Import work from year 2013-2014
This commit is contained in:
Benjamin Bertrand
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4e/DS/4eD/12_litt_frac_triCerc/12_litt_frac_triCerc.pdf
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4e/DS/4eD/12_litt_frac_triCerc/12_litt_frac_triCerc.pdf
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4e/DS/4eD/12_litt_frac_triCerc/12_litt_frac_triCerc.tex
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4e/DS/4eD/12_litt_frac_triCerc/12_litt_frac_triCerc.tex
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\documentclass[a4paper,10pt]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classDS}
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\usepackage{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/2013_2014}
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% Title Page
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\titre{4}
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% \quatreC \quatreD \troisB \troisPro
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\classe{\quatreD}
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\date{18 décembre 2013}
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%\duree{1 heure}
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\sujet{%{{infos.subj%}}}
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% DS DSCorr DM DMCorr Corr
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\typedoc{DS}
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\begin{document}
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\maketitle
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Le barème est donné à titre indicatif, il pourra être modifié.
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\begin{Exo}[6]
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% Copié de http://euler.ac-versailles.fr/eulerwikis/attach/Yann_Bourit/tri_rect_cercles_%E9quations_a.pdf
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$[AB]$ est un segment de 10cm.$C$ un point du segment $[AB]$ tel que $AC = 6cm$. $\mathcal{C}1$ est le cercle de diamètre $[AC]$ et $\mathcal{C}2$ est le cercle de diamètre $[CB]$.
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\begin{enumerate}
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\item Tracer la figure.
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\item Placer $D$ un point du cercle $\mathcal{C}1$ different de $A$ et $C$. Puis placer le point $E$, le point d'intersection entre le cercle $\mathcal{C}2$ et $(CD)$.
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\item Quelle est la nature du triangle $ADC$?
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\item Quelle est la nature du triangle $BEC$?
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\item Démontrer que $(AC)$ et $(EB)$ sont parallèles.
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\end{enumerate}
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\end{Exo}
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\begin{Exo}[6]
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\begin{minipage}[h]{0.4\textwidth}
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\includegraphics[scale=0.2]{./fig/rectangle.pdf}
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\end{minipage}
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\begin{minipage}[h]{0.6\textwidth}
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\begin{enumerate}
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\item Exprimer $AD$ en fonction de $x$.
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\item Expliquer pourquoi l'aire du rectangle $ABCD$ est égale à $21x$.
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\item Expliquer pourquoi le périmètre du rectangle $ABCD$ est égale à $6x + 14$.
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\item Si $x = 2$, quelle est l'aire du rectangle $ABCD$?
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\item Si $x = 1,5$, quel est le périmètre du rectangle $ABCD$?
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\end{enumerate}
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\end{minipage}
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\end{Exo}
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\begin{Exo}[3]
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Simplifier les fractions suivantes:
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\begin{eqnarray*}
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A & = & %{{ exo.frac1() %}} \\
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B & = & %{{ exo.frac3() %}} \\
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C & = & %{{ exo.frac4() %}}
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\end{eqnarray*}
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\end{Exo}
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\begin{Exo}[2]
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Évaluer les expressions suivantes:
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\begin{eqnarray*}
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%{{ exo.exp1(letter = "A")%}} \\
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%{{ exo.exp2(letter = "B") %}}
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\end{eqnarray*}
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\end{Exo}
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\begin{Exo}[2]
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Simplifier les expressions suivantes
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%\begin{eqnarray*}
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% I & = &
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% J & = &
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%\end{eqnarray*}
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\end{Exo}
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%\begin{Exo}[bonus]
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%
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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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BIN
4e/DS/4eD/12_litt_frac_triCerc/12_litt_frac_triCerc_1.pdf
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4e/DS/4eD/12_litt_frac_triCerc/12_litt_frac_triCerc_1.pdf
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4e/DS/4eD/12_litt_frac_triCerc/12_litt_frac_triCerc_1.tex
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4e/DS/4eD/12_litt_frac_triCerc/12_litt_frac_triCerc_1.tex
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\documentclass[a4paper,12pt]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classDS}
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\usepackage{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/2013_2014}
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||||
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||||
% Title Page
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\titre{4}
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||||
% \quatreC \quatreD \troisB \troisPro
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||||
\classe{\quatreD}
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||||
\date{18 décembre 2013}
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||||
\duree{1 heure}
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\sujet{1}
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% DS DSCorr DM DMCorr Corr
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\typedoc{DS}
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\begin{document}
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\maketitle
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Le barème est donné à titre indicatif, il pourra être modifié.
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\begin{Exo}[6]
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% Copié de http://euler.ac-versailles.fr/eulerwikis/attach/Yann_Bourit/tri_rect_cercles_%E9quations_a.pdf
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$[AB]$ est un segment de 10cm. $C$ un point du segment $[AB]$ tel que $AC =$ 6cm. $\mathcal{C}_1$ est le cercle de diamètre $[AC]$ et $\mathcal{C}_2$ est le cercle de diamètre $[CB]$.
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\begin{enumerate}
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\item Tracer la figure.
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\item Placer $D$ un point du cercle $\mathcal{C}_1$ different de $A$ et $C$. Puis placer le point $E$, le point d'intersection entre le cercle $\mathcal{C}_2$ et $(CD)$.
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\item Quelle est la nature du triangle $ADC$?
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\item Quelle est la nature du triangle $BEC$?
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\item Démontrer que $(AC)$ et $(EB)$ sont parallèles.
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\end{enumerate}
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\end{Exo}
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\begin{Exo}[6]
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\begin{minipage}[h]{0.4\textwidth}
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\includegraphics[scale=0.2]{./fig/rectangle.pdf}
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\end{minipage}
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\begin{minipage}[h]{0.6\textwidth}
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\begin{enumerate}
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\item Exprimer $AD$ en fonction de $x$.
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\item Expliquer pourquoi l'aire du rectangle $ABCD$ est égale à $15x$.
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\item Expliquer pourquoi le périmètre du rectangle $ABCD$ est égale à $6x + 10$.
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\item Si $x = 2$, quelle est l'aire du rectangle $ABCD$?
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\item Si $x = 1,5$, quel est le périmètre du rectangle $ABCD$?
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\end{enumerate}
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\end{minipage}
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\end{Exo}
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\begin{Exo}[3]
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Simplifier les fractions suivantes:
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\begin{eqnarray*}
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A & = & -\frac{3}{10}-\frac{7}{10} \\
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B & = & \frac{2}{5}-\frac{-4}{3} \\
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C & = & 1-\frac{-1}{7}
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\end{eqnarray*}
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\end{Exo}
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\begin{Exo}[2]
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Évaluer les expressions suivantes:
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\begin{eqnarray*}
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A = 5x + 3 & \mbox{avec} & x = 1 \\
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B = -3x(-2x + 4) & \mbox{avec} & x = 3
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\end{eqnarray*}
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\end{Exo}
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\begin{Exo}[2]
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Simplifier les expressions suivantes
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\begin{eqnarray*}
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I & = & 4x \times (-2) \times 5\\
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J & = & 3x + 4 - 2x - 8 + 5x
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\end{eqnarray*}
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\end{Exo}
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%\begin{Exo}[bonus]
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%
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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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BIN
4e/DS/4eD/12_litt_frac_triCerc/12_litt_frac_triCerc_1_.pdf
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BIN
4e/DS/4eD/12_litt_frac_triCerc/12_litt_frac_triCerc_1_.pdf
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4e/DS/4eD/12_litt_frac_triCerc/12_litt_frac_triCerc_1_.tex
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4e/DS/4eD/12_litt_frac_triCerc/12_litt_frac_triCerc_1_.tex
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\documentclass[a4paper,12pt]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classDS}
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\usepackage{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/2013_2014}
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||||
|
||||
% Title Page
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||||
\titre{4}
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||||
% \quatreC \quatreD \troisB \troisPro
|
||||
\classe{\quatreD}
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||||
\date{18 décembre 2013}
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||||
\duree{1 heure}
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||||
\sujet{1}
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||||
% DS DSCorr DM DMCorr Corr
|
||||
\typedoc{DS}
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||||
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||||
\begin{document}
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\maketitle
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Le barème est donné à titre indicatif, il pourra être modifié.
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||||
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||||
\begin{Exo}[6]
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% Copié de http://euler.ac-versailles.fr/eulerwikis/attach/Yann_Bourit/tri_rect_cercles_%E9quations_a.pdf
|
||||
$[AB]$ est un segment de 10cm. $C$ un point du segment $[AB]$ tel que $AC =$ 6cm. $\mathcal{C}_1$ est le cercle de diamètre $[AC]$ et $\mathcal{C}_2$ est le cercle de diamètre $[CB]$.
|
||||
\begin{enumerate}
|
||||
\item Tracer la figure.
|
||||
\item Placer $D$ un point du cercle $\mathcal{C}_1$ different de $A$ et $C$. Puis placer le point $E$, le point d'intersection entre le cercle $\mathcal{C}_2$ et $(CD)$.
|
||||
\item Quelle est la nature du triangle $ADC$?
|
||||
\item Quelle est la nature du triangle $BEC$?
|
||||
\item Démontrer que $(AC)$ et $(EB)$ sont parallèles.
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}[6]
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||||
\begin{minipage}[h]{0.4\textwidth}
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||||
\includegraphics[scale=0.2]{./fig/rectangle.pdf}
|
||||
\end{minipage}
|
||||
\begin{minipage}[h]{0.6\textwidth}
|
||||
\begin{enumerate}
|
||||
\item Exprimer $AD$ en fonction de $x$.
|
||||
\item Expliquer pourquoi l'aire du rectangle $ABCD$ est égale à $15x$.
|
||||
\item Expliquer pourquoi le périmètre du rectangle $ABCD$ est égale à $6x + 10$.
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||||
\item Si $x = 2$, quelle est l'aire du rectangle $ABCD$?
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||||
\item Si $x = 1,5$, quel est le périmètre du rectangle $ABCD$?
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||||
\end{enumerate}
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||||
\end{minipage}
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||||
\end{Exo}
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||||
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\begin{Exo}[3]
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Simplifier, sans utiliser de nombres à virgule, les fractions suivantes:
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||||
\begin{eqnarray*}
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A & = & -\frac{3}{10}-\frac{7}{10} \\
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B & = & \frac{2}{5}-\frac{-4}{3} \\
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C & = & 1-\frac{-1}{7}
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\end{eqnarray*}
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\end{Exo}
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\begin{Exo}[2]
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Évaluer les expressions suivantes:
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\begin{eqnarray*}
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A = 5x + 3 & \mbox{avec} & x = -1 \\
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B = -3x(-2x + 4) & \mbox{avec} & x = 3
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\end{eqnarray*}
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\end{Exo}
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\begin{Exo}[2]
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Simplifier les expressions suivantes
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\begin{eqnarray*}
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I & = & 4x \times (-2) \times 5\\
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J & = & 3x + 4 - 2x - 8 + 5x
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\end{eqnarray*}
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\end{Exo}
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\clearpage
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\begin{Exo}
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\exo{Bonus}
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On crée des motifs de la façon suivante:
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\begin{center}
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\includegraphics[scale=0.4]{./fig/carre.pdf}
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\end{center}
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\begin{enumerate}
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\item Dessiner le motif 5. Combien y a-t-il de petits carrés?
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\item Combien de petits carrés y a-t-il dans le motif $n$?
