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zwQ@2>dHs;Q=8e-`X*yzXU3e(YW@!OTo-!1x_Mg%K8aZ1Pg!onC#ksb?y1FCrEX|}Q z+gFOkAUT5huq>Xk0v;z7(-B*ipTAjd9d$5LWERfo;@ZDebI;*YJ?FM+AAVg^6W0 z)78v%S@U{HuxHfiYvmlvw?2a~oXx!obrwrm27Q6#LR$yJnl;W^f0mgto;Le|EY-*Yw>XdxLHM*xkbd; z*f_X^+1bUonT3T#*w}S|HBmM{WS%E&WD3iF= zC*TzY8rd2H{{fATpijVT4ePpsG1bD-XMi4j{a{>Y5{E3@k1I`2a?gLiM1#&KybT-q z$3n+%Fso4g6h3P*a&UapF?^HnGV>rqJ{*cQir-oE@mp}G6-AK4LP-~e*{bQ!>Mu&@J|VJRrY Multiplier par 4 > Soustraire 1 > Ajouter le nombre de départ > Soustraire 2 } @@ -10,11 +45,11 @@ \textbf{Programme B:} Choisir un nombre > Multiplier par 5 > Enlever 3 } -\medskip + \medskip - Abdou pense "\textit{Ces 2 programmes donnent toujours le même résultat.}". + Abdou pense "\textit{Ces 2 programmes donnent toujours le même résultat.}". - Qu'en pensez vous? + Qu'en pensez vous? \end{exercise} \begin{exercise}[subtitle={Pyramide additive}, step={4}, origin={D'anciennes choses}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }] @@ -28,7 +63,7 @@ \end{minipage} \begin{minipage}{0.45\linewidth} \flushright - \begin{tikzpicture} + \begin{tikzpicture}[scale=0.8] \draw (4,5)--(6,5)--(6,4)--(4,4)--cycle; \draw (3,4)--(5,4)--(5,3)--(3,3)--cycle; \draw (5,4)--(7,4)--(7,3)--(5,3)--cycle; @@ -44,3 +79,129 @@ \end{tikzpicture} \end{minipage} \end{exercise} + +\begin{exercise}[subtitle={Réduction}, step={4}, origin={Du chapeau}, topics={ Fraction Developpement Litteral }, tags={ Fractions, Developpement }] + $x$ représente n'importe quel nombre. Réduire les expressions suivantes + \begin{multicols}{3} + \begin{enumerate} + + \item A = $x + 1 + x - 4$ + \begin{solution} + \end{solution} + + \item B = $x + 6 + 3 + x - 6$ + \begin{solution} + + \end{solution} + + \item C = $-3 x + 5 + 5 x$ + \begin{solution} + \begin{eqnarray*} + A & = & -3 x + 5 + 5 x \\ + A & = & -3 x + 5 x + 5 \\ + A & = & ( -3 + 5 ) x + 5 \\ + A & = & 2 x + 5 + \end{eqnarray*} + \end{solution} + + + \item D = $-4 + 2 x - 10 - 10 x$ + \begin{solution} + \begin{eqnarray*} + A & = & -4 + 2 x - 10 - 10 x \\ + A & = & 2 x - 4 - 10 - 10 x \\ + A & = & 2 x - 14 - 10 x \\ + A & = & 2 x - 10 x - 14 \\ + A & = & ( 2 - 10 ) x - 14 \\ + A & = & -8 x - 14 + \end{eqnarray*} + \end{solution} + + \item E = $-1 - 8 + 8 x + 6 - 4 x$ + \begin{solution} + \begin{eqnarray*} + A & = & -1 - 8 + 8 x + 6 - 4 x \\ + A & = & -9 + 8 x + 6 - 4 x \\ + A & = & 8 x - 9 + 6 - 4 x \\ + A & = & 8 x - 3 - 4 x \\ + A & = & 8 x - 4 x - 3 \\ + A & = & ( 8 - 4 ) x - 3 \\ + A & = & 4 x - 3 + \end{eqnarray*} + \end{solution} + + \item E = $x^{ 2 } + 3 + 3 x + 3 - 10 x$ + \begin{solution} + \begin{eqnarray*} + A & = & x^{ 2 } + 3 + 3 x + 3 - 10 x \\ + A & = & x^{ 2 } + 3 x + 3 + 3 - 10 x \\ + A & = & x^{ 2 } + 3 x + 6 - 10 x \\ + A & = & x^{ 2 } + 3 x - 10 x + 6 \\ + A & = & x^{ 2 } + ( 3 - 10 ) x + 6 \\ + A & = & x^{ 2 } - 7 x + 6 + \end{eqnarray*} + \end{solution} + + + \item F = $-6 x^{ 2 } + 9 - 2 x - 2 - 6 x$ + \begin{solution} + \begin{eqnarray*} + A & = & -6 x^{ 2 } + 9 - 2 x - 2 - 6 x \\ + A & = & -6 x^{ 2 } - 2 x + 9 - 2 - 6 x \\ + A & = & -6 x^{ 2 } - 2 x + 7 - 6 x \\ + A & = & -6 x^{ 2 } - 2 x - 6 x + 7 \\ + A & = & -6 x^{ 2 } + ( -2 - 6 ) x + 7 \\ + A & = & -6 x^{ 2 } - 8 x + 7 + \end{eqnarray*} + \end{solution} + + \item G = $3 x^{ 2 } + 1 x^{ 2 } - 9 x - 9 + 3 x$ + \begin{solution} + \begin{eqnarray*} + A & = & 3 x^{ 2 } + 1 x^{ 2 } - 9 x - 9 + 3 x \\ + A & = & 3 x^{ 2 } + x^{ 2 } - 9 x - 9 + 3 x \\ + A & = & ( 3 + 1 ) x^{ 2 } - 9 x - 9 + 3 x \\ + A & = & 4 x^{ 2 } - 9 x - 9 + 3 x \\ + A & = & 4 x^{ 2 } - 9 x + 3 x - 9 \\ + A & = & 4 x^{ 2 } + ( -9 + 3 ) x - 9 \\ + A & = & 4 x^{ 2 } - 6 x - 9 + \end{eqnarray*} + \end{solution} + + \item G = $-2 x^{ 2 } + 7 - 6 x - 6 x^{ 2 } - 2 x$ + \begin{solution} + \begin{eqnarray*} + A & = & -2 x^{ 2 } + 7 - 6 x - 6 x^{ 2 } - 2 x \\ + A & = & -2 x^{ 2 } - 6 x + 7 - 6 x^{ 2 } - 2 x \\ + A & = & -2 x^{ 2 } - 6 x^{ 2 } - 6 x + 7 - 2 x \\ + A & = & ( -2 - 6 ) x^{ 2 } - 6 x + 7 - 2 x \\ + A & = & -8 x^{ 2 } - 6 x + 7 - 2 x \\ + A & = & -8 x^{ 2 } - 6 x - 2 x + 7 \\ + A & = & -8 x^{ 2 } + ( -6 - 2 ) x + 7 \\ + A & = & -8 x^{ 2 } - 8 x + 7 + \end{eqnarray*} + \end{solution} + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{solution} + \begin{enumerate} + \item + \begin{eqnarray*} + A & = & x + 1 + x - 4 \\ + A & = & x + x + 1 - 4 \\ + A & = & ( 1 + 1 ) x + 1 - 4 \\ + A & = & 2 x - 3 + \end{eqnarray*} + \item + \begin{eqnarray*} + B & = & x + 6 + 3 + x - 6 \\ + B & = & x + 9 + x - 6 \\ + B & = & x + x + 9 - 6 \\ + B & = & ( 1 + 1 ) x + 9 - 6 \\ + B & = & 2 x + 3 + \end{eqnarray*} + \end{enumerate} +\end{solution} +