Why is there only one question on the second page? Using Exam Class

Question

I am trying to format this exam; however, the number of question per page is horrible. There is no logical reason why there is only one question on the second page and several on the next page and only two on the last and third page.

Can anyone please explain how to properly space the question so there is enough white space to work the problems?

\documentclass[12pt]{exam}
\usepackage{graphicx}
\usepackage{amssymb}
\usepackage{epstopdf}
\usepackage{amsmath}
\usepackage{paralist}
\usepackage{enumerate}
\usepackage{wrapfig}
\usepackage{xcolor}
\usepackage{graphicx}

\newcommand{\Lim}[1]{\raisebox{0.5ex}{\scalebox{0.8}{$\displaystyle \lim_{#1}\;$}}}
% \pagebreak[10]
\printanswers


\pagestyle{headandfoot}
\runningheadrule
\firstpageheader{AP Calculus Practice Exam A1}{  }{Senior 2}
\firstpageheadrule
\runningheader{AP Calculus Practice Exam A1} { Page \thepage\ of \numpages} {Senior 2 }
\firstpagefooter{}{}{Page \thepage\ of \numpages}
\runningfooter{}{\iflastpage{End of exam}{Please go on to the next page\ldots}}{Page \thepage\ of \numpages}
% For a visual definition of these parameters, see
% \textwidth = 6.5 in
% \textheight = 9 in
% \oddsidemargin = 0.0 in
% \evensidemargin = 0.0 in
% \topmargin = 0.0 in           
% \headheight = 0.0 in          
% \headsep = 0.0 in


% These problems were taken from Calculus Problem Book AP exams.
\begin{document}
\begin{titlepage}


  \begin{center}
    \textsc{\LARGE A.P. Practice Test:A1}\\[0.5cm]


    \textsc{\LARGE Multiple-Choice}\\[0.5cm]


    \textsc{\LARGE No Calculators}\\[0.5cm]


    Time - 40 minutes\\

  \end{center}

  \vfill







  \emph{Directions}: Solve each of the following problems, using the available space for scratch work. After examining the form of the choices, decide which is best of the choices given and clearly circle the choice.  Do not spend too much time on any one problem.



  \vfill
  \begin{center} Good Luck\! \end{center}






\end{titlepage}





% These problems were taken from Calculus Problem Book AP exams.

\begin{questions}
  % A.P. Calculus Test One Section One Problem 1
  \begin{samepage}
    \question Which of the following is continuous at $x = 0$ ?
    \begin{center}
      \begin{parts}
        \renewcommand{\thepartno}{\Roman{partno}}
        \part $f\left(x\right) = \vert x \vert$
        \part $f\left(x\right) = e^{x}$
        \part $f\left(x\right) = \ln\left(e^{x} - 1 \right)$
      \end{parts}
    \end{center}
    \begin{oneparchoices}
      \choice I only
      \choice II only
      \CorrectChoice I and II only
      \choice II and III only
      \choice none
    \end{oneparchoices}
  \end{samepage}
  \vspace{\stretch{8}}




  \begin{samepage}
    \hrule
    % A.P. Calculus Test One Section One Problem 2
    \question The graph of a function $f$ is reflected across the $x$-axis and then shifted up 2 units. Which of the following describes this transformation of $f$? \begin{choices}
      \renewcommand{\thepartno}{\Alph{partno}}
      \choice $-f\left(x\right)$
      \choice $f\left(x\right) + 2$
      \choice $-f\left(x + 2 \right)$
      \choice $-f\left(x - 2 \right)$
      \CorrectChoice $-f\left(x\right) + 2$
    \end{choices}
  \end{samepage}
  \vspace{\stretch{8}}




  \begin{samepage}
    \hrule
    % A.P. Calculus Test One Section One Problem 3
    \question Which of the following functions is \textit{not} continuous for all real numbers $x$?
    \begin{choices}
      \renewcommand{\thepartno}{\Alph{partno}}
      \choice $f\left(x\right) = x^{1/3}$
      \CorrectChoice $f\left(x\right) = \dfrac{2}{\left(x + 1\right)^4}$
      \choice $f\left(x\right) = \vert x + 1 \vert$
      \choice $f\left(x\right) = \sqrt{1 + e^x}$
      \choice $f\left(x\right) = \dfrac{x - 3}{x^2 + 9}$
    \end{choices}

  \end{samepage}
  \vspace{\stretch{8}}




  \begin{samepage}
    \hrule
    % A.P. Calculus Test One Section One Problem 4
    \question $\Lim{x \to 1} \dfrac{\ln x}{x}$ is
    \begin{choices}
      \renewcommand{\thepartno}{\Alph{partno}}
      \choice 1
      \CorrectChoice 0
      \choice $e$
      \choice $-e$
      \choice nonexistent
    \end{choices}

  \end{samepage}
  \vspace{\stretch{8}}




  \begin{samepage}
    \hrule
    % A.P. Calculus Test One Section One Problem 5
    \question $\Lim{x \to 0} \left( \dfrac{1}{x} + \dfrac{1}{x^2} \right) = $
    \begin{choices}
      \renewcommand{\thepartno}{\Alph{partno}}
      \choice 0
      \choice $\dfrac{1}{2}$
      \choice 1
      \choice 2
      \CorrectChoice $\infty$
    \end{choices}

  \end{samepage}
  \vspace{\stretch{8}}




  \begin{samepage}
    \hrule
    % A.P. Calculus Test One Section One Problem 6
    \question $\Lim{x \to \infty} \dfrac{x^3 - 4x + 1}{2x^3 - 5} =  $
    \begin{choices}
      \renewcommand{\thepartno}{\Alph{partno}}
      \choice $-\dfrac{1}{5}$
      \CorrectChoice $\dfrac{1}{2}$
      \choice $\dfrac{2}{3}$
      \choice 1
      \choice Does not exist
    \end{choices}

  \end{samepage}
  \vspace{\stretch{8}}



  \newpage
  \begin{samepage}

    % A.P. Calculus Test One Section One Problem 7
    \question For what value of $k$ does $\Lim{x \to 4} \dfrac{x^2 - x + k}{x - 4}$ exist?
    \begin{choices}
      \renewcommand{\thepartno}{\Alph{partno}}
      \CorrectChoice -12
      \choice -4
      \choice 3
      \choice 7
      \choice No such value exists
    \end{choices}

  \end{samepage}
  \vspace{\stretch{8}}




  \begin{samepage}
    \hrule
    % A.P. Calculus Test One Section One Problem 8
    \question $\Lim{x \to 0} \dfrac{\tan x}{x} = $
    \begin{choices}
      \renewcommand{\thepartno}{\Alph{partno}}
      \choice -1
      \choice $-\dfrac{1}{2}$
      \choice 0
      \choice $-\dfrac{1}{2}$
      \CorrectChoice 1
    \end{choices}

  \end{samepage}
  \vspace{\stretch{8}}




  \begin{samepage}
    \hrule
    % A.P. Calculus Test One Section One Problem 9
    \question Suppose $f$ is defined as
    \[f\left(x\right) = \begin{cases} \dfrac{\vert x \vert - 2}{x - 2} & x \neq 2 \\ k & x = 2 \end{cases}\]
    Then the value of $k$ for which $f\left(x\right)$ is continuous for all real values of $x$ is $k = $
    \begin{choices}
      \renewcommand{\thepartno}{\Alph{partno}}
      \choice -2
      \choice -1
      \choice 0
      \CorrectChoice 1
      \choice 2
    \end{choices}

  \end{samepage}
  \vspace{\stretch{8}}



  \newpage
  \begin{samepage}
    % \hrule
    % A.P. Calculus Test One Section One Problem 10
    \question The average rate of change of $f\left(x\right) = x^3$ over the interval $[a,b]$ is
    \begin{choices}
      \renewcommand{\thepartno}{\Alph{partno}}
      \choice $3b + 3a$
      \CorrectChoice $b^2 + ab + a^2$
      \choice $\dfrac{b^2 + a^2}{2}$
      \choice $\dfrac{b^3 + a^3}{2}$
      \choice $\dfrac{b^4 - a^4}{4\left(b - a\right)}$
    \end{choices}

  \end{samepage}
  \vspace{\stretch{8}}




  \begin{samepage}
    \hrule
    % A.P. Calculus Test One Section One Problem 11
    \question The function
    \[ G\left(x\right) = \begin{cases} x - 5 & x > 2 \\
      -5   & x = 2 \\
      5x - 13 & x < 2 \end{cases} \]
    is not continuous at $x = 2$ because
    \begin{choices}
      \renewcommand{\thepartno}{\Alph{partno}}
      \choice $G\left(2\right)$ is not defined
      \choice $\Lim{x \to 2} G\left(x\right)$ does not exist
      \CorrectChoice $\Lim{x \to 2} G\left(x\right) \neq G\left(2\right)$
      \choice $G\left(2\right) \neq -5$
      \choice None of the above
    \end{choices}

  \end{samepage}
  \vspace{\stretch{8}}




  \begin{samepage}
    \hrule
    % A.P. Calculus Test One Section One Problem 12
    \question $\Lim{x \to -2} \dfrac{\sqrt{2x + 5} -1}{x + 2} = $
    \begin{choices}
      \renewcommand{\thepartno}{\Alph{partno}}
      \CorrectChoice 1
      \choice 0
      \choice $\infty$
      \choice $-\infty$
      \choice Does not exist
    \end{choices}

  \end{samepage}
  \vspace{\stretch{8}}



  \newpage
  \begin{samepage}
    % \hrule
    % A.P. Calculus Test One Section One Problem 13
    \question The Intermediate Value Theorem states that given a continuous function $f$ defined on a closed interval $[a,b]$ for which 0 is between $f\left(a\right)$ and $f\left(b\right)$, there exists a point $c$ between $a$ and $b$ such that
    \begin{choices}
      \renewcommand{\thepartno}{\Alph{partno}}
      \choice $c = a - b$
      \choice $f\left(a\right) = f\left(b\right)$
      \CorrectChoice $f\left(c\right) = 0$
      \choice $f\left(0\right) = c$
      \choice $c = 0$
    \end{choices}

  \end{samepage}
  \vspace{\stretch{8}}


  \begin{samepage}
    \hrule
    % A.P. Calculus Test One Section One Problem 14
    \question The function $t\left(x\right) = 2^x - \dfrac{\vert x - 3\vert}{x - 3}$ has
    \begin{choices}
      \renewcommand{\thepartno}{\Alph{partno}}
      \choice a removable discontinuity at $x = 3$
      \choice an infinite discontinuity at $x = 3$
      \CorrectChoice a jump discontinuity at $x = 3$
      \choice no discontinuities
      \choice a removable discontinuity at $x = 0$ and an infinite discontinuity at $x = 3$
    \end{choices}

