AMC

For simple questions (a single correct answer), one uses the following model:

\begin{question}{identifier}
  Here is the question...
  \begin{choices}
    \correctchoice{The correct answer}
    \wrongchoice{A wrong answer}
    \wrongchoice{Another wrong answer}
  \end{choices}
\end{question}

Multiple questions (those for which no, one, or several answers can be correct) use the questionmult environment instead of question.

One can sometimes require some open questions to be added to the subject. One way to do so is to reserve boxes use to the teacher for these questions. After the exam, the teacher reads the completed answer sheets and tick the boxes according to the answers written by the students for open questions. He will then scan the sheets and let AMC correct the multiple choice questions and integrate the open questions scores into the marks.

\begin{question}{open}
  Define \emph{inflation}.
  \AMCOpen{lines=5}{\wrongchoice[W]{w}\scoring{0}\wrongchoice[P]{p}\scoring{1}\correctchoice[C]{c}\scoring{2}}
\end{question}

In this example, the teacher will get three boxes. If the first (labeled W for wrong) is ticked, the student will get 0 points. If the second (labeled P for partial) is ticked, the student will get 1 point. If the third (labeled C for correct) is ticked, the student will get 2 points.

The first argument to \AMCOpen is a comma separated list of options. The available options are:

	Tip
	Use the command \savebox, outside the onecopy command, to display a longer text with linebreaks. \newsavebox{\correcbox} \savebox{\correcbox}{\parbox{5cm}{\color{red}{Here a linebreak\\or\\here...}}} Call out the boxe's contents: \AMCOpen{lines=4,lineheight=0.15cm, answer= \usebox{\correcbox}}{the scoring}

	Warning
	If the answer contains a comma or the equal sign, text must be bracketed by braces. If the answer contains commands \command or definitions \def, you must add \protect. \FPeval\aRandomVariable{round(3+8*random,2)} \FPeval\aCalculateVariable{round(\aRandomVariable*9.81,2)} \AMCOpen{answer={m=\protect\SI{\aRandomVariable}{\kilo\gram},% P=\protect\SI{\aCalculateVariable}{\newton}}{the scoring}

You can set other default values (for the whole exam) for all these parameters using the command \AMCopenOpts, like

\AMCopenOpts{boxframerule=2pt,boxframerulecol=red}

Moreover, a little text can be written in the marking area to tell the students not to tick these boxes, redefining the \AMCotextReserved command, as:

\def\AMCotextReserved{\emph{Reserved}}

When using separate answer sheets, the text added to each open question can also be defined, as:

\def\AMCotextGoto{\par{\bf\emph{Please write the answer on the separate answer sheet.}}}

Tip

if the number of boxes is significant, use this tip (\parbox) to force a linebreak. \AMCOpen{lines=6}{ \hbox{\parbox{8.5cm}{ \wrongchoice[F]{F}\scoring{0} \wrongchoice[1]{1}\scoring{1} \wrongchoice[2]{2}\scoring{2} \wrongchoice[3]{3}\scoring{3} \wrongchoice[4]{4}\scoring{4} \wrongchoice[5]{5}\scoring{5} \wrongchoice[6]{6}\scoring{6} \wrongchoice[7]{7}\scoring{7} \wrongchoice[8]{8}\scoring{8} \wrongchoice[9]{9}\scoring{9} \correctchoice[10]{10}\scoring{10} }} }

When the answer to the question is not supposed to be taken into account in the grading, one uses the \QuestionIndicative command, as in the following example:

\begin{question}{difficulty}\QuestionIndicative
  \scoring{auto=0,v=-1,e=-2}
  Did you find this class easy or difficult? Please answer on a scale from 0 (very difficult) to 5
  (very easy).
  \begin{choiceshoriz}[o]
    \correctchoice{0}
    \correctchoice{1}
    \correctchoice{2}
    \correctchoice{3}
    \correctchoice{4}
    \correctchoice{5}
  \end{choiceshoriz}
\end{question}

	Important
	One must use a different identifier for every question. An identifier can be made of digits, letters, and simple characters (but do not use e.g. underscores, braces or brackets, that have a special meaning in LaTeX files). Don't end your question identifier with an integer enclosed in square brackets, as this syntax is reserved to codes input.

The style of the identifier may be

group.identifier

or

group:identifier

(see Language package) to get the total of a one group of questions when exporting notes (see Exporting the scores list).

