2015-2016/3e/Expression_litterale/Equation_premier_degree/Exo_tech.tex

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\documentclass[a5paper,12pt, table]{/media/documents/Cours/Prof/Enseignements/tools/style/classDS}
\usepackage{/media/documents/Cours/Prof/Enseignements/2015_2016}
% Title Page
\titre{Équation du premier degré - Exercices}
% \seconde \premiereS \PSTMG \TSTMG
\classe{Troisième}
\date{Mars 2016}
\geometry{left=10mm,right=10mm, bottom= 10mm, top=10mm}
%\printanswers
\begin{document}
\begin{Exo}
Résoudre les équations suivantes
\begin{multicols}{2}
\begin{enumerate}
\Block{set e = randint(10,100)}
\Block{set f = randint(e,100)}
\item $x + \Var{e} = \Var{f}$
\begin{solution}
$x = \Var{f} - \Var{e} = \Var{f-e}$
\end{solution}
\Block{set e = randint(10,100)}
\Block{set f = randint(1,e)}
\item $x + \Var{e} = \Var{f}$
\begin{solution}
~ $x = \Var{f} - \Var{e} = \Var{f-e}$
\end{solution}
\Block{set e = randint(10,100)}
\Block{set f = randint(1,e)}
\item $a - \Var{e} = \Var{f}$
\begin{solution}
~ $a = \Var{f} + \Var{e} = \Var{f+e}$
\end{solution}
\Block{set e = randint(10,100)}
\Block{set f = randint(10,100)}
\item $\Var{e}x = \Var{f}$
\begin{solution}
~ $x = \frac{\Var{f}}{\Var{e}} = \Var{f/e}$
\end{solution}
\Block{set e = randint(10,100)}
\Block{set f = randint(10,100)}
\item $\Var{e}y = \Var{f}$
\begin{solution}
~ $y = \frac{\Var{f}}{\Var{e}} = \Var{f/e}$
\end{solution}
\Block{set e = randint(10,100)}
\Block{set f = randint(e,100)}
\item $x + \Var{e} = \Var{f}$
\begin{solution}
$x = \Var{f} - \Var{e} = \Var{f-e}$
\end{solution}
\Block{set e = randint(10,100)}
\Block{set f = randint(1,e)}
\item $x + \Var{e} = \Var{f}$
\begin{solution}
~ $x = \Var{f} - \Var{e} = \Var{f-e}$
\end{solution}
\Block{set e = randint(10,100)}
\Block{set f = randint(1,e)}
\item $a - \Var{e} = \Var{f}$
\begin{solution}
~ $a = \Var{f} + \Var{e} = \Var{f+e}$
\end{solution}
\Block{set e = randint(10,100)}
\Block{set f = randint(10,100)}
\item $\Var{e}x = \Var{f}$
\begin{solution}
~ $x = \frac{\Var{f}}{\Var{e}} = \Var{f/e}$
\end{solution}
\Block{set e = randint(10,100)}
\Block{set f = randint(10,100)}
\item $\Var{e}y = \Var{f}$
\begin{solution}
~ $y = \frac{\Var{f}}{\Var{e}} = \Var{f/e}$
\end{solution}
\end{enumerate}
\end{multicols}
\end{Exo}
\begin{Exo}
Résoudre les équations suivantes
\begin{multicols}{2}
\begin{enumerate}
\Block{set e = randint(10,100)}
\Block{set f = 0}
\Block{set g = randint(2,10)}
\item $\Var{g}x + \Var{e} = \Var{f}$
\begin{solution}
$x = \frac{\Var{f} - \Var{e}}{\Var{g}} = \Var{(f-e)/g}$
\end{solution}
\Block{set e = randint(10,100)}
\Block{set f = randint(10,100)}
\Block{set g = randint(2,10)}
\item $\Var{g}x + \Var{e} = \Var{f}$
\begin{solution}
$x = \frac{\Var{f} - \Var{e}}{\Var{g}} = \Var{(f-e)/g}$
\end{solution}
\Block{set e = randint(10,100)}
\Block{set f = randint(10,100)}
\Block{set g = randint(2,10)}
\item $\Var{g}x + \Var{e} = \Var{f}$
\begin{solution}
$x = \frac{\Var{f} - \Var{e}}{\Var{g}} = \Var{(f-e)/g}$
\end{solution}
\Block{set e = randint(10,100)}
\Block{set f = randint(10,100)}
\Block{set g = randint(4,10)}
\Block{set h = randint(2,g)}
\item $\Var{g}x + \Var{e} = \Var{h}x + \Var{f}$
\begin{solution}
$x = \frac{\Var{f} - \Var{e}}{\Var{g} - \Var{h}} = \Var{(f-e)/(g-h)}$
\end{solution}
\Block{set e = randint(10,100)}
\Block{set f = randint(10,100)}
\Block{set g = randint(4,10)}
\Block{set h = randint(2,g)}
\item $\Var{g}x + \Var{e} = \Var{h}x + \Var{f}$
\begin{solution}
$x = \frac{\Var{f} - \Var{e}}{\Var{g} - \Var{h}} = \Var{(f-e)/(g-h)}$
\end{solution}
\Block{set e = randint(10,100)}
\Block{set f = 0}
\Block{set g = randint(2,10)}
\item $\Var{g}x - \Var{e} = \Var{f}$
\begin{solution}
$x = \frac{\Var{f} + \Var{e}}{\Var{g}} = \Var{(f+e)/g}$
\end{solution}
\Block{set e = randint(10,100)}
\Block{set f = randint(10,100)}
\Block{set g = randint(2,10)}
\item $\Var{g}x + \Var{e} = \Var{f}$
\begin{solution}
$x = \frac{\Var{f} - \Var{e}}{\Var{g}} = \Var{(f-e)/g}$
\end{solution}
\Block{set e = randint(10,100)}
\Block{set f = randint(10,100)}
\Block{set g = randint(2,7)}
\Block{set h = randint(g,15)}
\item $\Var{g}x + \Var{e} = \Var{h}x + \Var{f}$
\begin{solution}
$x = \frac{\Var{f} - \Var{e}}{\Var{g} - \Var{h}} = \Var{(f-e)/(g-h)}$
\end{solution}
\Block{set e = randint(10,100)}
\Block{set f = randint(10,100)}
\Block{set g = randint(2,7)}
\Block{set h = randint(g,10)}
\item $\Var{g}x + \Var{e} = \Var{h}x + \Var{f}$
\begin{solution}
$x = \frac{\Var{f} - \Var{e}}{\Var{g} - \Var{h}} = \Var{(f-e)/(g-h)}$
\end{solution}
\Block{set e = randint(10,100)}
\Block{set f = randint(10,100)}
\Block{set g = randint(2,6)}
\Block{set h = randint(-10, 0)}
\item $\Var{g}x + \Var{e} = \Var{h}x + \Var{f}$
\begin{solution}
$x = \frac{\Var{f} - \Var{e}}{\Var{g} - \Var{h}} = \Var{(f-e)/(g-h)}$
\end{solution}
\end{enumerate}
\end{multicols}
\end{Exo}
\begin{Exo}
Voici deux programmes de calculs
\fbox{\colorbox{base2}{
\begin{minipage}[h]{0.4\textwidth}
\textbf{Programme A} \\
Choisir un nombre \\
Multiplier par 5 \\
Ajouter 3
\end{minipage}
}
}
\fbox{\colorbox{base2}{
\begin{minipage}[h]{0.4\textwidth}
\textbf{Programme B} \\
Choisir un nombre \\
Doubler \\
Enlever 10
\end{minipage}
}
}
\begin{enumerate}
\item Est-ce que ces deux programmes donnent toujours le même résultat?
\item Quelle valeur faut-il choisir pour obtenir 3 pour chaque programme? \textit{On demande de trouver ce résultat avec une équation}
\item Trouver la valeur de départ pour que ces deux programmes donnent le même résultat.
\end{enumerate}
\end{Exo}
\end{document}
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