\documentclass[a4paper,10pt]{article} \usepackage{myXsim} \title{Technique: Evaluer et reduire} \tribe{Troisième} \date{Novembre 2017} \pagestyle{empty} \begin{document} \begin{exercise} Évaluer les expressions suivantes \begin{multicols}{3} \begin{enumerate} \item $- x - 5$ en $x = 6$ \begin{solution} \begin{eqnarray*} A & = & - 6 - 5 \\ A & = & -6 - 5 \\ A & = & -11 \end{eqnarray*} \end{solution} \item $- x + 8$ en $x = 1$ \begin{solution} \begin{eqnarray*} A & = & - 1 + 8 \\ A & = & -1 + 8 \\ A & = & 7 \end{eqnarray*} \end{solution} \item $- x + 8$ en $x = 3$ \begin{solution} \begin{eqnarray*} A & = & - 3 + 8 \\ A & = & -3 + 8 \\ A & = & 5 \end{eqnarray*} \end{solution} \item $-10 x^{ 2 } + x - 6$ en $x = 7$ \begin{solution} \begin{eqnarray*} A & = & -10 \times 7^{ 2 } + 7 - 6 \\ A & = & -10 \times 49 + 7 - 6 \\ A & = & -490 + 7 - 6 \\ A & = & -483 - 6 \\ A & = & -489 \end{eqnarray*} \end{solution} \item $-10 x^{ 2 } + x - 6$ en $x = -5$ \begin{solution} \begin{eqnarray*} A & = & -10 \times ( -5 )^{ 2 } - 5 - 6 \\ A & = & -10 \times 25 - 5 - 6 \\ A & = & -250 - 5 - 6 \\ A & = & -255 - 6 \\ A & = & -261 \end{eqnarray*} \end{solution} \item $-10 x^{ 2 } + x + 10$ en $x = 8$ \begin{solution} \begin{eqnarray*} A & = & -10 \times 8^{ 2 } + 8 + 10 \\ A & = & -10 \times 64 + 8 + 10 \\ A & = & -640 + 8 + 10 \\ A & = & -632 + 10 \\ A & = & -622 \end{eqnarray*} \end{solution} \item $-7 x ( x - ( -7 ) )$ en $x = -10$ \item $-7 x ( x - ( -7 ) )$ en $x = -10$ \item $( 8 x + 7 ) ( -5 - 2 x )$ en $x = -2$ \end{enumerate} \end{multicols} \end{exercise} \begin{exercise} Réduis les expressions suivantes \begin{multicols}{3} \begin{enumerate} \item A = $x + 1 + x - 4$ \begin{solution} \begin{eqnarray*} A & = & x + 1 + x - 4 \\ A & = & x + x + 1 - 4 \\ A & = & ( 1 + 1 ) x + 1 - 4 \\ A & = & 2 x - 3 \end{eqnarray*} \end{solution} \item B = $x + 6 + 3 + x - 6$ \begin{solution} \begin{eqnarray*} A & = & x + 6 + 3 + x - 6 \\ A & = & x + 9 + x - 6 \\ A & = & x + x + 9 - 6 \\ A & = & ( 1 + 1 ) x + 9 - 6 \\ A & = & 2 x + 3 \end{eqnarray*} \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} \vfill \printexercise{exercise}{1} \printexercise{exercise}{2} \vfill \printexercise{exercise}{1} \printexercise{exercise}{2} \end{document} %%% Local Variables: %%% mode: latex %%% TeX-master: "master" %%% End: