Import work from year 2013-2014
This commit is contained in:
Benjamin Bertrand
BIN
3e/Nombres_Calculs/Arithmetique/Conn/Conn1007.pdf
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3e/Nombres_Calculs/Arithmetique/Conn/Conn1007.pdf
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3e/Nombres_Calculs/Arithmetique/Conn/Conn1007.tex
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3e/Nombres_Calculs/Arithmetique/Conn/Conn1007.tex
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\documentclass{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classConn}
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% Title Page
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\title{}
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\author{}
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\date{}
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\begin{document}
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\begin{multicols}{2}
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Nom - Prénom - classe:
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\section{Connaissance}
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Compléter les phases ou formules suivantes
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\begin{itemize}
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\renewcommand{\labelitemi}{$\star$}
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\item $a$, $b$ et $k$ trois nombres entiers positifs tels que $a = k \times b$. On dit alors que
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\begin{center}
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\item $a$ est un \hspace{5cm} de $b$
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\end{center}
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\vspace{1cm}
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\item Donner les divieurs de 12
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\vspace{5cm}
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\item Écrire le théorème de Thalès avec un dessin qui lui correspond.
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\end{itemize}
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\columnbreak
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Nom - Prénom - classe:
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\section{Connaissance}
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Compléter les phases ou formules suivantes
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\begin{itemize}
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\renewcommand{\labelitemi}{$\star$}
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\item $a$, $b$ et $k$ trois nombres entiers positifs tels que $a = k \times b$. On dit alors que
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\begin{center}
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\item $b$ est un \hspace{5cm} de $a$
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\end{center}
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\vspace{1cm}
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\item Donner les divieurs de 16
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\vspace{5cm}
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\item Écrire le théorème de Thalès avec un dessin qui lui correspond.
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\end{itemize}
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\end{multicols}
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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/Nombres_Calculs/Equation/decouverte/corr_meuble_t.pdf
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3e/Nombres_Calculs/Equation/decouverte/corr_meuble_t.pdf
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3e/Nombres_Calculs/Equation/decouverte/corr_meuble_t.tex
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3e/Nombres_Calculs/Equation/decouverte/corr_meuble_t.tex
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\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
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%\usepackage{multicol}
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\usepackage{tikz}
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\usepackage{enumerate}
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\usepackage{fancybox}
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% Title Page
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\title{Système d'équations - Exercices}
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\author{}
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\date{}
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\fancyhead[L]{Troisième}
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\fancyhead[C]{\Thetitle}
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\fancyhead[R]{\thepage}
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\begin{document}
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\thispagestyle{fancy}
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\begin{enumerate}
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\item
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\begin{eqnarray*}
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\left\{
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\begin{array}{lcl}
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2x + 4y &=& -2\\
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4x + 5y &=& 5
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\end{array}
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\right.
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\end{eqnarray*}
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On veut égaliser lei nombre de $x$. Pour cela on multiplie la première équation par 2
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\begin{eqnarray*}
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\left\{
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\begin{array}{lcl}
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4x + 8y &=& -4\\
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4x + 5y &=& 5
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\end{array}
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\right.
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\end{eqnarray*}
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On fait la différence entre ces deux équations.
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\begin{eqnarray*}
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0x + 3y & = & -9 \\
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y &=& \frac{-9}{3} = -3
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\end{eqnarray*}
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On remplace $y$ par -3 dans la première équation
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\begin{eqnarray*}
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2x + 4\times (-3) & = & -2 \\
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2x - 12 &=& -2 \\
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2x &=& -2 + 12 = 10 \\
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x &=& \frac{10}{2} = 5
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\end{eqnarray*}
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Les solutions du système d'équations sont $x=5$ et $y=-3$.
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\eject
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\item
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\begin{eqnarray*}
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\left\{
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\begin{array}{lcl}
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3x + 2y &=& 75 \hspace{1cm} \times 5\\
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5x + 5y &=& 90 \hspace{1cm} \times 3
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\end{array}
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\right.
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\end{eqnarray*}
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On veut égaliser le nombre de $x$ dans la première et la deuxième équation. Pour cela on multiplie la première équation par 5 et la deuxième par 3.
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\begin{eqnarray*}
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\left\{
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\begin{array}{lcl}
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15x + 10y &=& 375 \\
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15x + 15y &=& 270
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\end{array}
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\right.
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\end{eqnarray*}
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On fait la différence entre les deux équations
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\begin{eqnarray*}
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0x - 5y & = & 105\\
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y &=& \frac{105}{-5} = -21
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\end{eqnarray*}
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On remplace $y$ par -21 dans la première équation.
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\begin{eqnarray*}
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3x + 2\times(-21) & = & 75\\
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3x + (-42) &=& 75 \\
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3x &=& 75 + 42 = 117\\
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x &=& \frac{117}{3} = 39
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\end{eqnarray*}
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Les solutions du système d'équations sont $x=39$ et $y=-21$.
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\eject
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\item
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\begin{eqnarray*}
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\left\{
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\begin{array}{lcl}
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6x + 3y &=& 114 \hspace{1cm} \times 3 \\
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4x + 9y &=& 307
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\end{array}
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\right.
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\end{eqnarray*}
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On veut égaliser le nombre de $y$ dans la première et la deuxième équation. Pour cela on multiplie la première équation par 3
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\begin{eqnarray*}
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\left\{
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\begin{array}{lcl}
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18x + 9y &=& 342 \\
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4x + 9y &=& 307
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\end{array}
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\right.
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\end{eqnarray*}
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On fait la différence entre les deux équations
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\begin{eqnarray*}
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14x + 0y &=& 35\\
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x&=& \frac{35}{14} = 2,5
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\end{eqnarray*}
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On remplace $x$ par 2,5 dans la première équation.
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\begin{eqnarray*}
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6\times2.5 + 3y &=&114 \\
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15 + 3y &=& 114 \\
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3y &=& 114 -15 = 99 \\
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y&=& \frac{99}{3} = 33
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\end{eqnarray*}
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Les solutions du système d'équations sont $x=2,5$ et $y=33$.
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\eject
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\item
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\begin{eqnarray*}
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\left\{
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\begin{array}{lcl}
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6x + 44y &=& 755 \hspace{1cm} \times 5 \\
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30x - 7y &=& 143
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\end{array}
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\right.
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\end{eqnarray*}
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On veut égaliser le nombre de $x$ dans la première et la deuxième équation. Pour cela on multiplie la première équation par 5
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\begin{eqnarray*}
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\left\{
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\begin{array}{lcl}
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30x + 220 y &=& 3775 \\
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30x - 7y &=& 143
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\end{array}
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\right.
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\end{eqnarray*}
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On fait la différence entre les deux équations
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\begin{eqnarray*}
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0x + 227y &=& 3632\\
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y&=& \frac{3632}{227} = 16
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\end{eqnarray*}
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On remplace $y$ par 16 dans la première équation.
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\begin{eqnarray*}
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6x + 44\times16 &=& 755 \\
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6x + 704 &=& 755 \\
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6x &=& 755-704 = 51 \\
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x&=& \frac{51}{6} = 8,5
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\end{eqnarray*}
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Les solutions du système d'équations sont $x=8,5$ et $y=16$.
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\eject
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\end{enumerate}
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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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BIN
3e/Nombres_Calculs/Equation/decouverte/exo_decouv.pdf
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3e/Nombres_Calculs/Equation/decouverte/exo_decouv.pdf
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3e/Nombres_Calculs/Equation/decouverte/exo_decouv.tex
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3e/Nombres_Calculs/Equation/decouverte/exo_decouv.tex
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\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
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%\usepackage{multicol}
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||||
\usepackage{tikz}
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||||
\usepackage{fancybox}
|
||||
|
||||
% Title Page
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\title{Système d'équations - Exercices}
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\author{}
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\date{}
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||||
\fancyhead[L]{Troisième}
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\fancyhead[C]{\Thetitle}
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\fancyhead[R]{\thepage}
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\begin{document}
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\thispagestyle{fancy}
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\begin{Exo}
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Deux compositions de meubles sont exposées dans un magasin.
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\includegraphics[scale=0.3]{./fig/meubles}
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Les prix possibles des meubles sont 25\euro\;, 50\euro\;, 75\euro\; et 100\euro.
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\begin{minipage}{0.25\textwidth}
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Quel est le prix de cette composition?
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\end{minipage}
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\begin{minipage}{0.15\textwidth}
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\includegraphics[scale=0.2]{./fig/meubles2}
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\end{minipage}
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\end{Exo}
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\begin{Exo}
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Un joaillier vend des colliers dont le prix dépend uniquement des perles posées dessus. Voici trois colliers qu'il a en vitrine:
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\begin{center}
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\includegraphics[scale=0.4]{./fig/coliers}
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\end{center}
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Quel est le prix du troisième collier?
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\end{Exo}
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\eject
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\begin{Exo}
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Pour les motifs du carrelage d'une salle de bain, l'artisan propose deux motifs différents:
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\begin{center}
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\includegraphics[scale=0.3]{./fig/triangles}
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\end{center}
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Les triangles gris n'ont pas le même prix que les triangles blancs. \textbf{Quel est le prix d'un triangle blanc? Et celui d'un triangle noir?}
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\end{Exo}
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\begin{Exo}
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Charles et Sarah ont acheté des bonbons.
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\begin{itemize}
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\item Charles a acheté 4 \textit{paquets de chewing gums} et 4 \textit{oursons}, il a payé 10\euro.
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\item Sarah a acheté 2 \textit{paquets de chewing gum} et 6 \textit{oursons}, elle a payé 7\euro.
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\end{itemize}
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\textbf{Combien coûte un ourson? Et le paquets de chewing gums?}
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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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||||
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BIN
3e/Nombres_Calculs/Equation/decouverte/fig/coliers.pdf
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3e/Nombres_Calculs/Equation/decouverte/fig/coliers.pdf
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3e/Nombres_Calculs/Equation/decouverte/fig/coliers.svg
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3e/Nombres_Calculs/Equation/decouverte/fig/coliers.svg
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47
3e/Nombres_Calculs/Equation/decouverte/index.rst
Normal file
47
3e/Nombres_Calculs/Equation/decouverte/index.rst
Normal file
@@ -0,0 +1,47 @@
|
||||
Notes sur des exercices pour commencer les équations
|
||||
####################################################
|
||||
|
||||
:date: 2014-07-01
|
||||
:modified: 2014-07-01
|
||||
:tags: Nombres Calculs, Équations
|
||||
:category: 3e
|
||||
:authors: Benjamin Bertrand
|
||||
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
|
||||
|
||||
|
||||
|
||||
`Lien vers corr_meuble_t.pdf <corr_meuble_t.pdf>`_
|
||||
|
||||
`Lien vers meubles.pdf <meubles.pdf>`_
|
||||
|
||||
`Lien vers meubles_t.tex <meubles_t.tex>`_
|
||||
|
||||
`Lien vers meubles.tex <meubles.tex>`_
|
||||
|
||||
`Lien vers meubles_b.tex <meubles_b.tex>`_
|
||||
|
||||
`Lien vers exo_decouv.tex <exo_decouv.tex>`_
|
||||
|
||||
`Lien vers exo_decouv.pdf <exo_decouv.pdf>`_
|
||||
|
||||
`Lien vers corr_meuble_t.tex <corr_meuble_t.tex>`_
|
||||
|
||||
`Lien vers meubles_b.pdf <meubles_b.pdf>`_
|
||||
|
||||
`Lien vers meubles_t.pdf <meubles_t.pdf>`_
|
||||
|
||||
`Lien vers fig/coliers.pdf <fig/coliers.pdf>`_
|
||||
|
||||
`Lien vers fig/meubles_b1.pdf <fig/meubles_b1.pdf>`_
|
||||
|
||||
`Lien vers fig/meubles_b2.pdf <fig/meubles_b2.pdf>`_
|
||||
|
||||
`Lien vers fig/meubles.pdf <fig/meubles.pdf>`_
|
||||
|
||||
`Lien vers fig/triangles.pdf <fig/triangles.pdf>`_
|
||||
|
||||
`Lien vers fig/meubles2.pdf <fig/meubles2.pdf>`_
|
||||
|
||||
`Lien vers fig/coliers2.pdf <fig/coliers2.pdf>`_
|
||||
|
||||
`Lien vers fig/meubles_t.pdf <fig/meubles_t.pdf>`_
|
||||
BIN
3e/Nombres_Calculs/Equation/decouverte/meubles.pdf
Normal file
BIN
3e/Nombres_Calculs/Equation/decouverte/meubles.pdf
Normal file
Binary file not shown.
39
3e/Nombres_Calculs/Equation/decouverte/meubles.tex
Normal file
39
3e/Nombres_Calculs/Equation/decouverte/meubles.tex
Normal file
@@ -0,0 +1,39 @@
|
||||
\documentclass[a4paper,10pt]{beamer}
|
||||
\usepackage[utf8]{inputenc}
|
||||
\usepackage[french]{babel}
|
||||
\usepackage{graphicx}
|
||||
\usepackage{thumbpdf}
|
||||
\usepackage{wasysym}
|
||||
\usepackage{ucs}
|
||||
\usepackage{pgf,pgfarrows,pgfnodes,pgfautomata,pgfheaps,pgfshade}
|
||||
\usepackage{verbatim}
|
||||
\usepackage{subfig}
|
||||
\usepackage{amssymb}
|
||||
\usepackage{tikz}
|
||||
\usepackage{enumerate}
|
||||
\usepackage{eurosym}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\begin{frame}{Prix d'une cuisine}
|
||||
|
||||
Deux compositions de meubles sont exposées dans un magasin.
|
||||
\begin{center}
|
||||
\includegraphics[scale=0.2]{./fig/meubles}
|
||||
\end{center}
|
||||
|
||||
Les prix possibles des meubles sont 25\euro\;, 50\euro\;, 75\euro\; et 100\euro.
|
||||
|
||||
\begin{minipage}{0.5\textwidth}
|
||||
Quel est le prix de cette composition?
|
||||
\end{minipage}
|
||||
\begin{minipage}{0.4\textwidth}
|
||||
\includegraphics[scale=0.2]{./fig/meubles2}
|
||||
\end{minipage}
|
||||
|
||||
|
||||
|
||||
|
||||
\end{frame}
|
||||
|
||||
\end{document}
|
||||
BIN
3e/Nombres_Calculs/Equation/decouverte/meubles_b.pdf
Normal file
BIN
3e/Nombres_Calculs/Equation/decouverte/meubles_b.pdf
Normal file
Binary file not shown.
43
3e/Nombres_Calculs/Equation/decouverte/meubles_b.tex
Normal file
43
3e/Nombres_Calculs/Equation/decouverte/meubles_b.tex
Normal file
@@ -0,0 +1,43 @@
|
||||
\documentclass[a4paper,10pt]{beamer}
|
||||
\usepackage[utf8]{inputenc}
|
||||
\usepackage[french]{babel}
|
||||
\usepackage{graphicx}
|
||||
\usepackage{thumbpdf}
|
||||
\usepackage{wasysym}
|
||||
\usepackage{ucs}
|
||||
\usepackage{pgf,pgfarrows,pgfnodes,pgfautomata,pgfheaps,pgfshade}
|
||||
\usepackage{verbatim}
|
||||
\usepackage{subfig}
|
||||
\usepackage{amssymb}
|
||||
\usepackage{tikz}
|
||||
\usepackage{enumerate}
|
||||
\usepackage{eurosym}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\begin{frame}{Prix d'une cuisine}
|
||||
|
||||
\begin{itemize}
|
||||
\item
|
||||
Deux compositions de meubles sont exposées dans un magasin.
|
||||
\begin{center}
|
||||
\includegraphics[scale=0.2]{./fig/meubles_b1}
|
||||
\end{center}
|
||||
|
||||
En combinant les deux compositions, retrouver le prix d'un petit meuble carré. En déduire le prix d'un grand meuble gris.
|
||||
|
||||
\item<2-> Mêmes questions pour les compositions suivantes
|
||||
\begin{center}
|
||||
\includegraphics[scale=0.2]{./fig/meubles_b2}
|
||||
\end{center}
|
||||
|
||||
|
||||
\end{itemize}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\end{frame}
|
||||
|
||||
\end{document}
|
||||
BIN
3e/Nombres_Calculs/Equation/decouverte/meubles_t.pdf
Normal file
BIN
3e/Nombres_Calculs/Equation/decouverte/meubles_t.pdf
Normal file
Binary file not shown.
