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\documentclass[10pt,a4paper,portrait,french]{article}
 
%%%%% PACKAGES LANGUE %%%%%
\usepackage{ProfCollege}
\usepackage{babel} % sans option => langue définie dans la classe du document
\usepackage{fp}

%%%%% SPÉCIFICITÉS A.M.C. %%%%%
%\usepackage[francais,bloc,completemulti]{automultiplechoice} 
%   remarque : avec completmulti => "aucune réponse ne convient" en +
 \usepackage[francais,insidebox,bloc]{automultiplechoice}

%%%%% PACKAGES MISE EN PAGE %%%%%
 \usepackage{wrapfig}  
 \usepackage{fancybox}  % pour \doublebox \shadowbox  \ovalbox \Ovalbox
 \usepackage{setspace}
% Pour la gestion des fontes.
\usepackage{unicode-math}
% Par exemple, une fonte sans serif pour les briques Scratch.
\newfontfamily\myfontScratch[]{FreeSans}

%%%%% PACKAGES FIGURES %%%%%
%\usepackage{pstricks,pst-plot,pstricks-add}
%   POUR PSTRICKS d'où compilation sans PDFLateX mais : dvi, dvi2ps, ps2PDF...
%   MAIS ON PRÉFÉRERA UTILISER TIKZ...
\usetikzlibrary{babel,arrows,calc,fit,patterns,plotmarks,shapes.geometric,shapes.misc,shapes.symbols,shapes.arrows,shapes.callouts, shapes.multipart, shapes.gates.logic.US,shapes.gates.logic.IEC, er, automata,backgrounds,chains,topaths,trees,petri,mindmap,matrix, calendar, folding,fadings,through,positioning,scopes,decorations.fractals,decorations.shapes,decorations.text,decorations.pathmorphing,decorations.pathreplacing,decorations.footprints,decorations.markings,shadows}
\usepackage{graphicx} % pour inclure une image avec une échelle

%%%%% PACKAGES MATHS %%%%%
 \usepackage{amsmath}
 \usepackage{amsfonts}
 \usepackage{eurosym}
 \usepackage{frcursive}
 \newcommand{\Vcurs}{\begin{cursive}V\end{cursive}}
 \usepackage[normalem]{ulem} % pour souligner

%%%%% AUTRES %%%%%
%\renewcommand{\AMCStudentNumber}{100}

%%%%% Librairies utilisées par Mathgraphe32 %%%% 
%\usetikzlibrary{patterns}
\usepackage{fix-cm}
\usepackage{textcomp}

%%%%% PERSONNALISATION %%%%%
\renewcommand{\multiSymbole}{$\begin{smallmatrix}\circ\bullet\bullet \\ 
                 \circ\bullet\circ \end{smallmatrix}$\noindent} % par défaut $\clubsuit$
%\renewcommand{\multiSymbole}{\textbf{(! Évent. plusieurs réponses !)}\noindent} % si on veut être plus explicite ; par défaut $\clubsuit$

\renewcommand{\AMCbeginQuestion}[2]{\noindent{\colorbox{gray!20}{\bf#1}}#2}

%\renewcommand{\AMCIntervalFormat}[2]{\texttt{[}#1\,;\,#2\texttt{[}} 
                                               % Crochets plus nets, virgule...
%\AMCboxDimensions{size=1.7ex,down=.2ex} %% taille des cases à cocher diminuée

\newcommand{\collerVertic}{\vspace{-3mm}} % évite un trop grand espace vertical
\newcommand{\Prio}{\fbox{\textbf{PRIORITAIRE}} \noindent} % 
\newcommand{\enligne}{\def\AMCanswer##1##2{\hfill ##1 ##2}} % pour avoir les réponses à la suite de la question, sur la même ligne, alignées à droite. S'utilise avec  \begin{reponsesperso}   \bonne{}  \end{reponsesperso}
\newcommand{\Degre}{\ensuremath{^\circ}}

% pour écrire les codes Sacoche entourés (dans les tableaux de correction)
\newcommand{\textcircledd}[1]{\tikz[baseline=(letter.base)]\node[draw,circle,inner sep=1pt] (letter) {#1};}
\newcommand{\VV}{\textcircledd{VV}\:}
\newcommand{\V}{\textcircledd{V}\:}
\newcommand{\R}{\textcircledd{R}\:}
\newcommand{\RR}{\textcircledd{RR}\:}
\newcommand{\NE}{\textcircledd{NE}\:}
\newcommand{\NF}{\textcircledd{NF}\:}

