225 lines
7.7 KiB
TeX
225 lines
7.7 KiB
TeX
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\documentclass[a4paper,10pt]{article}
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\usepackage{myXsim}
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\title{Technique: Evaluer et reduire}
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\tribe{Troisième}
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\date{Novembre 2017}
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\pagestyle{empty}
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\begin{document}
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\begin{exercise}
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Évaluer les expressions suivantes
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\begin{multicols}{3}
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\begin{enumerate}
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\item $- x - 5$ en $x = 6$
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\begin{solution}
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\begin{eqnarray*}
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A & = & - 6 - 5 \\
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A & = & -6 - 5 \\
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A & = & -11
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\end{eqnarray*}
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\end{solution}
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\item $- x + 8$ en $x = 1$
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\begin{solution}
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\begin{eqnarray*}
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A & = & - 1 + 8 \\
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A & = & -1 + 8 \\
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A & = & 7
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\end{eqnarray*}
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\end{solution}
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\item $- x + 8$ en $x = 3$
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\begin{solution}
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\begin{eqnarray*}
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A & = & - 3 + 8 \\
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A & = & -3 + 8 \\
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A & = & 5
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\end{eqnarray*}
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\end{solution}
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\item $-10 x^{ 2 } + x - 6$ en $x = 7$
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\begin{solution}
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\begin{eqnarray*}
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A & = & -10 \times 7^{ 2 } + 7 - 6 \\
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A & = & -10 \times 49 + 7 - 6 \\
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A & = & -490 + 7 - 6 \\
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A & = & -483 - 6 \\
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A & = & -489
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\end{eqnarray*}
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\end{solution}
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\item $-10 x^{ 2 } + x - 6$ en $x = -5$
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\begin{solution}
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\begin{eqnarray*}
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A & = & -10 \times ( -5 )^{ 2 } - 5 - 6 \\
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A & = & -10 \times 25 - 5 - 6 \\
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A & = & -250 - 5 - 6 \\
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A & = & -255 - 6 \\
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A & = & -261
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\end{eqnarray*}
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\end{solution}
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\item $-10 x^{ 2 } + x + 10$ en $x = 8$
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\begin{solution}
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\begin{eqnarray*}
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A & = & -10 \times 8^{ 2 } + 8 + 10 \\
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A & = & -10 \times 64 + 8 + 10 \\
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A & = & -640 + 8 + 10 \\
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A & = & -632 + 10 \\
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A & = & -622
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\end{eqnarray*}
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\end{solution}
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\item $-7 x ( x - ( -7 ) )$ en $x = -10$
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\item $-7 x ( x - ( -7 ) )$ en $x = -10$
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\item $( 8 x + 7 ) ( -5 - 2 x )$ en $x = -2$
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\end{enumerate}
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\end{multicols}
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\end{exercise}
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\begin{exercise}
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Réduis les expressions suivantes
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\begin{multicols}{3}
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\begin{enumerate}
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\item A = $x + 1 + x - 4$
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\begin{solution}
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\begin{eqnarray*}
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A & = & x + 1 + x - 4 \\
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A & = & x + x + 1 - 4 \\
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A & = & ( 1 + 1 ) x + 1 - 4 \\
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A & = & 2 x - 3
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\end{eqnarray*}
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\end{solution}
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\item B = $x + 6 + 3 + x - 6$
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\begin{solution}
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\begin{eqnarray*}
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A & = & x + 6 + 3 + x - 6 \\
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A & = & x + 9 + x - 6 \\
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A & = & x + x + 9 - 6 \\
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A & = & ( 1 + 1 ) x + 9 - 6 \\
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A & = & 2 x + 3
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\end{eqnarray*}
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\end{solution}
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\item C = $-3 x + 5 + 5 x$
