item on the test awards 2 points for each correct answer, for a maximum possible score of 100 points.
    
    \item Non-graphing calculators are allowed. TI-84 or similar, including smart devices, are prohibited. 

    
    \item One half-page formula sheet printed in black ink and showing the instructor's authorization may be used. Any other form of aid is not allowed. 
    
    \item Mere suspicion of cheating, sharing calculators or using any unfair means of aid is enough to get your test withdrawn.
        
    \item When you are done, turn in the examination, your \textit{scantron} and your formula sheet. Failure to do so will result in an automatic failing grade.


    
\end{itemize} }}}
\vspace{0.2in}
\end{center}
\vspace{0.15in}
\runningheadrule \extraheadheight{0.14in}

\lhead{\ifcontinuation{Question \ContinuedQuestion\ continues\ldots}{}}
\runningheader{Precalculus}{Final Examination}{Spring 2018}
\runningfooter{4th Semester}
              {\thepage\ of \numpages}
              {Version A}
\vspace{0.15in}

\vspace{0.1in}

%-comment out the next line to display point value for each question -%
\nopointsinmargin
\setlength\linefillthickness{0.1pt}
\setlength\answerlinelength{0.1in}
\end{coverpages}

\parbox{6in}{\textsc{{SIDE A}}

\vspace{0.15in}

\parbox{5in}{
{\textsc{\textbf{Part I.} True or False Questions.}}}}

\vspace{0.15in}
\hrule 
\vspace{0.1in}
\begin{questions}

\question Differential Calculus is the branch of mathematics dedicated to the study of rates of change.

\begin{oneparchoices}
    \CorrectChoice True
    \choice False
\end{oneparchoices}

\question The domain of a function \(f(x)\) is the set of all the values of \(x\) for which \(f(x)\) is defined.

\begin{oneparchoices}
    \CorrectChoice True
    \choice False
\end{oneparchoices}

\question The base of a natural logarithm, \(\ln\),  is \(e\).

\begin{oneparchoices}
    \CorrectChoice True
    \choice False
\end{oneparchoices}

\question $\sqrt{3}$ is an irrational number 

\begin{oneparchoices}
    \CorrectChoice True
    \choice False
\end{oneparchoices}

\question $f(x) = |x|$ is continuous for all real numbers.

\begin{oneparchoices}
    \CorrectChoice True
    \choice False
\end{oneparchoices}

\question  If $(x+a)$ is a factor of \(p(x)\), then $x=a$ is a solution to $p(x)$ 

\begin{oneparchoices}
    \choice True
    \CorrectChoice False
\end{oneparchoices}


\question  If  $f(x)=g^{-1}(x)$, then $f(x)$ has the same domain of  $g(x)$ and $g^{-1}(x)$ has the same range of $f^{-1}(x)$

\begin{oneparchoices}
    \choice True
    \CorrectChoice False
\end{oneparchoices}

\question  All continuous functions are differentiable over their domain

\begin{oneparchoices}
    \CorrectChoice True
    \choice False
\end{oneparchoices}

\question  Polynomial functions are differentiable on \((-\infty,\infty)\).

\begin{oneparchoices}
    \CorrectChoice True
    \choice False
\end{oneparchoices}


\question  If $\lim_{x\to a} =$ does not exist, then $x=a$ must be undefined.

\begin{oneparchoices}
    \choice True
    \CorrectChoice False
\end{oneparchoices}

\vspace{0.2in}

\parbox{6in}{\textsc{\textbf{Part II.} Multiple Choice Questions.}}
\vspace{0.1in}
\hrule
\vspace{0.1in}


\question Simplify $\sqrt{500} - \sqrt{80}$
    \begin{choices}
            \choice $5\sqrt{5}$
            \CorrectChoice $6\sqrt{5}$
            \choice $10\sqrt{5}$
            \choice $16\sqrt{5}$
            \choice $25$
    \end{choices}
    
\question The vertex of the parabola $y=(x-2)^2$ is located at
        \begin{choices}
            \choice $(-2,0)$
            \CorrectChoice $(2,0)$
            \choice $(-2,-2)$
            \choice $(0, 0)$
            \choice none of the above
        \end{choices}
        
\pagebreak

\question If a polynomial function of degree 2 has an absolute maximum, then this point must also be a
        \begin{choices}
            \choice tangent line
            \CorrectChoice vertex
            \choice inflection point
            \choice absolute minimum 
            \choice none of the above
        \end{choices}
\vspace{0.10in}