%%pour afficher ailleurs que dans une question
\makeatletter
\newcommand{\AffichageSiCorrige}[1]{\ifAMC@correc #1\fi}
\makeatother

%%%%% TAILLES %%%%%
 \usepackage{geometry} 
 \geometry{headsep=0.3cm, left=1.5cm,right=1.5cm,top=2.4cm,bottom=1.5cm}
 \DecimalMathComma 
 %\setlength{\columnseprule}{0.25pt} % ligne de séparation des colonnes
 \setlength{\columnsep}{50pt} % séparation entre les colonnes
 
 \AMCcodeHspace=.4em % réduction de la taille des cases pour le code élève
 \AMCcodeVspace=.4em 
% \AMCcodeBoxSep=.1em
 
 \def\AMCotextReserved{\emph{Ne rien cocher, réservé au prof !}}
 
%%%%%% Définition des barèmes 
\baremeDefautS{
	e=0.0001,	% incohérence (plusieurs réponses données à 0,0001 pour définir des manquements au respect de consignes)
	b=1,		% bonne réponse 1
	m=-0.01,	% mauvaise réponse 0,01 pour différencier de la 
	v=0} 		% non réponse qui reste à 0

\baremeDefautM{formula=((NBC-NMC)/NB)*((NBC-NMC)/NB>0)} % nombre de bonnes réponses cochées minorées des mauvaises réponses cochées, ramenées à 1, et ramenée à 0 si résultat négatif.

%%%%%%%%% Paramètres pour réponses à construire 
\AMCinterIrep=0pt \AMCinterBrep=.5ex \AMCinterIquest=0pt \AMCinterBquest=3ex \AMCpostOquest=7mm \setlength{\AMChorizAnswerSep}{3em plus 4em} \setlength{\AMChorizBoxSep}{1em}
 
\setdefaultgroupmode{fixed} 
 
\begin{document}
\AMCrandomseed{458101}   % On choisit les "graines" pour initialiser le "hasard"
\FPseed=12345678
% attention tout de même à ne mettre à jour que les corrections et pas les sujets en cas de modifications postérieures à l'édition des sujets 

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\element{trigo}{ 
	\begin{question}{R.fig1}
		Dans un triangle MNP rectangle en P, on cherche à relier les longueurs MN et NP et l'angle $\widehat{MNP}$. Quelle propriété utiliser ? Il peut être utile de faire un dessin.
		\begin{reponseshoriz}
		\mauvaise{sinus}
		\bonne{cosinus}
		\mauvaise{tangente}
		\mauvaise{Pythagore}
		\mauvaise{Thalès}
		\end{reponseshoriz}
	\end{question}
}

\element{trigo}{ 
	\begin{question}{R.fig2}
		Dans un triangle MNP rectangle en P, on cherche à relier les longueurs NP et MP et la longueur MN. Quelle propriété utiliser ? Il peut être utile de faire un dessin.
		\begin{reponseshoriz}
		\mauvaise{tangente}
		\mauvaise{cosinus}
		\mauvaise{sinus}
		\bonne{Pythagore}
		\mauvaise{Thalès}
		\end{reponseshoriz}
	\end{question}
}

\element{Courstrigo}{
  \begin{questionmultx}{R.sin}\bareme{mz=1}
	 \begin{reponsesperso}[o]
    	$\sin \widehat{ABC} = \dfrac{\bonne[a]{}\mauvaise[b]{}\bonne[c]{}  }{\mauvaise[a]{}\bonne[b]{}\bonne[c]{} }  $ ? 
  \end{reponsesperso}
 
 \end{questionmultx}
}
\element{Courstrigo}{
  \begin{questionmultx}{R.cos}\bareme{mz=1}
	 \begin{reponsesperso}[o]
    	$\cos \widehat{ABC} = \dfrac{\bonne[a]{}\bonne[b]{}\mauvaise[c]{}  }{\mauvaise[a]{}\bonne[b]{}\bonne[c]{} }  $ ? 
  \end{reponsesperso}
 
 \end{questionmultx}
}
\element{Courstrigo}{
  \begin{questionmultx}{R.tan}\bareme{mz=1}
  	 \begin{reponsesperso}[o]
    	$\tan \widehat{ABC} = \dfrac{\bonne[a]{}\mauvaise[b]{}\bonne[c]{}  }{\bonne[a]{}\bonne[b]{}\mauvaise[c]{} }  $ ? 
  \end{reponsesperso}
 
 \end{questionmultx}
}
\element{trigo}{
	\begin{minipage}{0.30\linewidth}
		\textbf{Exercice :}
				