103
3e/Nombres_Calculs/Equation/decouverte/meubles_t.tex
Normal file
103
3e/Nombres_Calculs/Equation/decouverte/meubles_t.tex
Normal file
@@ -0,0 +1,103 @@
|
||||
\documentclass[a4paper,10pt]{beamer}
|
||||
\usepackage[utf8]{inputenc}
|
||||
\usepackage[french]{babel}
|
||||
\usepackage{graphicx}
|
||||
\usepackage{thumbpdf}
|
||||
\usepackage{wasysym}
|
||||
\usepackage{ucs}
|
||||
\usepackage{pgf,pgfarrows,pgfnodes,pgfautomata,pgfheaps,pgfshade}
|
||||
\usepackage{verbatim}
|
||||
\usepackage{subfig}
|
||||
\usepackage{amssymb}
|
||||
\usepackage{tikz}
|
||||
\usepackage{enumerate}
|
||||
\usepackage{eurosym}
|
||||
\usepackage{multicol}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\begin{frame}{Méthode par combinaison}
|
||||
|
||||
\begin{center}
|
||||
$ \left\{
|
||||
\begin{array}{lcl}
|
||||
3x + 4y &=& 195 \\
|
||||
4x + 5y &=& 249
|
||||
\end{array}
|
||||
\right.$
|
||||
|
||||
\end{center}
|
||||
|
||||
\vfill
|
||||
|
||||
\onslide<2->{
|
||||
Composition de meubles correspondante
|
||||
|
||||
\includegraphics[scale=0.2]{./fig/meubles_t}
|
||||
|
||||
\textbf{Comment faire pour avoir le même nombre de meubles $X$?}
|
||||
}
|
||||
|
||||
\vfill
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Éxercices}
|
||||
|
||||
\begin{multicols}{2}
|
||||
|
||||
\begin{enumerate}[a)]
|
||||
\item $ \left\{
|
||||
\begin{array}{lcl}
|
||||
2x + 4y &=& -2\\
|
||||
4x + 5y &=& 5
|
||||
\end{array}
|
||||
\right.$
|
||||
% x = 5 et y = -3
|
||||
|
||||
\vspace{0.5cm}
|
||||
\onslide<2>{x=5 et y = -3}
|
||||
\vspace{0.5cm}
|
||||
|
||||
\item $ \left\{
|
||||
\begin{array}{lcl}
|
||||
3x + 2y &=& 75 \\
|
||||
5x + 5y &=& 90
|
||||
\end{array}
|
||||
\right.$
|
||||
% x = -3 et y = 21
|
||||
|
||||
\vspace{0.5cm}
|
||||
\onslide<2>{x=-3 et y = 21}
|
||||
\vspace{0.5cm}
|
||||
|
||||
\item $ \left\{
|
||||
\begin{array}{lcl}
|
||||
6x + 3y &=& 114 \\
|
||||
4x + 9y &=& 307
|
||||
\end{array}
|
||||
\right.$
|
||||
%x = 2.5 et y = 33
|
||||
|
||||
\vspace{0.5cm}
|
||||
\onslide<2>{x=2.5 et y = 33}
|
||||
\vspace{0.5cm}
|
||||
|
||||
\item $ \left\{
|
||||
\begin{array}{lcl}
|
||||
6 x + 44 y &=& 755 \\
|
||||
30 x - 7y &=& 143
|
||||
\end{array}
|
||||
\right.$
|
||||
%x = 8.5 et y = 16
|
||||
|
||||
\vspace{0.5cm}
|
||||
\onslide<2>{x=8.5 et y = 16}
|
||||
\vspace{0.5cm}
|
||||
|
||||
\end{enumerate}
|
||||
|
||||
\end{multicols}
|
||||
|
||||
\end{frame}
|
||||
|
||||
\end{document}
|
||||
BIN
3e/Nombres_Calculs/Equation/exo/corr_77.pdf
Normal file
BIN
3e/Nombres_Calculs/Equation/exo/corr_77.pdf
Normal file
Binary file not shown.
62
3e/Nombres_Calculs/Equation/exo/corr_77.tex
Normal file
62
3e/Nombres_Calculs/Equation/exo/corr_77.tex
Normal file
@@ -0,0 +1,62 @@
|
||||
\documentclass[a4paper,10pt]{beamer}
|
||||
\usepackage[utf8]{inputenc}
|
||||
\usepackage[french]{babel}
|
||||
\usepackage{graphicx}
|
||||
\usepackage{thumbpdf}
|
||||
\usepackage{wasysym}
|
||||
\usepackage{ucs}
|
||||
\usepackage{pgf,pgfarrows,pgfnodes,pgfautomata,pgfheaps,pgfshade}
|
||||
\usepackage{verbatim}
|
||||
\usepackage{subfig}
|
||||
\usepackage{amssymb}
|
||||
\usepackage{tikz}
|
||||
\usepackage{enumerate}
|
||||
\usepackage{eurosym}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\begin{frame}{Solutions du 5p77}
|
||||
|
||||
\begin{itemize}
|
||||
\item
|
||||
$ \left\{
|
||||
\begin{array}{lcl}
|
||||
x - 3y &=& 2 \\
|
||||
2x - 7y &=& 6
|
||||
\end{array}
|
||||
\right.$
|
||||
\hfill Solutions $x = -2$ et $y=-4$
|
||||
\vfill
|
||||
\item
|
||||
$ \left\{
|
||||
\begin{array}{lcl}
|
||||
5x - 2y &=& -7 \\
|
||||
3x + y &=& -2
|
||||
\end{array}
|
||||
\right.$
|
||||
\hfill Solutions $x = -1$ et $y=1$
|
||||
\vfill
|
||||
\item
|
||||
$ \left\{
|
||||
\begin{array}{lcl}
|
||||
6x + y &=& 8 \\
|
||||
10x + 7y &=& -8
|
||||
\end{array}
|
||||
\right.$
|
||||
\hfill Solutions $x = 2$ et $y=-4$
|
||||
\vfill
|
||||
\item
|
||||
$ \left\{
|
||||
\begin{array}{lcl}
|
||||
7x + 4y &=& -5 \\
|
||||
x + 3y &=& 9
|
||||
\end{array}
|
||||
\right.$
|
||||
\hfill Solutions $x = 4$ et $y=-3$
|
||||
\end{itemize}
|
||||
|
||||
|
||||
|
||||
\end{frame}
|
||||
|
||||
\end{document}
|
||||
19
3e/Nombres_Calculs/Equation/exo/index.rst
Normal file
19
3e/Nombres_Calculs/Equation/exo/index.rst
Normal file
@@ -0,0 +1,19 @@
|
||||
Notes sur des exercices autour des systèmes d'équations
|
||||
#######################################################
|
||||
|
||||
:date: 2014-07-01
|
||||
:modified: 2014-07-01
|
||||
:tags: Nombres Calculs,Exo, Équations
|
||||
:category: 3e
|
||||
:authors: Benjamin Bertrand
|
||||
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
|
||||
|
||||
|
||||
|
||||
`Lien vers methode_subs.pdf <methode_subs.pdf>`_
|
||||
|
||||
`Lien vers corr_77.tex <corr_77.tex>`_
|
||||
|
||||
`Lien vers corr_77.pdf <corr_77.pdf>`_
|
||||
|
||||
`Lien vers methode_subs.tex <methode_subs.tex>`_
|
||||
BIN
3e/Nombres_Calculs/Equation/exo/methode_subs.pdf
Normal file
BIN
3e/Nombres_Calculs/Equation/exo/methode_subs.pdf
Normal file
Binary file not shown.
106
3e/Nombres_Calculs/Equation/exo/methode_subs.tex
Normal file
106
3e/Nombres_Calculs/Equation/exo/methode_subs.tex
Normal file
@@ -0,0 +1,106 @@
|
||||
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
|
||||
|
||||
%\usepackage{multicol}
|
||||
\usepackage{tikz}
|
||||
\usepackage{fancybox}
|
||||
|
||||
% Title Page
|
||||
\title{Fonction affine - Exercices}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
\fancyhead[L]{Troisième}
|
||||
\fancyhead[C]{\Thetitle}
|
||||
\fancyhead[R]{\thepage}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\thispagestyle{fancy}
|
||||
|
||||
\begin{Exo}
|
||||
\begin{center}
|
||||
\framebox{\parbox{0.45\textwidth}{
|
||||
\textbf{Résoudre un système d'équations: par substitution}
|
||||
|
||||
Résolution de $ \left\{
|
||||
\begin{array}{lcl}
|
||||
2x + 2y &=& 250 \\
|
||||
x + 3y &=& 225
|
||||
\end{array}
|
||||
\right.$
|
||||
|
||||
La deuxième équation nous donne $x = 225 - 3y$. On remplace donc $x$ par $225 - 3y$ dans la première équation.
|
||||
|
||||
\begin{eqnarray*}
|
||||
2(225 - 3y) + 2y & = & 250 \hspace{1cm} \mbox{Équation que l'on sait résoudre} \\
|
||||
550 - 6y + 2y &=& 250 \hspace{1cm} \mbox{On développe puis simplifie}\\
|
||||
550 - 4y &=& 250 \\
|
||||
-4y &=& 250 - 550 = -300 \\
|
||||
y &=& \frac{-300}{-4} = 75
|
||||
\end{eqnarray*}
|
||||
On peut donc remplacer $y$ dans la deuxième équation pour trouver $x$
|
||||
\begin{eqnarray*}
|
||||
x & = & 225 - 3y \\
|
||||
x &=& 225 - 3\times 75 = 50
|
||||
\end{eqnarray*}
|
||||
Donc $(50,75)$ est une solution du système d'équation.
|
||||
}}
|
||||
\end{center}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
En utilisant la méthode de substitution, résoudre le système d'équation suivant:
|
||||
\begin{eqnarray*}
|
||||
\left\{
|
||||
\begin{array}{lcl}
|
||||
3x + 4y &=& 38 \\
|
||||
x + 2y &=& 17
|
||||
\end{array}
|
||||
\right.
|
||||
\end{eqnarray*}
|
||||
La \parbox{2cm}{\dotfill} équation nous donne $x = \parbox{2cm}{\dotfill}$. On remplace donc $x$ par \parbox{2cm}{\dotfill} dans la \parbox{2cm}{\dotfill} équation.
|
||||
|
||||
\begin{eqnarray*}
|
||||
3(\parbox{2cm}{\dotfill}) + 4y & = & 38 \hspace{1cm} \mbox{Équation que l'on sait résoudre} \\[0.5cm]
|
||||
\parbox{2cm}{\dotfill}+ 4y &=& 38 \hspace{1cm} \mbox{On développe puis simplifie}\\[0.5cm]
|
||||
\parbox{2cm}{\dotfill} &=& 38 \\[0.5cm]
|
||||
\parbox{2cm}{\dotfill}&=& \parbox{2cm}{\dotfill} \\[0.5cm]
|
||||
y &=& \parbox{2cm}{\dotfill}
|
||||
\end{eqnarray*}
|
||||
On peut donc remplacer $y$ dans la deuxième équation pour trouver $x$
|
||||
\begin{eqnarray*}
|
||||
x & = & \parbox{2cm}{\dotfill} \\[0.5cm]
|
||||
x &=& \parbox{2cm}{\dotfill}
|
||||
\end{eqnarray*}
|
||||
Donc $(\parbox{1cm}{\dotfill},\parbox{1cm}{\dotfill})$ est une solution du système d'équation.
|
||||
|
||||
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
Résoudre le système d'équations suivant avec le méthode par substitution.
|
||||
\begin{eqnarray*}
|
||||
\left\{
|
||||
\begin{array}{lcl}
|
||||
5x + y &=& 21 \\
|
||||
2x + 6y &=& 42
|
||||
\end{array}
|
||||
\right.
|
||||
\end{eqnarray*}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
Pour classer des photos, un magasin propose deux types de rangement, des albums ou des boîtes.
|
||||
|
||||
Léa achète 6boites et 5 albums et paie 57\euro. Hugo achète une boite et 3 albums et paie 22,5\euro. \textbf{Quel est le prix d'une boite? Quel est le prix d'un album?}
|
||||
\end{Exo}
|
||||
|
||||
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
BIN
3e/Nombres_Calculs/Factorisation/Conn/Conn0916.pdf
Normal file
BIN
3e/Nombres_Calculs/Factorisation/Conn/Conn0916.pdf
Normal file
Binary file not shown.
94
3e/Nombres_Calculs/Factorisation/Conn/Conn0916.tex
Normal file
94
3e/Nombres_Calculs/Factorisation/Conn/Conn0916.tex
Normal file
@@ -0,0 +1,94 @@
|
||||
\documentclass{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classConn}
|
||||
|
||||
|
||||
% Title Page
|
||||
\title{}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
|
||||
\begin{document}
|
||||
|
||||
\begin{multicols}{2}
|
||||
|
||||
Nom - Prénom - classe:
|
||||
\section{Connaissance}
|
||||
|
||||
Compléter les phases ou formules suivantes
|
||||
|
||||
\begin{itemize}
|
||||
\renewcommand{\labelitemi}{$\star$}
|
||||
\item Une \textbf{expression littéralle} est \dotfill
|
||||
\vspace{1cm}
|
||||
\item \textbf{Développer} c'est \dotfill
|
||||
\vspace{2cm}
|
||||
\item $a,b,k$ sont trois nombres.
|
||||
\begin{eqnarray*}
|
||||
k\times a + k \times b & = & \dots
|
||||
\end{eqnarray*}
|
||||
|
||||
\end{itemize}
|
||||
|
||||
|
||||
Nom - Prénom - classe:
|
||||
\section{Connaissance}
|
||||
|
||||
Compléter les phases ou formules suivantes
|
||||
|
||||
\begin{itemize}
|
||||
\renewcommand{\labelitemi}{$\star$}
|
||||
\item Une \textbf{expression littéralle} est \dotfill
|
||||
\vspace{1cm}
|
||||
\item \textbf{Factoriser} c'est \dotfill
|
||||
\vspace{2cm}
|
||||
\item $a,b,k$ sont trois nombres.
|
||||
\begin{eqnarray*}
|
||||
k\times a + k \times b & = & \dots
|
||||
\end{eqnarray*}
|
||||
|
||||
\end{itemize}
|
||||
|
||||
\columnbreak
|
||||
|
||||
Nom - Prénom - classe:
|
||||
\section{Connaissance}
|
||||
|
||||
Compléter les phases ou formules suivantes
|
||||
|
||||
\begin{itemize}
|
||||
\renewcommand{\labelitemi}{$\star$}
|
||||
\item Une \textbf{expression littéralle} est \dotfill
|
||||
\vspace{1cm}
|
||||
\item \textbf{Développer} c'est \dotfill
|
||||
\vspace{1.5cm}
|
||||
\item $a,b,c,d$ sont quatre nombres.
|
||||
\begin{eqnarray*}
|
||||
(a+b)(c+d) & = & \dots
|
||||
\end{eqnarray*}
|
||||
|
||||
\end{itemize}
|
||||
|
||||
Nom - Prénom - classe:
|
||||
\section{Connaissance}
|
||||
|
||||
Compléter les phases ou formules suivantes
|
||||
|
||||
\begin{itemize}
|
||||
\renewcommand{\labelitemi}{$\star$}
|
||||
\item Une \textbf{expression littéralle} est \dotfill
|
||||
\vspace{1cm}
|
||||
\item \textbf{Factoriser} c'est \dotfill
|
||||
\vspace{2cm}
|
||||
\item $a,b,c,d$ sont quatre nombres.
|
||||
\begin{eqnarray*}
|
||||
(a+b)(c+d) & = & \dots
|
||||
\end{eqnarray*}
|
||||
|
||||
\end{itemize}
|
||||
\end{multicols}
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
BIN
3e/Nombres_Calculs/Inequations/activite/act_op_ineq.pdf
Normal file
BIN
3e/Nombres_Calculs/Inequations/activite/act_op_ineq.pdf
Normal file
Binary file not shown.