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\item Combien de petits carrés y a-t-il dans le motif 10 000?
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\end{enumerate}
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\end{Exo}
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\section*{Table de multiplication}
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\begin{center}
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\begin{tabular}{|c||c|c|c|c|c|c|c|c|c|c|}
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\hline
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Multiplié par & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
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\hline
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\hline
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1 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
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\hline
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2 & 2 & 4 & 6 & 8 & 10 & 12 & 14 & 16 & 18 & 20 \\
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\hline
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3 & 3 & 6 & 9 & 12 & 15 & 18 & 21 & 24 & 27 & 30 \\
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\hline
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4 & 4 & 8 & 12 & 16 & 20 & 24 & 28 & 32 & 36 & 40 \\
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\hline
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5 & 5 & 10 & 15 & 20 & 25 & 30 & 35 & 40 & 45 & 50 \\
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\hline
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6 & 6 & 12 & 18 & 24 & 30 & 36 & 42 & 48 & 54 & 60 \\
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\hline
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7 & 7 & 14 & 21 & 28 & 35 & 42 & 49 & 56 & 63 & 70 \\
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\hline
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8 & 8 & 16 & 24 & 32 & 40 & 48 & 56 & 64 & 72 & 80 \\
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\hline
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9 & 9 & 18 & 27 & 36 & 45 & 54 & 63 & 72 & 81 & 90 \\
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\hline
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10 & 10 & 20 & 30 & 40 & 50 & 60 & 70 & 80 & 90 & 100 \\
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\hline
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\end{tabular}
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\end{center}
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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
4e/DS/4eD/12_litt_frac_triCerc/12_litt_frac_triCerc_2.pdf
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BIN
4e/DS/4eD/12_litt_frac_triCerc/12_litt_frac_triCerc_2.pdf
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Binary file not shown.
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4e/DS/4eD/12_litt_frac_triCerc/12_litt_frac_triCerc_2.tex
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4e/DS/4eD/12_litt_frac_triCerc/12_litt_frac_triCerc_2.tex
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@@ -0,0 +1,115 @@
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\documentclass[a4paper,10pt]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classDS}
|
||||
\usepackage{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/2013_2014}
|
||||
|
||||
% Title Page
|
||||
\titre{4}
|
||||
% \quatreC \quatreD \troisB \troisPro
|
||||
\classe{\quatreD}
|
||||
\date{18 décembre 2013}
|
||||
\duree{1 heure}
|
||||
\sujet{2}
|
||||
% DS DSCorr DM DMCorr Corr
|
||||
\typedoc{DS}
|
||||
|
||||
\begin{document}
|
||||
\maketitle
|
||||
|
||||
Le barème est donné à titre indicatif, il pourra être modifié.
|
||||
|
||||
\begin{Exo}[6]
|
||||
% Copié de http://euler.ac-versailles.fr/eulerwikis/attach/Yann_Bourit/tri_rect_cercles_%E9quations_a.pdf
|
||||
$[AB]$ est un segment de $10cm$. $C$ un point du segment $[AB]$ tel que $AC = 6cm$. $\mathcal{C}1$ est le cercle de diamètre $[AC]$ et $\mathcal{C}2$ est le cercle de diamètre $[CB]$.
|
||||
\begin{enumerate}
|
||||
\item Tracer la figure.
|
||||
\item Placer $D$ un point du cercle $\mathcal{C}1$ different de $A$ et $C$. Puis placer le point $E$, le point d'intersection entre le cercle $\mathcal{C}2$ et $(CD)$.
|
||||
\item Quelle est la nature du triangle $ADC$?
|
||||
\item Quelle est la nature du triangle $BEC$?
|
||||
\item Démontrer que $(AC)$ et $(EB)$ sont parallèles.
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}[6]
|
||||
\begin{minipage}[h]{0.4\textwidth}
|
||||
\includegraphics[scale=0.2]{./fig/rectangle.pdf}
|
||||
\end{minipage}
|
||||
\begin{minipage}[h]{0.6\textwidth}
|
||||
\begin{enumerate}
|
||||
\item Exprimer $AD$ en fonction de $x$.
|
||||
\item Expliquer pourquoi l'aire du rectangle $ABCD$ est égale à $15x$.
|
||||
\item Expliquer pourquoi le périmètre du rectangle $ABCD$ est égale à $6x + 10$.
|
||||
\item Si $x = 3$, quelle est l'aire du rectangle $ABCD$?
|
||||
\item Si $x = 0,5$, quel est le périmètre du rectangle $ABCD$?