To put the answers on two columns, one can use the multicol package: load it in the preamble (just after the reference to the package automultiplechoice for instance) with

\usepackage{multicol}

and include the choices environment inside a multicols environment in the following manner:

\begin{multicols}{2}
  \begin{choices}
    \correctchoice{The correct answer}
    \wrongchoice{A wrong answer}
    \wrongchoice{Another wrong answer}
  \end{choices}
\end{multicols}

For even shorter answers, one can require questions to be printed following one another, using the choiceshoriz environment instead of choices.

To put answers on several columns (and thus save space), one can embed the choices environment in a multicols environment, using the LaTeX package multicol.

If, moreover, the answers do not fit into a single line, an answer might be split over several columns, which might be a little puzzling for the reader. The \AMCBoxedAnswers command was defined in order to prevent this phenomenon, by embedding each answer into a box. Here is an example of use:

\begin{question}{two columns}
  What is a bird ?
  \begin{multicols}{2}\AMCBoxedAnswers
    \begin{choices}
      \correctchoice{It is an animal with wings, laying eggs. There are birds with all sorts of colors.}
      \wrongchoice{It is a large piece of furniture, made of wood, and used most of the time to store
      household linen}
      \wrongchoice{It is a steam machine devised to seal cans at high speed.}
    \end{choices}
  \end{multicols}
\end{question}

Let us note that it is also possible to parameterize the vertical space between two answer blocks, thanks to the dimension AMCinterBrep:

\AMCinterBrep=.5ex

Sometimes this is not necessary to write some long text to describe answers, and one letter or symbol is enough. When using a separate answer sheet, it is quite annoying to print the boxes both on the question and on the answer sheet. In such cases, use \AMCBoxOnly instead of the choices environment:

\begin{question}{arm}
  Which letter shows the \textit{arm} on the diagram?
  \AMCBoxOnly{ordered=true}{\wrongchoice[A]{}\correctchoice[B]{}%
    \wrongchoice[C]{}\wrongchoice[D]{}}
\end{question}

The first argument to \AMCBoxOnly is a comma separated list of options. The available options are:

To provide explanation for the answers of a question, one can use the \explain command. The explanations are optional and are only displayed in the Solution and Catalog file.

	Warning
	Not displayed in the individual solution. To get around this, type in preamble: \makeatletter \renewcommand{\explain}[1]{% \ifAMC@correc% \AMCif@env{question}{\par\noindent{\AMC@loc@explain#1}}{\AMC@error@explain}\vspace{1ex}% \else% \AMCif@env{question}{}{\AMC@error@explain}% \fi% } \makeatother

Here is a simple example:

\begin{question}{explanation}
  Which has the highest elevation among the following?
  \begin{choices}
      \correctchoice{Sagarmatha}
      \wrongchoice{K2}
      \wrongchoice{Mont Blanc}
      \wrongchoice{Aconcagua}
  \end{choices}
  \explain{Sagarmatha which literally means `Head of sky' is the native name of
           Mount Everest, the highest mountain in the world.}
\end{question}

	Note
	The explain command must be typed inside question like environments only. This includes question, questionmult and questionmultx environments.

By default this command prints Explanation: before each explanations. This behavior can be changed using the \AMCtext command (see section the section called “Customizing some texts inserted by AMC”).

If you want to change this default behavior only for some questions and not for all just use the \AMCtext command before the \explain command as in the following example:

\begin{question}{elevation}
  Which has the highest elevation among the following?
  \begin{choices}
      \correctchoice{Sagarmatha}
      \wrongchoice{K2}
      \wrongchoice{Mont Blanc}
      \wrongchoice{Aconcagua}
  \end{choices}
  \explain{Sagarmatha which literally means `Head of sky' is the native name of
         Mount Everest, the highest mountain in the world.}
\end{question}

\begin{question}{odd}
  Pick the odd one out.
  \begin{choices}
      \correctchoice{Kilimanjaro}
      \wrongchoice{Himalayas}
      \wrongchoice{Alps}
      \wrongchoice{Andes}
  \end{choices}
  \AMCtext{explain}{\textit{\textbf{Reason: }}}
  \explain{Kilimanjaro is a mountain while the rest are mountain ranges.}
\end{question}

\begin{questionmult}{himalaya}
  Among the following which is in the Himalayas?
  \begin{choices}
      \correctchoice{Mount Everest}
      \correctchoice{K2}
      \wrongchoice{Mont Blanc}
      \wrongchoice{Aconcagua}
  \end{choices}
  \explain{Aconcagua is located in the Andes mountain range while Mont Blanc
                 is located in the Alps.}
\end{questionmult}

This will now print Explanation: before the explanations of first and third question but Reason: before the explanation of second question.

