\documentclass[addpoints, 12pt, a4paper]{exam}%answers,
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\noindent
\borders\\[1.5cm]
\noindent\hspace*{0.2cm}
\exo{Exercice 1: Droite dans le plan \hspace{2mm} (9 pts)}\\
\hspace*{0.2cm}Le plan est rapporté à un repère orthonormé \((O,\vec i, \vec  j)\). Soient les points
\(A(2,2)\), \(B(1,-1)\) et \(C(2,1)\)
\begin{questions}
\question
\begin{parts}
\part[1]
Déterminer les couples de coordonnées des vecteurs \(\overrightarrow{AB}\) et \(\overrightarrow{BC}\)
\part[1]
Montrer que les points \(A\), \(B\) et \(C\) sont non alignés
\end{parts}
\question[2]
Determiner une équation cartésienne de la droite \(D\left(R(1,2),\vec u (-2,1)\right)\)
\question[2]
Determiner une équation cartésienne de la droite \((HG)\) telle que \(H(2,1)\) et \(G(1,3)\)
\question[1]
Vérifier que les deux droites \((D)\) et \((HG)\) sont sécantes
\question[2]
Determiner leur point d'intersection.
\end{questions}
\noindent\hspace*{0.2cm}
\exo{Exercice 2: Calcul et ordre dans ~$\mathbb{R}$~ \hspace{2mm} (11 pts)}\\
\stamp{16.5}{0.5}
\hspace*{0.2cm}\textbf{\underline{Remarque:} Les questions sont indépendantes}
\begin{questions}
\question[2]
Factoriser : \(A=x^3-8+4(x^2-4)-3x+6\) et \(B=16x^2-(5x-3)^2\)
\question[1]
Determiner \(I\cap J\) et \(I\cup J\) tel que \(I=[-2,3[\) et \(J=]2,6]\)
\question[3]
Résoudre les équations \(|3x-4|=2\) et \(|x-1|=|3-2x|\)
\question[2]
Determiner les ensmbles suivants: \(A=\{x\in\mathbb{R}/|x-3|<1\}\) et \(B=\{x\in\mathbb{R}/|3-x|>2\}\)
\question[3]
Soient \(I=[-2,3[\) et \(J=]2,6]\)\\
Soient ~$x\in I$~ et ~$y\in J$~ encadrer ~$A=x^2+y^2-3x+2y-7$~
\end{questions}
\textcolor{white}{.}\hfill
{\scalebox{3}{\textbf{\textcolor{blue}{\calligra Good Luck!}}}}~~~~~
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