\question Find the vertical asymptote of $f(x)=\dfrac{x}{-x^2-2x}$.
        \begin{choices}
        \choice $x = 1/2$
        \CorrectChoice $x=-2$
        \choice $x=4$
        \choice $x = -1/4$
        \choice $x=2$
        \end{choices}
    \vspace{0.10in}

\question Which of the following has a vertical asymptote at $x=0$? 
\begin{choices}
        \choice  $e^x$
        \CorrectChoice $\ln{x}$
        \choice $|x|$
        \choice $\sin{x}$
        \choice ${x}$
 \end{choices}
\vspace{0.1in}

\question Which of the following best describes the function $f(x) = \dfrac{3x^2}{5x+25}$
    \begin{choices}
         \choice polynomial
         \CorrectChoice rational
         \choice quadratic
         \choice asymptotic
         \choice transcendental
    \end{choices}
    
\vspace{0.10in}

\question Consider \(f(x) = \dfrac{x}{x^2+8x+16}\). 
Determine the values of $x$ where $f(x)$ is discontinuous.
 \begin{choices}
            \choice $x=0$
            \choice $x=0,4$
            \CorrectChoice $x=4$
            \choice $x=3,4$
            \choice $x=1,4$
 \end{choices}

\question The domain of $f(x) = \dfrac{1}{x^2}$ is:
    \begin{choices}
            \CorrectChoice $(-\infty,0) \cup (0, \infty)$
            \choice $[0, \infty)$
            \choice $(-\infty, 0]$
            \choice $(-\infty, 1]$
   \choice $\mathbb{R}, x \ne 0$

            \end{choices}
            
 \question The domain of $f(x) = \dfrac{1}{1+x^2}$ is:
 \begin{choices}
     \CorrectChoice $(-\infty, \infty)$
     \choice $[0, \infty)$
     \choice $(-\infty, 0]$
     \choice $(-\infty, 1]$
     \choice $\mathbb{R}, x \ne 0$
\end{choices}

\pagebreak
        
\question Classify the discontinuity in  $ \displaystyle \frac{(x+1)(x-3)}{(x-4)}$ 
\begin{choices}
        \choice infinite at $x=3$, removable at $x=4$
        \choice removable at $x=3$ and $x=4$
         \CorrectChoice  infinite at $x=4$
        \choice removable at $x=3$, infinite at $x=1$
        \choice jump at $x=4$ and $x=1$
\end{choices}
    \vspace{0.10in}
    
\question if $f=e^x$ and $g=x^2$, then $e^{x^2}$ =  
 \begin{choices}
            \choice $f\circ f $
            \choice $g\circ f$
            \CorrectChoice $f\circ g$
            \choice $f/g$
            \choice $fg$
\end{choices}
    \vspace{0.10in}

\question The inverse function of $f(x) = (x+3)^2$ is  $f^{-1}(x)=$   
  \begin{choices}
            \choice $\sqrt{x+3} +2 $
            \choice $\sqrt{x-3}  $
            \choice $x^2 - 3$
            \CorrectChoice $\sqrt{x}-3$
            \choice $\sqrt{x-2}+3$
 \end{choices}
    \vspace{0.10in}

\question All of the following are characteristic of non-polynomial functions, except: 
\begin{choices}
	\CorrectChoice Minima and maxima
	\choice Asymptotes
	\choice Sharp turns
	\choice Jumps or gaps
	\choice none is correct
\end{choices}

\question Find the derivative of a polynomial $p(x)$ with roots $x=0, x=1$ and $x=3$; \(p'(x)\) = 
\begin{choices}
    \choice $3x^2-8x-3$
    \choice $3x^3+8x$
    \CorrectChoice $3x^2-8x+3$
    \choice $x^2-3x$
    \choice $x^2+x+3$
\end{choices}   

        
\vspace{0.10in}
\question Find $\lim_{x\to\infty} e^{-\sqrt{x}}$ 

\begin{oneparchoices}
        \choice  $\infty \qquad \ \ $
        \choice  $-\infty \qquad$ 
        \CorrectChoice  $0 \qquad$ 
        \choice  $e \qquad$
        \choice  Does not exist $\qquad$
        \end{oneparchoices}
\vspace{0.15in}

