Control n 2: Calcul et ordre dans IR et droite dans le plan (B)
📅 December 19, 2024 | 👁️ Views: 176
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\exo{Exercice 1: Droite dans le plan \hspace{2mm} (8 pts)}\\
\hspace*{0.2cm}Le plan est rapporté à un repère orthonormé \((O,\vec i, \vec j)\). Soient les points
\(A(2,2)\), \(B(-2,2)\) et \(C(2,3)\)
\begin{questions}
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Déterminer la nature du triangle ~$ABC$~
\part[1]
Déterminer les coordonnées du point ~$D$~ tel que ~$\overrightarrow{AD}=2\overrightarrow{BC}$~
\end{parts}
\question[2]
Determiner une équation cartésienne de la droite ~$(AB)$~
\question[2]
Determiner une équation cartésienne de la droite ~$(\Delta)$~ parallèle à ~$(AB)$~ passant par ~$C$~
\question[1]
Donner une représentation paramétrique de la droite ~$(BC)$~
\end{questions}
\noindent\hspace*{0.2cm}
\exo{Exercice 2: Calcul et ordre dans ~$\mathbb{R}$ ~(12 pts)}\\
\stamp{16}{0}
\hspace*{0.2cm}\textbf{\underline{Remarque:} Les questions sont indépendantes}
\begin{questions}
\question[3]
Soient \( x\in[-2,3[ \) et \(y\in]2,6]\), \hspace*{0.5cm}encadrer ~$A=\frac{2x+6y+3}{x+5y}$~
\question[3]
Résoudre les équations \(|-3x+7|=-2\) ~et~ \(|x+5|=|3-2x|\)
\question
Soient les ensmbles : \(A=\{x\in\mathbb{R}/|x+3|<1\}\) et \(B=\{x\in\mathbb{R}/|3-x|>1\}\)
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\part[2]
Determiner les ensmbles ~$A$~ et ~$B$~
\part[2]
Déterminer ~$A\cap B$ et $ A\cup B$~
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\question[2]
Factoriser : \(A=3\sqrt3x^3-8-4x(3x^2-4)\) et \(B=5x^2-(5x-3)^2+\sqrt5x+5x-3\)
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