39
3e/Nombres_Calculs/Inequations/activite/act_op_ineq.tex
Normal file
39
3e/Nombres_Calculs/Inequations/activite/act_op_ineq.tex
Normal file
@@ -0,0 +1,39 @@
|
||||
\documentclass[a4paper,10pt]{beamer}
|
||||
\usepackage[utf8]{inputenc}
|
||||
\usepackage[french]{babel}
|
||||
\usepackage{graphicx}
|
||||
\usepackage{thumbpdf}
|
||||
\usepackage{wasysym}
|
||||
\usepackage{ucs}
|
||||
\usepackage{pgf,pgfarrows,pgfnodes,pgfautomata,pgfheaps,pgfshade}
|
||||
\usepackage{verbatim}
|
||||
\usepackage{subfig}
|
||||
\usepackage{amssymb}
|
||||
\usepackage{tikz}
|
||||
\usepackage{enumerate}
|
||||
\usepackage{array}
|
||||
|
||||
\renewcommand{\arraystretch}{3}
|
||||
\setlength{\tabcolsep}{10pt}
|
||||
|
||||
\begin{document}
|
||||
\begin{frame}{Opérations et inégalités.}
|
||||
|
||||
\begin{tabular}{|m{4cm}|*{4}{m{1cm}|}}
|
||||
\hline
|
||||
Inégalité & -3 & +4 & $\times 2$ & $\times (-1)$ \\
|
||||
\hline
|
||||
$4 \leq 7$ & & & &\\
|
||||
\hline
|
||||
$6 > 1$ & & & &\\
|
||||
\hline
|
||||
$4 \geq -1$ & & & &\\
|
||||
\hline
|
||||
Sens de l'inégalité changé? &&&& \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
|
||||
|
||||
\end{frame}
|
||||
|
||||
\end{document}
|
||||
15
3e/Nombres_Calculs/Inequations/activite/index.rst
Normal file
15
3e/Nombres_Calculs/Inequations/activite/index.rst
Normal file
@@ -0,0 +1,15 @@
|
||||
Notes sur une activité autour des inéquations pour les 3e
|
||||
#########################################################
|
||||
|
||||
:date: 2014-07-01
|
||||
:modified: 2014-07-01
|
||||
:tags: Nombres Calculs, Inequations
|
||||
:category: 3e
|
||||
:authors: Benjamin Bertrand
|
||||
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
|
||||
|
||||
|
||||
|
||||
`Lien vers act_op_ineq.tex <act_op_ineq.tex>`_
|
||||
|
||||
`Lien vers act_op_ineq.pdf <act_op_ineq.pdf>`_
|
||||
BIN
3e/Nombres_Calculs/Inequations/exo/fig/axe.pdf
Normal file
BIN
3e/Nombres_Calculs/Inequations/exo/fig/axe.pdf
Normal file
Binary file not shown.
312
3e/Nombres_Calculs/Inequations/exo/fig/axe.svg
Normal file
312
3e/Nombres_Calculs/Inequations/exo/fig/axe.svg
Normal file
@@ -0,0 +1,312 @@
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After Width: | Height: | Size: 13 KiB |
BIN
3e/Nombres_Calculs/Inequations/exo/fig/axe_1.pdf
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3e/Nombres_Calculs/Inequations/exo/fig/axe_2.pdf
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3e/Nombres_Calculs/Inequations/exo/fig/axe_3.pdf
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3e/Nombres_Calculs/Inequations/exo/fig/axe_3.pdf
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3e/Nombres_Calculs/Inequations/exo/fig/axe_4.pdf
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3e/Nombres_Calculs/Inequations/exo/fig/axe_4.pdf
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3e/Nombres_Calculs/Inequations/exo/fig/axe_5.pdf
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3e/Nombres_Calculs/Inequations/exo/fig/axe_5.pdf
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39
3e/Nombres_Calculs/Inequations/exo/index.rst
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39
3e/Nombres_Calculs/Inequations/exo/index.rst
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|
||||
Notes sur des fiches d'exercices autour des inéquations
|
||||
#######################################################
|
||||
|
||||
:date: 2014-07-01
|
||||
:modified: 2014-07-01
|
||||
:tags: Nombres Calculs,Exo, Inequations
|
||||
:category: 3e
|
||||
:authors: Benjamin Bertrand
|
||||
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
|
||||
|
||||
|
||||
|
||||
`Lien vers inequations_1.pdf <inequations_1.pdf>`_
|
||||
|
||||
`Lien vers inequations_1.tex <inequations_1.tex>`_
|
||||
|
||||
`Lien vers slideCorr_17p92.tex <slideCorr_17p92.tex>`_
|
||||
|
||||
`Lien vers inequations_3.pdf <inequations_3.pdf>`_
|
||||
|
||||
`Lien vers inequations_2.tex <inequations_2.tex>`_
|
||||
|
||||
`Lien vers inequations_3.tex <inequations_3.tex>`_
|
||||
|
||||
`Lien vers inequations_2.pdf <inequations_2.pdf>`_
|
||||
|
||||
`Lien vers slideCorr_17p92.pdf <slideCorr_17p92.pdf>`_
|
||||
|
||||
`Lien vers fig/axe.pdf <fig/axe.pdf>`_
|
||||
|
||||
`Lien vers fig/axe_1.pdf <fig/axe_1.pdf>`_
|
||||
|
||||
`Lien vers fig/axe_3.pdf <fig/axe_3.pdf>`_
|
||||
|
||||
`Lien vers fig/axe_5.pdf <fig/axe_5.pdf>`_
|
||||
|
||||
`Lien vers fig/axe_2.pdf <fig/axe_2.pdf>`_
|
||||
|
||||
`Lien vers fig/axe_4.pdf <fig/axe_4.pdf>`_
|
||||
BIN
3e/Nombres_Calculs/Inequations/exo/inequations_1.pdf
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3e/Nombres_Calculs/Inequations/exo/inequations_1.pdf
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110
3e/Nombres_Calculs/Inequations/exo/inequations_1.tex
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110
3e/Nombres_Calculs/Inequations/exo/inequations_1.tex
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@@ -0,0 +1,110 @@
|
||||
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
|
||||
|
||||
\usepackage{multicol}
|
||||
|
||||
% Title Page
|
||||
\title{Inéquations- Exercices}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
\fancyhead[L]{Troisième}
|
||||
\fancyhead[C]{\Thetitle}
|
||||
\fancyhead[R]{\thepage}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\thispagestyle{fancy}
|
||||
|
||||
\begin{Exo}
|
||||
Traduire en français les expressions mathématiques suivantes
|
||||
\begin{multicols}{2}
|
||||
|
||||
\begin{enumerate}
|
||||
\item $5 \leq 9$
|
||||
\item $23 \geq 9$
|
||||
\item $x \leq 6$
|
||||
\item $3 > x$
|
||||
\columnbreak
|
||||
\item $5x > 1$
|
||||
\item $x < y$
|
||||
\item $2x > 4x$
|
||||
\item $4y \leq 9$
|
||||
\end{enumerate}
|
||||
|
||||
\end{multicols}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
\begin{enumerate}
|
||||
\item Dire si les phrases suivantes sont justes en justifiant.
|
||||
\begin{itemize}
|
||||
\item Si $x = 2$ alors $x \leq 4$.
|
||||
\item Si $x = 2,32$ alors $x \geq 2$.
|
||||
\item Si $x = 4$ alors $2x > 8$.
|
||||
\item Si $x = 6$ alors $3x - 4 \geq 14$.
|
||||
\item Si $x = 2$ alors $3x + 1 < 4x -1$.
|
||||
\item Si $a = 1$ alors $\frac{1}{3}a \leq 0.5$.
|
||||
\end{itemize}
|
||||
|
||||
\item Trouver une valeur de $x$ pour que les inéquations suivantes soient vraies.
|
||||
\begin{multicols}{2}
|
||||
\begin{enumerate}
|
||||
\item $x \leq 9$
|
||||
\item $23 \geq 9x$
|
||||
\item $x \leq 6$
|
||||
\item $3 > x$
|
||||
\columnbreak
|
||||
\item $5x > 1$
|
||||
\item $x + 4 < 2$
|
||||
\item $2x > 4x$
|
||||
\item $4x \leq 9$
|
||||
\end{enumerate}
|
||||
\end{multicols}
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
\eject
|
||||
|
||||
\begin{Exo}
|
||||
\begin{enumerate}
|
||||
\item Surligner les valeurs possibles pour $x$ dans les inéquations suivantes.
|
||||
\begin{enumerate}
|
||||
\item $x \geq 1$
|
||||
\includegraphics[scale=0.4]{./fig/axe_1.pdf}
|
||||
\item $x < 2$
|
||||
\includegraphics[scale=0.4]{./fig/axe.pdf}
|
||||
\item $x > -3$
|
||||
\includegraphics[scale=0.4]{./fig/axe.pdf}
|
||||
\item $x \leq 4$
|
||||
\includegraphics[scale=0.4]{./fig/axe.pdf}
|
||||
\item $x < 1$
|
||||
\includegraphics[scale=0.4]{./fig/axe.pdf}
|
||||
\end{enumerate}
|
||||
|
||||
\item Écrire l'inéquation qui correspond au graphique.
|
||||
\begin{enumerate}
|
||||
\item
|
||||
\includegraphics[scale=0.3]{./fig/axe_2.pdf} \parbox{2cm}{\dotfill}
|
||||
\item
|
||||
\includegraphics[scale=0.3]{./fig/axe_3.pdf} \parbox{2cm}{\dotfill}
|
||||
\item
|
||||
\includegraphics[scale=0.3]{./fig/axe_4.pdf} \parbox{2cm}{\dotfill}
|
||||
\item
|
||||
\includegraphics[scale=0.3]{./fig/axe_5.pdf} \parbox{2cm}{\dotfill}
|
||||
\end{enumerate}
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
\exo{31p94}
|
||||
\exo{30p94}
|
||||
|
||||
\end{Exo}
|
||||
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
BIN
3e/Nombres_Calculs/Inequations/exo/inequations_2.pdf
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3e/Nombres_Calculs/Inequations/exo/inequations_2.pdf
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96
3e/Nombres_Calculs/Inequations/exo/inequations_2.tex
Normal file
96
3e/Nombres_Calculs/Inequations/exo/inequations_2.tex
Normal file
@@ -0,0 +1,96 @@
|
||||
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
|
||||
|
||||
\usepackage{multicol}
|
||||
|
||||
% Title Page
|
||||
\title{Inéquations- Exercices}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
\fancyhead[L]{Troisième}
|
||||
\fancyhead[C]{\Thetitle}
|
||||
\fancyhead[R]{\thepage}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\thispagestyle{fancy}
|
||||
|
||||
\begin{Exo}
|
||||
Surligner les valeurs possibles pour $x$ dans les inéquations suivantes.
|
||||
\begin{enumerate}
|
||||
\item $x \geq -1$
|
||||
\includegraphics[scale=0.4]{./fig/axe.pdf}
|
||||
\item $x < -2$
|
||||
\includegraphics[scale=0.4]{./fig/axe.pdf}
|
||||
\item $x \leq 3$
|
||||
\includegraphics[scale=0.4]{./fig/axe.pdf}
|
||||
\item $x \leq 5$
|
||||
\includegraphics[scale=0.4]{./fig/axe.pdf}
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
Donner trois valeurs possibles pour $x$ puis représenter graphiquement les solutions des inéquations suivantes.
|
||||
\begin{enumerate}
|
||||
\item $x + 3 \leq 6$: \hspace{1cm} Valeurs possibles: \parbox{1cm}{\dotfill}, \parbox{1cm}{\dotfill}, \parbox{1cm}{\dotfill}
|
||||
|
||||
\includegraphics[scale=0.4]{./fig/axe.pdf}
|
||||
\item $x - 1 \geq -2$: \hspace{1cm} Valeurs possibles: \parbox{1cm}{\dotfill}, \parbox{1cm}{\dotfill}, \parbox{1cm}{\dotfill}
|
||||
|
||||
\includegraphics[scale=0.4]{./fig/axe.pdf}
|
||||
\item $x + 10 \leq 5$: \hspace{1cm} Valeurs possibles: \parbox{1cm}{\dotfill}, \parbox{1cm}{\dotfill}, \parbox{1cm}{\dotfill}
|
||||
|
||||
\includegraphics[scale=0.4]{./fig/axe.pdf}
|
||||
\item $x \leq 6 - x$: \hspace{1cm} Valeurs possibles: \parbox{1cm}{\dotfill}, \parbox{1cm}{\dotfill}, \parbox{1cm}{\dotfill}
|
||||
|
||||
\includegraphics[scale=0.4]{./fig/axe.pdf}
|
||||
\end{enumerate}
|
||||
|
||||
\end{Exo}
|
||||
|
||||
\eject
|
||||
|
||||
\setcounter{exo}{0}
|
||||
|
||||
\begin{Exo}
|
||||
Surligner les valeurs possibles pour $x$ dans les inéquations suivantes.
|
||||
\begin{enumerate}
|
||||
\item $x \geq -1$
|
||||
\includegraphics[scale=0.4]{./fig/axe.pdf}
|
||||
\item $x < -2$
|
||||
\includegraphics[scale=0.4]{./fig/axe.pdf}
|
||||
\item $x \leq 3$
|
||||
\includegraphics[scale=0.4]{./fig/axe.pdf}
|
||||
\item $x \leq 5$
|
||||
\includegraphics[scale=0.4]{./fig/axe.pdf}
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
Donner trois valeurs possibles pour $x$ puis représenter graphiquement les solutions des inéquations suivantes.
|
||||
\begin{enumerate}
|
||||
\item $x + 3 \leq 6$: \hspace{1cm} Valeurs possibles: \parbox{1cm}{\dotfill}, \parbox{1cm}{\dotfill}, \parbox{1cm}{\dotfill}
|
||||
|
||||
\includegraphics[scale=0.4]{./fig/axe.pdf}
|
||||
\item $x - 1 \geq -2$: \hspace{1cm} Valeurs possibles: \parbox{1cm}{\dotfill}, \parbox{1cm}{\dotfill}, \parbox{1cm}{\dotfill}
|
||||
|
||||
\includegraphics[scale=0.4]{./fig/axe.pdf}
|
||||
\item $x + 10 \leq 5$: \hspace{1cm} Valeurs possibles: \parbox{1cm}{\dotfill}, \parbox{1cm}{\dotfill}, \parbox{1cm}{\dotfill}
|
||||
|
||||
\includegraphics[scale=0.4]{./fig/axe.pdf}
|
||||
\item $x \leq 6 - x$: \hspace{1cm} Valeurs possibles: \parbox{1cm}{\dotfill}, \parbox{1cm}{\dotfill}, \parbox{1cm}{\dotfill}
|
||||
|
||||
\includegraphics[scale=0.4]{./fig/axe.pdf}
|
||||
\end{enumerate}
|
||||
|
||||
\end{Exo}
|
||||
|
||||
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
BIN
3e/Nombres_Calculs/Inequations/exo/inequations_3.pdf
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3e/Nombres_Calculs/Inequations/exo/inequations_3.pdf
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102
3e/Nombres_Calculs/Inequations/exo/inequations_3.tex
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102
3e/Nombres_Calculs/Inequations/exo/inequations_3.tex
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|
||||
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
|
||||
|
||||
%\usepackage{multicol}
|
||||
\usepackage{tikz}
|
||||
\usepackage{fancybox}
|
||||
|
||||
% Title Page
|
||||
\title{Inéquations 3 - Exercices}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
\fancyhead[L]{Troisième}
|
||||
\fancyhead[C]{\Thetitle}
|
||||
\fancyhead[R]{\thepage}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\thispagestyle{fancy}
|
||||
|
||||
\begin{Exo}
|
||||
\begin{center}
|
||||
\framebox{\parbox{0.45\textwidth}{
|
||||
Résoudre l'inéquation $3x + 5 > 0$ et représenter graphiquement les solutions.
|
||||
\begin{eqnarray*}
|
||||
3x + 5 > 0 & \hspace{1cm} & \mbox{On ajoute l'opposé de 5} \\
|
||||
3x + 5 \mathbf{+ (-5)} > \mathbf{-5} && \\
|
||||
3x > -5 & \hspace{1cm} & \mbox{On multiplie par l'inverse de 3 \colorbox{lightgray}{positif}} \\
|
||||
\mathbf{\frac{1}{3} \times }3x > \mathbf{ \frac{1}{3} \times }(-5) && \mbox{On ne change pas le sens de l'inégalité}\\
|
||||
x > \frac{-5}{3}
|
||||
\end{eqnarray*}
|
||||
La solution est $x > \frac{-5}{3}$.
|
||||
|
||||
\begin{tikzpicture}
|
||||
\draw[->, very thick] (-5,0) -- (6,0);
|
||||
\foreach \x in {-5,-4,...,5} {
|
||||
\draw(\x,0) node[below] {\x} node {|};
|
||||
}
|
||||
\draw[color=red, line width = 5pt] ({-5/3}, 0) node[scale=2.5]{]} node[above left, scale = 1.3] {$\frac{-5}{3}$} -- (6,0);
|
||||
|
||||
\end{tikzpicture}
|
||||
}}
|
||||
\end{center}
|
||||
\begin{center}
|
||||
\framebox{\parbox{0.45\textwidth}{
|
||||
Résoudre l'inéquation $-5x + 4 > 0$ et représenter graphiquement les solutions.