		Soit ABC un triangle rectangle en A. On note a, b et c les longueurs respectives BC, AC et AB. 
		\begin{center}
		\begin{tikzpicture}
		\definecolor{hhhhhh}{rgb}{0,0,0}
		\clip (5,0) rectangle (0,4.17);
		\fill[color=black] (4.34,1.288) circle (0.047);
		\node at (4.198, 1.241) [align=left,inner sep = 0pt, outer sep = 0pt,below right,black,font= \sf \fontsize {0.5cm} {0.5cm}  \selectfont] {$\text{A}$};
		\fill[color=black] (0.684,1.288) circle (0.047);
		\node at (0.118, 1.83) [align=left,inner sep = 0pt, outer sep = 0pt,below right,black,font= \sf \fontsize {0.5cm} {0.5cm}  \selectfont] {$\text{B}$};
		\draw [color=black , line width = 0.17](4.34,1.288)--(0.684,1.288);
		\fill[color=black] (4.34,3.199) circle (0.047);
		\node at (4.292, 3.671) [align=left,inner sep = 0pt, outer sep = 0pt,below right,black,font= \sf \fontsize {0.5cm} {0.5cm}  \selectfont] {$\text{C}$};
		\draw [color=black , line width = 0.17](0.684,1.288)--(4.34,3.199);
		\draw [color=black , line width = 0.17](4.34,1.288)--(4.34,3.199);
		\node at (2.335, 2.915) [align=left,below right ,black,,font= \sf \fontsize {0.5cm} {0.5cm} \selectfont] {a};
		\node at (4.458, 2.491) [align=left,below right ,black,,font= \sf \fontsize {0.5cm} {0.5cm} \selectfont] {b};
		\node at (2.406, 1.335) [align=left,below right ,black,,font= \sf \fontsize {0.5cm} {0.5cm} \selectfont] {c};
		\end{tikzpicture}
		\end{center}
	\end{minipage}
	\hfill
	\begin{minipage}{0.60\linewidth}
	Barrez les cases des formules suivantes de manière à ce que \textbf{la formule restant visible soit correcte} :
	\vfill	
	\restituegroupe{Courstrigo} 
	\vfill
	\end{minipage}	
		
}

\element{trigo}{ 
	\textbf{EXERCICE :} 		
	Dans un triangle GHI rectangle en G, on sait que $GH=75$ et $\widehat{IHG}=37^\circ$. On cherche à calculer HI.\\ \medskip
	\begin{question}{T.Fig1}
		\collerVertic
		\AMCOpen{lineup=true, lineuptext={Tâche 1 : Faire une figure codée à main levée  :}, dots=false}{\mauvaise[RR]{RR}\bareme{1}\mauvaise[R]{R}\bareme{2}\mauvaise[V]{V}\bareme{3}\bonne[VV]{VV}\bareme{4}}
		\collerVertic
	\end{question}

	\vspace{2cm}

	
	\begin{multicols}{2}
		\begin{question}{T.Fdir} % traduire en fraction 
			Tâche 2 : Noircir la case de la formule que vous utiliserez :
			\begin{reponseshoriz}
				\bonne{$\cos 37=\frac{75}{IH} \phantom{\dfrac{1}{1}}$}
				\mauvaise{$\cos 37=\frac{IH}{75}\phantom{\dfrac{1}{1}} $}
				\mauvaise{$\cos \widehat{IHG}=\frac{37}{75} \phantom{\dfrac{1}{1}}$}
				\mauvaise{$\sin 37=\frac{75}{IH} \phantom{\dfrac{1}{1}}$}
				\mauvaise{$\sin 37=\frac{IH}{75} \phantom{\dfrac{1}{1}}$}
				\mauvaise{$\sin \widehat{IHG}=\frac{37}{75}\phantom{\dfrac{1}{1}} $}
			\end{reponseshoriz}
		\end{question}	
	
		\begin{questionmultx}{T.Rdir} % Utiliser la proportionnalité, si traduire est OK
			Tâche 3 : Calculer HI et noircir dans l'ordre ses chiffres des dizaines, des unités et des dixièmes :
			
			\begin{minipage}{0.25\textwidth}
				\begin{tabular}{r}
				Dizaines → \\[0.15cm]
				Unités → \\[0.7cm]
				Dixièmes → \\
				\end{tabular}
			\end{minipage}
			\begin{minipage}{0.3\textwidth}
				\AMCnumericChoices{93.9}{digits=3,decimals=1,sign=false,borderwidth=0pt,backgroundcol=lightgray,scoreexact=1,exact=1}
			\end{minipage}
		\end{questionmultx}
	\end{multicols}
	\vfill
}