To keep the original order of the answers and prevent shuffling for this specific question, one can use the o option of the choices environment, replacing line 3 by the following:

\begin{choices}[o]

\begin{question}{color}
  Which color?
  \begin{choiceshoriz}
    \wrongchoice{red}
    \wrongchoice{blue}
    \wrongchoice{yellow}
    \lastchoices
    \correctchoice{transparent}
    \wrongchoice{can't say}
  \end{choiceshoriz}
\end{question}

\begin{questionmult}{number}
  How many?
  \begin{choiceshoriz}
    \wrongchoice{none}
    \correctchoice{one}
    \wrongchoice{two}
    \wrongchoice{three}
    \lastchoices
    \correctchoice{not so much}
    \wrongchoice{a lot}
  \end{choiceshoriz}
\end{questionmult}

see the section called “Coding the result”

Let us note that it is also possible to parameterize the vertical space between many answer blocks, thanks to the dimension AMCinterIrep:

\AMCinterIrep=.75ex

Type this command after \begin{document} and before the command \onecopy :

\AMCsetScoreZone{width=1.5em,height=1.5ex,depth=.5ex,position=margins}

The variables width, height, depth describe the dimensions of the box marking and its location on the sheet.

The position value may be equal to : none, question, margin, margins.

Type this command after \begin{document} and before the command \onecopy :

\AMCsetScoreZoneAnswerSheet{width=1.5em,height=1.5ex,depth=.5ex,position=question}

The variables width, height, depth describe the dimensions of the box marking and its location on the sheet.

The position value may be equal to : none, question, margin, margins.

	Warning
	The option margins does not work with AMC-TXT. Don't type one of those commands after printing.

The display of answers can be modified in the same fashion, if one uses the choicescustom environment instead of choices or choiceshoriz, redefining the three following LaTeX macros:

\def\AMCbeginAnswer{}
\def\AMCendAnswer{}
\def\AMCanswer#1#2{#1 #2}

Example 1

The check boxes can be used to penalize students who delay their copy, for example (8 points less for a small delay and 20 points less for an exaggerated delay). It will be enough to include at the desired place (for example in the header, something like this):

\fcolorbox{black}{gray}{\insertDelay}

the command \insertDelay is defined outside from \onecopy :

\def\insertDelay{ %
{\def\AMCbeginQuestion##1##2{}\AMCnobloc%
 \begin{questionmult}{00delay}
 \AMCnoCompleteMulti\AMCdontAnnotate%
 \def\AMCbeginAnswer{}\def\AMCendAnswer{}%
Holded~\begin{choicescustom}[o]\wrongchoice{R1~}\scoring{b=0,m=-8}\wrongchoice{R2}\scoringb=0,m=-20}\end{choicescustom}%
 \end{questionmult}}%
}

• the command \def\AMCbeginQuestion##1##2{} (combined with the use of the reponsesperso environment) allows AMC to write not "Question XX".

• \def\AMCbeginAnswer{}\def\AMCendAnswer{} also refine the result.

• \AMCnoCompleteMulti allows to tell AMC not to add the answer "none of these answers is correct" despite the use of questionmult.

• \AMCdontAnnotate ask AMC not to annotate these boxes there.

	Important
	Inside the commande \onecopy, double the #. \def\AMCanswer##1##2{##1 ##2} \def\AMCbeginQuestion##1##2{}

\begin{questionmultx}{formula}\scoring{mz=2}\AMCnoCompleteMulti
How is the identity function defined?
  \begin{choicescustom}[o]
    \[f(x)=\correctchoice[$y$]{}\wrongchoice{[$x$]{}\correctchoice[$+$]{}\correctchoice[$x^2$]{}\]
  \end{choicescustom}
\end{questionmultx}

One can also change spacing redefining the following dimensions (here are the default values):

\AMCinterIrep=0pt
\AMCinterBrep=.5ex
\AMCinterIquest=0pt
\AMCinterBquest=3ex
\AMCpostOquest=7mm
\setlength{\AMChorizAnswerSep}{3em plus 4em}
\setlength{\AMChorizBoxSep}{1em}

These dimensions are the vertical space between questions (quest) or answers (rep), in boxed mode (B, with \AMCBoxedAnswers or box package option) or standard mode (I) and the space left after an open question. The two last lengths are used in environment: choicescustom

Margins were chosen so that the document prints correctly on most printers. If your printer reduces, you can use the command geometry from laTex package geometry. For example, In order to narrow the top margin's copies, we can use \geometry{top=3cm} instead the default value 3.5cm, just before \begin{document}.