|
||||
\begin{eqnarray*}
|
||||
-5x + 4 > 0 & \hspace{1cm} & \mbox{On ajoute l'opposé de 4} \\
|
||||
-5x + 4 \mathbf{+ (-4)} > \mathbf{-4} && \\
|
||||
-5x > -4 & \hspace{1cm} & \mbox{On multiplie par l'inverse de -5 \colorbox{lightgray}{négatif}} \\
|
||||
\mathbf{\frac{1}{-5} \times }-5x \colorbox{lightgray}{<} \mathbf{ \frac{1}{-5} \times }(-4) && \mbox{On a changé le sens de l'inégalité}\\
|
||||
x < \frac{-4}{-5} = \frac{4}{5}
|
||||
\end{eqnarray*}
|
||||
La solution est $x < \frac{4}{5}$.
|
||||
|
||||
\begin{tikzpicture}
|
||||
\draw[->, very thick] (-2,0) -- (6,0);
|
||||
\foreach \x in {-2,-1,...,5} {
|
||||
\draw(\x,0) node[below] {\x} node {|};
|
||||
}
|
||||
\draw[color=red, line width = 5pt] (-2,0) --({4/5}, 0)node[scale=2.5]{[} node[above right, scale = 1.3] {$\frac{4}{5}$} ;
|
||||
|
||||
\end{tikzpicture}
|
||||
}}
|
||||
\end{center}
|
||||
|
||||
\begin{enumerate}
|
||||
\item Résoudre puis représenter les solutions de l'inéquation $4x + 7 > 0$.
|
||||
\begin{eqnarray*}
|
||||
4x + 7 > 0 & \hspace{0.5cm} & \mbox{On ajoute l'opposé de \parbox{1cm}{\dotfill}} \\[0.5cm]
|
||||
4x + 7 + \parbox{1.5cm}{\dotfill}> \parbox{1.5cm}{\dotfill}&& \\[0.5cm]
|
||||
4x > \parbox{1cm}{\dotfill}& \hspace{0.5cm} & \mbox{On multiplie par l'inverse de \parbox{1cm}{\dotfill}} \\[0.5cm]
|
||||
\parbox{1.5cm}{\dotfill} \times 4x \ovalbox{\begin{minipage}{0.3cm}\hfill\vspace{0.5cm}\end{minipage}} \parbox{1.5cm}{\dotfill} \times \parbox{1cm}{\dotfill} && \mbox{On \parbox{2cm}{\dotfill} le sens de l'inégalité} \\[0.5cm]
|
||||
x \ovalbox{\begin{minipage}{0.3cm}\hfill\vspace{0.5cm}\end{minipage}} \frac{\parbox{1cm}{\dotfill}}{\parbox{1cm}{\dotfill}}
|
||||
\end{eqnarray*}
|
||||
La solution est \parbox{2cm}{\dotfill}.
|
||||
\\[0.5cm]
|
||||
\begin{tikzpicture}
|
||||
\draw[->, very thick] (-4,0) -- (6,0);
|
||||
\foreach \x in {-4,-3,...,5} {
|
||||
\draw(\x,0) node[below] {\x} node {|};
|
||||
}
|
||||
\end{tikzpicture}
|
||||
\item Résoudre puis représenter les solutions des inéquations suivantes
|
||||
\begin{enumerate}
|
||||
\item $3x + 2 \geq 0$
|
||||
\item $5x - 10 \leq 0$
|
||||
\item $-3x + 9 > 0$
|
||||
\item $-2 x - 6 < 0$
|
||||
\item $3x + 4 > 7 $
|
||||
\item $-5x - 8 \geq 2$
|
||||
|
||||
\end{enumerate}
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
BIN
3e/Nombres_Calculs/Inequations/exo/slideCorr_17p92.pdf
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3e/Nombres_Calculs/Inequations/exo/slideCorr_17p92.pdf
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73
3e/Nombres_Calculs/Inequations/exo/slideCorr_17p92.tex
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73
3e/Nombres_Calculs/Inequations/exo/slideCorr_17p92.tex
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@@ -0,0 +1,73 @@
|
||||
\documentclass[a4paper,10pt]{beamer}
|
||||
\usepackage[utf8]{inputenc}
|
||||
\usepackage[french]{babel}
|
||||
\usepackage{graphicx}
|
||||
\usepackage{thumbpdf}
|
||||
\usepackage{wasysym}
|
||||
\usepackage{ucs}
|
||||
\usepackage{pgf,pgfarrows,pgfnodes,pgfautomata,pgfheaps,pgfshade}
|
||||
\usepackage{verbatim}
|
||||
\usepackage{subfig}
|
||||
\usepackage{amssymb}
|
||||
\usepackage{tikz}
|
||||
\usepackage{enumerate}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\begin{frame}{Solution l'exercice 17 p 93}
|
||||
|
||||
\begin{enumerate}[a.]
|
||||
\item $x + 7 < 12$ \hspace{2cm} Autre inéquation correspondante:
|
||||
|
||||
\begin{tikzpicture}
|
||||
\draw[->, very thick] (-2.5,0) -- (7,0);
|
||||
\foreach \x in {-2,-1,...,6} {
|
||||
\draw(\x,0) node[below] {\x} node {+};
|
||||
}
|
||||
\end{tikzpicture}
|
||||
\item $5 + x \leq -9$ \hspace{2cm} Autre inéquation correspondante:
|
||||
|
||||
\begin{tikzpicture}
|
||||
\draw[->, very thick] (-17.5,0) -- (-8,0);
|
||||
\foreach \x in {-17,-16,...,-9} {
|
||||
\draw(\x,0) node[below] {\x} node {+};
|
||||
}
|
||||
\end{tikzpicture}
|
||||
\item $t - 7 > 0$ \hspace{2cm} Autre inéquation correspondante:
|
||||
|
||||
\begin{tikzpicture}
|
||||
\draw[->, very thick] (1.5,0) -- (10,0);
|
||||
\foreach \x in {2,3,...,9} {
|
||||
\draw(\x,0) node[below] {\x} node {+};
|
||||
}
|
||||
\end{tikzpicture}
|
||||
\item $y + 1 \geq 1,5$ \hspace{2cm} Autre inéquation correspondante:
|
||||
|
||||
\begin{tikzpicture}
|
||||
\draw[->, very thick] (-2.5,0) -- (7,0);
|
||||
\foreach \x in {-2,-1,...,6} {
|
||||
\draw(\x,0) node[below] {\x} node {+};
|
||||
}
|
||||
\end{tikzpicture}
|
||||
\item $10 + x > -20$ \hspace{2cm} Autre inéquation correspondante:
|
||||
|
||||
\begin{tikzpicture}
|
||||
\draw[->, very thick] (-6.5,0) -- (3.5,0);
|
||||
\foreach \x in {-60,-50,...,30} {
|
||||
\draw({\x/10},0) node[below] {\x} node {+};
|
||||
}
|
||||
\end{tikzpicture}
|
||||
\item $t - 51 < -30$ \hspace{2cm} Autre inéquation correspondante:
|
||||
|
||||
\begin{tikzpicture}
|
||||
\draw[->, very thick] (15.5,0) -- (25,0);
|
||||
\foreach \x in {16,17,...,25} {
|
||||
\draw(\x,0) node[below] {\x} node {+};
|
||||
}
|
||||
\end{tikzpicture}
|
||||
|
||||
\end{enumerate}
|
||||
|
||||
\end{frame}
|
||||
|
||||
\end{document}
|
||||
15
3e/Nombres_Calculs/Puissance/Decouverte/index.rst
Normal file
15
3e/Nombres_Calculs/Puissance/Decouverte/index.rst
Normal file
@@ -0,0 +1,15 @@
|
||||
Notes sur une activité de (re)découverte des puissances
|
||||
#######################################################
|
||||
|
||||
:date: 2014-07-01
|
||||
:modified: 2014-07-01
|
||||
:tags: Nombres Calculs
|
||||
:category: 3e
|
||||
:authors: Benjamin Bertrand
|
||||
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
|
||||
|
||||
|
||||
|
||||
`Lien vers redecouverte_puiss.tex <redecouverte_puiss.tex>`_
|
||||
|
||||
`Lien vers redecouverte_puiss.pdf <redecouverte_puiss.pdf>`_
|
||||
BIN
3e/Nombres_Calculs/Puissance/Decouverte/redecouverte_puiss.pdf
Normal file
BIN
3e/Nombres_Calculs/Puissance/Decouverte/redecouverte_puiss.pdf
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108
3e/Nombres_Calculs/Puissance/Decouverte/redecouverte_puiss.tex
Normal file
108
3e/Nombres_Calculs/Puissance/Decouverte/redecouverte_puiss.tex
Normal file
@@ -0,0 +1,108 @@
|
||||
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
|
||||
|
||||
% Title Page
|
||||
\title{Puissances - Exercices}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
\fancyhead[L]{Troisième}
|
||||
\fancyhead[C]{\Thetitle}
|
||||
\fancyhead[R]{\thepage}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\thispagestyle{fancy}
|
||||
|
||||
\begin{Exo}
|
||||
Un laboratoire fait des recherches sur le développemeent d'une population de bactéries. Ils observent que le nombre de bactéries est multiplié par 3 toutes les heures. En vous aidant du tableau determiner le nombre de bactéries qu'il y aura au bout de 24h s'il y a une seule bactérie au début.
|
||||
|
||||
\begin{center}
|
||||
\begin{tabular}{|c|*{12}{c|}}
|
||||
\hline
|
||||
Heure & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 \\
|
||||
\hline
|
||||
Bactéries & & & & & & & & & & & &\\
|
||||
\hline
|
||||
\end{tabular}
|
||||
|
||||
\begin{tabular}{|c|*{12}{c|}}
|
||||
\hline
|
||||
Heure & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 & 22 & 23 & 24 \\
|
||||
\hline
|
||||
Bactéries & & & & & & & & & & & &\\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
On rappelle que l'on peut réduire des ecritures en utilisant les puissances. Par exemple,
|
||||
\begin{eqnarray*}
|
||||
2^4 & = & 2 \times 2 \times 2 \times 2
|
||||
\end{eqnarray*}
|
||||
En utilisant cette écriture, réécrire le nombre de bactéries au bout de 24h puis de 48h.
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
Réécrire avec des multiplications les puissances suivantes
|
||||
\begin{eqnarray*}
|
||||
2^5 & = \parbox{1cm}{\dotfill} \\
|
||||
6^7 & = \parbox{1cm}{\dotfill} \\
|
||||
3^5 & = \parbox{1cm}{\dotfill} \\
|
||||
2^{10} & = \parbox{1cm}{\dotfill} \\
|
||||
5^1 & = \parbox{1cm}{\dotfill} \\
|
||||
2^0 & = \parbox{1cm}{\dotfill}
|
||||
\end{eqnarray*}
|
||||
\end{Exo}
|
||||
\eject
|
||||
|
||||
\begin{Exo}
|
||||
\begin{enumerate}
|
||||
\item
|
||||
En passant par l'écriture avec les $\times$, mettre les multiplications suivantes sous la forme $a^n$
|
||||
\begin{eqnarray*}
|
||||
2^3\times2^4 =& 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 &= 2^7\\
|
||||
3^4 \times 3^5 =& \parbox{5cm}{\dotfill} & = 3^{\parbox{1cm}{\dotfill}} \\
|
||||
6^2 \times 6^3 =& \parbox{5cm}{\dotfill} & = 6^{\parbox{1cm}{\dotfill}} \\
|
||||
9 \times 9^6 =& \parbox{5cm}{\dotfill} & = 9^{\parbox{1cm}{\dotfill}} \\
|
||||
5^4 \times 5^3 =& \parbox{5cm}{\dotfill} & = 5^{\parbox{1cm}{\dotfill}} \\
|
||||
2^7 \times 2^0 =& \parbox{5cm}{\dotfill} & = 2^{\parbox{1cm}{\dotfill}} \\
|
||||
\end{eqnarray*}
|
||||
\item
|
||||
Donner une idée pour completer la formule suivante
|
||||
\begin{eqnarray*}
|
||||
a^n \times a^m & = & a^{\parbox{1cm}{\dotfill}}
|
||||
\end{eqnarray*}
|
||||
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
\begin{enumerate}
|
||||
\item
|
||||
En passant par l'écriture avec les $\times$, mettre les multiplications suivantes sous la forme $a^n$
|
||||
\begin{eqnarray*}
|
||||
(2^3)^4 &=& 2^3 \times 2^3 \times 2^3 \times 2^3\\
|
||||
&=& 2\times2\times2 \quad \times\quad2\times2\times2 \quad \times\quad2\times2\times2 \quad \times\quad2\times2\times2\\
|
||||
&=& 2^{12} \\
|
||||
\end{eqnarray*}
|
||||
\begin{eqnarray*}
|
||||
(3^2)^5 =& \parbox{5cm}{\dotfill} & = 3^{\parbox{1cm}{\dotfill}} \\
|
||||
(5^4)^2 =& \parbox{5cm}{\dotfill} & = 5^{\parbox{1cm}{\dotfill}} \\
|
||||
(6^1)^7 =& \parbox{5cm}{\dotfill} & = 6^{\parbox{1cm}{\dotfill}} \\
|
||||
(9^2)^3 =& \parbox{5cm}{\dotfill} & = 9^{\parbox{1cm}{\dotfill}} \\
|
||||
(2^{12})^0 =& \parbox{5cm}{\dotfill} & = 2^{\parbox{1cm}{\dotfill}} \\
|
||||
\end{eqnarray*}
|
||||
\item
|
||||
Donner une idée pour completer la formule suivante
|
||||
\begin{eqnarray*}
|
||||
(a^n)^m & = & a^{\parbox{1cm}{\dotfill}}
|
||||
\end{eqnarray*}
|
||||
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
15
3e/Nombres_Calculs/Puissance/fiches_exo/index.rst
Normal file
15
3e/Nombres_Calculs/Puissance/fiches_exo/index.rst
Normal file
@@ -0,0 +1,15 @@
|
||||
Notes sur une fiche d'exercices autour des puissances
|
||||
#####################################################
|
||||
|
||||
:date: 2014-07-01
|
||||
:modified: 2014-07-01
|
||||
:tags: Nombres Calculs, Exo
|
||||
:category: 3e
|
||||
:authors: Benjamin Bertrand
|
||||
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
|
||||
|
||||
|
||||
|
||||
`Lien vers puissances_1.pdf <puissances_1.pdf>`_
|
||||
|
||||
`Lien vers puissances_1.tex <puissances_1.tex>`_
|
||||
BIN
3e/Nombres_Calculs/Puissance/fiches_exo/puissances_1.pdf
Normal file
BIN
3e/Nombres_Calculs/Puissance/fiches_exo/puissances_1.pdf
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119
3e/Nombres_Calculs/Puissance/fiches_exo/puissances_1.tex
Normal file
119
3e/Nombres_Calculs/Puissance/fiches_exo/puissances_1.tex
Normal file
@@ -0,0 +1,119 @@
|
||||
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
|
||||
\usepackage{multicol}
|
||||
|
||||
% Title Page
|
||||
\title{Puissances - Exercices}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
\fancyhead[L]{Troisième}
|
||||
\fancyhead[C]{\Thetitle}
|
||||
\fancyhead[R]{\thepage}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\thispagestyle{fancy}
|
||||
|
||||
\begin{Exo}
|
||||
\begin{enumerate}
|
||||
\item Completer les formules suivantes
|
||||
\begin{eqnarray*}
|
||||
a^m \times a^n = \parbox{2cm}{\dotfill} \hspace{1cm} \left( a^n \right)^m =\parbox{2cm}{\dotfill} \\[0.5cm]
|
||||
a^{-n} = \parbox{3cm}{\dotfill} = \frac{1}{a^{\parbox{1cm}{\dotfill}}}
|
||||
\end{eqnarray*}
|
||||
\vspace{-1cm}
|
||||
\item Mettre les nombres suivants sous la forme $a^n$
|
||||
\begin{multicols}{2}
|
||||
\begin{eqnarray*}
|
||||
2^{13} \times 2^5 = \parbox{1cm}{\dotfill} =\parbox{1cm}{\dotfill} \\[0.5cm]
|
||||
6^{3} \times 6^5 = \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill} \\[0.5cm]
|
||||
5^{10} \times 5^{-7} = \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill} \\[0.5cm]
|
||||
10^{-5} \times 10^6 = \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill} \\[0.5cm]
|
||||
11^{-33} \times 11^9 = \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill} \\[0.5cm]
|
||||
2^4 \times 2^5 \times 2^7 = \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill}
|
||||
\end{eqnarray*}
|
||||
\columnbreak
|
||||
\begin{eqnarray*}
|
||||
2^9 \times \frac{1}{2^6} = \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill} \\[0.5cm]
|
||||
6^5 \times \frac{1}{6^9} = \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill} \\[0.5cm]
|
||||
5^6\times \frac{1}{5^2} = \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill} \\[0.5cm]
|
||||
10^{-4} \times 10^5 \times \frac{1}{10^7} = \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill} \\[0.5cm]
|
||||
\left( 3^4 \right)^6 = \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill}
|
||||
\end{eqnarray*}
|
||||
\end{multicols}
|
||||
|
||||
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
\vspace{-1cm}
|
||||
\begin{Exo}
|
||||
\begin{enumerate}
|
||||
\item Réécrire avec des multiplications puis mettre sous la forme $a^n$
|
||||
|
||||
\begin{eqnarray*}
|
||||
\frac{2^5}{2^3} = \frac{\parbox{3cm}{\dotfill}}{\parbox{3cm}{\dotfill}} = 2^{\parbox{1cm}{\dotfill}} \\[0.5cm]
|
||||
\frac{10^4}{10^2} = \frac{\parbox{3cm}{\dotfill}}{\parbox{3cm}{\dotfill}} = 2^{\parbox{1cm}{\dotfill}} \\[0.5cm]
|
||||
\frac{3^4}{3^5} = \frac{\parbox{3cm}{\dotfill}}{\parbox{3cm}{\dotfill}} = 2^{\parbox{1cm}{\dotfill}}
|
||||
\end{eqnarray*}
|
||||
\begin{eqnarray*}
|
||||
\frac{2^4}{2^5} = \frac{\parbox{3cm}{\dotfill}}{\parbox{3cm}{\dotfill}} = 2^{\parbox{1cm}{\dotfill}} \\[0.5cm]
|
||||
\end{eqnarray*}
|
||||
\vspace{-1cm}
|
||||
\item Donner une idée pour completer la formule suivante
|
||||
\begin{eqnarray*}
|
||||
\frac{a^n}{a^m} & = & a^{\parbox{1cm}{\dotfill}}
|
||||
\end{eqnarray*}
|
||||
|
||||
\end{enumerate}
|
||||
|
||||
|
||||
\end{Exo}
|
||||
%\eject
|
||||
|
||||
\begin{Exo}
|
||||
Mettre les expressions suivantes sous la forme $a^n$
|
||||
|
||||
\begin{multicols}{3}
|
||||
\begin{eqnarray*}
|
||||
\frac{2^5 \times 2^7}{2^5} \\[0.5cm]
|
||||
\frac{2^7 \times 2^2}{2^9} \\[0.5cm]
|
||||
\frac{2^5}{ 2^4 \times 2^5} \\[0.5cm]
|
||||
\frac{2^{-5} \times 2^{3}}{2^5} \\[0.5cm]
|
||||
\frac{2^5 \times 2^9}{2^2 \times 2^6} \\[0.5cm]
|
||||
\frac{2^{-5} \times 2^3}{2^{-5}}
|
||||
\end{eqnarray*}
|
||||
\columnbreak
|
||||
\begin{eqnarray*}
|
||||
\frac{10^4 \times 10^8}{10^2} \\[0.5cm]
|
||||
\frac{10^8 \times 10^7}{10^{15}} \\[0.5cm]
|
||||
\frac{10^6}{ 10^3 \times 10^5} \\[0.5cm]
|
||||
\frac{10^{-5} \times 10^{3} \times 10^6}{10^{33}} \\[0.5cm]
|
||||
\frac{10^5 \times 10^5}{10 \times 10^4} \\[0.5cm]
|
||||
\frac{10^{-5} \times 10^3}{10^{-5} \times 10^4 \times 10^{-2}}
|
||||
\end{eqnarray*}
|
||||
\columnbreak
|
||||
\begin{eqnarray*}
|
||||
\frac{5^5 \times 5^2}{5^2} \\[0.5cm]
|
||||
\frac{3^5 \times 3^5}{3^{-5} \times 3^5} \\[0.5cm]
|
||||
\frac{8^3 \times 8^{-7}}{8^5} \\[0.5cm]
|
||||
\frac{13^5 \times 13^3}{13} \\[0.5cm]
|
||||
\frac{1^5 \times 1^7}{1^5} \\[0.5cm]
|
||||
\frac{21^5 \times 21^7 \times 21^5}{21^5}
|
||||
\end{eqnarray*}
|
||||
\end{multicols}
|
||||
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
\exo{10p106}
|
||||
\end{Exo}
|
||||
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
BIN
3e/Nombres_Calculs/Puissance/scientifique/corr_scient_ex3.pdf
Normal file
BIN
3e/Nombres_Calculs/Puissance/scientifique/corr_scient_ex3.pdf
Normal file
Binary file not shown.