%resolution inverse

\element{trigo}{ 
	\textbf{EXERCICE :} 		
	Dans un triangle GHI rectangle en H, on sait que $HI=23$ et $GH=17$. On cherche à calculer $\widehat{IGH}$. \\ \medskip
	\begin{question}{T.Fig2}
		\collerVertic
		\AMCOpen{lineup=true, lineuptext={Tâche 1 : Faire une figure codée à main levée  :}, dots=false}{\mauvaise[RR]{RR}\bareme{1}\mauvaise[R]{R}\bareme{2}\mauvaise[V]{V}\bareme{3}\bonne[VV]{VV}\bareme{4}}
		\collerVertic
	\end{question}

	\vspace{2cm}

	
	\begin{multicols}{2}
		\begin{question}{T.Finv} % traduire en fraction 
			Tâche 2 : Noircir la case de la formule que vous utiliserez :
			\begin{reponseshoriz}
				\bonne{$\tan \widehat{IGH}=\frac{23}{17}	\phantom{\dfrac{1}{1}}$}
				\mauvaise{$\tan 17=\frac{\widehat{IGH}}{23}	\phantom{\dfrac{1}{1}}$}
				\mauvaise{$\cos \widehat{IGH}=\frac{17}{23} \phantom{\dfrac{1}{1}}$}
				\mauvaise{$\widehat{IGH}=\tan\frac{17}{23}	\phantom{\dfrac{1}{1}}$}
				\mauvaise{$\widehat{IGH}=\frac{17}{23}		\phantom{\dfrac{1}{1}}$}
				\mauvaise{$\sin \widehat{IGH}=\frac{17}{23}	\phantom{\dfrac{1}{1}}$}
			\end{reponseshoriz}
		\end{question}	
	
		\begin{questionmultx}{T.Rinv} % Utiliser la proportionnalité, si traduire est OK
			Tâche 3 : Calculer $\widehat{IGH}$ et noircir dans l'ordre ses chiffres des dizaines et des unités :
			
			\begin{minipage}{0.25\textwidth}
				\vspace*{0.15cm}
				\begin{tabular}{r}
				Dizaines → \\[0.15cm]
				Unités → \\[0.15cm]
				\end{tabular}
			\end{minipage}
			\begin{minipage}{0.3\textwidth}
				\AMCnumericChoices{53}{digits=2,decimals=0,sign=false,borderwidth=0pt,backgroundcol=lightgray,scoreexact=1,exact=1}
			\end{minipage}
		\end{questionmultx}
	\end{multicols}
	\vfill
}

% issue de MATHALEA 3G32-1

\element{angle}{
En considérant que le rayon de la Terre est de 6370 km, quelle est la longueur du $a=44$e parallèle Nord au kilomètre près ?
}
\element{angle}{
En considérant que le rayon de la Terre est de 6370 km, quelle est la longueur du $a=72$e parallèle Nord au kilomètre près ?
}
\element{angle}{
En considérant que le rayon de la Terre est de 6370 km, quelle est la longueur du $a=28$e parallèle Nord au kilomètre près ?
}

\element{trigo}{
%	\vspace{5mm}

	\textbf{EXERCICE :}
	{\mathversion{bold}
	\begin{tikzpicture}[baseline,scale = 0.5]

		\tikzset{
		  point/.style={
			thick,
			draw,
			cross out,
			inner sep=0pt,
			minimum width=5pt,
			minimum height=5pt,
		  },
		}
		\clip (-8,-6) rectangle (8,6);
			
		\draw[color={{gray}},opacity = 0.8,fill opacity = 0.4,preaction={fill,color = {gray}}] (0,5) circle (0.1);
		