  \end{samepage}
  \vspace{\stretch{8}}




  \begin{samepage}
    \hrule
    % A.P. Calculus Test One Section One Problem 15
    \question Find the values of $c$ so that the function
    \[  h\left(x\right) = \begin{cases} c^2 - x^2 & x < 2 \\
      x + c     &  x \geq 2 \end{cases}\]
    is continuous everywhere
    \begin{choices}
      \renewcommand{\thepartno}{\Alph{partno}}
      \choice -3,-2
      \choice 2,3
      \CorrectChoice -2, 3
      \choice -3, 2
      \choice There are no such values
    \end{choices}

  \end{samepage}
  \vspace{\stretch{8}}



  \newpage
  \begin{samepage}
    % \hrule
    % A.P. Calculus Test Two Section One Problem 4
    \question If $F\left(x\right) = x \sin x$, then find $F^{\prime}\left(\dfrac{3\pi}{2}\right)$
    \begin{choices}
      \renewcommand{\thepartno}{\Alph{partno}}
      \choice 0
      \choice 1
      \CorrectChoice -1
      \choice $\dfrac{3\pi}{2}$
      \choice $-\dfrac{3\pi}{2}$
    \end{choices}

  \end{samepage}
  \vspace{\stretch{8}}




  \begin{samepage}
    \hrule
    % Calculus Problem Book A.P. Calculus Test Three Question 8
    \question The position of a particle moving on the $x$-axis, starting at time $t=0$, is given by $x\left(t\right) = \left(t-a\right)^3\left(t-b\right)$, where $0 < a < b$. Which of the following statements are true?
    \begin{center} \begin{parts}
        \renewcommand{\thepartno}{\Roman{partno}}
        \part The particle is at a positive position on the $x$-axis at time $t = \dfrac{a + b}{2}$
        \part The particle is at rest at $t = a$
        \part The particle is moving to the right at time $t=b$
      \end{parts}\end{center}
    \begin{choices}
      \renewcommand{\thepartno}{\Alph{partno}}
      \choice I only
      \choice II only
      \CorrectChoice III only
      \choice I and II only
      \choice II and III only
    \end{choices}

  \end{samepage}
  \vspace{\stretch{8}}




  \begin{samepage}
    \hrule
    % Calculus Problem Book A.P. Calculus Test Three Page 96  Question 14
    \question Let $f$ be a twice-differentiable function of $x$ such that, when $x = c$, $f$ is decreasing, concave up, and has an $x$-intercept. Which of the following is true?
    \begin{choices}
      \renewcommand{\thepartno}{\Alph{partno}}
      \choice $f\left(c\right) < f^{\prime}\left(c\right) < f^{\prime \prime}\left(c\right)$
      \choice $f\left(c\right) < f^{\prime \prime}\left(c\right)< f^{\prime}\left(c\right) $
      \CorrectChoice $ f^{\prime}\left(c\right) < f\left(c\right)< f^{\prime \prime}\left(c\right)$
      \choice $ f^{\prime}\left(c\right) < f^{\prime \prime}\left(c\right) < f\left(c\right) $
      \choice $f^{\prime \prime}\left(c\right) < f\left(c\right) <  f^{\prime}\left(c\right) $
    \end{choices}

  \end{samepage}
  \vspace{\stretch{8}}

  % \newpage
  \begin{samepage}
    % \hrule
    % Calculus Problem Book A.P. Calculus Test Four Section One Question 3
    \question Let $f\left(x\right)$ be defined as below. Evaluate $\int_0^6 f\left(x\right)\,\mathrm{d}x$ 

    \[f\left(x\right) = \begin{cases} x & 0<x\leq 2 \\ 1 & 2 < x \leq 4 \\ \frac{x}{2} &  4 < x \leq 6 

    \end{cases}\]

    \begin{choices}
      \renewcommand{\thepartno}{\Alph{partno}}
      \choice 5
      \choice 6
      \choice 7 
      \choice 8 
      \CorrectChoice 9
    \end{choices}
  \end{samepage}
  \vspace{\stretch{8}}


  \begin{samepage}
    \hrule
    % Calculus Problem Book A.P. Calculus Test Five Section One Question 4
    \question Solve the differential equation $\frac{\mathrm{d}y}{\mathrm{d}x} = y$ with the initial condition that $y\left(0\right) =1.$ From your solution, find the value of $y\left(e\right)$
    \begin{choices}
      \renewcommand{\thepartno}{\Alph{partno}}
      \CorrectChoice $e^e$
      \choice $e$
      \choice $e-1$
      \choice $e^e - 1$
      \choice $e^2$
    \end{choices}
  \end{samepage}
  \vspace{\stretch{8}}


\end{questions}
\end{document}

Answer 1

Consider defining a few simple pieces of markup to help your document's readability, and don't use samepage for this; AFAIK, it doesn't provide any useful functionality. I replace it with a minipage environment within the myquestion environment I define.

Using enumitem, a successor/alternative to enumerate, I also define a new list type pickmulti for questions where you pick among several choices. For these questions, I also define labels and use references so you can change the numbering scheme at any time.

pickmulti doing its work:

\documentclass[12pt]{exam}
\usepackage{amssymb, amsmath}
\usepackage{enumitem}
\usepackage{graphicx}

\newcommand{\Lim}[1]{\raisebox{0.5ex}{\scalebox{0.8}{$\displaystyle\lim_{#1}\;$}}}
% ^ Reconsider this how you typeset this.

