$ \newcommand{\parallele}{\sslash} \newcommand{\para}{\sslash} \newcommand{\er}{\textsuperscript{er}\ } \newcommand{\eme}{\textsuperscript{ème}\ } \newcommand{\ere}{\textsuperscript{ère}\ } \newcommand{\snd}{\textsuperscript{nd}\ } \newcommand{\snde}{\textsuperscript{nde}\ } \newcommand{\iem}{\textsuperscript{ième}\ } \newcommand{\x}{\times} \newcommand{\ie}{\leqslant} \newcommand{\se}{\geqslant} \newcommand{\qqquad}{\quad\qquad} \newcommand{\N}{\mathbb N} \newcommand{\Z}{\mathbb Z} \newcommand{\D}{\mathbb D} \newcommand{\Q}{\mathbb Q} \newcommand{\R}{\mathbb R} \newcommand{\C}{\mathbb C} \newcommand{\F}{\mathbb F} \newcommand{\K}{\mathbb K} \newcommand{\U}{\mathbb U} %\newcommand{\Code}[1]{ {\verb+#1+} } \newcommand{\Code}[1]{{\ttfamily #1}} %\newcommand{\partent}{\mathsf{ent}} \newcommand{\E}{\mathsf{E}} %\newcommand{\alea}{\verb?alea?} \newcommand{\partent}{\text{\Code{ent}} } \newcommand{\alea}{\text{\Code{alea}} } \newcommand{\epsi}{\varepsilon} % epsilonn \newcommand{\f}{\othervarphi} % fonction phi \newcommand{\g}{\gamma} \newcommand{\al}{\alpha} \newcommand{\de}{\delta} \newcommand{\De}{\Delta} \newcommand{\Ga}{\Gamma} \newcommand{\La}{\Lambda} \newcommand{\la}{\lambda} \renewcommand{\o}{\otheromega} \newcommand{\si}{\sigma} \newcommand{\Ta}{\Theta} \newcommand{\teta}{\theta} \renewcommand{\O}{\Omega} \newcommand{\prive}{\setminus}%{\backslash} \newcommand{\union}{\cup} \newcommand{\inter}{\cap} \newcommand{\vide}{\varnothing} \newcommand{\card}{\mathop{\rm card}\nolimits} \newcommand{\paire}[2]{\{#1\, ;\, #2\}} \newcommand{\Paire}[2]{\left\{#1\, ;\, #2\right\}} \newcommand{\enstrois}[3]{\{#1\, ;\, #2\, ;\, #3\}} \newcommand{\Enstrois}[3]{\left\{#1\, ;\, #2\, ;\, #3\right\}} \newcommand{\ensquatre}[4]{\{#1\, ;\, #2\, ;\, #3\, ;\, #4\}} \newcommand{\Ensquatre}[4]{\left\{#1\, ;\, #2\, ;\, #3\, ;\, #4\right\}} \newcommand{\triplet}[3]{(#1\, ;\, #2\, ;\, #3)} \newcommand{\quadruplet}[4]{(#1\, ;\, #2\, ;\, #3\, ; #4)} \newcommand{\nuplet}[2]{(#1\, ;\,\ldots\, ;\, #2)} \newcommand{\Nuplet}[2]{\left(#1\, ;\,\ldots\, ;\, #2\right)} \newcommand{\ensemble}[2]{\{#1\, ;\,\ldots\, ;\, #2\}} \newcommand{\interieur}[1]{\ring{#1}} \newcommand{\ens}[1]{\left\{\,#1\,\right\}} \newcommand{\tq}{ \ \ \textrm{t.q} \ \ } \newcommand{\tqc}{ \textrm{t.q} } \newcommand{\Frac}[2]{\frac{\disp #1}{\disp #2}} \newcommand{\tvi}[2]{\vrule height #1 depth #2 width 0pt} \newcommand{\rond}{\circ} \newcommand{\ps}{\cdot} \newcommand{\ovra}[3]{\mkern #1mu\overrightarrow{\mkern -#1mu #2\mkern -#3mu}\mkern #3mu} \newcommand{\ovla}[3]{\mkern #1mu\overleftarrow{\mkern -#1mu #2\mkern -#3mu}\mkern #3mu} \newcommand{\delim}[3]{\raise #1\hbox{$\left #2\vbox to #3{}\right.