@@ -0,0 +1,46 @@
|
||||
\documentclass[a4paper,10pt]{beamer}
|
||||
\usepackage[utf8]{inputenc}
|
||||
\usepackage[french]{babel}
|
||||
\usepackage{graphicx}
|
||||
\usepackage{thumbpdf}
|
||||
\usepackage{wasysym}
|
||||
\usepackage{ucs}
|
||||
\usepackage{pgf,pgfarrows,pgfnodes,pgfautomata,pgfheaps,pgfshade}
|
||||
\usepackage{verbatim}
|
||||
\usepackage{subfig}
|
||||
\usepackage{amssymb}
|
||||
\usepackage{enumitem}
|
||||
\usepackage{multicol}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\begin{frame}{Solution l'exercice 3}
|
||||
\begin{multicols}{2}
|
||||
\begin{enumerate}[label=\alph* )]
|
||||
\item $ \displaystyle 2,99 \times 10^{25}$
|
||||
\\[1cm]
|
||||
\item $ 2,4936 \times 10^{4}$
|
||||
\\[1cm]
|
||||
\item $ 1,234 \times 10^{-12}$
|
||||
\\[1cm]
|
||||
\item $ 4.825 \times 10^{-6}$
|
||||
\\[1cm]
|
||||
\item $ 6,05 \times 10^{4}$
|
||||
\\[1cm]
|
||||
\columnbreak
|
||||
\item $ 4.02432 \times 10^{5}$
|
||||
\\[1cm]
|
||||
\item $ 3.414 \times 10^{-9}$
|
||||
\\[1cm]
|
||||
\item $ 3.504 \times {7}$
|
||||
\\[1cm]
|
||||
\item $ 2.231 \times 10^{10}$
|
||||
\\[1cm]
|
||||
\item $ 5.05045 \times 10^{-17}$
|
||||
\\[1cm]
|
||||
\end{enumerate}
|
||||
\end{multicols}
|
||||
\end{frame}
|
||||
|
||||
|
||||
\end{document}
|
||||
19
3e/Nombres_Calculs/Puissance/scientifique/index.rst
Normal file
19
3e/Nombres_Calculs/Puissance/scientifique/index.rst
Normal file
@@ -0,0 +1,19 @@
|
||||
Notes sur une fiche d'exercice autour de la notation scientifique
|
||||
#################################################################
|
||||
|
||||
:date: 2014-07-01
|
||||
:modified: 2014-07-01
|
||||
:tags: Nombres Calculs, Exo
|
||||
:category: 3e
|
||||
:authors: Benjamin Bertrand
|
||||
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
|
||||
|
||||
|
||||
|
||||
`Lien vers corr_scient_ex3.tex <corr_scient_ex3.tex>`_
|
||||
|
||||
`Lien vers scientifique.tex <scientifique.tex>`_
|
||||
|
||||
`Lien vers scientifique.pdf <scientifique.pdf>`_
|
||||
|
||||
`Lien vers corr_scient_ex3.pdf <corr_scient_ex3.pdf>`_
|
||||
BIN
3e/Nombres_Calculs/Puissance/scientifique/scientifique.pdf
Normal file
BIN
3e/Nombres_Calculs/Puissance/scientifique/scientifique.pdf
Normal file
Binary file not shown.
133
3e/Nombres_Calculs/Puissance/scientifique/scientifique.tex
Normal file
133
3e/Nombres_Calculs/Puissance/scientifique/scientifique.tex
Normal file
@@ -0,0 +1,133 @@
|
||||
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
|
||||
\usepackage{multicol}
|
||||
%\usepackage{enumitem}
|
||||
|
||||
% Title Page
|
||||
\title{Puissances - Exercices}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
\fancyhead[L]{Troisième}
|
||||
\fancyhead[C]{\Thetitle}
|
||||
\fancyhead[R]{\thepage}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\thispagestyle{fancy}
|
||||
|
||||
\begin{Exo}
|
||||
Mettre les expressions suivantes sous la forme $a^n$
|
||||
|
||||
\begin{multicols}{2}
|
||||
\begin{eqnarray*}
|
||||
10^{13} \times 10^5 \\[0.5cm]
|
||||
10^{3} \times 10^5 \\[0.5cm]
|
||||
10^{10} \times 10^{-7} \\[0.5cm]
|
||||
10^{-5} \times 10^6 \\[0.5cm]
|
||||
10^{-33} \times 10^9 \\[0.5cm]
|
||||
10^4 \times 10^5 \times 2^7
|
||||
\end{eqnarray*}
|
||||
\columnbreak
|
||||
\begin{eqnarray*}
|
||||
\frac{10^5 \times 10^2}{10^2} \\[0.5cm]
|
||||
\frac{10^9 \times 10^6}{10^{5}} \\[0.5cm]
|
||||
\frac{10^6}{ 10^3 \times 10^5} \\[0.5cm]
|
||||
\frac{10^{-1} \times 10^{8} \times 10^6}{10^{33}} \\[0.5cm]
|
||||
\frac{10^3 \times 10^5}{10 \times 10^4} \\[0.5cm]
|
||||
\frac{10^{-5} \times 10^3}{10^{-2} \times 10^3 \times 10^{-9}}
|
||||
\end{eqnarray*}
|
||||
\end{multicols}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
\begin{enumerate}
|
||||
\item Completer le tableau suivant sans utiliser la calculatrice
|
||||
\begin{tabular}{|c|*{7}{c|}}
|
||||
\hline
|
||||
$10^3$ & $10^2$ & $10^1$ & $10^0$ & $10^{-1}$ & $10^{-2}$ & $10^{-3}$ \\
|
||||
\hline
|
||||
1000 & \parbox{1cm}{\dotfill} & \parbox{1cm}{\dotfill} & \parbox{1cm}{\dotfill} & \parbox{1cm}{\dotfill} & \parbox{1cm}{\dotfill} & \parbox{1cm}{\dotfill} \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\item Donner la valeur numérique des nombres suivants
|
||||
\begin{multicols}{3}
|
||||
\begin{eqnarray*}
|
||||
4 \times 10^3 \\
|
||||
45 \times 10^2 \\
|
||||
56 \times 10^0 \\
|
||||
12 \times 10^7
|
||||
\end{eqnarray*}
|
||||
\columnbreak
|
||||
\begin{eqnarray*}
|
||||
5 \times 10^{-3} \\
|
||||
9 \times 10^{-1} \\
|
||||
45 \times 10^{-5} \\
|
||||
12345 \times 10^{-10}
|
||||
\end{eqnarray*}
|
||||
\columnbreak
|
||||
\begin{eqnarray*}
|
||||
2,7 \times 10^3 \\
|
||||
45,67 \times 10^4 \\
|
||||
51,45 \times 10^{-3} \\
|
||||
74,123 \times 10^2
|
||||
\end{eqnarray*}
|
||||
\end{multicols}
|
||||
\item Mettre en écriture scientifique les nombres suivants
|
||||
\begin{multicols}{3}
|
||||
\begin{eqnarray*}
|
||||
234 \\
|
||||
1234567 \\
|
||||
5867 \\
|
||||
98,7
|
||||
\end{eqnarray*}
|
||||
\columnbreak
|
||||
\begin{eqnarray*}
|
||||
0.03 \\
|
||||
0.056456 \\
|
||||
0.000123 \\
|
||||
0.0003450049
|
||||
\end{eqnarray*}
|
||||
\columnbreak
|
||||
\begin{eqnarray*}
|
||||
93,1234 \\
|
||||
2,45 \\
|
||||
98,456 \\
|
||||
965873,132
|
||||
\end{eqnarray*}
|
||||
\end{multicols}
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
%\eject
|
||||
|
||||
\begin{Exo}
|
||||
Mettre les expressions suivantes sous forme d'écriture scientifique.
|
||||
\begin{multicols}{2}
|
||||
\begin{enumerate}[label=\alph* )]
|
||||
\item $ \displaystyle 2,3 \times 10^2 \times 1,3 \times 10^{23}$
|
||||
\item $ \displaystyle \frac{6,234 \times 10^7}{2,5 \times 10^3}$
|
||||
\item $ \displaystyle \frac{123,4 \times 10^{-2}}{100 \times 10^{10}}$
|
||||
\item $ \displaystyle \frac{4,56 \times 10^3}{9,45 \times 10^8}$
|
||||
\item $ \displaystyle \frac{5,24 \times 10^7}{2,5 \times 10^3 \times 34,6 \times 10^{-2}}$
|
||||
\columnbreak
|
||||
\item $ \displaystyle \frac{5,24 \times 10^7 \times 2,4 \times 8 }{2,5 \times 10^3}$
|
||||
\item $ \displaystyle \frac{4,60 \times 10^{-4} \times 5,567 \times 2 }{1,5 \times 10^6}$
|
||||
\item $ \displaystyle \frac{0.004 \times 10^2}{2,5 \times 10^{-9} \times 456,6 \times 10^{-2}}$
|
||||
\item $ \displaystyle \frac{0,24 \times 10^7 \times 10^9}{3,23 \times 10^6 \times 33,3 \times 10^{-3}}$
|
||||
\item $ \displaystyle \frac{22,2222 \times 10^2}{2,2 \times 10^{22} \times 10^2 \times 0.002 \times 10^{-2}}$
|
||||
\end{enumerate}
|
||||
\end{multicols}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
\exo{37 p 109}
|
||||
\exo{34 p 109}
|
||||
\end{Exo}
|
||||
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
Binary file not shown.
@@ -0,0 +1,80 @@
|
||||
\documentclass{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classConn}
|
||||
|
||||
|
||||
% Title Page
|
||||
\title{}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
|
||||
\begin{document}
|
||||
|
||||
\begin{multicols}{2}
|
||||
|
||||
Nom - Prénom:
|
||||
\section{Connaissance}
|
||||
|
||||
\begin{enumerate}
|
||||
\item Donner les deux identités remarquables
|
||||
~\\[0.5cm]
|
||||
.\dotfill
|
||||
~\\[0.5cm]
|
||||
.\dotfill
|
||||
~\\[0.5cm]
|
||||
\item Mettre sous la forme $a^2$ en précisant la valeur de $a$
|
||||
\begin{eqnarray*}
|
||||
A = 25x^2 = \dots \hspace{2cm} a = \dots\\
|
||||
~\\[0.5cm]
|
||||
B = 64 = \dots \hspace{2cm} a = \dots
|
||||
\end{eqnarray*}
|
||||
\item Mettre sous la forme $2ab$ en précisant la valeur de $a$ et de $b$
|
||||
\begin{eqnarray*}
|
||||
C = 30x = \dots \hspace{2cm} a = \dots \hspace{1cm} b = \dots\\
|
||||
\end{eqnarray*}
|
||||
\item Donner la définition d'une \textbf{issue} d'une experience aléatoire:
|
||||
~\\[0.5cm]
|
||||
.\dotfill
|
||||
~\\[0.5cm]
|
||||
.\dotfill
|
||||
~\\[0.5cm]
|
||||
\end{enumerate}
|
||||
|
||||
|
||||
\columnbreak
|
||||
Nom - Prénom
|
||||
\section{Connaissance}
|
||||
|
||||
|
||||
\begin{enumerate}
|
||||
\item Donner les deux identités remarquables
|
||||
~\\[0.5cm]
|
||||
.\dotfill
|
||||
~\\[0.5cm]
|
||||
.\dotfill
|
||||
~\\[0.5cm]
|
||||
\item Mettre sous la forme $a^2$ en précisant la valeur de $a$
|
||||
\begin{eqnarray*}
|
||||
A = 49x^2 = \dots \hspace{2cm} a = \dots\\
|
||||
~\\[0.5cm]
|
||||
B = 100 = \dots \hspace{2cm} a = \dots
|
||||
\end{eqnarray*}
|
||||
\item Mettre sous la forme $2ab$ en précisant la valeur de $a$ et de $b$
|
||||
\begin{eqnarray*}
|
||||
C = 12x = \dots \hspace{2cm} a = \dots \hspace{1cm} b = \dots\\
|
||||
\end{eqnarray*}
|
||||
\item Donner la définition d'un \textbf{évènement} d'une experience aléatoire:
|
||||
~\\[0.5cm]
|
||||
.\dotfill
|
||||
~\\[0.5cm]
|
||||
.\dotfill
|
||||
~\\[0.5cm]
|
||||
\end{enumerate}
|
||||
|
||||
|
||||
\end{multicols}
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
Binary file not shown.