		\draw[color={{rgb,255:red,178;green,178;blue,178}},opacity = 0.8,fill opacity = 0.4,preaction={fill,color = {rgb,255:red,178;green,178;blue,178}}] (0,-5) circle (0.1);
		\draw[color={gray}, dotted ,opacity = 0.5] (2.51,4.66)--(2.51,4.66)--(2.27,4.7)--(1.96,4.73)--(1.59,4.75)--(1.17,4.76)--(0.72,4.75)--(0.25,4.73)--(-0.23,4.7)--(-0.71,4.66)--(-1.16,4.6)--(-1.58,4.54)--(-1.95,4.48)--(-2.26,4.4)--(-2.51,4.33);
		\draw[color={gray}] (-2.75,4.18)--(-2.75,4.12)--(-2.67,4.06)--(-2.51,4)--(-2.27,3.96)--(-1.96,3.93)--(-1.59,3.91)--(-1.17,3.9)--(-0.72,3.91)--(-0.25,3.93)--(0.23,3.96)--(0.71,4)--(1.16,4.06)--(1.58,4.12)--(1.95,4.18)--(2.26,4.26)--(2.5,4.33)--(2.67,4.4)--(2.75,4.48)--(2.75,4.54)--(2.67,4.6);
		\draw[color={gray}, dotted ,opacity = 0.5] (4.64,2.96)--(4.62,2.98)--(4.34,3.07)--(3.93,3.14)--(3.39,3.2)--(2.76,3.23)--(2.03,3.24)--(1.25,3.23)--(0.43,3.2)--(-0.4,3.14)--(-1.22,3.07)--(-2.01,2.98)--(-2.73,2.87)--(-3.37,2.75)--(-3.91,2.63)--(-4.33,2.5)--(-4.64,2.35);
		\draw[color={gray}] (-4.77,2.13)--(-4.62,2.02)--(-4.34,1.93)--(-3.93,1.86)--(-3.39,1.8)--(-2.76,1.77)--(-2.03,1.76)--(-1.25,1.77)--(-0.43,1.8)--(0.4,1.86)--(1.22,1.93)--(2.01,2.02)--(2.73,2.13)--(3.37,2.25)--(3.91,2.37)--(4.33,2.5)--(4.62,2.63)--(4.76,2.75)--(4.77,2.87);
		\draw[color={black},line width = 1.5, dotted ,opacity = 0.5] (5.45,0.47)--(5.34,0.55)--(5.01,0.66)--(4.53,0.74)--(3.92,0.8)--(3.18,0.84)--(2.35,0.86)--(1.45,0.84)--(0.5,0.8)--(-0.47,0.74)--(-1.41,0.66)--(-2.32,0.55)--(-3.16,0.43)--(-3.89,0.29)--(-4.52,0.15)--(-5,0)--(-5.45,-0.25);
		\draw[color={black},line width = 1.5] (-5.5,-0.43)--(-5.34,-0.55)--(-5.01,-0.66)--(-4.53,-0.74)--(-3.92,-0.8)--(-3.18,-0.84)--(-2.35,-0.86)--(-1.45,-0.84)--(-0.5,-0.8)--(0.47,-0.74)--(1.41,-0.66)--(2.32,-0.55)--(3.16,-0.43)--(3.89,-0.29)--(4.52,-0.15)--(5,0)--(5.33,0.15)--(5.5,0.29)--(5.5,0.43);
		\draw[color={gray}, dotted ,opacity = 0.5] (4.77,-2.15)--(4.77,-2.13)--(4.62,-2.02)--(4.34,-1.93)--(3.93,-1.86)--(3.39,-1.8)--(2.76,-1.77)--(2.03,-1.76)--(1.25,-1.77)--(0.43,-1.8)--(-0.4,-1.86)--(-1.22,-1.93)--(-2.01,-2.02)--(-2.73,-2.13)--(-3.37,-2.25)--(-3.91,-2.37)--(-4.33,-2.5)--(-4.62,-2.63)--(-4.77,-2.78);
		\draw[color={gray}] (-4.62,-2.98)--(-4.34,-3.07)--(-3.93,-3.14)--(-3.39,-3.2)--(-2.76,-3.23)--(-2.03,-3.24)--(-1.25,-3.23)--(-0.43,-3.2)--(0.4,-3.14)--(1.22,-3.07)--(2.01,-2.98)--(2.73,-2.87)--(3.37,-2.75)--(3.91,-2.63)--(4.33,-2.5)--(4.62,-2.37)--(4.76,-2.25);
		\draw[color={gray}, dotted ,opacity = 0.5] (2.74,-4.19)--(2.75,-4.18)--(2.75,-4.12)--(2.67,-4.06)--(2.51,-4)--(2.27,-3.96)--(1.96,-3.93)--(1.59,-3.91)--(1.17,-3.9)--(0.72,-3.91)--(0.25,-3.93)--(-0.23,-3.96)--(-0.71,-4)--(-1.16,-4.06)--(-1.58,-4.12)--(-1.95,-4.18)--(-2.26,-4.26)--(-2.5,-4.33)--(-2.67,-4.4)--(-2.75,-4.48)--(-2.74,-4.55);
		\draw[color={gray}] (-2.51,-4.66)--(-2.27,-4.7)--(-1.96,-4.73)--(-1.59,-4.75)--(-1.17,-4.76)--(-0.72,-4.75)--(-0.25,-4.73)--(0.23,-4.7)--(0.71,-4.66)--(1.16,-4.6)--(1.58,-4.54)--(1.95,-4.48)--(2.26,-4.4)--(2.5,-4.33)--(2.67,-4.26);
		\draw[color ={gray}] (0,5)--(0.48,5.01);
		\draw[color ={gray}] (-0.48,4.96)--(0,5);