\question Find $\displaystyle \lim_{x\rightarrow 0} 3\sqrt{2x+3}$

\begin{oneparchoices}
\CorrectChoice  $3\sqrt{3} \qquad$
        \choice  $9 \qquad \ \  $
        \choice  $-\sqrt{3} \ \  $ 
        \choice  $0\qquad$ 
        \choice  Does not exist
 \end{oneparchoices}
\vspace{0.1in}

\question Find \(\displaystyle \lim_{x\rightarrow 0}\dfrac{x^2+3x}{3x^2+4x}\) 

\begin{oneparchoices}
     	\CorrectChoice $\dfrac{3}{4} \qquad \ \  \ $
            \choice $-\infty \qquad$
            \choice $\dfrac{1}{3} \qquad$
            \choice $\infty \qquad$
            \choice $1 \qquad$
        \end{oneparchoices}
    \vspace{0.15in}
\pagebreak

\uplevel{ Consider function $f$ below:}

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%\begin{figure}[h]
%\begin{center}
%\includegraphics[width=1\textwidth,height=0.5\textheight,keepaspectratio]{limits-graph.png}
%\end{center}
%\end{figure}

\vspace{0.10in}
\question For what values of \(x\) is \(f(x)\) discontinuous?
   \begin{choices}
            \choice $0, 2, 3$
            \choice $0, 2, 4$
            \CorrectChoice $-2, 2, 3$
            \choice $-2, 2$
            \choice $3,5$
\end{choices}
 \vspace{0.1in}

\question Find \(f(2)\)
\begin{choices}
   	 \choice $2$
   	 \choice $1$
 	 \CorrectChoice $-1$
  	 \choice $0$
  	 \choice Undefined
\end{choices}
\vspace{0.1in}

\question Find the \(\lim_{x\to3} f(x) \) 
\begin{choices}
    \choice $3$
    \choice $2$
    \CorrectChoice $\infty$
   \choice 0
   \choice undetermined
\end{choices}
\vspace{0.2in}

\question Find \(\lim_{x\to2^{+}}f(x) \) 
\begin{choices}
  	  \choice 0
  	  \choice 1
  	  \CorrectChoice 1
  	 \choice $\infty$
   	\choice 2
\end{choices}
\vspace{0.1in}

\question Find \( \lim_{x\to2} f(x)\)
\begin{choices}
    	\choice 0
    	\choice 1
    	\CorrectChoice Does not exist
  	 \choice $\infty$
  	 \choice $2$
\end{choices}
\vspace{0.1in}


\question A right triangle has a  hypotenuse of length 6 and one leg of length $\sqrt{5}$. What is the length of the other leg?
  \begin{choices}
      \CorrectChoice $\sqrt{31}$
      \choice $21$
      \choice $\sqrt{41}$
      \choice $31$
      \choice $\sqrt{10}$
\end{choices}

\question Which of the following angles is coterminal to $325$º 
\begin{choices}
  	  \choice -45º
  	  \choice -25º
  	  \CorrectChoice -35º
 	   \choice 75º
  	  \choice 125º
\end{choices}

\question A triangle in the unit circle has a terminal point ${(\frac{1}{2},\frac{\sqrt{3}}{2})}$. What is $\theta$?
\begin{choices}
 	 \choice 30º
 	 \choice 120º
 	 \choice 45º 
  	\CorrectChoice 60º
  	\choice 210º
\end{choices}

\question Where does the terminal side of the angle $-320$º lie, if drawn in standard position?
\begin{choices}
    \CorrectChoice  Quadrant I
    \choice Quadrant II
    \choice Quadrant III
    \choice Quadrant IV
    \choice Standard position angles can't be negative
\end{choices}

\question Find the length of the arc, in cm,  formed by an angle of $\theta = 45$º if the distance from the terminal point to the center is $r=2 \ cm$

\begin{oneparchoices}
    \CorrectChoice  $\pi \qquad \ \ $
    \choice $\dfrac{\pi}{3} \qquad \ \ $
    \choice $\dfrac{4\pi}{3} \qquad \ \ $
    \choice  $\dfrac{2\pi}{3} \qquad \ \ $
    \choice  $\dfrac{3\pi}{2} \qquad \ \ $
\end{oneparchoices}

\question Find the area of a sector of a circle with radius 10 centimeters formed by the arc subtended from the angle \(\theta\)= \(\dfrac{\pi}{5}\)rad.
\begin{choices}
    \choice $5\pi \ cm^2$
    \choice $50\pi \  cm^2$
    \choice $25\pi \ cm^2$
    \CorrectChoice $10\pi \ cm^2$
    \choice $12.5\pi \ cm^2$
\end{choices}
\pagebreak

