DS9 pour les 601

This commit is contained in:
Bertrand Benjamin 2018-04-11 17:04:16 +03:00
parent 27d3e4b659
commit 074d615b66
4 changed files with 570 additions and 3 deletions

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\title{DS 9}
\tribe{Sixième}
\date{11 avril 2018}
\date{13 avril 2018}
\sujet{1}
\RequirePackage{contour}
\newcommand{\clockATick}[2]{%
% colors
\colorlet{minutes color}{blue!50!cyan!70!black}
\colorlet{bg hours 0}{yellow}
\colorlet{bg hours 1}{red!50}
\colorlet{hours color}{red!80!black}
% styles
\tikzset{
minutes/.style={circle,inner sep=0,text width=5mm,align=center,font=\bfseries},
minutes 0/.style={fill=minutes color,text=white,minutes},
minutes 1/.style={text=minutes color,fill=white,minutes},
minutes font/.style={font=\normalsize},
hours/.style={font=\fontsize{60}{66}\selectfont\bfseries,text=hours color,align=center},
mini hours font/.style={font=\fontsize{40}{46}\selectfont\bfseries},
}
% radii
\def\bigradius{80mm}
\def\minuteradius{75mm}
\def\hourradius{60mm}
\def\minihourminradius{25mm}
\def\minihourmaxradius{45mm}
\pgfmathsetmacro\minihourradius{(\minihourmaxradius + \minihourminradius)*.5}
\def\hourwidth{2mm}
\def\minutewidth{1mm}
% big circle
\filldraw [fill=white,draw=minutes color] (0,0) circle (\bigradius);
% minutes marks
\foreach \angle[count=\c from 0,evaluate={\c as \hourmark using notequal(int(mod(\c,5)),0)}]
in {0,6,...,354}{ \path (-\angle:\minuteradius) node[minutes \hourmark]{\c}; }
% hours marks
\foreach \angle[count=\c from 1,evaluate={\c as \col using int(mod(\c,2))}] in {30,60,...,360}{
\path (-\angle:\hourradius) node[hours]{\c};
\path[fill=bg hours \col]
(-\angle:\minihourminradius) -- (-\angle:\minihourmaxradius)
arc(-\angle:-\angle-30:\minihourmaxradius) -- (-\angle-30:\minihourminradius)
arc(-\angle-30:-\angle:\minihourminradius) -- cycle;
\path (-\angle-15:\minihourradius pt) node[mini hours font]{\textcolor{white}{\contour{hours color}{\c}}};
}
% hands
\pgfmathsetmacro\hourangle{-#1*30-#2*.5}
\pgfmathsetmacro\minuteangle{-#2*6}
\fill[rotate=\hourangle,fill=hours color] ++(0,\hourwidth) arc(90:270:\hourwidth) -- ++(50mm,0)
-- ++(\hourwidth,\hourwidth) -- ++(-\hourwidth,\hourwidth) -- ++(-50mm,0) -- cycle ;
\fill[rotate=\minuteangle,fill=minutes color] ++(0,\minutewidth) arc(90:270:\minutewidth) -- ++(70mm,0)
-- ++(\minutewidth,\minutewidth) -- ++(-\minutewidth,\minutewidth) -- ++(-70mm,0) -- cycle ;
}
\newcommand{\clockBTick}[2]{%
\draw (0,0) circle (2cm);
\foreach \angle / \label in
{0/3, 30/2, 60/1, 90/12, 120/11, 150/10, 180/9,
210/8, 240/7, 270/6, 300/5, 330/4}
{
\draw (\angle:1.8cm) -- (\angle:2cm);
\draw (\angle:1.4cm) node{\textsf{\label}};
}
\foreach \angle[count=\c from 0] in {0,6,...,354}
{
\draw (\angle:1.9cm) -- (\angle:2cm);
}
\draw[rotate=90] (0,0) -- (-#1*30-#2*30/60:0.7cm); % hours
