\documentclass[a4paper,12pt]{article}
\usepackage{myXsim}

\title{DS 9}
\tribe{Sixième}
\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

\maketitle
\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={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={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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