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\begin{solution}
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\begin{eqnarray*}
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A & = & -3 x + 5 + 5 x \\
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A & = & -3 x + 5 x + 5 \\
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A & = & ( -3 + 5 ) x + 5 \\
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A & = & 2 x + 5
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\end{eqnarray*}
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\end{solution}
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\item D = $-4 + 2 x - 10 - 10 x$
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\begin{solution}
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\begin{eqnarray*}
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A & = & -4 + 2 x - 10 - 10 x \\
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A & = & 2 x - 4 - 10 - 10 x \\
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A & = & 2 x - 14 - 10 x \\
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A & = & 2 x - 10 x - 14 \\
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A & = & ( 2 - 10 ) x - 14 \\
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A & = & -8 x - 14
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\end{eqnarray*}
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\end{solution}
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\item E = $-1 - 8 + 8 x + 6 - 4 x$
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\begin{solution}
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\begin{eqnarray*}
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A & = & -1 - 8 + 8 x + 6 - 4 x \\
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A & = & -9 + 8 x + 6 - 4 x \\
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A & = & 8 x - 9 + 6 - 4 x \\
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A & = & 8 x - 3 - 4 x \\
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A & = & 8 x - 4 x - 3 \\
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A & = & ( 8 - 4 ) x - 3 \\
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A & = & 4 x - 3
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\end{eqnarray*}
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\end{solution}
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\item E = $x^{ 2 } + 3 + 3 x + 3 - 10 x$
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\begin{solution}
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\begin{eqnarray*}
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A & = & x^{ 2 } + 3 + 3 x + 3 - 10 x \\
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A & = & x^{ 2 } + 3 x + 3 + 3 - 10 x \\
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A & = & x^{ 2 } + 3 x + 6 - 10 x \\
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A & = & x^{ 2 } + 3 x - 10 x + 6 \\
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A & = & x^{ 2 } + ( 3 - 10 ) x + 6 \\
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A & = & x^{ 2 } - 7 x + 6
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\end{eqnarray*}
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\end{solution}
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\item F = $-6 x^{ 2 } + 9 - 2 x - 2 - 6 x$
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\begin{solution}
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\begin{eqnarray*}
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A & = & -6 x^{ 2 } + 9 - 2 x - 2 - 6 x \\
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A & = & -6 x^{ 2 } - 2 x + 9 - 2 - 6 x \\
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A & = & -6 x^{ 2 } - 2 x + 7 - 6 x \\
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A & = & -6 x^{ 2 } - 2 x - 6 x + 7 \\
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A & = & -6 x^{ 2 } + ( -2 - 6 ) x + 7 \\
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A & = & -6 x^{ 2 } - 8 x + 7
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\end{eqnarray*}
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\end{solution}
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\item G = $3 x^{ 2 } + 1 x^{ 2 } - 9 x - 9 + 3 x$
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\begin{solution}
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\begin{eqnarray*}
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A & = & 3 x^{ 2 } + 1 x^{ 2 } - 9 x - 9 + 3 x \\
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A & = & 3 x^{ 2 } + x^{ 2 } - 9 x - 9 + 3 x \\
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A & = & ( 3 + 1 ) x^{ 2 } - 9 x - 9 + 3 x \\
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A & = & 4 x^{ 2 } - 9 x - 9 + 3 x \\
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A & = & 4 x^{ 2 } - 9 x + 3 x - 9 \\
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A & = & 4 x^{ 2 } + ( -9 + 3 ) x - 9 \\
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A & = & 4 x^{ 2 } - 6 x - 9
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\end{eqnarray*}
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\end{solution}
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\item G = $-2 x^{ 2 } + 7 - 6 x - 6 x^{ 2 } - 2 x$
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\begin{solution}
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\begin{eqnarray*}
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A & = & -2 x^{ 2 } + 7 - 6 x - 6 x^{ 2 } - 2 x \\
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A & = & -2 x^{ 2 } - 6 x + 7 - 6 x^{ 2 } - 2 x \\
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A & = & -2 x^{ 2 } - 6 x^{ 2 } - 6 x + 7 - 2 x \\
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A & = & ( -2 - 6 ) x^{ 2 } - 6 x + 7 - 2 x \\
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A & = & -8 x^{ 2 } - 6 x + 7 - 2 x \\
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A & = & -8 x^{ 2 } - 6 x - 2 x + 7 \\
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A & = & -8 x^{ 2 } + ( -6 - 2 ) x + 7 \\
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A & = & -8 x^{ 2 } - 8 x + 7
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\end{eqnarray*}
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\end{solution}
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\end{enumerate}
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\end{multicols}
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\end{exercise}
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\vfill
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\printexercise{exercise}{1}
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\printexercise{exercise}{2}
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\vfill
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\printexercise{exercise}{1}
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\printexercise{exercise}{2}
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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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