\printanswers

\newenvironment{myquestion}{%
  \ifodd\value{question}
    %\rule{\linewidth}{1pt}\par
    \hrule
    \vspace{1em}
  \fi
  \minipage{\linewidth}%
}{%
  \endminipage
  \vspace{\stretch{1}}%
  \ifodd\value{question}\else
    \newpage
  \fi
}

\newlist{pickmulti}{enumerate}{1}
\setlist[pickmulti]{
  label=\Roman*.,
  ref=(\Roman*)
}


%\pagestyle{headandfoot}
\firstpageheadrule
\firstpageheader{AP Calculus Practice Exam A1}{}{Senior 2}
\firstpagefooter{}{}{Page \thepage\ of \numpages}

\runningheadrule
\runningheader{AP Calculus Practice Exam A1}{Page \thepage\ of \numpages}{Senior 2}
\runningfooter{}{\iflastpage{End of exam}{Please go on to the next page\ldots}}{Page \thepage\ of \numpages}


% These problems were taken from Calculus Problem Book AP exams.
\begin{document}
\begin{titlepage}
  \begin{center}
    \LARGE\scshape
    \setlength\parskip{0.5cm}

    A.P. Practice Test: A1

    Multiple-Choice

    No Calculators

    Time: 40 minutes
  \end{center}

  \vfill

  \paragraph{Directions}
  Solve each of the following problems,
    using the available space for scratch work.
  After examining the form of the choices,
    decide which is best of the choices given and clearly circle the choice.
  Do not spend too much time on any one problem.

  \vfill

  \begin{center}
    Good Luck!
  \end{center}
\end{titlepage}

% These problems were taken from Calculus Problem Book AP exams.

\begin{questions}
  % A.P. Calculus Test One Section One Problem 1
  \begin{myquestion}
    \question
    Which of the following is continuous at $x = 0$?
    \begin{pickmulti}
      \item \label{q:cont:abs(x)}
        $f\left(x\right) = \vert x \vert$
      \item \label{q:cont:e**x}
        $f\left(x\right) = e^{x}$
      \item \label{q:cont:ln(e**x-1)}
        $f\left(x\right) = \ln\left(e^{x} - 1 \right)$
    \end{pickmulti}
    \begin{oneparchoices}
      \choice \ref{q:cont:abs(x)} only
      \choice \ref{q:cont:e**x} only
      \CorrectChoice \ref{q:cont:abs(x)} and \ref{q:cont:e**x} only
      \choice \ref{q:cont:e**x} and \ref{q:cont:ln(e**x-1)} only
      \choice none
    \end{oneparchoices}
  \end{myquestion}

  \begin{myquestion}
    % A.P. Calculus Test One Section One Problem 2
    \question
    The graph of a function $f$ is reflected across the $x$-axis and then shifted up 2 units.
    Which of the following describes this transformation of $f$?
    \begin{choices}
      \choice $-f\left(x\right)$
      \choice $f\left(x\right) + 2$
      \choice $-f\left(x + 2 \right)$
      \choice $-f\left(x - 2 \right)$
      \CorrectChoice $-f\left(x\right) + 2$
    \end{choices}
  \end{myquestion}

  \begin{myquestion}
    % A.P. Calculus Test One Section One Problem 3
    \question
    Which of the following functions is \emph{not} continuous for all real numbers $x$?
    \begin{choices}
      \choice $f\left(x\right) = x^{1/3}$
      \CorrectChoice $f\left(x\right) = \dfrac{2}{\left(x + 1\right)^4}$
      \choice $f\left(x\right) = \vert x + 1 \vert$
      \choice $f\left(x\right) = \sqrt{1 + e^x}$
      \choice $f\left(x\right) = \dfrac{x - 3}{x^2 + 9}$
    \end{choices}
  \end{myquestion}

  \begin{myquestion}
    % A.P. Calculus Test One Section One Problem 4
    \question $\Lim{x \to 1} \dfrac{\ln x}{x}$ is
    \begin{choices}
      \choice 1
      \CorrectChoice 0
      \choice $e$
      \choice $-e$
      \choice non-existent
    \end{choices}
  \end{myquestion}

  \begin{myquestion}
    % A.P. Calculus Test One Section One Problem 5
    \question $\Lim{x \to 0} \left( \dfrac{1}{x} + \dfrac{1}{x^2} \right) = $
    \begin{choices}
      \choice 0
      \choice $\dfrac{1}{2}$
      \choice 1
      \choice 2
      \CorrectChoice $\infty$
    \end{choices}
  \end{myquestion}

  \begin{myquestion}
    % A.P. Calculus Test One Section One Problem 6
    \question $\Lim{x \to \infty} \dfrac{x^3 - 4x + 1}{2x^3 - 5} =  $
    \begin{choices}
      \choice $-\dfrac{1}{5}$
      \CorrectChoice $\dfrac{1}{2}$
      \choice $\dfrac{2}{3}$
      \choice 1
      \choice Does not exist
    \end{choices}
  \end{myquestion}

  \begin{myquestion}
    % A.P. Calculus Test One Section One Problem 7
    \question For what value of $k$ does $\Lim{x \to 4} \dfrac{x^2 - x + k}{x - 4}$ exist?
    \begin{choices}
      \CorrectChoice $-12$
      \choice $-4$
      \choice 3
      \choice 7
      \choice No such value exists
    \end{choices}
  \end{myquestion}

  \begin{myquestion}
    % A.P. Calculus Test One Section One Problem 8
    \question $\Lim{x \to 0} \dfrac{\tan x}{x} = $
    \begin{choices}
      \choice $-1$
      \choice $-\dfrac{1}{2}$
      \choice 0
      \choice $-\dfrac{1}{2}$
      \CorrectChoice 1
    \end{choices}
  \end{myquestion}