\question Which of the following best describes what a derivative is?
\begin{choices}
	\CorrectChoice The slope of the tangent line or instantaneous rate of change
	\choice The slope of the secant line or average rate of change
	\choice The equation of a tangent line at a point
	\choice The equation of the tangent line anywhere on the curve
	\choice none of the above
\end{choices}

 \question Find the derivative of \(f(x) = x\ln{x}\)
\begin{choices}
	\choice \(x+x\ln{x}\)
	\CorrectChoice \(\ln{x} + 1\)
	\choice \(\ln{x}\)
	\choice \(\ln{x} + \frac{1}{x}\)
	\choice \(1 + \frac{1}{x}\)
\end{choices}

\question Find the derivative of  $f(x)=x -\dfrac{1}{x^{2}}$
	\begin{choices}
		\choice $1 + x^{3}$
		\choice $\dfrac{1}{x^{3}}$
		\CorrectChoice $1 + \dfrac{1}{x^{3}}$
		\choice $ \dfrac{1}{x^{-3}}$
		\choice $1-\dfrac{1}{2x}$
	\end{choices}

\question Differentiate $ f(x) =  2\sqrt{x}  $
	\begin{choices}
		\choice  $\dfrac{1}{2\sqrt{x}}$
		\choice $-\dfrac{\sqrt{x}}{2x}$
		\CorrectChoice $\dfrac{1}{\sqrt{x}}$
		\choice  $1/{2x}$
		\choice $2\sqrt{x}$
	\end{choices}

\question Find the slope of the line tangent to  $ \displaystyle \small y =-x^{-3}$ at $x=1$
            \begin{choices}
            \choice $m = 3/2$
            \choice $m = -3$
            \choice $m = 3/4$
            \choice  $m = -3/4$
            \CorrectChoice $m =3$
            \end{choices}

\question Find the equation of the line which at the point $(1,6)$ is tangent to the graph of\\ \(\displaystyle y=-4x^3+7x^2-9x+12\)
     \begin{choices}
            \choice $y=5x+1$
            \choice $y=-12x -9$
            \CorrectChoice $y=-7x+13$
            \choice $y=-4x+12$
            \choice $y=-24x-14$
     \end{choices}
\vspace{0.2in}
\question Find  $f'(2)$ given  $$f(x) = 3x^3 - 2x- 5$$
\begin{choices}
	\choice 64
	\CorrectChoice 34
	\choice 3
	\choice -3
	\choice 72
\end{choices}
\vspace{0.1in}

\question The trajectory of a body in motion is modeled by $$p(t) = 3t^3 - 2t^2 -18$$ Find the position of the body after 2 seconds.
\begin{choices}
	\choice $-9m \ m$
	\choice $-18 \ m$ 
	\CorrectChoice $-2 \ m$
	\choice $12 \ m$ 
	\choice $18 \ m$
\end{choices}
\vspace{0.2in}

\question Find the total displacement of this particle from the moment motion begins and  $t=3s$
\begin{choices}
	\choice $41 \ m$
	\choice $39 \ m$ 
	\CorrectChoice $28 \ m$
	\choice $43 \ m$
	\choice $45 \ m$ 
\end{choices}

\vspace{0.1in}
\question Find an equation for the velocity of the body
\begin{choices}
	\choice $6t^2 -8t -18 \ m/s$ 
	\choice $3t^2 -4t \ m/s$ 
	\CorrectChoice $9t^2 - 4t \  m/s$ 
	\choice $9t^2 + 4t -18 \ m/s$
	\choice  $9t^2 - 4$
\end{choices}
\vspace{0.1in}

\question Find the exact time at which the body's acceleration is $0  \ m/s^2$	
\begin{choices}
	\choice $\frac{1}{2} \ s $
	\choice $\frac{2}{3} \ s$
	\CorrectChoice $\frac{9}{2} \ s$
	\choice $\frac{1}{9} \ s$
\choice $\frac{5}{3} \ s$
\end{choices}

\question What is the best team in the world?
\begin{choices}
	\CorrectChoice Atletico Madrid
	\choice Real Madrid
	\choice Barcelona
	\choice Tigres
	\choice none of the above
\end{choices}

\vspace{0.10in}

\end{questions}
\end{document}
 

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