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		\draw[color={black}] (0.39,4.97)--(0.59,4.94)--(0.78,4.9)--(0.98,4.85)--(1.17,4.79)--(1.36,4.72)--(1.54,4.65)--(1.73,4.56)--(1.91,4.47)--(2.09,4.37)--(2.26,4.26)--(2.43,4.14)--(2.59,4.01)--(2.75,3.88)--(2.9,3.73)--(3.05,3.59)--(3.19,3.43)--(3.33,3.27)--(3.46,3.1)--(3.58,2.93)--(3.7,2.75)--(3.81,2.56)--(3.91,2.37)--(4.01,2.18)--(4.09,1.98)--(4.17,1.78)--(4.24,1.57)--(4.31,1.36)--(4.36,1.15)--(4.41,0.94)--(4.45,0.72)--(4.48,0.51)--(4.5,0.29)--(4.51,0.07)--(4.52,-0.15)--(4.51,-0.37)--(4.5,-0.58)--(4.48,-0.8)--(4.45,-1.01)--(4.41,-1.23)--(4.36,-1.44)--(4.31,-1.65)--(4.24,-1.85)--(4.17,-2.05)--(4.09,-2.25)--(4.01,-2.44)--(3.91,-2.63)--(3.81,-2.81)--(3.7,-2.99)--(3.58,-3.16)--(3.46,-3.33)--(3.33,-3.49)--(3.19,-3.64)--(3.05,-3.79)--(2.9,-3.93)--(2.75,-4.06)--(2.59,-4.18)--(2.43,-4.3)--(2.26,-4.4)--(2.09,-4.5)--(1.91,-4.59)--(1.73,-4.68)--(1.54,-4.75)--(1.36,-4.81)--(1.17,-4.87)--(0.98,-4.91);
		\draw[color={black},line width = 1.5] (-0.67,4.98)--(-1,4.91)--(-1.3,4.83)--(-1.55,4.75)--(-1.83,4.65)--(-2.06,4.55)--(-2.28,4.44)--(-2.51,4.33)--(-2.74,4.19)--(-2.96,4.06)--(-3.16,3.92)--(-3.35,3.77)--(-3.54,3.62)--(-3.72,3.45)--(-3.89,3.29)--(-4.06,3.11)--(-4.22,2.93)--(-4.37,2.75)--(-4.51,2.55)--(-4.64,2.35)--(-4.77,2.15)--(-4.88,1.94)--(-4.99,1.72)--(-5.08,1.51)--(-5.16,1.3)--(-5.23,1.08)--(-5.29,0.86)--(-5.34,0.64)--(-5.39,0.42)--(-5.42,0.2)--(-5.44,-0.02)--(-5.45,-0.25)--(-5.45,-0.47)--(-5.44,-0.69)--(-5.42,-0.91)--(-5.39,-1.13)--(-5.35,-1.35)--(-5.29,-1.56)--(-5.23,-1.77)--(-5.16,-1.98)--(-5.08,-2.18)--(-4.99,-2.38)--(-4.88,-2.58)--(-4.77,-2.78)--(-4.64,-2.96)--(-4.51,-3.15)--(-4.37,-3.32)--(-4.22,-3.49)--(-4.06,-3.65)--(-3.89,-3.8)--(-3.72,-3.94)--(-3.54,-4.08)--(-3.35,-4.21)--(-3.16,-4.33)--(-2.96,-4.45)--(-2.74,-4.55)--(-2.51,-4.66)--(-2.29,-4.74)--(-2.06,-4.82)--(-1.83,-4.89)--(-1.55,-4.95)--(-1.3,-5)--(-1,-5.04)--(-0.67,-5.06)--(-0.41,-5.07)--(-0.25,-5.07)--(-0.09,-5.06)--(0.08,-5.05)--(0.25,-5.04)--(0.4,-5.02)--(0.55,-5)--(0.67,-4.98)--(1,-4.91)--(1.3,-4.83)--(1.55,-4.75)--(1.83,-4.65)--(2.06,-4.55)--(2.28,-4.44)--(2.51,-4.33)--(2.74,-4.19)--(2.96,-4.06)--(3.16,-3.92)--(3.35,-3.77)--(3.54,-3.62)--(3.72,-3.45)--(3.89,-3.29)--(4.06,-3.11)--(4.22,-2.93)--(4.37,-2.75)--(4.51,-2.55)--(4.64,-2.35)--(4.77,-2.15)--(4.88,-1.94)--(4.99,-1.72)--(5.08,-1.51)--(5.16,-1.3)--(5.23,-1.08)--(5.29,-0.86)--(5.34,-0.64)--(5.39,-0.42)--(5.42,-0.2)--(5.44,0.02)--(5.45,0.25)--(5.45,0.47)--(5.44,0.69)--(5.42,0.91)--(5.39,1.13)--(5.35,1.35)--(5.29,1.56)--(5.23,1.77)--(5.16,1.98)--(5.08,2.18)--(4.99,2.38)--(4.88,2.58)--(4.77,2.78)--(4.64,2.96)--(4.51,3.15)--(4.37,3.32)--(4.22,3.49)--(4.06,3.65)--(3.89,3.8)--(3.72,3.94)--(3.54,4.08)--(3.35,4.21)--(3.16,4.33)--(2.96,4.45)--(2.74,4.55)--(2.51,4.66)--(2.29,4.74)--(2.06,4.82)--(1.83,4.89)--(1.55,4.95)--(1.3,5)--(1,5.04)--(0.67,5.06)--(0.51,5.07)--(0.31,5.06)--(0.11,5.06)--(-0.1,5.04)--(-0.31,5.02)--(-0.5,5)--(-0.68,4.97)--cycle;
		\draw[color ={black}, densely dash dot dot ] (0,-5)--(0,5);
		\draw[color ={black}, densely dash dot dot ] (0,3.26)--(4.18,3.56);
		\draw[color ={black}, densely dash dot dot ] (0,0)--(4.18,3.56);
		\draw[color ={black}] (0.55,3.3)--(0.55,2.8);\draw[color ={black}] (0.55,2.8)--(0,2.76);
		