|
||||
\end{enumerate}
|
||||
\end{minipage}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}[3]
|
||||
Simplifier les fractions suivantes:
|
||||
\begin{eqnarray*}
|
||||
A & = & -\frac{19}{9}+\frac{-14}{9} \\
|
||||
B & = & -\frac{-19}{4}-\frac{-17}{6} \\
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||||
C & = & -5+\frac{17}{10}
|
||||
\end{eqnarray*}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}[2]
|
||||
Évaluer les expressions suivantes:
|
||||
\begin{eqnarray*}
|
||||
A = 2x + 7 & \mbox{avec} & x = -9 \\
|
||||
B = 10x(2x + 1) & \mbox{avec} & x = 2
|
||||
\end{eqnarray*}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}[2]
|
||||
Simplifier les expressions suivantes
|
||||
\begin{eqnarray*}
|
||||
I & = & (-3) \times 2x \times (-5) \\
|
||||
J & = & 5 + 6x - 2x - 2x - 9
|
||||
\end{eqnarray*}
|
||||
\end{Exo}
|
||||
|
||||
%\begin{Exo}[bonus]
|
||||
%
|
||||
%\end{Exo}
|
||||
|
||||
\section*{Table de multiplication}
|
||||
|
||||
\begin{center}
|
||||
|
||||
\begin{tabular}{|c||c|c|c|c|c|c|c|c|c|c|}
|
||||
|
||||
\hline
|
||||
Multiplié par & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
|
||||
\hline
|
||||
\hline
|
||||
1 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
|
||||
\hline
|
||||
2 & 2 & 4 & 6 & 8 & 10 & 12 & 14 & 16 & 18 & 20 \\
|
||||
\hline
|
||||
3 & 3 & 6 & 9 & 12 & 15 & 18 & 21 & 24 & 27 & 30 \\
|
||||
\hline
|
||||
4 & 4 & 8 & 12 & 16 & 20 & 24 & 28 & 32 & 36 & 40 \\
|
||||
\hline
|
||||
5 & 5 & 10 & 15 & 20 & 25 & 30 & 35 & 40 & 45 & 50 \\
|
||||
\hline
|
||||
6 & 6 & 12 & 18 & 24 & 30 & 36 & 42 & 48 & 54 & 60 \\
|
||||
\hline
|
||||
7 & 7 & 14 & 21 & 28 & 35 & 42 & 49 & 56 & 63 & 70 \\
|
||||
\hline
|
||||
8 & 8 & 16 & 24 & 32 & 40 & 48 & 56 & 64 & 72 & 80 \\
|
||||
\hline
|
||||
9 & 9 & 18 & 27 & 36 & 45 & 54 & 63 & 72 & 81 & 90 \\
|
||||
\hline
|
||||
10 & 10 & 20 & 30 & 40 & 50 & 60 & 70 & 80 & 90 & 100 \\
|
||||
\hline
|
||||
|
||||
\end{tabular}
|
||||
|
||||
\end{center}
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
BIN
4e/DS/4eD/12_litt_frac_triCerc/12_litt_frac_triCerc_2_.pdf
Normal file
BIN
4e/DS/4eD/12_litt_frac_triCerc/12_litt_frac_triCerc_2_.pdf
Normal file
Binary file not shown.
126
4e/DS/4eD/12_litt_frac_triCerc/12_litt_frac_triCerc_2_.tex
Normal file
126
4e/DS/4eD/12_litt_frac_triCerc/12_litt_frac_triCerc_2_.tex
Normal file
@@ -0,0 +1,126 @@
|
||||
\documentclass[a4paper,10pt]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classDS}
|
||||
\usepackage{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/2013_2014}
|
||||
|
||||
% Title Page
|
||||
\titre{4}
|
||||
% \quatreC \quatreD \troisB \troisPro
|
||||
\classe{\quatreD}
|
||||
\date{18 décembre 2013}
|
||||
\duree{1 heure}
|
||||
\sujet{2}
|
||||
% DS DSCorr DM DMCorr Corr
|
||||
\typedoc{DS}
|
||||
|
||||
\begin{document}
|
||||
\maketitle
|
||||
|
||||
Le barème est donné à titre indicatif, il pourra être modifié.
|
||||
|
||||
\begin{Exo}[6]
|
||||
% Copié de http://euler.ac-versailles.fr/eulerwikis/attach/Yann_Bourit/tri_rect_cercles_%E9quations_a.pdf
|
||||
$[AB]$ est un segment de $10cm$. $C$ un point du segment $[AB]$ tel que $AC = 6cm$. $\mathcal{C}_1$ est le cercle de diamètre $[AC]$ et $\mathcal{C}_2$ est le cercle de diamètre $[CB]$.
|
||||
\begin{enumerate}
|
||||
\item Tracer la figure.
|
||||
\item Placer $D$ un point du cercle $\mathcal{C}_1$ different de $A$ et $C$. Puis placer le point $E$, le point d'intersection entre le cercle $\mathcal{C}_2$ et $(CD)$.
|
||||
\item Quelle est la nature du triangle $ADC$?
|
||||
\item Quelle est la nature du triangle $BEC$?
|
||||
\item Démontrer que $(AC)$ et $(EB)$ sont parallèles.
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}[6]
|
||||
\begin{minipage}[h]{0.4\textwidth}
|
||||
\includegraphics[scale=0.2]{./fig/rectangle.pdf}
|
||||
\end{minipage}
|
||||
\begin{minipage}[h]{0.6\textwidth}
|
||||
\begin{enumerate}
|
||||
\item Exprimer $AD$ en fonction de $x$.
|
||||
\item Expliquer pourquoi l'aire du rectangle $ABCD$ est égale à $15x$.
|
||||
\item Expliquer pourquoi le périmètre du rectangle $ABCD$ est égale à $6x + 10$.
|
||||
\item Si $x = 3$, quelle est l'aire du rectangle $ABCD$?
|
||||
\item Si $x = 0,5$, quel est le périmètre du rectangle $ABCD$?
|
||||
\end{enumerate}
|
||||
\end{minipage}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}[3]
|
||||
Simplifier, sans utiliser de nombres à virgule, les fractions suivantes:
|
||||
\begin{eqnarray*}
|
||||
A & = & -\frac{19}{9}+\frac{-14}{9} \\
|
||||
B & = & -\frac{-19}{4}-\frac{-17}{6} \\
|
||||
C & = & -5+\frac{17}{10}
|
||||
\end{eqnarray*}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}[2]
|
||||
Évaluer les expressions suivantes:
|
||||
\begin{eqnarray*}
|
||||
A = 2x + 7 & \mbox{avec} & x = -9 \\
|
||||
B = 10x(2x + 1) & \mbox{avec} & x = -2
|
||||
\end{eqnarray*}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}[2]
|
||||
Simplifier les expressions suivantes
|
||||
\begin{eqnarray*}
|
||||
I & = & (-3) \times 2x \times (-5) \\
|
||||
J & = & 5 + 6x - 2x - 2x - 9
|
||||
\end{eqnarray*}
|
||||
\end{Exo}
|
||||
|
||||
|
||||
\clearpage
|
||||
\begin{Exo}
|
||||
\exo{Bonus}
|
||||
On crée des motifs de la façon suivante:
|
||||
\begin{center}
|
||||
\includegraphics[scale=0.4]{./fig/carre.pdf}
|
||||
\end{center}
|
||||
\begin{enumerate}
|
||||
\item Dessiner le motif 5. Combien y a-t-il de petits carrés?
|
||||
\item Combien de petits carrés y a-t-il dans le motif $n$?
|
||||
\item Combien de petits carrés y a-t-il dans le motif 10 000?