  \begin{myquestion}
    % A.P. Calculus Test One Section One Problem 9
    \question
    Suppose $f$ is defined as
    \[
    f\left(x\right) =
    \begin{cases}
      \dfrac{\vert x \vert - 2}{x - 2} & x \neq 2 \\
      k & x = 2
    \end{cases}
    \]
    Then the value of $k$ for which $f\left(x\right)$ is continuous for all real values of $x$ is $k = $
    \begin{choices}
      \choice $-2$
      \choice $-1$
      \choice 0
      \CorrectChoice 1
      \choice 2
    \end{choices}
  \end{myquestion}

  \begin{myquestion}
    % A.P. Calculus Test One Section One Problem 10
    \question The average rate of change of $f\left(x\right) = x^3$ over the interval $[a,b]$ is
    \begin{choices}
      \choice $3b + 3a$
      \CorrectChoice $b^2 + ab + a^2$
      \choice $\dfrac{b^2 + a^2}{2}$
      \choice $\dfrac{b^3 + a^3}{2}$
      \choice $\dfrac{b^4 - a^4}{4\left(b - a\right)}$
    \end{choices}
  \end{myquestion}

  \begin{myquestion}
    % A.P. Calculus Test One Section One Problem 11
    \question The function
    \[
    G\left(x\right) =
    \begin{cases}
      x - 5 & x > 2 \\
      -5   & x = 2 \\
      5x - 13 & x < 2
    \end{cases}
    \]
    is not continuous at $x = 2$ because
    \begin{choices}
      \choice $G\left(2\right)$ is not defined
      \choice $\Lim{x \to 2} G\left(x\right)$ does not exist
      \CorrectChoice $\Lim{x \to 2} G\left(x\right) \neq G\left(2\right)$
      \choice $G\left(2\right) \neq -5$
      \choice None of the above
    \end{choices}
  \end{myquestion}

  \begin{myquestion}
    % A.P. Calculus Test One Section One Problem 12
    \question $\Lim{x \to -2} \dfrac{\sqrt{2x + 5} -1}{x + 2} = $
    \begin{choices}
      \CorrectChoice 1
      \choice 0
      \choice $\infty$
      \choice $-\infty$
      \choice Does not exist
    \end{choices}
  \end{myquestion}

  \begin{myquestion}
    % A.P. Calculus Test One Section One Problem 13
    \question
    The Intermediate Value Theorem states that given a continuous
    function $f$ defined on a closed interval $[a,b]$ for which 0 is
    between $f\left(a\right)$ and $f\left(b\right)$, there exists a
    point $c$ between $a$ and $b$ such that
    \begin{choices}
      \choice $c = a - b$
      \choice $f\left(a\right) = f\left(b\right)$
      \CorrectChoice $f\left(c\right) = 0$
      \choice $f\left(0\right) = c$
      \choice $c = 0$
    \end{choices}
  \end{myquestion}
  \begin{myquestion}
    % A.P. Calculus Test One Section One Problem 14
    \question The function $t\left(x\right) = 2^x - \dfrac{\vert x - 3\vert}{x - 3}$ has
    \begin{choices}
      \choice a removable discontinuity at $x = 3$
      \choice an infinite discontinuity at $x = 3$
      \CorrectChoice a jump discontinuity at $x = 3$
      \choice no discontinuities
      \choice a removable discontinuity at $x = 0$ and an infinite discontinuity at $x = 3$
    \end{choices}
  \end{myquestion}

  \begin{myquestion}
    % A.P. Calculus Test One Section One Problem 15
    \question Find the values of $c$ so that the function
    \[
    h\left(x\right) =
    \begin{cases}
      c^2 - x^2 & x < 2 \\
      x + c     &  x \geq 2
    \end{cases}
    \]
    is continuous everywhere
    \begin{choices}
      \choice $-3,-2$
      \choice 2,3
      \CorrectChoice $-2$, 3
      \choice $-3$, $2$
      \choice There are no such values
    \end{choices}
  \end{myquestion}

  \begin{myquestion}
    % A.P. Calculus Test Two Section One Problem 4
    \question If $F\left(x\right) = x \sin x$, then find $F^{\prime}\left(\dfrac{3\pi}{2}\right)$
    \begin{choices}
      \choice 0
      \choice 1
      \CorrectChoice $-1$
      \choice $\dfrac{3\pi}{2}$
      \choice $-\dfrac{3\pi}{2}$
    \end{choices}
  \end{myquestion}

  \begin{myquestion}
    % Calculus Problem Book A.P. Calculus Test Three Question 8
    \question
    The position of a particle moving on the $x$-axis, starting at
    time $t=0$, is given by $x\left(t\right) = \left( t - a \right)^3
    \left( t - b \right)$, where $0 < a < b$.  Which of the following
    statements are true?
    \begin{pickmulti}
    \item \label{q:part:opt:pos}
      The particle is at a positive position on the $x$-axis at time $t = \dfrac{a + b}{2}$
    \item \label{q:part:opt:rest}
      The particle is at rest at $t = a$
    \item \label{q:part:opt:right}
      The particle is moving to the right at time $t=b$
    \end{pickmulti}
    \begin{choices}
      \choice \ref{q:part:opt:pos} only
      \choice \ref{q:part:opt:rest} only
      \CorrectChoice \ref{q:part:opt:right} only
      \choice \ref{q:part:opt:pos} and \ref{q:part:opt:rest} only
      \choice \ref{q:part:opt:rest} and \ref{q:part:opt:right} only
    \end{choices}
  \end{myquestion}