@@ -0,0 +1,38 @@
|
||||
\documentclass[a4paper,10pt]{beamer}
|
||||
\usepackage[utf8]{inputenc}
|
||||
\usepackage[french]{babel}
|
||||
\usepackage{graphicx}
|
||||
\usepackage{thumbpdf}
|
||||
\usepackage{wasysym}
|
||||
\usepackage{ucs}
|
||||
\usepackage{pgf,pgfarrows,pgfnodes,pgfautomata,pgfheaps,pgfshade}
|
||||
\usepackage{verbatim}
|
||||
\usepackage{subfig}
|
||||
\usepackage{amssymb}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\begin{frame}{Solution l'exercice 1}
|
||||
\begin{itemize}
|
||||
\item La solution de l'équation $2x + 1 = 0$ est $\mathbf{x = \frac{-1}{2}}$
|
||||
\vfill
|
||||
\item La solution de l'équation $6x + 12 = 0$ est $\mathbf{x = -2}$
|
||||
\vfill
|
||||
\item La solution de l'équation $3x - 3 = 0$ est $\mathbf{x = 1}$
|
||||
\vfill
|
||||
\item La solution de l'équation $8x - 4 = 0$ est $\mathbf{x = \frac{1}{2}}$
|
||||
\vfill
|
||||
\item La solution de l'équation $-6x - 3 = 0$ est $\mathbf{x = \frac{-1}{2}}$
|
||||
\vfill
|
||||
\item La solution de l'équation $9 + 3x = 0$ est $\mathbf{x = -3}$
|
||||
\vfill
|
||||
\item La solution de l'équation $5 + 3x = 0$ est $\mathbf{x = \frac{-5}{3}}$
|
||||
\vfill
|
||||
\item La solution de l'équation $\frac{2}{3}x + 3 = 0$ est $\mathbf{x = \frac{-9}{2}}$
|
||||
\end{itemize}
|
||||
|
||||
|
||||
\end{frame}
|
||||
|
||||
|
||||
\end{document}
|
||||
Binary file not shown.
@@ -0,0 +1,37 @@
|
||||
\documentclass[a4paper,10pt]{beamer}
|
||||
\usepackage[utf8]{inputenc}
|
||||
\usepackage[french]{babel}
|
||||
\usepackage{graphicx}
|
||||
\usepackage{thumbpdf}
|
||||
\usepackage{wasysym}
|
||||
\usepackage{ucs}
|
||||
\usepackage{pgf,pgfarrows,pgfnodes,pgfautomata,pgfheaps,pgfshade}
|
||||
\usepackage{verbatim}
|
||||
\usepackage{subfig}
|
||||
\usepackage{amssymb}
|
||||
\usepackage{multicol}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\begin{frame}{Solutions de l'exercice 2}
|
||||
\begin{enumerate}
|
||||
\item Les solutions sont $x = \frac{-3}{2}$ et $x = \frac{-5}{4}$.
|
||||
\vfill
|
||||
\item Les solutions sont $x = \frac{-13}{6}$ et $x = \frac{-44}{5}$.
|
||||
\vfill
|
||||
\item Les solutions sont $x = \frac{1}{3}$ et $x = 9$.
|
||||
\vfill
|
||||
\item Les solutions sont $x = 3$ et $x = \frac{-1}{2}$.
|
||||
\vfill
|
||||
\item Les solutions sont $x = 1$ et $x = 2$.
|
||||
\vfill
|
||||
\item La solution est $x = \frac{-3}{2}$.
|
||||
\vfill
|
||||
\item Les solutions sont $x = \frac{-8}{3}$ et $x = \frac{8}{3}$.
|
||||
\vfill
|
||||
\item La solution est $x = \frac{1}{7}$.
|
||||
\end{enumerate}
|
||||
\end{frame}
|
||||
|
||||
|
||||
\end{document}
|
||||
@@ -0,0 +1,19 @@
|
||||
Notes sur correction
|
||||
####################
|
||||
|
||||
:date: 2014-07-01
|
||||
:modified: 2014-07-01
|
||||
:tags: Nombres Calculs
|
||||
:category: 3e
|
||||
:authors: Benjamin Bertrand
|
||||
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
|
||||
|
||||
|
||||
|
||||
`Lien vers corr_eq_1.tex <corr_eq_1.tex>`_
|
||||
|
||||
`Lien vers corr_eq_1.pdf <corr_eq_1.pdf>`_
|
||||
|
||||
`Lien vers corr_eq_2.tex <corr_eq_2.tex>`_
|
||||
|
||||
`Lien vers corr_eq_2.pdf <corr_eq_2.pdf>`_
|
||||
Binary file not shown.
@@ -0,0 +1,130 @@
|
||||
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
|
||||
|
||||
% Title Page
|
||||
\title{Identités remarquables - Exercices}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
\fancyhead[L]{Troisième}
|
||||
\fancyhead[C]{\Thetitle}
|
||||
\fancyhead[R]{\thepage}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\thispagestyle{fancy}
|
||||
|
||||
\begin{Exo}
|
||||
\begin{enumerate}
|
||||
\item Relier les expressions égales entres elles.
|
||||
|
||||
\begin{minipage}[c]{0.2\textwidth}
|
||||
\flushright
|
||||
$4x^2 + 4x + 1 \qquad \bullet$ \\[0.5cm]
|
||||
$64x^2 - 48x + 9 \qquad \bullet$ \\[0.5cm]
|
||||
$36x^2 + 60x + 25 \qquad \bullet$ \\[0.5cm]
|
||||
$36x^2 - 60x + 25 \qquad \bullet$
|
||||
|
||||
\end{minipage}
|
||||
\hspace{2cm}
|
||||
\begin{minipage}[c]{0.1\textwidth}
|
||||
\begin{itemize}
|
||||
\item $(8x - 3)^2$
|
||||
\item $(6x + 5)^2$
|
||||
\item $(2x + 1)^2$
|
||||
\item $(6x - 5)^2$
|
||||
\item $(36x + 25)^2$
|
||||
\item $(4x + 1)^2$
|
||||
\item $(2x - 1)^2$
|
||||
\item $(8x + 3)^2$
|
||||
\end{itemize}
|
||||
|
||||
\end{minipage}
|
||||
|
||||
\item Factoriser l'expression suivante
|
||||
\begin{eqnarray*}
|
||||
A & = & 25x^2 + 30x + 9
|
||||
\end{eqnarray*}
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
\vspace{1cm}
|
||||
|
||||
\begin{Exo}
|
||||
\begin{enumerate}
|
||||
\item Relier les expressions égales entres elles.
|
||||
|
||||
\begin{minipage}[c]{0.2\textwidth}
|
||||
\flushright
|
||||
$4x + 4x^2 + 1 \qquad \bullet$ \\[0.5cm]
|
||||
$9 - 48x + 64x^2 \qquad \bullet$ \\[0.5cm]
|
||||
$4 + 49x^2 - 28x \qquad \bullet$ \\[0.5cm]
|
||||
$16x + 16x^2 + 4 \qquad \bullet$
|
||||
\end{minipage}
|
||||
\hspace{2cm}
|
||||
\begin{minipage}[c]{0.1\textwidth}
|
||||
\begin{itemize}
|
||||
\item $(2x + 1)^2$
|
||||
\item $(8x - 3)^2$
|
||||
\item $(7x + 3)^2$
|
||||
\item $(2x + 4)^2$
|
||||
\item $(2x - 1)^2$
|
||||
\item $(3 - 7x)^2$
|
||||
\item $(2 + 4x)^2$
|
||||
\item $(8x + 3)^2$
|
||||
\end{itemize}
|
||||
|
||||
\end{minipage}
|
||||
|
||||
\item Factoriser les expressions suivantes
|
||||
\begin{eqnarray*}
|
||||
A & = & 4 + 25x^2 + 20x\\
|
||||
B & = & -72x + 81x^2 + 16
|
||||
\end{eqnarray*}
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
|
||||
\begin{Exo}
|
||||
\begin{enumerate}
|
||||
\item Relier les expressions égales entres elles.
|
||||
|
||||
\begin{minipage}[c]{0.2\textwidth}
|
||||
\flushright
|
||||
$x^2 + 2x + 1 \qquad \bullet$ \\[0.5cm]
|
||||
$2x^2 + 6\sqrt{2}x + 9 \qquad \bullet$ \\[0.5cm]
|
||||
$3x^2 + 4\sqrt{3}x + 4 \qquad \bullet$ \\[0.5cm]
|
||||
$9x^2 + 6\sqrt{2}x + 2 \qquad \bullet$
|
||||
|
||||
\end{minipage}
|
||||
\hspace{2cm}
|
||||
\begin{minipage}[c]{0.1\textwidth}
|
||||
\begin{itemize}
|
||||
\item $(x + 1)^2$
|
||||
\item $(\sqrt{2}x - 3)^2$
|
||||
\item $(\sqrt{2}x + 3)^2$
|
||||
\item $(3x - \sqrt{2})^2$
|
||||
\item $(x - 1)^2$
|
||||
\item $(\sqrt{3}x + 2)^2$
|
||||
\item $(3x + \sqrt{2})^2$
|
||||
\item $(\sqrt{3}x - 2)^2$
|
||||
\end{itemize}
|
||||
|
||||
\end{minipage}
|
||||
|
||||
\item Factoriser les expressions suivantes
|
||||
\begin{eqnarray*}
|
||||
A & = & 2x^2 + 8\sqrt{2}x + 16 \\
|
||||
B & = & 3x^2 + 10\sqrt{3}x + 25 \\
|
||||
C & = & 3x^2 + 2\sqrt{6}x + 2 \\
|
||||
\end{eqnarray*}
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
Binary file not shown.
@@ -0,0 +1,123 @@
|
||||
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
|
||||
|
||||
% Title Page
|
||||
\title{Identités remarquables - Exercices}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
\fancyhead[L]{Troisième}
|
||||
\fancyhead[C]{\Thetitle}
|
||||
\fancyhead[R]{\thepage}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\thispagestyle{fancy}
|
||||
|
||||
\begin{Exo}
|
||||
Rappeler les deux identités remarquables.
|
||||
\begin{eqnarray*}
|
||||
(a + b)^2 & = & \hspace{3cm} \\[0.5cm]
|
||||
(a - b)^2 & = & \hspace{3cm}
|
||||
\end{eqnarray*}
|
||||
|
||||
Développer puis réduire pour découvrir la 3e identité remarquable.
|
||||
|
||||
\begin{eqnarray*}
|
||||
(a + b)(a - b) & = & \parbox{1cm}{\dotfill} \times \parbox{1cm}{\dotfill} + \parbox{1cm}{\dotfill} \times \parbox{1cm}{\dotfill} + \parbox{1cm}{\dotfill} \times \parbox{1cm}{\dotfill} + \parbox{1cm}{\dotfill} \times \parbox{1cm}{\dotfill} \\[0.5cm]
|
||||
& = & \parbox{1cm}{\dotfill} + \parbox{1cm}{\dotfill} + \parbox{1cm}{\dotfill} + \parbox{1cm}{\dotfill} \\[0.5cm]
|
||||
& = & \parbox{1cm}{\dotfill} - \parbox{1cm}{\dotfill}
|
||||
\end{eqnarray*}
|
||||
|
||||
On en déduit la troisième identité remarquable
|
||||
\begin{center}
|
||||
\framebox{\parbox{0.2\textwidth}{
|
||||
\begin{eqnarray*}
|
||||
(a + b)(a - b) & = & \parbox{1cm}{\dotfill} - \parbox{1cm}{\dotfill}
|
||||
\end{eqnarray*}
|
||||
}}
|
||||
\end{center}
|
||||
|
||||
|
||||
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
\begin{enumerate}
|
||||
\item Relier les expressions égales entres elles (en utilisant la 3e identité remarquable).
|
||||
|
||||
\begin{minipage}[c]{0.2\textwidth}
|
||||
\flushright
|
||||
$(2x + 1)(2x - 1) \qquad \bullet$ \\[0.5cm]
|
||||
$(4x + 2)(4x - 2) \qquad \bullet$ \\[0.5cm]
|
||||
$(8x - 1)(8x + 1) \qquad \bullet$ \\[0.5cm]
|
||||
$(5 + 2x)(5 - 2x) \qquad \bullet$
|
||||
|
||||
\end{minipage}
|
||||
\hspace{1cm}
|
||||
\begin{minipage}[c]{0.2\textwidth}
|
||||
\begin{itemize}
|
||||
\item $4x^2 + 16x - 2$
|
||||
\item $4x^2 - 1$
|
||||
\item $4x - 1$
|
||||
\item $25 - 4x$
|
||||
\item $16x^2 - 4$
|
||||
\item $64x - 1$
|
||||
\item $4x^2 + 1$
|
||||
\item $4x - 25$
|
||||
\end{itemize}
|
||||
|
||||
\end{minipage}
|
||||
|
||||
\item Développer les expressions suivantes
|
||||
\begin{eqnarray*}
|
||||
A = (3x + 5)(3x - 5) \hspace{2cm} B = (7x - 4)(7x + 4)
|
||||
\end{eqnarray*}
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
\vspace{1cm}
|
||||
|
||||
\begin{Exo}
|
||||
\begin{enumerate}
|
||||
\item Relier les expressions égales entres elles.
|
||||
|
||||
\begin{minipage}[c]{0.15\textwidth}
|
||||
\flushright
|
||||
$4x^2 - 9 \qquad \bullet$ \\[0.5cm]
|
||||
$64x^2 - 16 \qquad \bullet$ \\[0.5cm]
|
||||
$49x^2 - 81\qquad \bullet$ \\[0.5cm]
|
||||
$36 - 9x^2 \qquad \bullet$
|
||||
\end{minipage}
|
||||
\hspace{2cm}
|
||||
\begin{minipage}[c]{0.2\textwidth}
|
||||
\begin{itemize}
|
||||
\item $(4x - 9)^2$
|
||||
\item $(3x + 6)(3x - 6)$
|
||||
\item $(7x + 9)(9 - 7x)$
|
||||
\item $(8x + 4)^2$
|
||||
\item $(4x + 9)(4x - 9)$
|
||||
\item $(7x + 9)(7x - 9)$
|
||||
\item $(8x - 4)(8x + 4)$
|
||||
\item $(6 - 3x)(6 + 3x)$
|
||||
\end{itemize}
|
||||
|
||||
\end{minipage}
|
||||
|
||||
\item Factoriser les expressions suivantes
|
||||
\begin{eqnarray*}
|
||||
A = 2x^2 - 9 \hspace{2cm} B = 9x^2 - 25 \\[0.5cm]
|
||||
C = 64x^2 - 1 \hspace{2cm} D = x^2 - 16
|
||||
\end{eqnarray*}
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
|
||||
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
Binary file not shown.
