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\noindent
\begin{tabularx}{\textwidth}{@{} lCr @{}}
    Lycee Taghzirt\textbf{/}Prof MOSAID &
    2024-2025\textbf{/Devoir 1 S01}\ccc{A}&
    TCSF  \textbf{/}2h\\
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\textbf{\underline{Exercice 1:}}(12pts)\\
\noindent
\begin{tabular}{>{\hfill}p{0.04\textwidth}|p{0.95\textwidth}}
     & 1. Soient les nombres $x=2420$ et $y=6930$\\
    2& \hspace*{0.5cm}a. Décomposer les deux nombres $x$ et $y$ en produits de facteurs premiers\\
    2& \hspace*{0.5cm}b. Déterminer $pgcd(x,y)$ et $ppcm(x,y)$\\
    2& \hspace*{0.5cm}c. Simplifier $\sqrt{5x}$ et $\sqrt{\frac{35y}{22}}$\\
    2& \hspace*{0.5cm}d. Utiliser l'algorithme d'euclid pour determiner $pgcd(x,y)$\\
    1& 2. Le nombre 371 est il un nombre premier ? justifier.\\
    2& 3. Soit $n\in \mathbb{N}$. Etudier la parité du nombre $a=n^2-n+1$\\
    1& 4. Déterminer l'ensemble des diviseurs de 42\\
\end{tabular}
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\noindent
\textbf{\underline{Exercice 2:}}(8pts)\\
\noindent
\begin{tabular}{>{\hfill}p{0.04\textwidth}|p{0.95\textwidth}}
    & Soit $ABC$ un triangle. Soient les points $I$, $J$ et $K$ tels que\\
    & \hspace*{1cm}$\overrightarrow{AI}=\frac{1}{2}\overrightarrow{AB}$~~~~;~~~~~
      $\overrightarrow{AJ}=\frac{2}{5}\overrightarrow{AC}$~~~~;~~~~~
      $\overrightarrow{BK}=-2\overrightarrow{BC}$\\
    3& 1. Construire une figure\\
    2& 2. Montrer que
      $\overrightarrow{IJ}=-\frac{1}{2}\overrightarrow{AB}+\frac{2}{5}\overrightarrow{AC}$~~~~et~~~~~
      $\overrightarrow{IK}=\frac{5}{2}\overrightarrow{AB}-2\overrightarrow{AC}$\\
    2& 3. Montrer que $\overrightarrow{IJ}$ et $\overrightarrow{IK}$ sont colinèaires\\
    1& 4. Montrer que les points I, J et K sont alignés.
\end{tabular}\\
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\textcolor{white}{.}\hfill \underline{MOSAID le \today}\\
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