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
\section*{Table de multiplication}
|
||||
|
||||
\begin{center}
|
||||
|
||||
\begin{tabular}{|c||c|c|c|c|c|c|c|c|c|c|}
|
||||
|
||||
\hline
|
||||
Multiplié par & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
|
||||
\hline
|
||||
\hline
|
||||
1 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
|
||||
\hline
|
||||
2 & 2 & 4 & 6 & 8 & 10 & 12 & 14 & 16 & 18 & 20 \\
|
||||
\hline
|
||||
3 & 3 & 6 & 9 & 12 & 15 & 18 & 21 & 24 & 27 & 30 \\
|
||||
\hline
|
||||
4 & 4 & 8 & 12 & 16 & 20 & 24 & 28 & 32 & 36 & 40 \\
|
||||
\hline
|
||||
5 & 5 & 10 & 15 & 20 & 25 & 30 & 35 & 40 & 45 & 50 \\
|
||||
\hline
|
||||
6 & 6 & 12 & 18 & 24 & 30 & 36 & 42 & 48 & 54 & 60 \\
|
||||
\hline
|
||||
7 & 7 & 14 & 21 & 28 & 35 & 42 & 49 & 56 & 63 & 70 \\
|
||||
\hline
|
||||
8 & 8 & 16 & 24 & 32 & 40 & 48 & 56 & 64 & 72 & 80 \\
|
||||
\hline
|
||||
9 & 9 & 18 & 27 & 36 & 45 & 54 & 63 & 72 & 81 & 90 \\
|
||||
\hline
|
||||
10 & 10 & 20 & 30 & 40 & 50 & 60 & 70 & 80 & 90 & 100 \\
|
||||
\hline
|
||||
|
||||
\end{tabular}
|
||||
|
||||
\end{center}
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
219
4e/DS/4eD/12_litt_frac_triCerc/add_frac.py
Normal file
219
4e/DS/4eD/12_litt_frac_triCerc/add_frac.py
Normal file
@@ -0,0 +1,219 @@
|
||||
#!/usr/bin/env python
|
||||
# encoding: utf-8
|
||||
|
||||
from random import randint, random
|
||||
|
||||
|
||||
|
||||
"""Classe which generate randomly fractions sums
|
||||
|
||||
Types of sums
|
||||
|
||||
1 -> b / a + c / a
|
||||
2 -> b / a + c / ka
|
||||
3 -> b / a + e / d
|
||||
4 -> f + b / a or b / a + f
|
||||
|
||||
where:
|
||||
a integer > 2
|
||||
b integer different from 0 (could be coprime with a)
|
||||
c integer different from 0 (could be coprime with a or ka)
|
||||
e integer different from 0 (could be coprime with d)
|
||||
d integer > 2 ( a not divisible by d and d not divisible by a)
|
||||
k integer > 2
|
||||
f integer different from 0
|
||||
|
||||
Signs can be mod
|
||||
|
||||
|
||||
"""
|
||||
|
||||
def a(min_ = 2, max_ = 10):
|
||||
"""Generate randomly a
|
||||
|
||||
:param min_: minimum value for a
|
||||
:param max_: maximum value for a
|
||||
:returns: a value
|
||||
|
||||
"""
|
||||
return randint(min_, max_)
|
||||
|
||||
def k(min_ = 2, max_ = 5):
|
||||
"""Generate randomly k
|
||||
|
||||
:param min_: minimum value for k
|
||||
:param max_: maximum value for k
|
||||
:returns: k value
|
||||
|
||||
"""
|
||||
return randint(min_, max_)
|
||||
|
||||
def b(a_ = 0, min_ = -20, max_ = 20):
|
||||
"""Generate randomly b
|
||||
|
||||
:param a: the value of a if b has to be coprime with a (default 0 which means not necessarily coprime)
|
||||
:param min_: minimum value for b (default -20)
|
||||
:param max_: maximum value for b (default 20)
|
||||
:returns: b value
|
||||
|
||||
"""
|
||||
b_ = 0
|
||||
while b_ == 0 or not coprime:
|
||||
b_ = randint(min_, max_)
|
||||
if a_ == 0:
|
||||
coprime = 1
|
||||
elif b_ != 0:
|
||||
gcd_ = gcd(abs(a_),abs(b_))
|
||||
coprime = (gcd_ == 1)
|
||||
|
||||
return b_
|
||||
|
||||
def c(a_ = 0, k_ = 1, min_ = -20, max_ = 20):
|
||||
"""Generate randomly c
|
||||
|
||||
:param a: the value of a if c has to be coprime with a (default 0 which means not necessarily coprime)
|
||||
:param k: the value of a if c has to be coprime with ak (default 0 which means not necessarily coprime)
|
||||
:param min_: minimum value for c (default -20)
|
||||
:param max_: maximum value for c (default 20)
|
||||
:returns: c value
|
||||
|
||||
"""
|
||||
return b(a_ = a_*k_, min_ = min_, max_ = max_)
|
||||
|
||||
def e(d_ = 0, min_ = -20, max_ = 20):
|
||||
"""Generate randomly e
|
||||
|
||||
:param d: the value of a if e has to be coprime with a (default 0 which means not necessarily coprime)
|
||||
:param min_: minimum value for e (default -20)
|
||||
:param max_: maximum value for e (default 20)
|
||||
:returns: e value
|
||||
|
||||
"""
|
||||
return b(a_ = d_, min_ = min_, max_ = max_)
|
||||
|
||||
def d(a_, min_ = 2, max_ = 10):
|
||||
"""Generate randomly d
|
||||
|
||||
:param a: the value of a
|
||||
:param min_: minimum value for d
|
||||
:param max_: maximum value for d
|
||||
:returns: d value
|
||||
|
||||
"""
|
||||
d_ = randint(min_, max_)
