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