import work from year 2016-2017
This commit is contained in:
Benjamin Bertrand
240
3e/Expression_litterale/Periode2/01_eval_red_tech.tex
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3e/Expression_litterale/Periode2/01_eval_red_tech.tex
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\documentclass[a4paper,10pt]{/media/documents/Cours/Prof/Enseignements/2016-2017/tools/style/classExo}
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\usepackage{/media/documents/Cours/Prof/Enseignements/2016-2017/theme}
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%\geometry{left=10mm,right=10mm, top=10mm, bottom=10mm}
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% Title Page
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\titre{Technique: Evaluer et reduire}
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% \seconde \premiereS \PSTMG \TSTMG
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\classe{Troisième}
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\date{Novembre 2016}
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%\duree{1 heure}
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\sujet{01}
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% DS DSCorr DM DMCorr Corr
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%\printanswers
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\pagestyle{empty}
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\newcommand{\lesexos}{%
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\begin{Exo}
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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{Exo}
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\begin{Exo}
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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{Exo}
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}
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\begin{document}
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\lesexos
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\setcounter{exo}{0}
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\vfill
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\ifprintanswers
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\else
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\lesexos
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\setcounter{exo}{0}
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\vfill
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\lesexos
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\setcounter{exo}{0}
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\vfill
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\fi
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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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3e/Expression_litterale/Periode2/all_eval_red_tech.pdf
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3e/Expression_litterale/Periode2/all_eval_red_tech.pdf
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3e/Expression_litterale/Periode2/corr_eval_red_tech.pdf
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3e/Expression_litterale/Periode2/formuleEuler.odt
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3e/Expression_litterale/Periode2/formuleEulerpyramides.odt
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3e/Expression_litterale/Periode2/index.rst
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3e/Expression_litterale/Periode2/index.rst
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Notes autour de la 3e période sur le calcul littéral pour les 3e: développer réduire
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####################################################################################
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:date: 2016-10-06
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:modified: 2016-10-06
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:tags: Calcul litteral
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:category: 3e
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:authors: Bertrand Benjamin
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:summary: Organisation de la période 2 pour le calcul littéral pour les 3e
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Séance 1
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--------
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Problèmes formule d'Euler (réduction d'expressions)
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Séance 2
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--------
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Exercices techniques de réduction
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Séance 3
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--------
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Programmes de calculs avec d'étranges coïncidences à explicité grâce au calcul littéral.
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Séance 4
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--------
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Programmes avec développements implicites.
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Explication de la technique de développement
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Exercices techniques de developpement.
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Séances suivantes
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-----------------
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Mélange de programmes de calculs et exercices techniques.
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3e/Expression_litterale/Periode2/pgm_cal_vers_expr_litt.odt
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3e/Expression_litterale/Periode2/pgm_cal_vers_expr_litt.odt
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3e/Expression_litterale/Periode2/pgm_calc_vers_developpement.odt
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3e/Expression_litterale/Periode2/pgm_calc_vers_developpement.tex
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3e/Expression_litterale/Periode2/pgm_calc_vers_developpement.tex
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\documentclass[a4paper,10pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/2016-2017/tools/style/classExo}
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\usepackage{/media/documents/Cours/Prof/Enseignements/2016-2017/theme}
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%\geometry{left=10mm,right=10mm, top=10mm, bottom=10mm}
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% Title Page
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\titre{Programme de calcul vers developpement}
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% \seconde \premiereS \PSTMG \TSTMG
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\classe{Troisième}
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\date{Décembre 2016}
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%\duree{1 heure}
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%\sujet{01}
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% DS DSCorr DM DMCorr Corr
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%\printanswers
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\pagestyle{empty}
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|
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\newcommand{\lesexos}{%
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\begin{Exo}
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Voici 2 programmes de cacluls.
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\Ovalbox{%
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\begin{minipage}{0.2\textwidth}
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\hspace{1cm}\textbf{Programme A}
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\begin{itemize}
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\item Choisir un nombre
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\item Multiplier par 4
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\item Soustraire 1
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\item Ajouter le nombre de départ
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\item Soustraire 2
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\end{itemize}
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\end{minipage}
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}
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\Ovalbox{%
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\begin{minipage}{0.2\textwidth}
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\hspace{1cm} \textbf{Programme B}
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\begin{itemize}
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\item Choisir un nombre
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\item Multiplier par 5
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\item Enlever 3
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\end{itemize}
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\end{minipage}
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||||
}
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\begin{enumerate}
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||||
\item Executer ces 2 programmes avec 4 nombres différents.
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\item Abdou pense
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\begin{center}
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\textit{Ces 2 programmes donnent toujours le même résultat.}
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||||
\end{center}
|
||||
Qu'en pensez vous?