|
||||
div = (not a_ % d_) or (not d_ % a_)
|
||||
while div:
|
||||
d_ = randint(min_, max_)
|
||||
div = (not a_ % d_) or (not d_ % a_)
|
||||
|
||||
return d_
|
||||
|
||||
def f(min_ = -10, max_ = 10):
|
||||
"""Generate randomly f
|
||||
|
||||
:param min_: minimum value for f
|
||||
:param max_: maximum value for f
|
||||
:returns: f value
|
||||
|
||||
"""
|
||||
f_ = randint(min_, max_)
|
||||
while f_ == 0:
|
||||
f_ = randint(min_, max_)
|
||||
|
||||
return f_
|
||||
|
||||
def plusOrMinus(p = 0.5):
|
||||
"""Return plus with prob p and minus otherwise
|
||||
"""
|
||||
pm = random()
|
||||
return "+"*(pm >= p) + "-"*(pm < p)
|
||||
|
||||
def nothingOrMinus(p = 0.5):
|
||||
"""Return nothing with prob p and minus otherwise
|
||||
"""
|
||||
pm = random()
|
||||
return ""*(pm >= p) + "-"*(pm < p)
|
||||
|
||||
def type1():
|
||||
"""@todo: Docstring for type1
|
||||
:returns: @todo
|
||||
|
||||
"""
|
||||
a_ = a()
|
||||
b_ = b(a_=a_)
|
||||
c_ = c(a_=a_)
|
||||
|
||||
return nothingOrMinus() + "\\frac{" + str(b_) + "}{" + str(a_) + "}" + plusOrMinus() + "\\frac{" + str(c_) + "}{" + str(a_) + "}"
|
||||
|
||||
def type2():
|
||||
"""@todo: Docstring for type2
|
||||
:returns: @todo
|
||||
|
||||
"""
|
||||
a_ = a()
|
||||
b_ = b(a_=a_)
|
||||
k_ = k()
|
||||
c_ = c(a_=a_, k_ = k_)
|
||||
|
||||
return nothingOrMinus() + "\\frac{" + str(b_) + "}{" + str(a_) + "}" + plusOrMinus() + "\\frac{" + str(c_) + "}{" + str(k_*a_) + "}"
|
||||
|
||||
def type3():
|
||||
"""@todo: Docstring for type3
|
||||
:returns: @todo
|
||||
|
||||
"""
|
||||
a_ = a()
|
||||
b_ = b(a_=a_)
|
||||
c_ = c(a_=a_)
|
||||
d_ = d(a_)
|
||||
|
||||
return nothingOrMinus() + "\\frac{" + str(b_) + "}{" + str(a_) + "}" + plusOrMinus() + "\\frac{" + str(c_) + "}{" + str(d_) + "}"
|
||||
|
||||
def type4():
|
||||
"""@todo: Docstring for type4
|
||||
:returns: @todo
|
||||
|
||||
"""
|
||||
a_ = a()
|
||||
b_ = b(a_=a_)
|
||||
f_ = f()
|
||||
|
||||
return str(f_) + plusOrMinus() + "\\frac{" + str(b_) + "}{" + str(a_) + "}"
|
||||
|
||||
def gcd(a_, b_):
|
||||
"""Compute gcd(a,b)
|
||||
|
||||
:param a: first number
|
||||
:param b: second number
|
||||
:returns: the gcd
|
||||
|
||||
"""
|
||||
if a_ > b_:
|
||||
c_ = a_ % b_
|
||||
else:
|
||||
c_ = b_ % a_
|
||||
|
||||
if c_ == 0:
|
||||
return min(a_,b_)
|
||||
elif a_ == 1:
|
||||
return b_
|
||||
elif b_ == 1:
|
||||
return a_
|
||||
else:
|
||||
return gcd(min(a_,b_), c_)
|
||||
|
||||
if __name__ == '__main__':
|
||||
# print(a())
|
||||
# print(b())
|
||||
# print(c())
|
||||
# print(d(3))
|
||||
# print(e())
|
||||
# print(f())
|
||||
print(type1())
|
||||
print(type2())
|
||||
print(type3())
|
||||
print(type4())
|
||||
|
||||
# Reglages pour 'vim'
|
||||
# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
|
||||
# cursor: 16 del
|
||||
163
4e/DS/4eD/12_litt_frac_triCerc/call_litt.py
Normal file
163
4e/DS/4eD/12_litt_frac_triCerc/call_litt.py
Normal file
@@ -0,0 +1,163 @@
|
||||
#!/usr/bin/env python
|
||||
# encoding: utf-8
|
||||
|
||||
from random import randint, uniform
|
||||
from math import sqrt
|
||||
from jinja2 import Template
|
||||
|
||||
"""
|
||||
Generate expression for litteral calculous
|
||||
|
||||
3 types of expression (a, b, c != 0, 1)
|
||||
1 -> ax + b and eval for x != -b / a
|
||||
2 -> ax(bx + c) and eval for x != 0 and x != -c / b
|
||||
3 -> ax^2 + b and eval for x != +-sqrt(b/a) (if a and b have same sign)
|
||||
"""
|
||||
|
||||
def gene_type1(min_ = -10, max_ = 10):
|
||||
"""@todo: Docstring for gene_type1
|
||||
|
||||
:param min_: @todo
|
||||
:param max_: @todo
|
||||
:returns: @todo
|
||||
|
||||
"""
|
||||
a, b = 0, 0
|
||||
while (b in [0]) or (a in [0, 1]):
|
||||
a = randint(min_, max_)
|
||||
b = randint(1, max_)
|
||||
|
||||
return "{}x + {}".format(a,b), [-b/a]
|
||||
|
||||
def gene_type2(min_, max_):
|
||||
"""@todo: Docstring for gene_type2
|
||||
|
||||
:param min_: @todo
|
||||
:param max_: @todo
|
||||
:returns: @todo
|
||||
|
||||
"""
|
||||
a, b, c = 0, 0, 0
|
||||
while (a in [0, 1]) or (b in [0, 1]) or c in [0]:
|
||||
a = randint(min_, max_)
|
||||
b = randint(min_, max_)
|
||||
c = randint(1, max_)
|
||||
|
||||
return "{}x({}x + {})".format(a,b,c), [0, -c/b]
|
||||
|
||||