\draw[rotate=90] (0,0) -- (-#2*6:1.2cm); % minutes
\path [fill=black] (0,0) circle (3pt);
\path [fill=red] (0,0) circle (1.5pt);
}
\newcommand{\clockA}{%
% colors
\colorlet{minutes color}{blue!50!cyan!70!black}
\colorlet{bg hours 0}{yellow}
\colorlet{bg hours 1}{red!50}
\colorlet{hours color}{red!80!black}
% styles
\tikzset{
minutes/.style={circle,inner sep=0,text width=5mm,align=center,font=\bfseries},
minutes 0/.style={fill=minutes color,text=white,minutes},
minutes 1/.style={text=minutes color,fill=white,minutes},
minutes font/.style={font=\normalsize},
hours/.style={font=\fontsize{60}{66}\selectfont\bfseries,text=hours color,align=center},
mini hours font/.style={font=\fontsize{40}{46}\selectfont\bfseries},
}
% radii
\def\bigradius{80mm}
\def\minuteradius{75mm}
\def\hourradius{60mm}
\def\minihourminradius{25mm}
\def\minihourmaxradius{45mm}
\pgfmathsetmacro\minihourradius{(\minihourmaxradius + \minihourminradius)*.5}
\def\hourwidth{2mm}
\def\minutewidth{1mm}
% big circle
\filldraw [fill=white,draw=minutes color] (0,0) circle (\bigradius);
% minutes marks
\foreach \angle[count=\c from 0,evaluate={\c as \hourmark using notequal(int(mod(\c,5)),0)}]
in {0,6,...,354}{ \path (-\angle:\minuteradius) node[minutes \hourmark]{\c}; }
% hours marks
\foreach \angle[count=\c from 1,evaluate={\c as \col using int(mod(\c,2))}] in {30,60,...,360}{
\path (-\angle:\hourradius) node[hours]{\c};
\path[fill=bg hours \col]
(-\angle:\minihourminradius) -- (-\angle:\minihourmaxradius)
arc(-\angle:-\angle-30:\minihourmaxradius) -- (-\angle-30:\minihourminradius)
arc(-\angle-30:-\angle:\minihourminradius) -- cycle;
\path (-\angle-15:\minihourradius pt) node[mini hours font]{\textcolor{white}{\contour{hours color}{\c}}};
}
\path [fill=black] (0,0) circle (3mm);
\path [fill=red] (0,0) circle (1.5mm);
}
\newcommand{\clockB}{%
\draw (0,0) circle (2cm);
\foreach \angle / \label in
{0/3, 30/2, 60/1, 90/12, 120/11, 150/10, 180/9,
210/8, 240/7, 270/6, 300/5, 330/4}
{
\draw (\angle:1.8cm) -- (\angle:2cm);
\draw (\angle:1.4cm) node{\textsf{\label}};
}
\foreach \angle[count=\c from 0] in {0,6,...,354}
{
\draw (\angle:1.9cm) -- (\angle:2cm);
}
\path [fill=black] (0,0) circle (3pt);
\path [fill=red] (0,0) circle (1.5pt);
}
\begin{document}
\competencesStatement
@ -15,18 +156,142 @@
\bigskip
\begin{exercise}[subtitle={Angle et mesures}]
\begin{enumerate}
\item \textbf{Mesurer} les angles de la figure.
\includegraphics[scale=0.9]{./fig/mes_angles-1}
\begin{center}
$\widehat{ABC} = ....$ \hfill
$\widehat{BCD} = ....$ \hfill
$\widehat{CDE} = ....$
\end{center}
\item Tracer la droite (d) parallèle à la droite $(AB)$ passant par le point $C$
\includegraphics[scale=0.9]{./fig/paral-1}
\end{enumerate}
\end{exercise}
\begin{exercise}[subtitle={L'heure}]
\begin{enumerate}
\item Quelle heure indique ces deux horloges?