  \begin{myquestion}
    % Calculus Problem Book A.P. Calculus Test Three Page 96  Question 14
    \question
    Let $f$ be a twice-differentiable function of $x$ such that, when
    $x = c$, $f$ is decreasing, concave up, and has an
    $x$-intercept.  Which of the following is true?
    \begin{choices}
      \choice $f\left(c\right) < f^{\prime}\left(c\right) < f^{\prime \prime}\left(c\right)$
      \choice $f\left(c\right) < f^{\prime \prime}\left(c\right)< f^{\prime}\left(c\right) $
      \CorrectChoice $ f^{\prime}\left(c\right) < f\left(c\right)< f^{\prime \prime}\left(c\right)$
      \choice $ f^{\prime}\left(c\right) < f^{\prime \prime}\left(c\right) < f\left(c\right) $
      \choice $f^{\prime \prime}\left(c\right) < f\left(c\right) <  f^{\prime}\left(c\right) $
    \end{choices}
  \end{myquestion}

  \begin{myquestion}
    % Calculus Problem Book A.P. Calculus Test Four Section One Question 3
    \question
    Let $f\left(x\right)$ be defined as below.
    Evaluate $\int_0^6 f\left(x\right)\,\mathrm{d}x$ where
    \[
    f\left(x\right) =
    \begin{cases}
      x & 0<x\leq 2 \\
      1 & 2 < x \leq 4 \\
      \frac{x}{2} & 4 < x \leq 6
    \end{cases}
    \]

    \begin{choices}
      \choice 5
      \choice 6
      \choice 7
      \choice 8
      \CorrectChoice 9
    \end{choices}
  \end{myquestion}
  \begin{myquestion}
    % Calculus Problem Book A.P. Calculus Test Five Section One Question 4
    \question
    Solve the differential equation $\frac{\mathrm{d}y}{\mathrm{d}x} = y$
      with the initial condition that $y\left(0\right) = 1$.
    From your solution, find the value of $y\left(e\right)$
    \begin{choices}
      \CorrectChoice $e^e$
      \choice $e$
      \choice $e-1$
      \choice $e^e - 1$
      \choice $e^2$
    \end{choices}
  \end{myquestion}
\end{questions}
\end{document}

Answer 2

I would put two questions per page, each with a \vfill between and a forced \newpage afterward (this can be automated; see below).

Using \vfill below each question leaves equal space within the same page. If you wish to have the same horizontal rule (\questiondiv) from one page to the next, that can also be achieved with some calculations.

\documentclass[12pt]{exam}% http://ctan.org/pkg/exam
\usepackage{amsmath}% http://ctan.org/pkg/amsmath

\printanswers

\pagestyle{headandfoot}
\runningheadrule
\firstpageheader{AP Calculus Practice Exam A1}{  }{Senior 2}
\firstpageheadrule
\runningheader{AP Calculus Practice Exam A1} { Page \thepage\ of \numpages} {Senior 2 }
\firstpagefooter{}{}{Page \thepage\ of \numpages}
\runningfooter{}{\iflastpage{End of exam}{Please go on to the next page\ldots}}{Page \thepage\ of \numpages}
% For a visual definition of these parameters, see
%\textwidth = 6.5 in
%\textheight = 9 in
%\oddsidemargin = 0.0 in
%\evensidemargin = 0.0 in
%\topmargin = 0.0 in            
%\headheight = 0.0 in           
%\headsep = 0.0 in

\newcommand{\questiondiv}{\hrule}
%These problems were taken from Calculus Problem Book AP exams.
\begin{document}
\begin{titlepage}

\begin{center}
  \textsc{\LARGE A.P. Practice Test: A1}\\[0.5cm]
  \textsc{\LARGE Multiple-Choice}\\[0.5cm]
  \textsc{\LARGE No Calculators}\\[0.5cm]
  Time - 40 minutes\\

\vfill

\emph{Directions}: Solve each of the following problems, using the available space for 
scratch work. After examining the form of the choices, decide which is best of the 
choices given and clearly circle the choice. Do not spend too much time on any one problem.

\vfill

Good Luck!
\end{center}

\end{titlepage}

%These problems were taken from Calculus Problem Book AP exams.

\begin{questions}
% A.P. Calculus Test One Section One Problem 1
  \question
  Which of the following is continuous at $x = 0$ ?
  \begin{parts}
    \renewcommand{\thepartno}{\Roman{partno}}
    \part $f(x) = \vert x \vert$
    \part $f(x) = e^{x}$
    \part $f(x) = \ln\bigl(e^{x} - 1 \bigr)$
  \end{parts}
  \begin{oneparchoices}
    \choice I only
    \choice II only
    \CorrectChoice I and II only
    \choice II and III only
    \choice none
  \end{oneparchoices}

  \vfill

  \questiondiv

% A.P. Calculus Test One Section One Problem 2
  \question
  The graph of a function~$f$ is reflected across the $x$-axis and then shifted 
  up~2 units. Which of the following describes this transformation of~$f$?
  \begin{choices}
    \renewcommand{\thepartno}{\Alph{partno}}
    \choice $-f(x)$
    \choice $f(x) + 2$
    \choice $-f(x + 2)$
    \choice $-f(x - 2)$
    \CorrectChoice $-f(x) + 2$
  \end{choices}