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||||
\end{enumerate}
|
||||
\end{Exo}
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\begin{Exo}
|
||||
\Ovalbox{%
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||||
\begin{minipage}{0.2\textwidth}
|
||||
\hspace{1cm}\textbf{Programme de calcul}
|
||||
\begin{itemize}
|
||||
\item Choisir un nombre
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||||
\item Multiplier par 2
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||||
\item Ajouter 3
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||||
\item Multiplier par 5
|
||||
\item Enlever 5 fois le nombre de départ
|
||||
\end{itemize}
|
||||
\end{minipage}
|
||||
}
|
||||
\begin{minipage}{0.2\textwidth}
|
||||
\begin{enumerate}
|
||||
\item Executer ce programme avec 4 nombres différents et faire une conjecture.
|
||||
\item Démontrer votre conjecture.
|
||||
\end{enumerate}
|
||||
\end{minipage}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
Voici 2 programmes de cacluls.
|
||||
|
||||
\hspace{1cm}
|
||||
\Ovalbox{%
|
||||
\begin{minipage}{0.2\textwidth}
|
||||
\hspace{1cm}\textbf{Programme A}
|
||||
\begin{itemize}
|
||||
\item Choisir un nombre
|
||||
\item Soustraire 1
|
||||
\item Multiplier par 4
|
||||
\item Ajouter le nombre de départ
|
||||
\item Soustraire 2
|
||||
\end{itemize}
|
||||
\end{minipage}
|
||||
}
|
||||
\hfill
|
||||
\Ovalbox{%
|
||||
\begin{minipage}{0.2\textwidth}
|
||||
\hspace{1cm} \textbf{Programme B}
|
||||
\begin{itemize}
|
||||
\item Choisir un nombre
|
||||
\item Soustraire 2
|
||||
\item Multiplier par 3
|
||||
\item Ajouter 2 fois le nombre de départ
|
||||
\end{itemize}
|
||||
\end{minipage}
|
||||
}
|
||||
\hspace{1cm}
|
||||
|
||||
\begin{enumerate}
|
||||
\item Executer ces 2 programmes avec 4 nombres différents.
|
||||
\item Quelle conjecture peut-on faire?
|
||||
\item Prouver la conjecture.
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
}
|
||||
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\begin{document}
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|
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\lesexos
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\setcounter{exo}{0}
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\vfill
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|
||||
\pagebreak
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|
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\lesexos
|
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\setcounter{exo}{0}
|
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\vfill
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|
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\end{document}
|
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|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
179
3e/Expression_litterale/Periode2/tpl_eval_red_tech.tex
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179
3e/Expression_litterale/Periode2/tpl_eval_red_tech.tex
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@@ -0,0 +1,179 @@
|
||||
\documentclass[a4paper,10pt]{/media/documents/Cours/Prof/Enseignements/2016-2017/tools/style/classExo}
|
||||
\usepackage{/media/documents/Cours/Prof/Enseignements/2016-2017/theme}
|
||||
%\geometry{left=10mm,right=10mm, top=10mm, bottom=10mm}
|
||||
|
||||
% Title Page
|
||||
\titre{Technique: Evaluer et reduire}
|
||||
% \seconde \premiereS \PSTMG \TSTMG
|
||||
\classe{Troisième}
|
||||
\date{Novembre 2016}
|
||||
%\duree{1 heure}
|
||||
\sujet{\Var{infos.num}}
|
||||
% DS DSCorr DM DMCorr Corr
|
||||
|
||||
%\printanswers
|
||||
\pagestyle{empty}
|
||||
|
||||
\newcommand{\lesexos}{%
|
||||
\begin{Exo}
|
||||
Évaluer les expressions suivantes
|
||||
|
||||
\begin{multicols}{3}
|
||||
\begin{enumerate}
|
||||
\Block{set P = Polynom.random(degree = 1)}
|
||||
\Block{set x = Expression.random("{a}")}
|
||||
\item $\Var{P}$ en $x = \Var{x}$
|
||||
\begin{solution}
|
||||
\begin{eqnarray*}
|
||||
\Var{P(x).explain()| calculus()}
|
||||
\end{eqnarray*}
|
||||
\end{solution}
|
||||
\Block{set P = Polynom.random(degree = 1)}
|
||||
\Block{set x = Expression.random("{a}")}
|
||||
\item $\Var{P}$ en $x = \Var{x}$
|
||||
\begin{solution}
|
||||
\begin{eqnarray*}
|
||||
\Var{P(x).explain()| calculus()}
|
||||
\end{eqnarray*}
|
||||
\end{solution}
|
||||
\Block{set x = Expression.random("{a}")}
|
||||
\item $\Var{P}$ en $x = \Var{x}$
|
||||