~
\vspace{1.5cm}
\hspace{1cm}
\begin{tikzpicture}[cap=round, rotate=90, transform canvas={scale=0.25}]
\clockATick{7}{30}
\end{tikzpicture}
\hspace{2cm}
............
\hspace{2.5cm}
\begin{tikzpicture}[cap=round, transform canvas={scale=0.9}]
\clockBTick{11}{15}
\end{tikzpicture}
\hspace{2cm}
............
\hspace{2.5cm}
\begin{tikzpicture}[cap=round, transform canvas={scale=0.9}]
\clockBTick{3}{55}
\end{tikzpicture}
\hspace{2cm}
............
\vspace{2cm}
\item Placer les aiguilles correctement.
~
\vspace{1.5cm}
\hspace{1cm}
\begin{tikzpicture}[cap=round, rotate=90, transform canvas={scale=0.25}]
\clockA
\end{tikzpicture}
\hspace{2cm}
10h20
\hspace{2.5cm}
\begin{tikzpicture}[cap=round, transform canvas={scale=0.9}]
\clockB
\end{tikzpicture}
\hspace{2cm}
9h54
\hspace{2.5cm}
\begin{tikzpicture}[cap=round, transform canvas={scale=0.9}]
\clockB
\end{tikzpicture}
\hspace{2cm}
1h34
\vspace{2cm}
\end{enumerate}
\end{exercise}
\clearpage
\begin{exercise}[subtitle={}]
\begin{exercise}[subtitle={Longueur d'un pas}]
\begin{enumerate}
\item Abdou a mesuré la longueur d'un de ses pas, 1 pas mesure 80cm.
\begin{enumerate}
\item Complète le tableau avec la mesure que vient de faire Abdou.
\begin{tabular}{|c|*{5}{p{2cm}|}}
\hline
Nombre de pas & & & & & \\
\hline
Distance (en cm) & & & & & \\
\hline
\end{tabular}
\item Il a mesuré que pour sortir de la salle d'histoire, il devrait faire 6pas. Quelle distance parcourt il pour sortir?
\\[0.2cm] .\dotfill
\item Il a mesuré que pour aller du cours de français au cours de math, il faisait 20pas. Cela fait combien de cm?
\\[0.2cm] .\dotfill
\item Quand il est rentré chez lui, il a compté 554 pas. Combien de km a-t-il parcouru?
\\[0.2cm] .\dotfill
\\[0.2cm] .\dotfill
\end{enumerate}
\end{enumerate}
\end{exercise}
\begin{exercise}[subtitle={Taille d'élèves}]
\begin{exercise}[subtitle={Tailles des élèves}]
Dans le tableau ci-dessous, on a reporté les tailles des élèves d'une classe de 6e.
\begin{tabular}{|c|*{5}{p{2cm}|}}
\hline
Élève & Mariam & Abdou & Roubouanti & Ikram & Faiz \\
\hline
Taille & 1,5m & 1,45m & 1,63m & 1,4m & 1,53m \\
\hline
\end{tabular}
\begin{enumerate}
\item Qui est la plus grande, Mariam ou Ikram?
\\[0.2cm] .\dotfill
\\[0.2cm] .\dotfill
\\[0.2cm] .\dotfill
\item Ranger en ordre croissant la taille des élèves.
\\[0.2cm] .\dotfill
\\[0.2cm] .\dotfill
\\[0.2cm] .\dotfill
\item Convertir la taille de Roubouanti en cm.
\\[0.2cm] .\dotfill
\item Convertir la taille de Abdou en km.