AMC automatically handles the number of pages for each subject. You can choose to fix a identical number of pages for each subject with the command \AMCaddpagesto{integer} to be called at a place you need to reach this number of pages (usually at the end of the copy description or between the question and the answer sheet).

This package sort in an ascending order the questions' numbers, the questions' pages or the labels' pages (the documentation http://mirrors.ctan.org/macros/latex/contrib/cleveref/cleveref.pdf).

	Warning
	This package must be loaded after the package automultiplechoice.

To use this package, a new command was created: \AMCstudentlabel.

\cref{\AMCstudentlabel{led},\AMCstudentlabel{lamp},\AMCstudentlabel{motor}}

led, lamp, motor are the created labels to reference the questions with the command \AMClabel{}.

The automultiplechoice package moreover defines a \AMCIntervals command which makes this kind of construction simpler, as illustrated in the next example:

\begin{question}{inf-expo-indep}
  \FPeval\VQa{trunc(2 + random * 4,0)}
  \FPeval\VQb{trunc(6 + random * 5,0)}
  \FPeval\VQr{VQa/(VQa+VQb)}

  Let $X$ and $Y$ be two independent random variables, following the exponential distribution with
respective parameters \VQa{} and \VQb{}.
  To which interval does the probability $\mathbb{P}[X<Y]$ belong ?

  \begin{multicols}{5}
    \begin{choices}[o]
      \AMCIntervals{\VQr}{0}{1}{0.1}  
    \end{choices}
  \end{multicols}
\end{question}

Note that the interval formatting can be changed redefining the \AMCintervalFormat command, which is originally defined as

\def\AMCIntervalFormat#1#2{[#1,\,#2[}

to follow local conventions (writing [a,b) instead of [a,b[ is for example a common usage).

The students can also be asked to code the numerical answer, using the \AMCnumericChoices command, as in the following example:

\begin{questionmultx}{sqrt}
  \FPeval\VQa{trunc(5+random*15,0)}
  \FPeval\VQs{VQa^0.5}
  Compute $\sqrt{\VQa}$ and round it with two digits after period.

  \AMCnumericChoices{\VQs}{digits=3,decimals=2,sign=true,
                 borderwidth=0pt,backgroundcol=lightgray,approx=5}
\end{questionmultx}

Note the use of questionmultx environment: we need this question to be multiple as several boxes has to be ticked, but we can’t say that several answers are correct, so we don’t show the symbol for multiple questions.

Options

Available options that can be used in the second argument of the \AMCnumericChoices command are the following (bool can be true or false, and color must be a color known by the xcolor package):

digits=num

gives the number of digits to request (defaults to 3).

decimals=num

gives the number of digits after period to request (defaults to 0). Note that when num is positive, the LaTeX package fp must be loaded.

base=num

gives the base for digits and decimals (defaults to 10).

significant=bool

if true, the numbers to code are the first significant digits from the first argument of \AMCnumericChoices. For example, the right answer to

\AMCnumericChoices{56945.23}{digits=2,significant=true}

is 57.

exponent=num

switch to scientific notation mode, with num digits for the exponent.

nozero=bool

if true, the choice 0 is removed for all digits.

May be useful when using \AMCnumericChoices to enter small (<10) positive values.

sign=bool

requests (or not) a signed value (defaults to true).

exposign=bool

same for the exponent sign.

strict=bool

if true, a box has to be ticked for every digit (even null digits) and for the sign. If false, if some digits has no ticked box, they will be set to zero. Defaults to false.

vertical=bool

if true, each digit is represented on one raw. If false (default), each digit is represented on one line.

expovertical=bool

if true, the mantissa is above the exponent. If false (default), the mantissa is beside the exponent.

reverse=bool

if true, place higher values of the digits on the top in vertical mode (defaults to true).

vhead=bool

if true, in vertical mode, a header is placed over all digits rows, made using the command \AMCntextVHead that is originally defined as

\def\AMCntextVHead#1{\emph{b#1}}

This default value is useful to number the binary digits.