  \vfill

  \newpage%\questiondiv

% A.P. Calculus Test One Section One Problem 3
  \question
  Which of the following functions is \emph{not\/} continuous for all real numbers~$x$?
  \begin{choices}
    \renewcommand{\thepartno}{\Alph{partno}}
    \choice $f(x) = x^{1/3}$
    \CorrectChoice $f(x) = \dfrac{2}{(x + 1)^4}$
    \choice $f(x) = \vert x + 1 \vert$
    \choice $f(x) = \sqrt{1 + e^x}$
    \choice $f(x) = \dfrac{x - 3}{x^2 + 9}$
  \end{choices}

  \vfill

  \questiondiv

% A.P. Calculus Test One Section One Problem 4
  \question
  $\displaystyle \lim_{x \to 1} \dfrac{\ln x}{x}$ is
  \begin{choices}
    \renewcommand{\thepartno}{\Alph{partno}}
    \choice 1
    \CorrectChoice 0
    \choice $e$
    \choice $-e$
    \choice nonexistent
  \end{choices}

  \vfill

  \newpage%\questiondiv

% A.P. Calculus Test One Section One Problem 5
  \question
  $\displaystyle \lim_{x \to 0} \biggl( \dfrac{1}{x} + \dfrac{1}{x^2} \biggr) = $
   \begin{choices}
    \renewcommand{\thepartno}{\Alph{partno}}
    \choice 0
    \choice $\dfrac{1}{2}$
    \choice 1
    \choice 2
    \CorrectChoice $\infty$
  \end{choices}

  \vfill

  \questiondiv

% A.P. Calculus Test One Section One Problem 6
  \question
  $\displaystyle \lim_{x \to \infty} \dfrac{x^3 - 4x + 1}{2x^3 - 5} =  $
  \begin{choices}
    \renewcommand{\thepartno}{\Alph{partno}}
    \choice $-\dfrac{1}{5}$
    \CorrectChoice $\dfrac{1}{2}$
    \choice $\dfrac{2}{3}$
    \choice 1
    \choice Does not exist
  \end{choices}

  \vfill

  \newpage%\questiondiv

% A.P. Calculus Test One Section One Problem 7
  \question
  For what value of~$k$ does $\displaystyle \lim_{x \to 4} \dfrac{x^2 - x + k}{x - 4}$ exist?
  \begin{choices}
    \renewcommand{\thepartno}{\Alph{partno}}
    \CorrectChoice -12
    \choice -4
    \choice 3
    \choice 7
    \choice No such value exists
  \end{choices}

  \vfill

  \questiondiv

% A.P. Calculus Test One Section One Problem 8
  \question
  $\displaystyle \lim_{x \to 0} \dfrac{\tan x}{x} = $
  \begin{choices}
    \renewcommand{\thepartno}{\Alph{partno}}
    \choice -1
    \choice $-\dfrac{1}{2}$
    \choice 0
    \choice $-\dfrac{1}{2}$
    \CorrectChoice 1
  \end{choices}

  \vfill

  \newpage%\questiondiv

% A.P. Calculus Test One Section One Problem 9
  \question
  Suppose~$f$ is defined as
  \[
    f(x) = \begin{cases}
      \dfrac{\vert x \vert - 2}{x - 2} & x \neq 2 \\
      k & x = 2
    \end{cases}
  \]
  Then the value of~$k$ for which~$f(x)$ is continuous for all real values of~$x$ is $k = $
  \begin{choices}
    \renewcommand{\thepartno}{\Alph{partno}}
    \choice -2
    \choice -1
    \choice 0
    \CorrectChoice 1
    \choice 2
  \end{choices}

  \vfill

  \questiondiv

% A.P. Calculus Test One Section One Problem 10
  \question
  The average rate of change of $f(x) = x^3$ over the interval $[a,b]$ is
  \begin{choices}
    \renewcommand{\thepartno}{\Alph{partno}}
    \choice $3b + 3a$
    \CorrectChoice $b^2 + ab + a^2$
    \choice $\dfrac{b^2 + a^2}{2}$
    \choice $\dfrac{b^3 + a^3}{2}$
    \choice $\dfrac{b^4 - a^4}{4(b - a)}$
  \end{choices}

  \vfill


  \newpage%\questiondiv

% A.P. Calculus Test One Section One Problem 11
  \question
  The function
  \[
    G(x) = \begin{cases} x - 5 & x > 2 \\
      -5   & x = 2 \\
      5x - 13 & x < 2
    \end{cases}
  \]
  is not continuous at $x = 2$ because
  \begin{choices}
    \renewcommand{\thepartno}{\Alph{partno}}
    \choice $G(2)$ is not defined
    \choice $\displaystyle \lim_{x \to 2} G(x)$ does not exist
    \CorrectChoice $\lim_{x \to 2} G(x) \neq G(2)$
    \choice $G(2) \neq -5$
    \choice None of the above
  \end{choices}

  \vfill

  \questiondiv

% A.P. Calculus Test One Section One Problem 12
  \question
  $\displaystyle \lim_{x \to -2} \dfrac{\sqrt{2x + 5} -1}{x + 2} = $
  \begin{choices}
    \renewcommand{\thepartno}{\Alph{partno}}
    \CorrectChoice 1
    \choice 0
    \choice $\infty$
    \choice $-\infty$
    \choice Does not exist
  \end{choices}

  \vfill

  \newpage%\questiondiv

% A.P. Calculus Test One Section One Problem 13
  \question
  The Intermediate Value Theorem states that given a continuous function~$f$ 
  defined on a closed interval $[a,b]$ for which~0 is between~$f(a)$ and~$f(b)$, 
  there exists a point~$c$ between~$a$ and~$b$ such that
  \begin{choices}
    \renewcommand{\thepartno}{\Alph{partno}}
    \choice $c = a - b$
    \choice $f(a) = f(b)$
    \CorrectChoice $f(c) = 0$
    \choice $f(0) = c$
    \choice $c = 0$
  \end{choices}

