Source Latex
sujet du devoir
\documentclass[12pt,onecolumn,a4paper]{article}
\usepackage[french]{babel}
\usepackage[utf8]{inputenc}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{enumerate}
\usepackage{array}
\usepackage{pst-all}
\usepackage{hyperref}
\hypersetup{
pdfauthor={Yoann Morel},
pdfsubject={Devoir de mathématiques de seconde},
pdftitle={Devoir de mathématiques de 2nde},
pdfkeywords={calcul algébrique, fractions, développer, factoriser, identités remarquables, racines carrées, radicaux}
}
\hypersetup{
colorlinks = true,
linkcolor = blue,
anchorcolor = red,
citecolor = blue,
filecolor = red,
urlcolor = red
}
\voffset=-1cm
% Raccourcis diverses:
\newcommand{\nwc}{\newcommand}
\nwc{\dsp}{\displaystyle}
\nwc{\bge}{\begin{equation}}\nwc{\ene}{\end{equation}}
\nwc{\bgar}{\begin{array}}\nwc{\enar}{\end{array}}
\nwc{\bgit}{\begin{itemize}}\nwc{\enit}{\end{itemize}}
\nwc{\bgen}{\begin{enumerate}}\nwc{\enen}{\end{enumerate}}
\nwc{\la}{\left\{}\nwc{\ra}{\right\}}
\nwc{\lp}{\left(}\nwc{\rp}{\right)}
\nwc{\lb}{\left[}\nwc{\rb}{\right]}
\nwc{\ul}{\underline}
\nwc{\tm}{\times}
\nwc{\V}{\overrightarrow}
\newcommand{\zb}{\mbox{$0\hspace{-0.67em}\mid$}}
\newcommand{\db}{\mbox{$\hspace{0.1em}|\hspace{-0.67em}\mid$}}
\newcommand{\ct}{\centerline}
\def\N{{\rm I\kern-.1567em N}}
\def\D{{\rm I\kern-.1567em D}}
\def\R{{\rm I\kern-.1567em R}}
\def\C{{\rm C\kern-4.7pt
\vrule height 7.7pt width 0.4pt depth -0.5pt \phantom {.}}}
\def\Q{\mathbb{Q}}
\def\Z{{\sf Z\kern-4.5pt Z}}
\def\euro{\mbox{\raisebox{.25ex}{{\it =}}\hspace{-.5em}{\sf C}}}
\newcounter{nex}[section]\setcounter{nex}{0}
\newenvironment{EX}{%
\stepcounter{nex}
\medskip{\noindent{{\bf Exercice }}\arabic{nex}}\hspace{0.5cm}
}{}
\nwc{\bgex}{\begin{EX}}\nwc{\enex}{\end{EX}}
\nwc{\bgfg}{\begin{figure}}\nwc{\enfg}{\end{figure}}
\nwc{\epsx}{\epsfxsize}\nwc{\epsy}{\epsfysize}
\nwc{\bgmp}{\begin{minipage}}\nwc{\enmp}{\end{minipage}}
\newenvironment{centerpage}{\vspace*{\fill}}{
\protect\vspace*{\fill}}
\setlength{\columnsep}{30pt} % default=10pt
\setlength{\columnseprule}{1pt} % default=0pt (no line)
\setlength{\headsep}{0in} % default=0.35in
\setlength{\parskip}{0ex}
\setlength{\parindent}{0mm}
\voffset=-1cm
\textheight=27.6cm
\textwidth=18.5cm
\topmargin=0cm
\headheight=-0.cm
\footskip=1.cm
\oddsidemargin=-1.cm
\usepackage{fancyhdr}
\pagestyle{fancyplain}
\setlength{\headheight}{0cm}
\renewcommand{\headrulewidth}{0pt}
\renewcommand{\footrulewidth}{.1pt}
\lfoot{Y. Morel - \href{https://xymaths.fr/Lycee/2nde/Mathematiques-2nde.php}{xymaths - 2nde}}
\cfoot{}
\rfoot{Devoir de mathématiques - \thepage/\pageref{LastPage}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\thispagestyle{empty}
\vspace*{-4em}
\qquad{\bf\large{Devoir de math\'ematiques}}
\setcounter{nex}{0}
\bgex
Exprimer sous la forme la plus simple possible, d'une seule fraction irr\'eductible, sans racine carrée au dénominateur, et les expressions algébriques développées:
%$a=\dfrac23-\dfrac15\tm\dfrac{2+\dfrac12}{2-\dfrac12}$
%\qquad
$a=\dfrac{3x+2}{2x-3}-1$
%\qquad
%$c=\dfrac{x-2}{2x-1}+\dfrac{2x+1}{x+2}$
\qquad
$b=\dfrac{x+\dfrac32}{x+\dfrac12}-1$