\\[0.2cm] .\dotfill
\end{enumerate}
\vspace{3cm}
\begin{tikzpicture}[scale=8]
\draw (0,0) -> (2.2, 0);
\foreach \x in {0,...,2} {%
\draw (\x,0) -- (\x, -0.1);
}
\foreach \x in {0,...,21} {%
\draw ({0.1*\x},0) -- ({0.1*\x}, -0.07);
}
\foreach \x in {0,...,210} {%
\draw ({0.01*\x},0) -- ({0.01*\x}, -0.03);
}
\end{tikzpicture}
\end{exercise}
\end{document}

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\documentclass[a4paper,12pt]{article}
\usepackage{myXsim}
\title{DS 9}
\tribe{Sixième}
\date{13 avril 2018}
\sujet{2}
\RequirePackage{contour}
\newcommand{\clockATick}[2]{%
% colors
\colorlet{minutes color}{blue!50!cyan!70!black}
\colorlet{bg hours 0}{yellow}
\colorlet{bg hours 1}{red!50}
\colorlet{hours color}{red!80!black}
% styles
\tikzset{
minutes/.style={circle,inner sep=0,text width=5mm,align=center,font=\bfseries},
minutes 0/.style={fill=minutes color,text=white,minutes},
minutes 1/.style={text=minutes color,fill=white,minutes},
minutes font/.style={font=\normalsize},
hours/.style={font=\fontsize{60}{66}\selectfont\bfseries,text=hours color,align=center},
mini hours font/.style={font=\fontsize{40}{46}\selectfont\bfseries},
}
% radii
\def\bigradius{80mm}
\def\minuteradius{75mm}
\def\hourradius{60mm}
\def\minihourminradius{25mm}
\def\minihourmaxradius{45mm}
\pgfmathsetmacro\minihourradius{(\minihourmaxradius + \minihourminradius)*.5}
\def\hourwidth{2mm}
\def\minutewidth{1mm}
% big circle
\filldraw [fill=white,draw=minutes color] (0,0) circle (\bigradius);
% minutes marks
\foreach \angle[count=\c from 0,evaluate={\c as \hourmark using notequal(int(mod(\c,5)),0)}]
in {0,6,...,354}{ \path (-\angle:\minuteradius) node[minutes \hourmark]{\c}; }
% hours marks
\foreach \angle[count=\c from 1,evaluate={\c as \col using int(mod(\c,2))}] in {30,60,...,360}{
\path (-\angle:\hourradius) node[hours]{\c};
\path[fill=bg hours \col]
(-\angle:\minihourminradius) -- (-\angle:\minihourmaxradius)
arc(-\angle:-\angle-30:\minihourmaxradius) -- (-\angle-30:\minihourminradius)
arc(-\angle-30:-\angle:\minihourminradius) -- cycle;
\path (-\angle-15:\minihourradius pt) node[mini hours font]{\textcolor{white}{\contour{hours color}{\c}}};
}
% hands
\pgfmathsetmacro\hourangle{-#1*30-#2*.5}
\pgfmathsetmacro\minuteangle{-#2*6}
\fill[rotate=\hourangle,fill=hours color] ++(0,\hourwidth) arc(90:270:\hourwidth) -- ++(50mm,0)
-- ++(\hourwidth,\hourwidth) -- ++(-\hourwidth,\hourwidth) -- ++(-50mm,0) -- cycle ;
\fill[rotate=\minuteangle,fill=minutes color] ++(0,\minutewidth) arc(90:270:\minutewidth) -- ++(70mm,0)
-- ++(\minutewidth,\minutewidth) -- ++(-\minutewidth,\minutewidth) -- ++(-70mm,0) -- cycle ;
}
\newcommand{\clockBTick}[2]{%
\draw (0,0) circle (2cm);
\foreach \angle / \label in
{0/3, 30/2, 60/1, 90/12, 120/11, 150/10, 180/9,
210/8, 240/7, 270/6, 300/5, 330/4}
{
\draw (\angle:1.8cm) -- (\angle:2cm);
\draw (\angle:1.4cm) node{\textsf{\label}};
}
\foreach \angle[count=\c from 0] in {0,6,...,354}
{
\draw (\angle:1.9cm) -- (\angle:2cm);