@@ -0,0 +1,127 @@
|
||||
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
|
||||
|
||||
% Title Page
|
||||
\title{Identités remarquables - Exercices}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
\fancyhead[L]{Troisième}
|
||||
\fancyhead[C]{\Thetitle}
|
||||
\fancyhead[R]{\thepage}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\thispagestyle{fancy}
|
||||
|
||||
\begin{Exo}
|
||||
Rappeler les trois identités remarquables.
|
||||
|
||||
\begin{center}
|
||||
\framebox{\parbox{0.4\textwidth}{
|
||||
\begin{eqnarray*}
|
||||
(a + b)^2 & = & \hspace{5cm} \\[0.5cm]
|
||||
(a - b)^2 & = & \hspace{5cm} \\[0.5cm]
|
||||
(a + b)(a - c) & = & \hspace{5cm}
|
||||
\end{eqnarray*}
|
||||
}}
|
||||
\end{center}
|
||||
|
||||
|
||||
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
\begin{enumerate}
|
||||
\item Relier les expressions égales entres elles (il faudra utiliser les 3 identités remarquables).
|
||||
|
||||
\begin{minipage}[c]{0.2\textwidth}
|
||||
\flushright
|
||||
$(2x + 1)(2x - 1) \qquad \bullet$ \\[0.5cm]
|
||||
$(4x + 2)^2 \qquad \bullet$ \\[0.5cm]
|
||||
$(8x - 1)(8x + 1) \qquad \bullet$ \\[0.5cm]
|
||||
$(5 - 2x)^2 \qquad \bullet$
|
||||
|
||||
\end{minipage}
|
||||
\hspace{1cm}
|
||||
\begin{minipage}[c]{0.2\textwidth}
|
||||
\begin{itemize}
|
||||
\item $25 + 20x + 4x^2$
|
||||
\item $16x^2 + 16x + 4$
|
||||
\item $4x^2 - 1$
|
||||
\item $16x^2 - 16x + 4$
|
||||
\item $64x^2 - 1$
|
||||
\item $64x^2 + 16x + 1$
|
||||
\item $4x^2 + 1$
|
||||
\item $25 - 20x + 4x^2$
|
||||
\end{itemize}
|
||||
|
||||
\end{minipage}
|
||||
|
||||
\item Développer les expressions suivantes en utilisant les identités remarquables.
|
||||
\begin{eqnarray*}
|
||||
A = (2x + 3)(2x - 3) &=& \parbox{3cm}{\dotfill} \\[0.5cm]
|
||||
B = (7x - 4)^2 &=& \parbox{3cm}{\dotfill}\\[0.5cm]
|
||||
C = (8x + 4)^2 &=& \parbox{3cm}{\dotfill}\\[0.5cm]
|
||||
D = (6x - 1)(6x + 1)&=&\parbox{3cm}{\dotfill}
|
||||
\end{eqnarray*}
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
\vspace{1cm}
|
||||
|
||||
\begin{Exo}
|
||||
\begin{enumerate}
|
||||
\item Relier les expressions égales entres elles.
|
||||
|
||||
\begin{minipage}[c]{0.15\textwidth}
|
||||
\flushright
|
||||
$16x^2 - 9 \qquad \bullet$ \\[0.5cm]
|
||||
$9x^2 - 24x + 16 \qquad \bullet$ \\[0.5cm]
|
||||
$49x^2 + 112x + 64\qquad \bullet$ \\[0.5cm]
|
||||
$1 - 25x^2 \qquad \bullet$
|
||||
\end{minipage}
|
||||
\hspace{2cm}
|
||||
\begin{minipage}[c]{0.2\textwidth}
|
||||
\begin{itemize}
|
||||
\item $(1 + 5x)(1 - 5x)$
|
||||
\item $(4x - 3)^2$
|
||||
\item $(4x - 3)(4x + 3)$
|
||||
\item $(3x + 4)^2$
|
||||
\item $(7x + 8)(7x - 8)$
|
||||
\item $(1 - 5x)^2$
|
||||
\item $(3x - 4)^2$
|
||||
\item $(7x + 8)^2$
|
||||
\end{itemize}
|
||||
|
||||
\end{minipage}
|
||||
|
||||
\item Factoriser les expressions suivantes
|
||||
\begin{eqnarray*}
|
||||
A = 9x^2 - 9 \hspace{2cm} B = 4x^2 + 12x + 9 \\[0.5cm]
|
||||
C = 100x^2 - 121 \hspace{2cm} D = 49x^2 - 84x + 36
|
||||
\end{eqnarray*}
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
En utilisant la troisième identité remarquable et en suivante l'exemple, factoriser les expressions suivantes.
|
||||
\begin{eqnarray*}
|
||||
A = (x + 2)^2 - 81 = (x + 2)^2 - 9^2 = (x + 2 + 9)(x + 2 - 9) = (x + 11)(x - 7) \\[0.5cm]
|
||||
\end{eqnarray*}
|
||||
\begin{eqnarray*}
|
||||
B = (x + 1)^2 - 4 &\hspace{2cm}& C = (x + 3)^2 - 9 \\[0.5cm]
|
||||
D = (2x + 1)^2 - 25 &\hspace{2cm}& E = 36 - (4x + 1)^2 \\[0.5cm]
|
||||
F = (2x - 1)^2 - (3x + 4)^2 &\hspace{2cm}& D = (3x - 1)^2 - (x + 1)^2
|
||||
\end{eqnarray*}
|
||||
\end{Exo}
|
||||
|
||||
|
||||
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
Binary file not shown.
@@ -0,0 +1,122 @@
|
||||
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
|
||||
|
||||
|
||||
% Title Page
|
||||
\title{Identités remarquables et équations- Exercices}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
\fancyhead[L]{Troisième}
|
||||
\fancyhead[C]{\Thetitle}
|
||||
\fancyhead[R]{\thepage}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\thispagestyle{fancy}
|
||||
|
||||
\begin{Exo}
|
||||
Rappeler les trois identités remarquables.
|
||||
|
||||
\begin{center}
|
||||
\framebox{\parbox{0.4\textwidth}{
|
||||
\begin{eqnarray*}
|
||||
(a + b)^2 & = & \hspace{5cm} \\[0.5cm]
|
||||
(a - b)^2 & = & \hspace{5cm} \\[0.5cm]
|
||||
(a + b)(a - c) & = & \hspace{5cm}
|
||||
\end{eqnarray*}
|
||||
}}
|
||||
\end{center}
|
||||
|
||||
|
||||
|
||||
\end{Exo}
|
||||
|
||||
|
||||
\begin{Exo}
|
||||
\begin{enumerate}
|
||||
\item Relier les expressions égales entres elles.
|
||||
|
||||
\begin{minipage}[c]{0.15\textwidth}
|
||||
\flushright
|
||||
$49x^2 + 126x + 81\qquad \bullet$ \\[0.5cm]
|
||||
$25x^2 - 16 \qquad \bullet$ \\[0.5cm]
|
||||
$x^2 - 8x + 16 \qquad \bullet$ \\[0.5cm]
|
||||
$100 - 4x^2 \qquad \bullet$
|
||||
\end{minipage}
|
||||
\hspace{2cm}
|
||||
\begin{minipage}[c]{0.2\textwidth}
|
||||
\begin{itemize}
|
||||
\item $(x - 4)^2$
|
||||
\item $(5x + 4)(5x - 4)$
|
||||
\item $(7x - 9)^2$
|
||||
\item $(x - 4)(x + 4)$
|
||||
\item $(7x + 9)^2$
|
||||
\item $(10 - 2x)(10 + 2x)$
|
||||
\item $(5x + 4)^2$
|
||||
\item $(2x - 10)(10 + 2x)$
|
||||
\end{itemize}
|
||||
|
||||
\end{minipage}
|
||||
|
||||
\item Factoriser les expressions suivantes
|
||||
\begin{eqnarray*}
|
||||
A = x^2 - 9 \hspace{2cm} B = x^2 + 6x + 9 \\[0.5cm]
|
||||
C = 9 - 4x^2 \hspace{2cm} D = 49x^2 + 84x + 36
|
||||
\end{eqnarray*}
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
En utilisant la troisième identité remarquable et en suivante l'exemple, factoriser les expressions suivantes.
|
||||
|
||||
\framebox{\parbox{0.45\textwidth}{
|
||||
\begin{eqnarray*}
|
||||
A = (x + 2)^2 - 81 = (x + 2)^2 - 9^2 = (x + 2 + 9)(x + 2 - 9) = (x + 11)(x - 7)
|
||||
\end{eqnarray*}
|
||||
}}
|
||||
\begin{eqnarray*}
|
||||
B = (2x + 5)^2 - 16 &\hspace{2cm}& C = (7x + 2)^2 - 2 \\[0.5cm]
|
||||
D = (-x - 1)^2 - 25 &\hspace{2cm}& E = (4x + 1)^2 - 49
|
||||
\end{eqnarray*}
|
||||
\begin{center}
|
||||
\framebox{\parbox{0.45\textwidth}{
|
||||
On rappelle que quand on enlève les parenthèses avec un signe "-" devant, il faut changer le signe de \textbf{TOUS} les éléments entre les parenthèses.
|
||||
\begin{eqnarray*}
|
||||
F = (x + 2)^2 - (3x + 4)^2 &=& \left[ x + 2 + 3x + 4 \right]\left[ x + 2 - \mathbf{(3x + 4)} \right] \\
|
||||
&=& \left[ x + 3x + 2 + 4 \right]\left[ x + 2 \mathbf{- 3x - 4} \right] \\
|
||||
&=& \left( 4x + 6 \right)\left( -2x - 2 \right)
|
||||
\end{eqnarray*}
|
||||
}}
|
||||
\end{center}
|
||||
\begin{eqnarray*}
|
||||
G = (2x + 1)^2 - (x + 2)^2 &\hspace{2cm}& H = (3x - 1)^2 - (5x + 2)^2 \\
|
||||
I = (4x + 3)^2 - (3x - 4)^2 &\hspace{2cm}& J = (3x - 1)^2 - (x - 2)^2
|
||||
\end{eqnarray*}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
Résoudre les équations suivantes
|
||||
|
||||
%\framebox{\parbox{0.45\textwidth}{
|
||||
% \begin{eqnarray*}
|
||||
% 2x = 5 \quad \mbox{ On divise par 2 }\quad \frac{2x}{2} = \frac{5}{2} \quad \mbox{ donc }\quad x = \frac{5}{2}
|
||||
% \end{eqnarray*}
|
||||
%}}
|
||||
\begin{eqnarray*}
|
||||
a) \qquad 3x = 4 \hspace{2cm} b) \qquad -5x = 7 \\
|
||||
c) \qquad x + 3 = 4 \hspace{2cm} d) \qquad 2 + x = 9 \\
|
||||
e) \qquad 3x + 2 = 3 \hspace{2cm} f) \qquad 3x - 2 = 5
|
||||
\end{eqnarray*}
|
||||
|
||||
\end{Exo}
|
||||
|
||||
|
||||
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
Binary file not shown.
@@ -0,0 +1,139 @@
|
||||
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
|
||||
|
||||
\usepackage{multicol}
|
||||
|
||||
% Title Page
|
||||
\title{Identités remarquables et équations- Exercices}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
\fancyhead[L]{Troisième}
|
||||
\fancyhead[C]{\Thetitle}
|
||||
\fancyhead[R]{\thepage}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\thispagestyle{empty}
|
||||
|
||||
\begin{Exo}
|
||||
\exo{Équations de degrés 1}
|
||||
|
||||
\begin{center}
|
||||
\framebox{\parbox{0.4\textwidth}{
|
||||
Résoudre l'équation $3x + 5 = 0$.
|
||||
\begin{eqnarray*}
|
||||
3x + 5 = 0 & \hspace{1cm} & \mbox{On ajoute l'opposé de 5} \\
|
||||
3x + 5 \mathbf{+ (-5)} = \mathbf{-5} && \\
|
||||
3x = -5 & \hspace{1cm} & \mbox{On multiplie par l'inverse de 3} \\
|
||||
\mathbf{\frac{1}{3} \times }3x = \mathbf{ \frac{1}{3} \times }(-5) && \\
|
||||
x = \frac{-5}{3}
|
||||
\end{eqnarray*}
|
||||
La solution est $x = \frac{-5}{3}$.
|
||||
}}
|
||||
\end{center}
|
||||
|
||||
\begin{enumerate}
|
||||
\item Résoudre l'équation $4x + 7 = 0$.
|
||||
\begin{eqnarray*}
|
||||
4x + 7 = 0 & \hspace{0.5cm} & \mbox{On ajoute l'opposé de \parbox{1cm}{\dotfill}} \\[0.5cm]
|
||||
4x + 7 + \parbox{1.5cm}{\dotfill}= \parbox{1.5cm}{\dotfill}&& \\[0.5cm]
|
||||
4x = \parbox{1cm}{\dotfill}& \hspace{0.5cm} & \mbox{On multiplie par l'inverse de \parbox{1cm}{\dotfill}} \\[0.5cm]
|
||||
\parbox{1.5cm}{\dotfill} \times 4x = \parbox{1.5cm}{\dotfill} \times \parbox{1cm}{\dotfill} && \\[0.5cm]
|
||||
x = \frac{\parbox{1cm}{\dotfill}}{\parbox{1cm}{\dotfill}}
|
||||
\end{eqnarray*}
|
||||
La solution est \parbox{2cm}{\dotfill}.
|
||||
|
||||
\item Résoudre les équations suivantes
|
||||
\begin{multicols}{2}
|
||||
\begin{enumerate}
|
||||
\item $2x + 1 = 0$
|
||||
\item $6x + 12 = 0$
|
||||
\item $3x - 3 = 0$
|
||||
\item $8x - 4 = 0$
|
||||
\columnbreak
|
||||
\item $-6x - 3 = 0$
|
||||
\item $9 + 3x = 0$
|
||||
\item $5 + 3x = 0$
|
||||
\item $\frac{2}{3}x + 3 = 0$
|
||||
\end{enumerate}
|
||||
\end{multicols}
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
\exo{Équation produit}
|
||||
\begin{center}
|
||||
\framebox{\parbox{0.45\textwidth}{
|
||||
Résoudre l'équation $(3x + 5)(2x + 4) = 0$.
|
||||
|
||||
$(3x + 5)(2x + 4) = 0$ donc
|
||||
\begin{center}
|
||||
$3x + 5 = 0$ \hspace{1cm} soit \hspace{1cm} $2x + 4 = 0$
|
||||
\end{center}
|
||||
|
||||
\begin{multicols}{2}
|
||||
Soit
|
||||
\begin{eqnarray*}
|
||||
3x + 5 = 0 \\
|
||||
3x + 5 \mathbf{+ (-5)} = \mathbf{-5}\\
|
||||
3x = -5 \\
|
||||
\mathbf{\frac{1}{3} \times } 3x = \mathbf{ \frac{1}{3} \times } (-5) \\
|
||||
x = \frac{-5}{3}
|
||||
\end{eqnarray*}
|
||||
|
||||
\columnbreak
|
||||
Soit
|
||||
\begin{eqnarray*}
|
||||
2x + 4 = 0 \\
|
||||
2x + 4 \mathbf{+ (-4)} = \mathbf{-4}\\
|
||||
2x = -4 \\
|
||||
\mathbf{ \frac{1}{2} \times } 2x =\mathbf{\frac{1}{2} \times } -4 \\
|
||||
x = \frac{-4}{2} = -2
|
||||
\end{eqnarray*}
|
||||
|
||||
\end{multicols}
|
||||
Les solutions sont $x = \frac{-5}{3}$ ou $x = -2$.
|
||||
}}
|
||||
\end{center}
|
||||
|
||||
Résoudre l'équation $(6x + 2)(3x + 4) = 0$.
|
||||
|
||||
$(6x + 2)(3x + 4) = 0$ donc
|
||||
\begin{center}
|
||||
\parbox{3cm}{\dotfill} = 0\hspace{1cm} soit \hspace{1cm} \parbox{3cm}{\dotfill} = 0
|
||||
\end{center}
|
||||
|
||||
\begin{multicols}{2}
|
||||
Soit
|
||||
\begin{eqnarray*}
|
||||
\parbox{2cm}{\dotfill} = 0 \\[0.3cm]
|
||||
\parbox{2cm}{\dotfill} = \parbox{2cm}{\dotfill} \\[0.3cm]
|
||||
\parbox{2cm}{\dotfill} = \parbox{2cm}{\dotfill} \\[0.3cm]
|
||||
\parbox{2cm}{\dotfill} = \parbox{2cm}{\dotfill} \\[0.3cm]
|
||||
x = \parbox{1cm}{\dotfill}
|
||||
\end{eqnarray*}
|
||||
|
||||
\columnbreak
|
||||
Soit
|
||||
\begin{eqnarray*}
|
||||
\parbox{2cm}{\dotfill} = 0 \\[0.3cm]
|
||||
\parbox{2cm}{\dotfill} = \parbox{2cm}{\dotfill} \\[0.3cm]
|
||||
\parbox{2cm}{\dotfill} = \parbox{2cm}{\dotfill} \\[0.3cm]
|
||||
\parbox{2cm}{\dotfill} = \parbox{2cm}{\dotfill} \\[0.3cm]
|
||||
x = \parbox{1cm}{\dotfill}
|
||||
\end{eqnarray*}
|
||||
|
||||
\end{multicols}
|
||||
Les solutions sont $x = \parbox{1cm}{\dotfill}$ ou $x = $\parbox{1cm}{\dotfill}.
|
||||
\end{Exo}
|
||||
|
||||
|
||||
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
Binary file not shown.