\qquad
$c=\dfrac{15}{\sqrt{5}}$
\qquad
$d=\lp\sqrt{12}-\sqrt{3}\rp^2$
\qquad
$e=(3\sqrt{2})^2-(\sqrt{2}-1)^2$
\qquad
$f=\dfrac{2}{2+\sqrt{3}}$
\qquad
%$g=\dfrac{\sqrt{3}+\sqrt{12}}{\sqrt{3}-\sqrt{12}}$
%\qquad
%$h=\dfrac{x(3x)^3}{9x^2}$
$g=(4x+12)\dfrac{\dfrac{x^2-16}{x+3}}{x-4}$
\enex
\bgex Factoriser:
$A(x)=(x+3)(2x-1)-(x+3)(x+2)$ \\[.6em]
$B(x)=(2x+1)^2-2x(2x+1)$
\qquad
$C(x)=(2x+1)+(x+2)(2x+1)$
\qquad
$D(x)=(x+3)^2-4$
\enex
\vfill
\hrulefill
\qquad{\bf\large{Devoir de math\'ematiques}}
\setcounter{nex}{0}
\bgex
Exprimer sous la forme la plus simple possible, d'une seule fraction irr\'eductible, sans racine carrée au dénominateur, et les expressions algébriques développées:
%$a=\dfrac23-\dfrac15\tm\dfrac{2+\dfrac12}{2-\dfrac12}$
%\qquad
$a=\dfrac{3x+2}{2x-3}-1$
%\qquad
%$c=\dfrac{x-2}{2x-1}+\dfrac{2x+1}{x+2}$
\qquad
$b=\dfrac{x+\dfrac32}{x+\dfrac12}-1$
\qquad
$c=\dfrac{15}{\sqrt{5}}$
\qquad
$d=\lp\sqrt{12}-\sqrt{3}\rp^2$
\qquad
$e=(3\sqrt{2})^2-(\sqrt{2}-1)^2$
\qquad
$f=\dfrac{2}{2+\sqrt{3}}$
\qquad
%$g=\dfrac{\sqrt{3}+\sqrt{12}}{\sqrt{3}-\sqrt{12}}$
%\qquad
%$h=\dfrac{x(3x)^3}{9x^2}$
$g=(4x+12)\dfrac{\dfrac{x^2-16}{x+3}}{x-4}$
\enex
\bgex Factoriser:
$A(x)=(x+3)(2x-1)-(x+3)(x+2)$ \\[.6em]
$B(x)=(2x+1)^2-2x(2x+1)$
\qquad
$C(x)=(2x+1)+(x+2)(2x+1)$
\qquad
$D(x)=(x+3)^2-4$
\enex
\vfill
\hrulefill
\qquad{\bf\large{Devoir de math\'ematiques}}
\setcounter{nex}{0}
\bgex
Exprimer sous la forme la plus simple possible, d'une seule fraction irr\'eductible, sans racine carrée au dénominateur, et les expressions algébriques développées:
%$a=\dfrac23-\dfrac15\tm\dfrac{2+\dfrac12}{2-\dfrac12}$
%\qquad
$a=\dfrac{3x+2}{2x-3}-1$
%\qquad
%$c=\dfrac{x-2}{2x-1}+\dfrac{2x+1}{x+2}$
\qquad
$b=\dfrac{x+\dfrac32}{x+\dfrac12}-1$
\qquad
$c=\dfrac{15}{\sqrt{5}}$
\qquad
$d=\lp\sqrt{12}-\sqrt{3}\rp^2$
\qquad
$e=(3\sqrt{2})^2-(\sqrt{2}-1)^2$
\qquad
$f=\dfrac{2}{2+\sqrt{3}}$
\qquad
%$g=\dfrac{\sqrt{3}+\sqrt{12}}{\sqrt{3}-\sqrt{12}}$
%\qquad
%$h=\dfrac{x(3x)^3}{9x^2}$
$g=(4x+12)\dfrac{\dfrac{x^2-16}{x+3}}{x-4}$
\enex
\bgex Factoriser:
$A(x)=(x+3)(2x-1)-(x+3)(x+2)$ \\[.6em]
$B(x)=(2x+1)^2-2x(2x+1)$
\qquad
$C(x)=(2x+1)+(x+2)(2x+1)$
\qquad
$D(x)=(x+3)^2-4$
\enex
\vfill
\hrulefill
\qquad{\bf\large{Devoir de math\'ematiques}}
\setcounter{nex}{0}
\bgex
Exprimer sous la forme la plus simple possible, d'une seule fraction irr\'eductible, sans racine carrée au dénominateur, et les expressions algébriques développées:
%$a=\dfrac23-\dfrac15\tm\dfrac{2+\dfrac12}{2-\dfrac12}$
%\qquad
$a=\dfrac{3x+2}{2x-3}-1$
%\qquad
%$c=\dfrac{x-2}{2x-1}+\dfrac{2x+1}{x+2}$
\qquad
$b=\dfrac{x+\dfrac32}{x+\dfrac12}-1$
\qquad
$c=\dfrac{15}{\sqrt{5}}$
\qquad
$d=\lp\sqrt{12}-\sqrt{3}\rp^2$
\qquad
$e=(3\sqrt{2})^2-(\sqrt{2}-1)^2$
\qquad
$f=\dfrac{2}{2+\sqrt{3}}$
\qquad
%$g=\dfrac{\sqrt{3}+\sqrt{12}}{\sqrt{3}-\sqrt{12}}$
%\qquad
%$h=\dfrac{x(3x)^3}{9x^2}$
$g=(4x+12)\dfrac{\dfrac{x^2-16}{x+3}}{x-4}$
\enex
\bgex Factoriser:
$A(x)=(x+3)(2x-1)-(x+3)(x+2)$ \\[.6em]
$B(x)=(2x+1)^2-2x(2x+1)$
\qquad
$C(x)=(2x+1)+(x+2)(2x+1)$
\qquad
$D(x)=(x+3)^2-4$
\enex
\label{LastPage}
\end{document}
Télécharger le fichier source