def gene_type3(min_ = -10, max_ = 10):
|
||||
"""@todo: Docstring for gene_type3
|
||||
|
||||
:param min_: @todo
|
||||
:param max_: @todo
|
||||
:returns: @todo
|
||||
|
||||
"""
|
||||
a, b = 0, 0
|
||||
while (b in [0]) or (a in [0, 1]):
|
||||
a = randint(min_, max_)
|
||||
b = randint(1, max_)
|
||||
|
||||
if a*(-b) > 0:
|
||||
VI = [-sqrt(-b/a), sqrt(-b/a)]
|
||||
else:
|
||||
VI = []
|
||||
|
||||
return "{}x^2 + {}".format(a,b), VI
|
||||
|
||||
def get_goodX(VI, approx = 0, min_ = -10, max_ = 10):
|
||||
"""@todo: Docstring for get_goodX
|
||||
|
||||
:param VI: @todo
|
||||
:returns: @todo
|
||||
|
||||
"""
|
||||
x = uniform(min_, max_)
|
||||
if approx == 0:
|
||||
x = int(x)
|
||||
else:
|
||||
x = round(x,approx)
|
||||
while x in VI:
|
||||
x = uniform(min_, max_)
|
||||
if approx == 0:
|
||||
x = int(x)
|
||||
else:
|
||||
x = round(x,approx)
|
||||
|
||||
return x
|
||||
|
||||
|
||||
|
||||
def fullExo(min_ = -10 , max_ = 10):
|
||||
"""Generate the whole exo
|
||||
|
||||
:param min_: @todo
|
||||
:param max_: @todo
|
||||
:returns: @todo
|
||||
|
||||
"""
|
||||
template = Template("""
|
||||
\\begin{equation*}
|
||||
A = {{type1}} \\qquad B = {{type2}} \\qquad C = {{type3}}
|
||||
\\end{equation*}
|
||||
|
||||
Évaluer $A$, $B$ et $C$ pour $x = {{x1}}$ puis $x = {{x2}}$""")
|
||||
|
||||
type1, VI1 = gene_type1(min_, max_)
|
||||
type2, VI2 = gene_type2(min_, max_)
|
||||
type3, VI3 = gene_type3(min_, max_)
|
||||
|
||||
VI = VI1 + VI2 + VI3
|
||||
|
||||
x1, x2 = get_goodX(VI), get_goodX(VI, approx = 1)
|
||||
|
||||
info = {"type1": type1, "type2": type2, "type3": type3, "x1":x1, "x2":x2}
|
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|
||||
exo = template.render(**info)
|
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|
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return exo
|
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|
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def exp1(min_ = -10, max_ = 10, letter = "A"):
|
||||
"""@todo: Docstring for exp1
|
||||
|
||||
:param min: @todo
|
||||
:param max: @todo
|
||||
:returns: @todo
|
||||
|
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"""
|
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exp, VI = gene_type1(min_,max_)
|
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x = get_goodX(VI)
|
||||
|
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tpl = Template("{{A}} = {{exp}} & \\mbox{avec} & x = {{x}}")
|
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|
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return tpl.render(A = letter, exp = exp, x = x)
|
||||
|
||||
def exp2(min_ = -10, max_ = 10, letter = "A"):
|
||||
"""@todo: Docstring for exp1
|
||||
|
||||
:param min: @todo
|
||||
:param max: @todo
|
||||
:returns: @todo
|
||||
|
||||
"""
|
||||
exp, VI = gene_type2(min_,max_)
|
||||
x = get_goodX(VI)
|
||||
|
||||
tpl = Template("{{A}} = {{exp}} & \\mbox{avec} & x = {{x}}")
|
||||
|
||||
return tpl.render(A = letter, exp = exp, x = x)
|
||||
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
print(fullExo())
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
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# -----------------------------
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# Reglages pour 'vim'
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# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
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# cursor: 16 del
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41
4e/DS/4eD/12_litt_frac_triCerc/index.rst
Normal file
41
4e/DS/4eD/12_litt_frac_triCerc/index.rst
Normal file
@@ -0,0 +1,41 @@
|
||||
Notes sur 12 litt frac triCerc
|
||||
##############################
|
||||
|
||||
:date: 2014-07-01
|
||||
:modified: 2014-07-01
|
||||
:tags: DS
|
||||
:category: 4e
|
||||
:authors: Benjamin Bertrand
|
||||
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
|
||||
|
||||
|
||||
|
||||
`Lien vers 12_litt_frac_triCerc_2_.pdf <12_litt_frac_triCerc_2_.pdf>`_
|
||||
|
||||
`Lien vers 12_litt_frac_triCerc.pdf <12_litt_frac_triCerc.pdf>`_
|
||||
|
||||
`Lien vers 12_litt_frac_triCerc_1.pdf <12_litt_frac_triCerc_1.pdf>`_
|
||||
|
||||
`Lien vers 12_litt_frac_triCerc_1.tex <12_litt_frac_triCerc_1.tex>`_
