\documentclass[a4paper,12pt,landscape]{exam}

% ─────────────────────────────────────────────────────────────────
% default_preamble.tex — packages + command definitions
% Everything here is placed BEFORE \begin{document}.
% ─────────────────────────────────────────────────────────────────

\usepackage[left=1.3cm,right=1.3cm,top=1cm,bottom=1cm]{geometry}
\usepackage[utf8]{inputenc}
\usepackage{fontspec}
\usepackage{amsmath, amsfonts, amssymb, amsthm}
\usepackage{graphicx}
\usepackage{xcolor}
\usepackage{multicol}
\usepackage{enumitem}
\usepackage{mathrsfs}
\usepackage{colortbl}
\usepackage{varwidth}
\usepackage[most]{tcolorbox}
\tcbuselibrary{skins,breakable}
\usepackage{tikz,tkz-euclide}
\usetikzlibrary{calc}
\usetikzlibrary{shadows}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\usepackage{tabularx, array, booktabs}
\usepackage{multirow}
\usepackage{array}
\usepackage{setspace}
\usepackage{hyperref}
\hypersetup{colorlinks=true, urlcolor=magenta}





% Language variables for French exams
\def\professor{R. MOSAID}  % Should be R. MOSAID not {{R. MOSAID}}
\def\classname{TCSHF}
\def\examtitle{Devoir 01\ccc{B} \hspace*{1cm} Nom:\fff{3}}
\def\schoolname{Lycée Taghzirt}
\def\academicyear{2026/2027}
\def\subject{Mathématiques}
\def\duration{2h}
\def\secondtitle{\small{}}
\def\province{}
\def\logo{\includegraphics[width=\linewidth]{images/logo-men.png}}
\def\wsite{\href{https://www.mosaid.xyz}{\textcolor{magenta}{\texttt{www.mosaid.xyz}}}}
\def\ddate{\hfill \number\day/\number\month/\number\year~~}



\newcommand{\shadowhead}{%
  \noindent
  \begin{tikzpicture}
    \node[
      fill=white,
      draw=black,
      rounded corners=2pt,
      inner sep=6pt,
      drop shadow={opacity=0.4}
    ]{%
      \begin{minipage}{0.98\columnwidth}
        \centering
        \renewcommand{\arraystretch}{1.1}
        \begin{tabularx}{\columnwidth}{@{}X X@{}}
          \schoolname
          &
          \hfill\academicyear
          \\[2pt]

          \multicolumn{2}{c}{%
            \normalsize\textbf{\examtitle}
          }
          \\[2pt]

          \textit{\professor}
          &
          \hfill\classname
        \end{tabularx}
      \end{minipage}
    };
  \end{tikzpicture}
}


% Exercise Theme 1: TikZ shadow title
\newcommand{\exothemeone}[1]{%
\par\vspace{0pt}\noindent\leavevmode
\begin{tikzpicture}[baseline=(text.base)]
    \node[] (text) at (0,0) {\textbf{#1}};
    \fill[black] ([xshift=0.1cm, yshift=-0.1cm]text.south west)
                 rectangle ([xshift=0.1cm, yshift=-0.1cm]text.north east);
    \draw[fill=white] (text.south west) rectangle (text.north east);
    \node[] at (text) {\textbf{#1}};
\end{tikzpicture}\\[0.2cm]
}

\newcommand{\printexo}[3]{%
  \if\relax\detokenize{#2}\relax
    \def\fulltitle{Exercice #1}%
  \else
    \def\fulltitle{Exercice #1~#2}%
  \fi
  \exothemeone{\fulltitle}%
  \noindent #3%
  \vspace{0.2cm}%
}



% --- Colors ---
\definecolor{maroon}{cmyk}{0,0.87,0.68,0.32}
\definecolor{pBlue}{RGB}{102, 53, 153}

\definecolor{myblue}{HTML}{1D2A6E}
\definecolor{myred}{HTML}{A97E77}
\definecolor{mybrown}{HTML}{B35823}
\definecolor{gold}{HTML}{B48920}
\definecolor{myorange}{HTML}{ED8C2B}
\definecolor{col}{RGB}{45, 136, 119}
\definecolor{MainRed}{rgb}{.8, .1, .1}
\definecolor{winered}{rgb}{0.5,0,0}
\definecolor{JungleGreen}{HTML}{29AB87}

\definecolor{myblue3}{RGB}{36, 57, 126}
\definecolor{mygray}{RGB}{112,121,139}
\definecolor{LemonGlacier}{RGB}{253,255,0}
\colorlet{myblue3}{red!75!black}

\definecolor{lightgray}{gray}{0.6}
\definecolor{arrowblue}{RGB}{0,140,180}
\definecolor{bannerblue}{RGB}{210,240,240}