		\draw[color ={{black}},line width = 0.6666666666666666,opacity = 0.8] (-0.2,3.46)--(0.2,3.06);
		\draw[color ={{black}},line width = 0.6666666666666666,opacity = 0.8] (-0.2,3.06)--(0.2,3.46);
		\draw[color ={{black}},line width = 0.6666666666666666,opacity = 0.8] (3.98,3.76)--(4.38,3.36);
		\draw[color ={{black}},line width = 0.6666666666666666,opacity = 0.8] (3.98,3.36)--(4.38,3.76);
		\draw[color ={{black}},line width = 0.6666666666666666,opacity = 0.8] (-0.2,0.2)--(0.2,-0.2);
		\draw[color ={{black}},line width = 0.6666666666666666,opacity = 0.8] (-0.2,-0.2)--(0.2,0.2);
		\draw[color ={{black}},line width = 0.6666666666666666,opacity = 0.8] (5.3,0.49)--(5.7,0.09);
		\draw[color ={{black}},line width = 0.6666666666666666,opacity = 0.8] (5.3,0.09)--(5.7,0.49);
		
		\draw (0,3.26) node[left] {$H$};
		\draw (4.18,3.56) node[above right] {$P$};
		\draw (0,0) node[above left] {$O$};
		\draw (5.5,0.29) node[right] {$M$};
	
		\draw[color={red}] (4.18,3.56)--(4.14,3.45)--(3.97,3.34)--(3.68,3.23)--(3.28,3.12)--(2.78,3.01)--(2.2,2.91)--(1.55,2.82)--(0.85,2.75)--(0.12,2.69)--(-0.61,2.64)--(-1.32,2.62)--(-1.99,2.62)--(-2.6,2.63)--(-3.13,2.67)--(-3.56,2.72)--(-3.89,2.79)--(-4.1,2.88)--(-4.18,2.97);
		\draw[color={red}, densely dash dot dot ,opacity = 0.9] (4.18,3.56)--(4.1,3.65)--(3.89,3.74)--(3.56,3.81)--(3.13,3.86)--(2.6,3.89)--(1.99,3.91)--(1.32,3.91)--(0.61,3.88)--(-0.12,3.84)--(-0.85,3.78)--(-1.55,3.71)--(-2.2,3.62)--(-2.78,3.52)--(-3.28,3.41)--(-3.68,3.3)--(-3.97,3.19)--(-4.14,3.08)--(-4.18,2.97);
		\draw[color ={black}, densely dash dot dot ] (0,0)--(5.5,0.29);
		