|
||||
|
||||
`Lien vers 12_litt_frac_triCerc_2.tex <12_litt_frac_triCerc_2.tex>`_
|
||||
|
||||
`Lien vers 12_litt_frac_triCerc_1_.tex <12_litt_frac_triCerc_1_.tex>`_
|
||||
|
||||
`Lien vers number_rotation.py <number_rotation.py>`_
|
||||
|
||||
`Lien vers 12_litt_frac_triCerc_2_.tex <12_litt_frac_triCerc_2_.tex>`_
|
||||
|
||||
`Lien vers 12_litt_frac_triCerc.tex <12_litt_frac_triCerc.tex>`_
|
||||
|
||||
`Lien vers call_litt.py <call_litt.py>`_
|
||||
|
||||
`Lien vers 12_litt_frac_triCerc_2.pdf <12_litt_frac_triCerc_2.pdf>`_
|
||||
|
||||
`Lien vers 12_litt_frac_triCerc_1_.pdf <12_litt_frac_triCerc_1_.pdf>`_
|
||||
|
||||
`Lien vers add_frac.py <add_frac.py>`_
|
||||
|
||||
`Lien vers fig/rectangle.pdf <fig/rectangle.pdf>`_
|
||||
|
||||
`Lien vers fig/carre.pdf <fig/carre.pdf>`_
|
||||
90
4e/DS/4eD/12_litt_frac_triCerc/number_rotation.py
Executable file
90
4e/DS/4eD/12_litt_frac_triCerc/number_rotation.py
Executable file
@@ -0,0 +1,90 @@
|
||||
#!/usr/bin/env python
|
||||
# encoding: utf-8
|
||||
|
||||
import jinja2, random, os
|
||||
import sys
|
||||
import optparse
|
||||
|
||||
def randfloat(approx = 1, low = 0, up = 10):
|
||||
""" return a random number between low and up with approx floating points """
|
||||
ans = random.random()
|
||||
ans = ans*(up - low) + low
|
||||
ans = round(ans, approx)
|
||||
return ans
|
||||
|
||||
random.randfloat = randfloat
|
||||
|
||||
def gaussRandomlist(mu = 0, sigma = 1, size = 10, manip = lambda x:x):
|
||||
""" return a list of a gaussian sample """
|
||||
ans = []
|
||||
for i in range(size):
|
||||
ans += [manip(random.gauss(mu,sigma))]
|
||||
return ans
|
||||
|
||||
random.gaussRandomlist = gaussRandomlist
|
||||
|
||||
def gaussRandomlist_strInt(mu = 0, sigma = 1, size = 10):
|
||||
return gaussRandomlist(mu, sigma, size, manip = lambda x: str(int(x)))
|
||||
|
||||
random.gaussRandomlist_strInt = gaussRandomlist_strInt
|
||||
|
||||
# ------------------
|
||||
# Spécial exo!
|
||||
|
||||
from add_frac import type1, type3, type4
|
||||
exo = {"frac1": type1, "frac3": type3, "frac4": type4}
|
||||
|
||||
from call_litt import exp1, exp2
|
||||
exo["exp1"] = exp1
|
||||
exo["exp2"] = exp2
|
||||
|
||||
|
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report_renderer = jinja2.Environment(
|
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block_start_string = '%{',
|
||||
block_end_string = '%}',
|
||||
variable_start_string = '%{{',
|
||||
variable_end_string = '%}}',
|
||||
loader = jinja2.FileSystemLoader(os.path.abspath('.'))
|
||||
)
|
||||
|
||||
def main(options):
|
||||
template = report_renderer.get_template(options.template)
|
||||
|
||||
if options.output:
|
||||
output_basename = options.output
|
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else:
|
||||
tpl_base = os.path.splitext(options.template)[0]
|
||||
output_basename = tpl_base + "_"
|
||||
|
||||
|
||||
for subj in range(options.num_subj):
|
||||
subj = subj+1
|
||||
dest = output_basename + str(subj) + '.tex'
|
||||
with open( dest, 'w') as f:
|
||||
f.write(template.render(random = random, infos = {"subj" : subj}, exo = exo))
|
||||
os.system("pdflatex " + dest)
|
||||
|
||||
if not options.dirty:
|
||||
os.system("rm *.aux *.log")
|
||||
|
||||
if __name__ == '__main__':
|
||||
|
||||
|
||||
parser = optparse.OptionParser()
|
||||
parser.add_option("-t","--tempalte",action="store",type="string",dest="template", help="File with template")
|
||||
parser.add_option("-o","--output",action="store",type="string",dest="output",help="Base name for output (without .tex or any extension))")
|
||||
parser.add_option("-n","--number_subjects", action="store",type="int", dest="num_subj", default = 2, help="The number of subjects to make")
|
||||
parser.add_option("-d","--dirty", action="store_true", dest="dirty", help="Do not clean after compilation")
|
||||
|
||||
(options, args) = parser.parse_args()
|
||||
|
||||
if not options.template:
|
||||
print("I need a template!")
|
||||
sys.exit(0)
|
||||
|
||||
main(options)
|
||||
|
||||
# -----------------------------
|
||||
# Reglages pour 'vim'
|
||||
# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
|
||||
# cursor: 16 del
|
||||
Reference in New Issue
Block a user