@@ -0,0 +1,132 @@
|
||||
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
|
||||
|
||||
\usepackage{multicol}
|
||||
|
||||
% Title Page
|
||||
\title{Identités remarquables et équations- Exercices}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
\fancyhead[L]{Troisième}
|
||||
\fancyhead[C]{\Thetitle}
|
||||
\fancyhead[R]{\thepage}
|
||||
|
||||
|
||||
\begin{document}
|
||||
\thispagestyle{fancy}
|
||||
|
||||
|
||||
\begin{Exo}
|
||||
\exo{Équation produit}
|
||||
\begin{center}
|
||||
\framebox{\parbox{0.45\textwidth}{
|
||||
Résoudre l'équation $(3x + 5)(2x + 4) = 0$.
|
||||
|
||||
$(3x + 5)(2x + 4) = 0$ donc
|
||||
\begin{center}
|
||||
$3x + 5 = 0$ \hspace{1cm} soit \hspace{1cm} $2x + 4 = 0$
|
||||
\end{center}
|
||||
|
||||
\begin{multicols}{2}
|
||||
Soit
|
||||
\begin{eqnarray*}
|
||||
3x + 5 = 0 \\
|
||||
3x + 5 \mathbf{+ (-5)} = \mathbf{-5}\\
|
||||
3x = -5 \\
|
||||
\mathbf{\frac{1}{3} \times } 3x = \mathbf{ \frac{1}{3} \times } (-5) \\
|
||||
x = \frac{-5}{3}
|
||||
\end{eqnarray*}
|
||||
|
||||
\columnbreak
|
||||
Soit
|
||||
\begin{eqnarray*}
|
||||
2x + 4 = 0 \\
|
||||
2x + 4 \mathbf{+ (-4)} = \mathbf{-4}\\
|
||||
2x = -4 \\
|
||||
\mathbf{ \frac{1}{2} \times } 2x =\mathbf{\frac{1}{2} \times } -4 \\
|
||||
x = \frac{-4}{2} = -2
|
||||
\end{eqnarray*}
|
||||
|
||||
\end{multicols}
|
||||
Les solutions sont $x = \frac{-5}{3}$ ou $x = -2$.
|
||||
}}
|
||||
\end{center}
|
||||
|
||||
Résoudre l'équation $(2x + 2)(5x + 10) = 0$.
|
||||
|
||||
$(2x + 2)(5x + 10) = 0$ donc
|
||||
\begin{center}
|
||||
\parbox{4cm}{\dotfill} = 0\hspace{1cm} soit \hspace{1cm} \parbox{4cm}{\dotfill} = 0
|
||||
\end{center}
|
||||
|
||||
\begin{multicols}{2}
|
||||
Soit
|
||||
\begin{eqnarray*}
|
||||
\parbox{2cm}{\dotfill} = 0 \\[0.5cm]
|
||||
\parbox{2cm}{\dotfill} = \parbox{2cm}{\dotfill} \\[0.5cm]
|
||||
\parbox{2cm}{\dotfill} = \parbox{2cm}{\dotfill} \\[0.5cm]
|
||||
\parbox{2cm}{\dotfill} = \parbox{2cm}{\dotfill} \\[0.5cm]
|
||||
x = \parbox{1cm}{\dotfill}
|
||||
\end{eqnarray*}
|
||||
|
||||
\columnbreak
|
||||
Soit
|
||||
\begin{eqnarray*}
|
||||
\parbox{2cm}{\dotfill} = 0 \\[0.5cm]
|
||||
\parbox{2cm}{\dotfill} = \parbox{2cm}{\dotfill} \\[0.5cm]
|
||||
\parbox{2cm}{\dotfill} = \parbox{2cm}{\dotfill} \\[0.5cm]
|
||||
\parbox{2cm}{\dotfill} = \parbox{2cm}{\dotfill} \\[0.5cm]
|
||||
x = \parbox{1cm}{\dotfill}
|
||||
\end{eqnarray*}
|
||||
|
||||
\end{multicols}
|
||||
Les solutions sont $x = \parbox{1cm}{\dotfill}$ ou $x = $\parbox{1cm}{\dotfill}.
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
Résoudre les équations suivantes
|
||||
\begin{multicols}{2}
|
||||
\begin{enumerate}
|
||||
\item $(2x + 3)(4x + 5) = 0$
|
||||
\item $(6x + 13)(44x + 5) = 0$
|
||||
\item $(12x - 4)(54x + 6) = 0$
|
||||
\item $(x - 3)(-4x - 2) = 0$
|
||||
\columnbreak
|
||||
|
||||
\item $(x - 1)(x - 2) = 0$
|
||||
\item $(2x + 3)^2 = 0$
|
||||
\item $(3x + 8)(3x - 8) = 0$
|
||||
\item $(7x - 1)^2 = 0$
|
||||
\end{enumerate}
|
||||
\end{multicols}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
Voici trois expressions
|
||||
\begin{eqnarray*}
|
||||
A = 9x^2 - 16 \hspace{1cm} B = 4x^2 + 24x + 9 \\
|
||||
C = (x + 1)(2x - 4) + (x + 1)(7x + 2)
|
||||
\end{eqnarray*}
|
||||
\begin{enumerate}
|
||||
\item Factoriser les trois expressions
|
||||
\item En utilisant la forme de l'énoncé, développer $C$.
|
||||
\item En utilisant la forme factorisée, résoudre les équations
|
||||
\begin{eqnarray*}
|
||||
A = 0 \hspace{1cm} B = 0 \hspace{1cm} C = 0
|
||||
\end{eqnarray*}
|
||||
|
||||
\end{enumerate}
|
||||
|
||||
\end{Exo}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
@@ -0,0 +1,37 @@
|
||||
Notes sur des fiches d'exercices autour des identites remarquables
|
||||
##################################################################
|
||||
|
||||
:date: 2014-07-01
|
||||
:modified: 2014-07-01
|
||||
:tags: Nombres Calculs, Identités Remarquables
|
||||
:category: 3e
|
||||
:authors: Benjamin Bertrand
|
||||
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
|
||||
|
||||
|
||||
|
||||
`Lien vers exo_id_rmq_eq_2.pdf <exo_id_rmq_eq_2.pdf>`_
|
||||
|
||||
`Lien vers exo_id_rmq_4.tex <exo_id_rmq_4.tex>`_
|
||||
|
||||
`Lien vers exo_id_rmq.pdf <exo_id_rmq.pdf>`_
|
||||
|
||||
`Lien vers exo_id_rmq.tex <exo_id_rmq.tex>`_
|
||||
|
||||
`Lien vers exo_id_rmq_4.pdf <exo_id_rmq_4.pdf>`_
|
||||
|
||||
`Lien vers exo_id_rmq_2.tex <exo_id_rmq_2.tex>`_
|
||||
|
||||
`Lien vers exo_id_rmq_3.pdf <exo_id_rmq_3.pdf>`_
|
||||
|
||||
`Lien vers exo_id_rmq_eq_2.tex <exo_id_rmq_eq_2.tex>`_
|
||||
|
||||
`Lien vers exo_id_rmq_eq_1.pdf <exo_id_rmq_eq_1.pdf>`_
|
||||
|
||||
`Lien vers exo_id_rmq_eq_1.tex <exo_id_rmq_eq_1.tex>`_
|
||||
|
||||
`Lien vers exo_id_rmq_2.pdf <exo_id_rmq_2.pdf>`_
|
||||
|
||||
`Lien vers exo_id_rmq_3.tex <exo_id_rmq_3.tex>`_
|
||||
|
||||
Il semblerait que la première étape qui consiste à relier les expressions justes aident les élèves.
|
||||
BIN
3e/Nombres_Calculs/racine_carree/Conn/Conn1202.pdf
Normal file
BIN
3e/Nombres_Calculs/racine_carree/Conn/Conn1202.pdf
Normal file
Binary file not shown.
108
3e/Nombres_Calculs/racine_carree/Conn/Conn1202.tex
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3e/Nombres_Calculs/racine_carree/Conn/Conn1202.tex
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|
||||
\documentclass{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classConn}
|
||||
|
||||
|
||||
% Title Page
|
||||
\title{}
|
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\author{}
|
||||
\date{}
|
||||
|
||||
|
||||
\begin{document}
|
||||
|
||||
\begin{multicols}{2}
|
||||
|
||||
Nom - Prénom:
|
||||
\section{Connaissance}
|
||||
|
||||
\begin{enumerate}
|
||||
\item La racine carré d'un nombre \rule{2cm}{0.5pt} $a$ est notée \rule{2cm}{0.5pt}
|
||||
\vspace{0.5cm}
|
||||
|
||||
\item Si $a$ et $b$ sont deux nombres \rule{2cm}{0.5pt} alors
|
||||
\begin{equation*}
|
||||
\sqrt{a\times b} = \rule{3cm}{0.5pt}
|
||||
\end{equation*}
|
||||
|
||||
\item Si $a$ est positif, combien de solution a l'équation suivante $x^2 = a$?
|
||||
\vspace{0.5cm}
|
||||
|
||||
Qui sont: \rule{2cm}{0.5pt}
|
||||
|
||||
\item Donner la définition du PGCD:
|
||||
\vspace{0.5cm}
|
||||
\end{enumerate}
|
||||
\vspace{0.5cm}
|
||||
|
||||
Nom - Prénom:
|
||||
\section{Connaissance}
|
||||
|
||||
\begin{enumerate}
|
||||
\item Donner la définition du PGCD:
|
||||
\vspace{0.5cm}
|
||||
|
||||
\item La racine carré d'un nombre \rule{2cm}{0.5pt} $a$ est notée \rule{2cm}{0.5pt}
|
||||
\vspace{0.5cm}
|
||||
|
||||
\item Si $a$ et $b$ sont deux nombres \rule{2cm}{0.5pt} alors
|
||||
\begin{equation*}
|
||||
\sqrt{a\times b} = \rule{3cm}{0.5pt}
|
||||
\end{equation*}
|
||||
|
||||
\item Si $a$ est positif, combien de solution a l'équation suivante $x^2 = a$?
|
||||
\vspace{0.5cm}
|
||||
|
||||
Qui sont: \rule{2cm}{0.5pt}
|
||||
\end{enumerate}
|
||||
|
||||
\columnbreak
|
||||
Nom - Prénom
|
||||
\section{Connaissance}
|
||||
|
||||
\begin{enumerate}
|
||||
\item La racine carré d'un nombre \rule{2cm}{0.5pt} $a$ est notée \rule{2cm}{0.5pt}
|
||||
\vspace{0.5cm}
|
||||
|
||||
\item Si $a$ et $b$ sont deux nombres \rule{2cm}{0.5pt} alors
|
||||
\begin{equation*}
|
||||
\frac{\sqrt{a}}{\sqrt{b}} = \rule{3cm}{0.5pt}
|
||||
\end{equation*}
|
||||
|
||||
\item Si $a$ est negatif, combien de solution a l'équation suivante $x^2 = a$?
|
||||
\vspace{0.5cm}
|
||||
|
||||
Qui sont: \rule{2cm}{0.5pt}
|
||||
\item Donner la définition du PGCD:
|
||||
\vspace{0.5cm}
|
||||
\end{enumerate}
|
||||
\vspace{0.5cm}
|
||||
|
||||
Nom - Prénom
|
||||
\section{Connaissance}
|
||||
|
||||
\begin{enumerate}
|
||||
\item Donner la définition du PGCD:
|
||||
\vspace{0.5cm}
|
||||
|
||||
\item La racine carré d'un nombre \rule{2cm}{0.5pt} $a$ est notée \rule{2cm}{0.5pt}
|
||||
\vspace{0.5cm}
|
||||
|
||||
\item Si $a$ et $b$ sont deux nombres \rule{2cm}{0.5pt} alors
|
||||
\begin{equation*}
|
||||
\frac{\sqrt{a}}{\sqrt{b}} = \rule{3cm}{0.5pt}
|
||||
\end{equation*}
|
||||
|
||||
\item Si $a$ est negatif, combien de solution a l'équation suivante $x^2 = a$?
|
||||
\vspace{0.5cm}
|
||||
|
||||
Qui sont: \rule{2cm}{0.5pt}
|
||||
|
||||
|
||||
\end{enumerate}
|
||||
|
||||
\end{multicols}
|
||||
\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:
|
||||
BIN
3e/Nombres_Calculs/racine_carree/Conn0217/Conn0217.pdf
Normal file
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3e/Nombres_Calculs/racine_carree/Conn0217/Conn0217.pdf
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105
3e/Nombres_Calculs/racine_carree/Conn0217/Conn0217.tex
Normal file
105
3e/Nombres_Calculs/racine_carree/Conn0217/Conn0217.tex
Normal file
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|
||||
\documentclass{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classConn}
|
||||
|
||||
|
||||
% Title Page
|
||||
\title{}
|
||||
\author{}
|
||||
\date{}
|
||||
|
||||
|
||||
\begin{document}
|
||||
|
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\begin{multicols}{2}
|
||||
|
||||
Nom - Prénom:
|
||||
\section{Connaissance}
|
||||
|
||||
\begin{enumerate}
|
||||
\item Si $a$ et $b$ sont deux nombres \rule{2cm}{0.5pt} alors
|
||||
\begin{equation*}
|
||||
\sqrt{a\times b} = \rule{3cm}{0.5pt}
|
||||
\end{equation*}
|
||||
\vfill
|
||||
|
||||
\item Énoncer le théorème qui permet de démontrer dans le dessin suivant que le triangle est rectangle.
|
||||
|
||||
\begin{minipage}[h]{0.2\textwidth}
|
||||
\includegraphics[scale=0.15]{./fig/triCercle}
|
||||
\end{minipage}
|
||||
\begin{minipage}[h]{0.25\textwidth}
|
||||
~\\[0.5cm]
|
||||
Si \dotfill
|
||||
~\\[0.5cm]
|
||||
.\dotfill
|
||||
~\\[0.5cm]
|
||||
Alors \dotfill
|
||||
|
||||
\end{minipage}
|
||||
\vfill
|
||||
|
||||
\item Quel théorème permet de calculer $AB$ dans le dessin suivant (il n'est pas demander d'écrire le théorème). Quelles hypothèses a-t-on besoin pour pouvoir appliquer le théorème?
|
||||
|
||||
\begin{minipage}[h]{0.2\textwidth}
|
||||
\includegraphics[scale=0.2]{./fig/thales}
|
||||
\end{minipage}
|
||||
\begin{minipage}[h]{0.25\textwidth}
|
||||
~\\[0.5cm]
|
||||
Nom du théorème: \dotfill
|
||||
~\\[0.5cm]
|
||||
Hypothèses: \dotfill
|
||||
~\\[0.5cm]
|
||||
.\dotfill
|
||||
\end{minipage}
|
||||
|
||||
\end{enumerate}
|
||||
|
||||
\vfill
|
||||
|
||||
Nom - Prénom:
|
||||
\section{Connaissance}
|
||||
|
||||
\begin{enumerate}
|
||||
\item Si $a$ et $b$ sont deux nombres \rule{2cm}{0.5pt} alors
|
||||
\begin{equation*}
|
||||
\sqrt{\frac{a}{b}} = \rule{3cm}{0.5pt}
|
||||
\end{equation*}
|
||||
\vfill
|
||||
|
||||
\item Quel théorème permet de démontrer que les droites $(BC)$ et $(DE)$ sont parallèles avec le dessin suivant. Quelles sont les hypothèses de ce théorème.
|
||||
|
||||
\begin{minipage}[h]{0.2\textwidth}
|
||||
\includegraphics[scale=0.2]{./fig/recipthales}
|
||||
\end{minipage}
|
||||
\begin{minipage}[h]{0.25\textwidth}
|
||||
~\\[0.5cm]
|
||||
Nom du théorème: \dotfill
|
||||
~\\[0.5cm]
|
||||
Hypothèses: \dotfill
|
||||
~\\[0.5cm]
|
||||
.\dotfill
|
||||
\end{minipage}
|
||||
\vfill
|
||||
|
||||
\item Quel théorème permet de calculer $AB$ dans le dessin suivant (il n'est pas demander d'écrire le théorème). De quelles longueurs aura-t-on besoin?
|
||||
|
||||
\begin{minipage}[h]{0.2\textwidth}
|
||||
\includegraphics[scale=0.15]{./fig/triangleRectABC}
|
||||
\end{minipage}
|
||||
\begin{minipage}[h]{0.25\textwidth}
|
||||
~\\[0.5cm]
|
||||
Nom du théorème: \dotfill
|
||||
~\\[0.5cm]
|
||||
Longueurs nécessaires: \dotfill
|
||||
~\\[0.5cm]
|
||||
.\dotfill
|
||||
\end{minipage}
|
||||
|
||||
\end{enumerate}
|
||||
|
||||
\end{multicols}
|
||||
\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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BIN
3e/Nombres_Calculs/racine_carree/Conn0217/fig/recipthales.pdf
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BIN
3e/Nombres_Calculs/racine_carree/Conn0217/fig/recipthales.pdf
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BIN
3e/Nombres_Calculs/racine_carree/Conn0217/fig/thales.pdf
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BIN
3e/Nombres_Calculs/racine_carree/Conn0217/fig/thales.pdf
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176
3e/Nombres_Calculs/racine_carree/Conn0217/fig/thales.svg
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176
3e/Nombres_Calculs/racine_carree/Conn0217/fig/thales.svg
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