% Exam-specific settings and custom definitions
% This file is generated in the current working directory
% Edit this file to customize your exam settings



% Define column type for centered cells
\newcolumntype{Y}{>{\centering\arraybackslash}X}
\newcolumntype{M}[1]{@{}>{\centering\arraybackslash}m{#1}@{}}

\newcommand{\tb}{\tikz[baseline=-0.6ex]{\fill (0,0) circle (2pt);}~}

\newcommand{\ccc}[1]{
    \begin{tikzpicture}[overlay, remember picture]
        \node[circle, inner sep=3pt, draw=black, outer sep=0pt] at (0.5,0.2) {#1};
    \end{tikzpicture}
}


\newcommand{\circled}[1]{%
  \tikz[baseline=(char.base)]{
    \node[shape=circle,draw,inner sep=1pt, font=\bf] (char) {#1};}%
}


% --- Margin offsets for note placement ---
\def\rnotemargin{-1.5}   % distance from right edge of text block
\def\lnotemargin{0.5}   % distance from left edge of text block


% --- Note number placed 1cm from page edge (right margin) ---
\newcommand{\rnote}[1]{%
  \tikz[remember picture,overlay,baseline=(text.base)]{%
    % a tiny anchor at the current line baseline
    \node (text) at (0,0) {};%
    % coordinate 1cm left of the physical page right edge
    \coordinate (marg) at ($(current page.east)+(\rnotemargin,0)$);%
    % place the marker using x from 'marg' and y from 'text.base'
    \node[anchor=base west,
      font=\small\bfseries,
      fill=yellow!30,
      draw=black,
      circle,
      minimum width=18pt,
      minimum height=18pt,
      text width=18pt,   % force fixed width
      align=center,      % center text inside
      inner sep=0pt      % prevent expansion
    ] at (marg |- text.base) {$#1$};%
  }%
}

% --- Note number placed 1cm from page edge (left margin) ---
\newcommand{\note}[1]{%
  \tikz[remember picture,overlay,baseline=(text.base)]{%
    % a tiny anchor at the current line baseline
    \node (text) at (0,0) {};%
    % coordinate 1cm left of the physical page right edge
    \coordinate (marg) at ($(current page.west)+(\lnotemargin,0)$);%
    % place the marker using x from 'marg' and y from 'text.base'
    \node[anchor=base west,
      font=\small\bfseries,
      fill=yellow!30,
      draw=black,
      circle,
      minimum width=18pt,
      minimum height=18pt,
      text width=18pt,   % force fixed width
      align=center,      % center text inside
      inner sep=0pt      % prevent expansion
    ] at (marg |- text.base) {$#1$};%
  }%
}




% Document spacing
\setstretch{1.3}

% Math display style
\everymath{\displaystyle}

\mathversion{bold}

%\AtBeginDocument{\fontsize{15}{17}\selectfont}

\newcommand{\fff}[1]{\makebox[#1cm]{\dotfill}}

\newcommand{\dfp}[1]{\dotfill (\bf{#1 pt})}

\SetEnumitemKey{tight}{
    leftmargin=*,
    itemsep=0pt,
    topsep=0pt,
    parsep=0pt,
    partopsep=0pt,
    before=\vspace{-2pt},   % reduce space before
    after=\vspace{-2pt}     % reduce space after
}

\newcommand{\VMargin}[1]{%
  \begin{tikzpicture}[remember picture,overlay]
    \draw[line width=1pt]
      ([xshift=#1]current page.north west) --
      ([xshift=#1]current page.south west);
  \end{tikzpicture}%
}

\newcommand{\VMarginRight}[1]{%
  \begin{tikzpicture}[remember picture,overlay]
    \draw[line width=0.6pt]
      ([xshift=-#1]current page.north east) --
      ([xshift=-#1]current page.south east);
  \end{tikzpicture}%
}



% Custom theorem environments (uncomment if needed)
% \newtheorem{theorem}{Theorem}
% \newtheorem{lemma}{Lemma}
% \newtheorem{corollary}{Corollary}

% Custom exercise environments (uncomment if needed)
% \newenvironment{solution}{\begin{proof}[Solution]}{\end{proof}}
% \newenvironment{remark}{\begin{proof}[Remark]}{\end{proof}}

% Custom commands for this exam (add your own below)
% \newcommand{\answerline}[1]{\underline{\hspace{#1}}}
% \newcommand{\points}[1]{\hfill(\mbox{#1 points})}

% Additional packages (uncomment if needed)
% \usepackage{siunitx} % For SI units
% \usepackage{chemformula} % For chemical formulas
% \usepackage{circuitikz} % For circuit diagrams