Default value is false.

hspace=space

sets the horizontal space between boxes (defaults to .5em).

vspace=space

sets the vertical space between boxes (defaults to 1ex).

borderwidth=space

sets the width of the frame border around all the boxes (defaults to 1mm).

bordercol=color

sets the color of the frame (defaults to lightgray).

backgroundcol=color

sets the background color (defaults to white).

Tsign=text

sets the text to print at the top of the boxes to set the sign (Can also be redefined by \def\AMCntextSign{text}, and defaults to be empty).

Tpoint=text

sets the text for the period. Can also be redefined by \def\AMCdecimalPoint{text}, and defaults to \raisebox{1ex}{\bf .}.

Texponent=text

sets the text that separates mantissa and exponent. Can also be redefined by \def\AMCexponent{text}, and defaults to $\times10$\textasciicircum.

scoring=bool

if true, a scoring strategy is given to AMC for this question. Defaults to true.

scoreexact=num

gives the score for an exact answer (defaults to 2).

exact=num

sets the maximal distance to the correct integer value (value without the decimal point) for an answer to be said exact and be rewarded to scoreexact points (defaults to 0).

scoreapprox=num

gives the score for an approximative answer (defaults to 1).

approx=num

sets the maximal distance to the correct integer value (value without the decimal point) for an answer to be said approximative and be rewarded to scoreapprox points (defaults to 0).

	Warning
	AMC converts all numbers (decimals included) to integers (simply removing the decimal point) before subtracting them and comparing with approx. As an example, with decimals=2, if the correct answer is 3.14 and the given answer is 3.2, then the integer difference is 320-314=6, so that the student gets scoreapprox points only if approx is 6 or greater.

scorewrong=num

gives the score for an wrong answer (defaults to 0).

keepas=text

keeps the value entered by the student for future use with alsocorrect in another question.

All following questions must follow the lexicographic order of IDs

alsocorrect=text

gives another acceptable answer, that can be based on the values entered by the student in the previous questions. The formula use perl code:

+, -, *, /, ** (power)

 \begin{question}{carre-a}
    \QuestionIndicative
    Choose any number.
    \begin{reponseshoriz}[o]
      \wronhchoice{2}\scoring{2,setglobal.Number=2}
      \wronhchoice{3}\scoring{3,setglobal.Number=3}
      \wronhchoice{4}\scoring{4,setglobal.Number=4}
      \wronhchoice{5}\scoring{5,setglobal.Number=5}
    \end{reponseshoriz}
  \end{question}
  
  \begin{questionmultx}{carre-b}
    \AMCdontAnnotate\bareme{MAX=2}
    What is his square?
    \AMCnumericChoices{}{digits=2,approx=1,alsocorrect=Number**2}
  \end{questionmultx}



  \begin{minipage}{.3\linewidth}
    \begin{tikzpicture}
      \draw[fill=blue!50] (0,0) ellipse (1.5 and 0.2);
      \draw (1.5,0) -- (0,5) -- (-1.5,0);
      \draw (1.6,0) -- (2,0);
      \draw (1.6,5) -- (2,5);
      \draw[<->] (1.8,0) -- (1.8,5);
      \node[right] at (1.8,2.5) {$h=5$};
      \draw (0,-0.4) -- (0,-0.8);
      \draw (1.5,-0.4) -- (1.5,-0.8);
      \draw[<->] (0,-0.6) -- (1.5,-0.6);
      \node[below] at (0.75,-0.6) {$r=1.5$};
      \draw[fill=black] (0,0) circle (0.02);
    \end{tikzpicture}
  \end{minipage}
  \begin{minipage}{.65\linewidth}
    \begin{questionmultx}{cone-a}
      What is the area of the blue disc?
      \AMCnumericChoices{pi*1.5^2}{digits=3,decimals=2,exponent=2,approx=2,sign=false,
      exposign=true,expovertical=true,keepas=Surface}
    \end{questionmultx}
        
    \begin{questionmultx}{cone-b}
      What is the volume of the cone?
      \AMCnumericChoices{pi*1.5^2*5/3}{digits=3,decimals=2,exponent=2,approx=2,sign=false,
      exposign=true,expovertical=true,alsocorrect=Surface*5/3}
    \end{questionmultx}
  \end{minipage}  



  \begin{questionmultx}{pipi2-a}
    What is the value of$\pi$ ?
    \AMCnumericChoices{pi}{digits=3,decimals=2,sign=false,keepas=Pi}
  \end{questionmultx}

  \begin{questionmultx}{pipi2-b}
    What is the value  $\pi^2$ ?
    \AMCnumericChoices{pi^2}{digits=3,decimals=2,sign=false,approx=1,alsocorrect=Pi**2}
  \end{questionmultx}  

