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% Title Page
\titre{Équation du premier degré - Exercices}
% \seconde \premiereS \PSTMG \TSTMG
\classe{Troisième}
\date{Mars 2016}

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\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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