		\draw [color={black}] (1.858167379925286,0.7397391352237604) node[anchor = center,scale=1] {$a$} ;
		\draw[color={black}] (1.4978855565722522,0.07961695430141896) arc (3.04:40.37:1.5) ;
\end{tikzpicture}
	}
\\
	\restituegroupe[1]{angle}	
	\vspace{7.5cm}

	\begin{question}{T.Choix}
	\collerVertic
	\AMCOpen{lineup=true, lineuptext={Choisir un cadre adapté}, dots=false}{\mauvaise[RR]{RR}\bareme{1}\mauvaise[R]{R}\bareme{2}\mauvaise[V]{V}\bareme{3}\bonne[VV]{VV}\bareme{4}}
	\collerVertic
	\end{question}

	\begin{question}{T.Prop} 
	\collerVertic
	\AMCOpen{lineup=true, lineuptext={Utiliser la proportionnalité},dots=false}{\mauvaise[RR]{RR}\scoring{1}\mauvaise[R]{R}\scoring{2}\mauvaise[V]{V}\scoring{3}\bonne[VV]{VV}\scoring{4}}
	\collerVertic
	\end{question}

	\begin{question}{T.trigo} 
	\collerVertic
	\AMCOpen{lineup=true, lineuptext={Traduire par une fonction},dots=false}{\mauvaise[RR]{RR}\scoring{1}\mauvaise[R]{R}\scoring{2}\mauvaise[V]{V}\scoring{3}\bonne[VV]{VV}\scoring{4}}
	\collerVertic
	\end{question}

	\begin{question}{T.unite} 
	\collerVertic
	\AMCOpen{lineup=true, lineuptext={Utiliser une unité adaptée},dots=false}{\mauvaise[RR]{RR}\scoring{1}\mauvaise[R]{R}\scoring{2}\mauvaise[V]{V}\scoring{3}\bonne[VV]{VV}\scoring{4}}
	\collerVertic
	\end{question}

	\begin{question}{T.Expl} 
	\collerVertic
	\AMCOpen{lineup=true, lineuptext={Expliquer par écrit},dots=false}{\mauvaise[RR]{RR}\scoring{1}\mauvaise[R]{R}\scoring{2}\mauvaise[V]{V}\scoring{3}\bonne[VV]{VV}\scoring{4}}
	\collerVertic
	\explain{Plusieurs valeurs différentes de l'angle $a$ étaient proposées suivant les sujets, mais la résolution pouvait se faire de la manière suivante :
	
	Pour trouver la longueur du $a^e$ parallèle, il faut trouver le rayon HP de ce cercle de centre H passant par P.
	HPO est un triangle rectangle en H, avec OP = rayon de la Terre = 6 370 km.
  	Comme (HP) // (OM), et que $\widehat{MOP}$ et $\widehat{HPO}$ sont alternes internes, on a de plus $\widehat{HPO}=\widehat{MOP}=a$.
	Donc dans le triangle HPO, on a~:
	$$\cos{a} = \dfrac{HP}{OP}$$ soit aussi $$\cos{a} = \dfrac{HP}{6370}$$ et $$ HP = 6370 \times \cos{a} \text{km} $$ 
	Donc la longueur du $a^e$ parallèle est $2\times\pi\times HP$ soit à 1 km près :
	\begin{enumerate}
		\item si $a=28\Degre$ alors l = \num{35339} km.
		\item si $a=44\Degre$ alors l = \num{28791} km.		
		\item si $a=78\Degre$ alors l = \num{8321} km.
	\end{enumerate}}
	\end{question}
}


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\exemplaire{1}{   % <========================  /!\ PENSER À ADAPTER /!\  ==  %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% pour alléger la couleur des lettres dans les cases et les réduire
\def\AMCchoiceLabelFormat##1{\textcolor{black!70}{{\tiny ##1}}}  
% pour revenir dans le cas normal à une case à cocher blanche
\def\AMCchoiceLabel##1{}


REMPLIR avec un stylo NOIR la ou les cases pour chaque question. Si vous devez modifier un choix, NE PAS chercher à redessiner la case cochée par erreur, mettez simplement un coup de "blanc" dessus.
	
Les questions qui ne commencent PAS par le symbole \multiSymbole \ n'ont qu'une SEULE case correcte.
Les questions qui commencent par le symbole \multiSymbole \ PEUVENT comporter plusieurs cases correctes (mais ce n'est pas obligatoire).
	
\textbf{Attention, la plupart des questions nécessitent des calculs qui sont à faire au brouillon. Il est fortement déconseillé de répondre au hasard !}
		
%%%%% QUESTIONS MÉLANGÉES %%%%% 
	
\colorbox{gray!20}{\textbf{PARTIE A : Trigonométrie  \hspace{11cm} (20 min)}}
	
\restituegroupe{trigo}	

}% Fin du bloc \exemplaire

\end{document}