  \vfill

  \questiondiv

% A.P. Calculus Test One Section One Problem 14
  \question
  The function $t(x) = 2^x - \dfrac{\vert x - 3\vert}{x - 3}$ has
  \begin{choices}
    \renewcommand{\thepartno}{\Alph{partno}}
    \choice a removable discontinuity at $x = 3$
    \choice an infinite discontinuity at $x = 3$
    \CorrectChoice a jump discontinuity at $x = 3$
    \choice no discontinuities
    \choice a removable discontinuity at $x = 0$ and an infinite discontinuity at $x = 3$
  \end{choices}

  \vfill

  \newpage%\questiondiv

% A.P. Calculus Test One Section One Problem 15
  \question
  Find the values of~$c$ so that the function
  \[
    h(x) = \begin{cases}
      c^2 - x^2 & x < 2 \\
      x + c     &  x \geq 2
    \end{cases}
  \]
  is continuous everywhere
  \begin{choices}
    \renewcommand{\thepartno}{\Alph{partno}}
    \choice $-3,-2$
    \choice $2,3$
    \CorrectChoice $-2, 3$
    \choice $-3,2$
    \choice There are no such values
  \end{choices}

  \vfill

  \questiondiv

% A.P. Calculus Test Two Section One Problem 4
  \question
  If $F(x) = x \sin x$, then find $F^{\prime}F(\tfrac{3\pi}{2})$
  \begin{choices}
    \renewcommand{\thepartno}{\Alph{partno}}
    \choice 0
    \choice 1
    \CorrectChoice $-1$
    \choice $\tfrac{3\pi}{2}$
    \choice $-\tfrac{3\pi}{2}$
  \end{choices}

  \vfill

  \newpage%\questiondiv

% Calculus Problem Book A.P. Calculus Test Three Question 8
  \question
  The position of a particle moving on the $x$-axis, starting at time $t=0$, 
  is given by $x(t) = (t-a)^3(t-b)$, where $0 < a < b$. Which of the following 
  statements are true?
  \begin{parts}
    \renewcommand{\thepartno}{\Roman{partno}}
    \part The particle is at a positive position on the $x$-axis at time $t = \dfrac{a + b}{2}$
    \part The particle is at rest at $t = a$
    \part The particle is moving to the right at time $t=b$
  \end{parts}
  \begin{choices}
    \renewcommand{\thepartno}{\Alph{partno}}
    \choice I only
    \choice II only
    \CorrectChoice III only
    \choice I and II only
    \choice II and III only
  \end{choices}

  \vfill

  \questiondiv

% Calculus Problem Book A.P. Calculus Test Three Page 96  Question 14
  \question
  Let~$f$ be a twice-differentiable function of~$x$ such that, when 
  $x = c$,~$f$ is decreasing, concave up, and has an $x$-intercept. Which of the following is true?
  \begin{choices}
    \renewcommand{\thepartno}{\Alph{partno}}
    \choice $f(c) < f'(c) < f''(c)$
    \choice $f(c) < f''(c)< f'(c)$
    \CorrectChoice $f'(c) < f(c) < f''(c)$
    \choice $f'(c) < f''(c) < f(c)$
    \choice $f''(c) < f(c) <  f'(c)$
  \end{choices}

  \vfill

  \newpage%\questiondiv

%Calculus Problem Book A.P. Calculus Test Four Section One Question 3
  \question
  Let~$f(x)$ be defined as below. Evaluate $\int_0^6 f(x)\,\mathrm{d}x$ 
  \[
    f(x) = \begin{cases}
      x & 0 < x \leq 2 \\
      1 & 2 < x \leq 4 \\
      \frac{x}{2} &  4 < x \leq 6
    \end{cases}
  \]
  \begin{choices}
    \renewcommand{\thepartno}{\Alph{partno}}
    \choice 5
    \choice 6
    \choice 7 
    \choice 8 
    \CorrectChoice 9
  \end{choices}

  \vfill

  \questiondiv

% Calculus Problem Book A.P. Calculus Test Five Section One Question 4
  \question
  Solve the differential equation $\frac{\mathrm{d}y}{\mathrm{d}x} = y$ with 
  the initial condition that $y(0) = 1.$ From your solution, find the value of~$y(e)$
  \begin{choices}
    \renewcommand{\thepartno}{\Alph{partno}}
    \CorrectChoice $e^e$
    \choice $e$
    \choice $e-1$
    \choice $e^e - 1$
    \choice $e^2$
  \end{choices}

  \vfill
\end{questions}
\end{document}

For automation, remove the \vfill...\newpage...\questiondiv content between \questions, and add the following to your preamble:

\let\oldquestions\questions
\renewcommand{\questions}{%
  \oldquestions%
  \let\oldquestion\question%
  \renewcommand{\question}{%
    \ifnum\value{question}>0% Not at first question
      \par\vfill% Insert space for question
      \ifodd\value{question}% Busy with an odd-numbered question
        \questiondiv% Insert \question division (\hrule)
      \else
        \clearpage% Insert page break
      \fi
    \fi
    \oldquestion% Issue regular question
  }
}
\let\endoldquestions\endquestions
\renewcommand{\endquestions}{%
  \vfill% Add space for last question
  \endoldquestions%
}

The above adapts the questions environment and inserts the appropriate division/page break/vertical fill depending on the question number.