\begin{solution}
|
||||
\begin{eqnarray*}
|
||||
\Var{P(x).explain()| calculus()}
|
||||
\end{eqnarray*}
|
||||
\end{solution}
|
||||
|
||||
\Block{set P = Polynom.random(degree = 2)}
|
||||
\Block{set x = Expression.random("{a}")}
|
||||
\item $\Var{P}$ en $x = \Var{x}$
|
||||
\begin{solution}
|
||||
\begin{eqnarray*}
|
||||
\Var{P(x).explain()| calculus()}
|
||||
\end{eqnarray*}
|
||||
\end{solution}
|
||||
\Block{set x = Expression.random("{a}")}
|
||||
\item $\Var{P}$ en $x = \Var{x}$
|
||||
\begin{solution}
|
||||
\begin{eqnarray*}
|
||||
\Var{P(x).explain()| calculus()}
|
||||
\end{eqnarray*}
|
||||
\end{solution}
|
||||
\Block{set P = Polynom.random(degree = 2)}
|
||||
\Block{set x = Expression.random("{a}")}
|
||||
\item $\Var{P}$ en $x = \Var{x}$
|
||||
\begin{solution}
|
||||
\begin{eqnarray*}
|
||||
\Var{P(x).explain()| calculus()}
|
||||
\end{eqnarray*}
|
||||
\end{solution}
|
||||
\Block{set P = Expression.random("{a} x * (x - {b})")}
|
||||
\Block{set x = Expression.random("{a}")}
|
||||
\item $\Var{P}$ en $x = \Var{x}$
|
||||
\Block{set x = Expression.random("{a}")}
|
||||
\item $\Var{P}$ en $x = \Var{x}$
|
||||
\Block{set P = Expression.random("({a}x + {b})({c} + {d}x)")}
|
||||
\Block{set x = Expression.random("{a}")}
|
||||
\item $\Var{P}$ en $x = \Var{x}$
|
||||
\end{enumerate}
|
||||
\end{multicols}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
Réduis les expressions suivantes
|
||||
|
||||
\begin{multicols}{3}
|
||||
\begin{enumerate}
|
||||
\Block{set A = Expression.random("x + {a} + x - {b}")}
|
||||
\item A = $\Var{A}$
|
||||
\begin{solution}
|
||||
\begin{eqnarray*}
|
||||
\Var{A.simplify().explain() | calculus()}
|
||||
\end{eqnarray*}
|
||||
\end{solution}
|
||||
\Block{set B = Expression.random("x + {a} + {c} + x - {b}")}
|
||||
\item B = $\Var{B}$
|
||||
\begin{solution}
|
||||
\begin{eqnarray*}
|
||||
\Var{B.simplify().explain() | calculus()}
|
||||
\end{eqnarray*}
|
||||
\end{solution}
|
||||
\Block{set C = Expression.random("{a}x + {c} + {d}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
|
||||
\item C = $\Var{C}$
|
||||
\begin{solution}
|
||||
\begin{eqnarray*}
|
||||
\Var{C.simplify().explain() | calculus()}
|
||||
\end{eqnarray*}
|
||||
\end{solution}
|
||||
|
||||
\Block{set D = Expression.random("{b} + {a}x + {c} + {d}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
|
||||
\item D = $\Var{D}$
|
||||
\begin{solution}
|
||||
\begin{eqnarray*}
|
||||
\Var{D.simplify().explain() | calculus()}
|
||||
\end{eqnarray*}
|
||||
\end{solution}
|
||||
\Block{set E = Expression.random("({b} - {a}) + {a}x + {c} + {d}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
|
||||
\item E = $\Var{E}$
|
||||
\begin{solution}
|
||||
\begin{eqnarray*}
|
||||
\Var{E.simplify().explain() | calculus()}
|
||||
\end{eqnarray*}
|
||||
\end{solution}
|
||||
\Block{set E = Expression.random("x^2 + {c} + {d}x + {d} + {a}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
|
||||
\item E = $\Var{E}$
|
||||
\begin{solution}
|
||||
\begin{eqnarray*}
|
||||
\Var{E.simplify().explain() | calculus()}
|
||||
\end{eqnarray*}
|
||||
\end{solution}
|
||||
|
||||
\Block{set F = Expression.random("{a}x^2 + {c} + {d}x + {d} + {a}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
|
||||
\item F = $\Var{F}$
|
||||
\begin{solution}
|
||||
\begin{eqnarray*}
|
||||
\Var{F.simplify().explain() | calculus()}
|
||||
\end{eqnarray*}
|
||||
\end{solution}
|
||||
\Block{set G = Expression.random("{a}x^2 + {c}x^2 + {d}x + {d} + {a}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
|
||||
\item G = $\Var{G}$
|
||||
\begin{solution}
|
||||
\begin{eqnarray*}
|
||||
\Var{G.simplify().explain() | calculus()}
|
||||
\end{eqnarray*}
|
||||
\end{solution}
|
||||
\Block{set G = Expression.random("{a}x^2 + {c}+ {d}x + {d}x^2 + {a}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
|
||||
\item G = $\Var{G}$
|
||||
\begin{solution}
|
||||
\begin{eqnarray*}
|
||||
\Var{G.simplify().explain() | calculus()}
|
||||
\end{eqnarray*}
|
||||
\end{solution}
|
||||
\end{enumerate}
|
||||
\end{multicols}
|
||||
\end{Exo}
|
||||
}
|
||||
|
||||
\begin{document}
|
||||
|
||||
\lesexos
|
||||
\setcounter{exo}{0}
|
||||
\vfill
|
||||
|
||||
\ifprintanswers
|
||||
\else
|
||||
\lesexos
|
||||
\setcounter{exo}{0}
|
||||
\vfill
|
||||
\lesexos
|
||||
\setcounter{exo}{0}
|
||||
\vfill
|
||||
\fi
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
Reference in New Issue
Block a user