% Page layout adjustments
% \setlength{\parindent}{0pt}
% \setlength{\parskip}{1em}

% Custom colors for this exam
% \definecolor{myblue}{RGB}{0,100,200}
% \definecolor{mygreen}{RGB}{0,150,0}

\def\nex{01}

% ----------------------------------------------------------------------
% ADD YOUR CUSTOM DEFINITIONS BELOW THIS LINE
% ----------------------------------------------------------------------

% Example:
\newcommand{\dif}{\mathrm{d}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\C}{\mathbb{C}}

% ── Exam class settings ──────────────────────────────────────
\pointsinmargin
\pointname{}
\pointformat{\textcolor{red}{\circled{\thepoints}}}
\colorfillwithdottedlines
\definecolor{FillWithDottedLinesColor}{gray}{0.7}
\unframedsolutions
\renewcommand{\solutiontitle}{%
  \noindent\textbf{\textcolor{green!70!black}{Solution}}\enspace}
\SolutionEmphasis{\itshape\small\color{red}}
% ─────────────────────────────────────────────────────────────


% ─────────────────────────────────────────────────────────────────
% default_wrapper.tex — the document body.
% Placed AFTER preamble / colors / definitions in _assemble().
% ─────────────────────────────────────────────────────────────────

\begin{document}



% ── Top of document (user block) ────────────────────────────────


% ── Header command (exam class only; article class uses fancyhdr)


% ── Two-column start
\setlength{\columnsep}{0.5cm}
\setlength{\columnseprule}{2pt}
\renewcommand{\columnseprulecolor}{\color{black}}
\begin{multicols}{2}[\raggedcolumns]
\vspace*{-\topskip}
% Header for first column
\noindent\shadowhead

% ── Main exercises
\VMargin{1.25cm}
\vspace*{-0.5cm}


\printexo{1}{(20 points) -- les questions sont indépendantes

}{\vspace*{-0.5cm}
\begin{questions}

  \question[3]
    Calculer et donner le résultat sous forme de fraction irréductible:\\
    ~\(
      A=\frac{\frac{5}{6}-\frac{1}{4}}
      {\frac{3}{2}+\frac{1}{3}}
    \)~
    \fff{7.5}\\[0.5cm]
    \fff{12}

  \question[2] Réduire l'expression suivante:\\
    ~\(
      B=5(2a-3b)-2(3a+b)-(-4a+4b)
    \)~\\
    \fff{12}\\
    \fff{12}\\
    \fff{12}

  \question[2] Factoriser les expressions suivantes:

    $C=15x^2y-10xy^2+5xy$\\[0.2cm]
    \fff{12}\\[0.3cm]
    $D=(a-4)(2b+1)+(a-4)(b-3)$\\[0.2cm]
    \fff{12}\\
    \fff{12}\\[0.3cm]
    $E=16x^2+40x+25$\\
    \fff{12}

  \question[2] Développer et réduire:

    $F=(2x-5)(x+3)$\\[0.2cm]
    \fff{12}\\
    \fff{12}\\[0.3cm]
    $G=(3x+2)^2$\\[0.2cm]
    \fff{12}

  \question[4]
    Simplifier l'expression suivante en utilisant les propriétés des puissances:
    ~\(
      H=\frac{a^{-2}\cdot(a^3b^{-2})^2\cdot b^5}
      {(a^{-1}b^3)^3\cdot b^{-4}}
    \)~
    \fff{5.5}\\[0.75cm]
    \fff{12}\\[0.5cm]
    \fff{12}

  \question[2]
    Déterminer le nombre $x$ pour que les quatre nombres
    $5,\quad x,\quad 12,\quad 8$
    soient proportionnels dans cet ordre.\\[0.3cm]
    \fff{12}\\[0.3cm]
    \fff{12}

  \question[2]
    Comparer les deux nombres suivants sans utiliser de valeur approchée:
    ~\(
      \sqrt{13}\quad\text{et}\quad 2\sqrt{3}
    \)~
    \fff{12}\\[0.3cm]
    \fff{12}\\[0.3cm]
    \fff{12}

  \question[3]
    Soient $-2\leq x\leq 3$ et $1\leq y\leq 4$. Encadrer $x+2y$ puis $2x-y$\\
    \fff{12}\\[0.3cm]
    \fff{12}\\[0.3cm]
    \fff{12}\\[0.3cm]
    \fff{12}

\end{questions}
}

% ── Between columns (if two-column)


% ── Repeat section



% ── Bottom message — inside column 2 (last column)


% ── Two-column end
\end{multicols}

% ── Bottom of document (user block) ─────────────────────────────




\end{document}