% Students question collection
%# Author Alejandro Gonzalez Recuenco and SKR students
%# e-mail <alejandrogonzalezrecuenco@gmail.com>

\documentclass{exam}
%SET-UP:
\usepackage{amsmath, physics, tikz, tcolorbox, graphicx}



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% DOCUMENT STARTS HERE
\begin{document}

\author{Everyone version \myversion}
\title{\textsc{Exam collection} --- mini-exam for \nickname\ of class \class}


\maketitle


\section{Word problems}

The two sections of questions are these ones


\subsection{Subsection 1}\begin{questions}


	\question What is a tangent line to a curve at a point $x = a$?

	\begin{choices}
		\choice A line that crosses a  curve once.
		\choice None of the other choices are correct.
		\choice A line that crosses a curve in two points.
		\CorrectChoice A line that has the same slope as the curve at the point $x = a$.
	\end{choices}
	\question What type of graph is the derivative of $f(x)= 5x^3+6x^2+5x-1$ graph?

	\begin{choices}
		\choice Line.
		\choice Circle.
		\choice Hyperbola.
		\CorrectChoice Parabola.
	\end{choices}

\end{questions}

\subsection{Subsection 2}
\begin{questions}


	\question test --- What is a tangent line to a curve at a point $x = a$?

	\begin{choices}
		\choice A line that crosses a  curve once.
		\choice None of the other choices are correct.
		\choice A line that crosses a curve in two points.
		\CorrectChoice A line that has the same slope as the curve at the point $x = a$.
	\end{choices}
	\question test --- What type of graph is the derivative of $f(x)= 5x^3+6x^2+5x-1$ graph?

	\begin{choices}
		\choice Line.
		\choice Circle.
		\choice Hyperbola.
		\CorrectChoice Parabola.
	\end{choices}

\end{questions}


\section{Easy}
The two sections of questions are these ones


\subsection{Subsection 1}\begin{questions}

	\question If $y=\cos5x$ find $\dv{y}{x}$.

	\begin{choices}
		\choice $\dv{y}{x} = 5\cos5x$.
		\choice $\dv{y}{x} = -2\sin5x$.
		\choice $\dv{y}{x} = 5\cos2x$.
		\CorrectChoice $\dv{y}{x} = -5\sin5x$.
	\end{choices}
	\question Given $y=2x^2-3x+5$, What is $\dv[2]{y}{x}$

	\begin{choices}
		\choice $\dv[2]{y}{x}=4x-3$
		\choice $\dv[2]{y}{x}=16x-12$
		\choice $\dv[2]{y}{x}=0$
		\CorrectChoice $\dv[2]{y}{x}=4$
	\end{choices}

\end{questions}

\subsection{Subsection 2}

\begin{questions}

	\question test --- If $y=\cos5x$ find $\dv{y}{x}$.

	\begin{choices}
		\choice $\dv{y}{x} = 5\cos5x$.
		\choice $\dv{y}{x} = -2\sin5x$.
		\choice $\dv{y}{x} = 5\cos2x$.
		\CorrectChoice $\dv{y}{x} = -5\sin5x$.
	\end{choices}
	second part of question
	\begin{choices}
		\choice test ---   $\dv{y}{x} = 5\cos5x$.
		\choice test ---   $\dv{y}{x} = -2\sin5x$.
		\choice test ---   $\dv{y}{x} = 5\cos2x$.
		\CorrectChoice test ---   $\dv{y}{x} = -5\sin5x$.
	\end{choices}
	\question test ---  Given $y=2x^2-3x+5$, What is $\dv[2]{y}{x}$

	\begin{choices}
		\choice $\dv[2]{y}{x}=4x-3$
		\choice $\dv[2]{y}{x}=16x-12$
		\choice $\dv[2]{y}{x}=0$
		\CorrectChoice $\dv[2]{y}{x}=4$
	\end{choices}

\end{questions}


\section{Medium}


\begin{questions}

	\question What is the derivative of f(x)=$(1-6x^2)^4$
	\begin{choices}
		\choice $4(1-6x^2)^3$
		\choice $4x(1-6x^2)^3$
		\choice $48x(1-6x^2)^3$
		\CorrectChoice $-48x(1-6x^2)^3 y$
	\end{choices}

	\question Find the derivative of $f(x) = \frac{x-1}{x+1}$

	\begin{choices}
		\choice $f'(x) = \frac{-2}{(x+1)^2}$
		\choice $f'(x) = \frac{2}{(x-1)^2}$
		\choice $f'(x) = \frac{-2}{(x-1)^2}$
		\CorrectChoice $f'(x) = \frac{2}{(x+1)^2}$
	\end{choices}

\end{questions}



\section{Hard}

\begin{questions}

	\question What is value of the $\displaystyle \lim_{h \to 0} \frac{f(x+h) -f(x)}{h}$ tells about the function?

	\begin{choices}
		\choice\label{choice:der1} The Slope of the graph.
		\choice\label{choice:der2} The critical point of the function , when the value of the limit is 0.
		\CorrectChoice Both options, \ref{choice:der1} and \ref{choice:der2}, are correct.
		\choice None of the above.
	\end{choices}

	\question What is the derivative of $f(x) = \arctan(2x)$ ?

	\begin{choices}
		\choice $\frac{2}{1 + x^{2}}$
		\choice $\frac{2}{2 + x^{2}}$
		\choice $\frac{2}{2 + 4x^{2}}$
		\CorrectChoice $\frac{2}{1 + 4x^{2}}$
	\end{choices}

\end{questions}

\section{Graphic problems}

\begin{questions}
	\question
	From the following graph find $\lim_{x \to -2 } f(x)$
	\par\nopagebreak

	\begin{choices}
		\choice $0$.
		\choice $5$.
		\choice $4$.
		\CorrectChoice undefined.
	\end{choices}

\end{questions}

\section{Bonus, integration}

\begin{questions}
	\question Find the area of the graph between f(x) = $x^4$ and f(x) = $(x-6)^4$

	\begin{choices}
		\choice $\frac{243}{5}$
		\choice $\frac{243}{10}$
		\choice $\frac{486}{10}$
		\CorrectChoice $\frac{486}{5}$
	\end{choices}
	\question Find the integral of $ 4x^3+3x^2 $

	\begin{choices}
		\choice $12x^2 + 6x$
		\choice $4x^2 + 3x$
		\choice $4x^4 + 3x^3 + c$
		\CorrectChoice $x^4 + x^3 +c$
	\end{choices}

\end{questions}

\end{document}