You can set other default values (for the whole exam) for all these parameters using the command \AMCnumericOpts, like

\AMCnumericOpts{scoreexact=3,borderwidth=2pt}

Moreover, the text added at the end of the questions using \AMCnumericChoices when not in the separate answer sheet (and when a separate answer sheet is requested by the separateanswersheet package option) can also be set redefining the \AMCntextGoto command, as:

\def\AMCntextGoto{\par{\bf\emph{Please code the answer on
                           the separate answer sheet.}}}

Here is an example with a simple computation:

\begin{question}{inverse}
  \pgfmathrandominteger{\x}{1}{50}

  How much is the reciprocal of $x=\x$?

  \begin{choices}
    \correctchoice{\pgfmathparse{1/\x}\pgfmathresult }
    \wrongchoice{\pgfmathparse{1/(\x +1))}\pgfmathresult}
    \wrongchoice{\pgfmathparse{cos(\x)} \pgfmathresult}
    \wrongchoice{\pgfmathparse{\x^(-0.5)}\pgfmathresult}
  \end{choices}
\end{question}

Here, the command \pgfmathparse makes the computation, and \pgfmathresult outputs the result.

Output formatting is also available with the command \pgfmathprintnumber, as in the following example (three digits after decimal point, and use of the comma as a decimal point).

\begin{question}{inverse3}
  \pgfmathrandominteger{\x}{1}{50}
  \pgfkeys{/pgf/number format/.cd,fixed,fixed zerofill,precision=3,use comma}
  How much is the reciprocal of $x=\pgfmathprintnumber{\x}$?

  \begin{choices}
    \correctchoice{\pgfmathparse{1/\x}\pgfmathprintnumber{\pgfmathresult}}
    \wrongchoice{\pgfmathparse{1/(\x +1))} \pgfmathprintnumber{\pgfmathresult}}
    \wrongchoice{\pgfmathparse{cos(\x)} \pgfmathprintnumber{\pgfmathresult}}
    \wrongchoice{\pgfmathparse{\x^(-0.5)} \pgfmathprintnumber{\pgfmathresult}}
  \end{choices}
\end{question}

	Note
	You can also use the \AMCIntervals and \AMCnumericChoices commands (see the section called “Choosing an interval” and the section called “Coding the result”)

The tikz package also allows to make (random or not) graphs.

\begin{questionmult}{graph}
  Let us consider the three functions which graphs are plotted below:
  \pgfmathrandominteger{\a}{2}{4}
  \begin{center}
    \begin{tikzpicture}[domain=0:4]
      \draw[very thin,color=gray] (-0.1,-4.1) grid (3.9,3.9);
      \draw[->] (-0.2,0) -- (4.2,0) node[right] {$x$};
      \draw[->] (0,-4.2) -- (0,4.2) node[above] {$f(x)$};
      \draw[color=red] plot (\x,{(1+\a/4)*\x-\a}) node[right] {$f_{1} (x)$};
      \draw[color=blue] plot (\x,{\a*sin(\x r)}) node[right] {$f_{2}(x)$};
      \draw[color=orange] plot (\x,{\a*cos(\x r)}) node[right] {$f_{3}(x)$};
    \end{tikzpicture}
  \end{center}
  Then:
  \begin{choices}
    \pgfmathrandominteger{\x0}{2}{4}
    \correctchoice{$f_{2}(\x0)$=\pgfmathparse{\a*sin(\x0 r)} \pgfmathprintnumber{\pgfmathresult}.}
    \correctchoice{$f_{3}(\x0)$=\pgfmathparse{\a*cos(\x0 r)} \pgfmathprintnumber{\pgfmathresult}.}
    \wrongchoice{La fonction $f_{1}(x)$ est une fonction linéaire.}
  \end{choices}
\end{questionmult}

To make pretty graphs, package pgfplots can also be useful.

With pgfmath, precision is limited, so that a "Arithmetic overflow" error can be encountered. Packages tikz and pgfplots allows to overcome this problem, using gnuplot as a backend. You need to install gnuplot on your system, and use LaTeX option --shell-escape. To this purpose, go to AMC preferences window, and set the LaTeX engine for your project to "pdflatex --shell-escape" (without the quotes).