}
\draw[rotate=90] (0,0) -- (-#1*30-#2*30/60:0.7cm); % hours
\draw[rotate=90] (0,0) -- (-#2*6:1.2cm); % minutes
\path [fill=black] (0,0) circle (3pt);
\path [fill=red] (0,0) circle (1.5pt);
}
\newcommand{\clockA}{%
% colors
\colorlet{minutes color}{blue!50!cyan!70!black}
\colorlet{bg hours 0}{yellow}
\colorlet{bg hours 1}{red!50}
\colorlet{hours color}{red!80!black}
% styles
\tikzset{
minutes/.style={circle,inner sep=0,text width=5mm,align=center,font=\bfseries},
minutes 0/.style={fill=minutes color,text=white,minutes},
minutes 1/.style={text=minutes color,fill=white,minutes},
minutes font/.style={font=\normalsize},
hours/.style={font=\fontsize{60}{66}\selectfont\bfseries,text=hours color,align=center},
mini hours font/.style={font=\fontsize{40}{46}\selectfont\bfseries},
}
% radii
\def\bigradius{80mm}
\def\minuteradius{75mm}
\def\hourradius{60mm}
\def\minihourminradius{25mm}
\def\minihourmaxradius{45mm}
\pgfmathsetmacro\minihourradius{(\minihourmaxradius + \minihourminradius)*.5}
\def\hourwidth{2mm}
\def\minutewidth{1mm}
% big circle
\filldraw [fill=white,draw=minutes color] (0,0) circle (\bigradius);
% minutes marks
\foreach \angle[count=\c from 0,evaluate={\c as \hourmark using notequal(int(mod(\c,5)),0)}]
in {0,6,...,354}{ \path (-\angle:\minuteradius) node[minutes \hourmark]{\c}; }
% hours marks
\foreach \angle[count=\c from 1,evaluate={\c as \col using int(mod(\c,2))}] in {30,60,...,360}{
\path (-\angle:\hourradius) node[hours]{\c};
\path[fill=bg hours \col]
(-\angle:\minihourminradius) -- (-\angle:\minihourmaxradius)
arc(-\angle:-\angle-30:\minihourmaxradius) -- (-\angle-30:\minihourminradius)
arc(-\angle-30:-\angle:\minihourminradius) -- cycle;
\path (-\angle-15:\minihourradius pt) node[mini hours font]{\textcolor{white}{\contour{hours color}{\c}}};
}
\path [fill=black] (0,0) circle (3mm);
\path [fill=red] (0,0) circle (1.5mm);
}
\newcommand{\clockB}{%
\draw (0,0) circle (2cm);
\foreach \angle / \label in
{0/3, 30/2, 60/1, 90/12, 120/11, 150/10, 180/9,
210/8, 240/7, 270/6, 300/5, 330/4}
{
\draw (\angle:1.8cm) -- (\angle:2cm);
\draw (\angle:1.4cm) node{\textsf{\label}};
}
\foreach \angle[count=\c from 0] in {0,6,...,354}
{
\draw (\angle:1.9cm) -- (\angle:2cm);
}
\path [fill=black] (0,0) circle (3pt);
\path [fill=red] (0,0) circle (1.5pt);
}
\begin{document}
\competencesStatement
\maketitle
\bigskip
\begin{exercise}[subtitle={L'heure}]
\begin{enumerate}
\item Quelle heure indique ces deux horloges?
~
\vspace{1.5cm}
\hspace{1cm}
\begin{tikzpicture}[cap=round, rotate=90, transform canvas={scale=0.25}]
\clockATick{1}{30}
\end{tikzpicture}
\hspace{2cm}
............
\hspace{2.5cm}
\begin{tikzpicture}[cap=round, transform canvas={scale=0.9}]
\clockBTick{8}{5}
\end{tikzpicture}
\hspace{2cm}
............
\hspace{2.5cm}
\begin{tikzpicture}[cap=round, transform canvas={scale=0.9}]
\clockBTick{10}{34}
\end{tikzpicture}
\hspace{2cm}
............
\vspace{2cm}
\item Placer les aiguilles correctement.
~
\vspace{1.5cm}
\hspace{1cm}
\begin{tikzpicture}[cap=round, rotate=90, transform canvas={scale=0.25}]
\clockA
\end{tikzpicture}
\hspace{2cm}
2h25
\hspace{2.5cm}
\begin{tikzpicture}[cap=round, transform canvas={scale=0.9}]
\clockB
\end{tikzpicture}
\hspace{2cm}
6h04
\hspace{2.5cm}
\begin{tikzpicture}[cap=round, transform canvas={scale=0.9}]
\clockB
\end{tikzpicture}
\hspace{2cm}
11h44
\vspace{2cm}
\end{enumerate}
\end{exercise}
\begin{exercise}[subtitle={Longueur d'un pas}]
\begin{enumerate}
\item Mariam a mesuré la longueur d'un de ses pas, 1 pas mesure 70cm.
\begin{enumerate}
\item Complète le tableau avec la mesure que vient de faire Abdou.
\begin{tabular}{|c|*{5}{p{2cm}|}}
\hline
Nombre de pas & & & & & \\
\hline
Distance (en cm) & & & & & \\
\hline
\end{tabular}
\item Elle a mesuré que pour sortir de la salle d'histoire, elle devrait faire 6pas. Quelle distance parcourt elle pour sortir?
\\[0.2cm] .\dotfill
\item Elle a mesuré que pour aller du cours de français au cours de math, elle faisait 20pas. Cela fait combien de cm?
\\[0.2cm] .\dotfill
\item Quand elle est rentré chez elle, elle a compté 554 pas. Combien de km a-t-elle parcouru?
\\[0.2cm] .\dotfill
\\[0.2cm] .\dotfill
\end{enumerate}
\end{enumerate}
\end{exercise}
\clearpage
\begin{exercise}[subtitle={Tailles des élèves}]
Dans le tableau ci-dessous, on a reporté les tailles des élèves d'une classe de 6e.
\begin{tabular}{|c|*{5}{p{2cm}|}}
\hline
Élève & Mariam & Abdou & Roubouanti & Ikram & Faiz \\
\hline
Taille & 1,5m & 1,45m & 1,63m & 1,4m & 1,53m \\
\hline
\end{tabular}
\begin{enumerate}
\item Qui est la plus grande, Mariam ou Ikram?
\\[0.2cm] .\dotfill
\\[0.2cm] .\dotfill
\\[0.2cm] .\dotfill
\item Ranger en ordre croissant la taille des élèves.
\\[0.2cm] .\dotfill
\\[0.2cm] .\dotfill
\\[0.2cm] .\dotfill
\item Convertir la taille de Faiz en cm.
\\[0.2cm] .\dotfill
\item Convertir la taille de Mariam en km.
\\[0.2cm] .\dotfill
\end{enumerate}
\vspace{3cm}
\begin{tikzpicture}[scale=8]
\draw (0,0) -> (2.2, 0);
\foreach \x in {0,...,2} {%
\draw (\x,0) -- (\x, -0.1);
}
\foreach \x in {0,...,21} {%
\draw ({0.1*\x},0) -- ({0.1*\x}, -0.07);
}
\foreach \x in {0,...,210} {%
\draw ({0.01*\x},0) -- ({0.01*\x}, -0.03);
}
\end{tikzpicture}
\end{exercise}
\begin{exercise}[subtitle={Angle et mesures}]
\begin{enumerate}
\item \textbf{Mesurer} les angles de la figure.
\includegraphics[scale=0.9]{./fig/mes_angles-2}
\begin{center}
$\widehat{ABC} = ....$ \hfill
$\widehat{BCD} = ....$ \hfill
$\widehat{CDE} = ....$
\end{center}
\item Tracer la droite (d) parallèle à la droite $(AB)$ passant par le point $C$
\includegraphics[scale=0.9]{./fig/paral-2}
\end{enumerate}
\end{exercise}
\end{document}
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