$}} \renewcommand{\(}{\left( } \renewcommand{\)}{\right) } \newcommand{\oc}{\left[} \newcommand{\fc}{\right]} \newcommand{\norme}[1]{\| #1 \|} \newcommand{\normebis}[1]{\delim{2pt}{\|}{9pt}\! #1\delim{2pt}{\|}{9pt}} \newcommand{\normetriple}[1]{\left |\kern -.07em\left\| #1\right |\kern -.07em\right\|} \newcommand{\valabs}[1]{\delim{2pt}{|}{9pt}#1\delim{2pt}{|}{9pt}} \newcommand{\Abs}[1]{\left \lvert#1\right \rvert} \newcommand{\dist}[2]{\textrm{d}(#1\textrm{;\,} #2)} \newcommand{\limit}[2]{\displaystyle\lim_{#1} #2} \newcommand{\limitx}[3]{\displaystyle\lim_{#1\to #2} #3} \newcommand{\limitxinf}[3]{\displaystyle\lim_{#1\build{\to}_{<}^{} #2} #3} \newcommand{\limitxsup}[3]{\displaystyle\lim_{#1\build{\to}_{>}^{} #2} #3} \newcommand{\tend}[2]{\displaystyle\build\longrightarrow_{#1\rightarrow #2}^{}} \newcommand{\ds}{\displaystyle} \newcommand{\fonc}[4]{#1\ :\begin{array}{rll} #2 &\to \\ x& \mapsto  \end{array}} \newcommand{\Fonc}[5]{#1\ :\begin{array}{rll} #2 &\to \\ #4& \mapsto  \end{array}} \newcommand{\limd}[2][x]{\ds\lim_{{#1\to #2}\atop{#1>#2}} } \newcommand{\limcd}[1]{\ds\lim_{#1^+} } \newcommand{\limg}[2][x]{\ds\lim_{{#1\to #2}\atop{#1<#2}} } \newcommand{\limcg}[1]{\ds\lim_{#1^-} } \newcommand{\limc}[1]{\ds\lim_{#1} } \newcommand{\lin}{\ds\lim_{n\to +\infty}} \newcommand{\Lim}[2][x]{\displaystyle{\lim_{#1 \to #2}}} \newcommand{\Li}[2]{\left.\begin{array}{lcr} #1\\ #2 \end{array}\right\}} \newcommand{\somme}[3][i]{\sum\limits_{\substack{#1=#2}}^{#3}} \newcommand{\Tendvers}[2][h]{\underset{#1\rightarrow #2}{\longrightarrow}} \newcommand{\un}{{(u_n)}_{n\in\N}\ } % suite un {(t_{n})}_{n\in\N} \newcommand{\unstar}{{(u_n)}_{n\in\N^{\ast}}\ } % suite un \newcommand{\vn}{{(v_n)}_{n\in\N}\ } %suite vn \newcommand{\wn}{{(w_n)}_{n\in\N}\ } %suite wn \newcommand{\tn}{{(t_n)}_{n\in\N}\ } %suite tn \newcommand{\sn}{{(s_n)}_{n\in\N}\ } %suite tn \newcommand{\rn}{{(r_n)}_{n\in\N}\ } %suite tn \newcommand{\xn}{{(x_n)}_{n\in\N}\ } %suite tn \newcommand{\yn}{{(y_n)}_{n\in\N}\ } %suite tn \newcommand{\zn}{{(z_n)}_{n\in\N}\ } %suite tn \newcommand{\an}{{(a_n)}_{n\in\N}\ } %suite tn \newcommand{\bn}{{(b_n)}_{n\in\N}\ } %suite tn \newcommand{\cn}{{(c_n)}_{n\in\N}\ } %suite tn \newcommand{\dn}{{(d_n)}_{n\in\N}\ } %suite tn \newcommand{\en}{{(e_n)}_{n\in\N}\ } %suite tn \newcommand{\enstar}{{(e_n)}_{n\in\N^{\ast}}\ } % suite un % % % % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Equivalent \newcommand{\equivalent}[1]{\build\sim_{#1}^{}} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% o et O \renewcommand{\o}[2]{\build o_{#1\to #2}^{}} \renewcommand{\O}[2]{\build O_{#1\to #2}^{}} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Displaystyle \newcommand{\disp}{\displaystyle} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Signes d'equivalence et d'implication \newcommand{\equivaut}{\Longleftrightarrow} \newcommand{\equi}{\Leftrightarrow} \newcommand{\implique}{\Longrightarrow} \newcommand{\impli}{\Rightarrow} \newcommand{\ssi}{\textrm{ \ ssi \ }} \newcommand{\idest}{\quad \textrm{i.e} \quad} \newcommand{\cad}{\quad \textrm{c-à-d} \quad} % \newcommand{\ssic}{\textrm{ssi} } \newcommand{\idestc}{\textrm{i.e} } \newcommand{\cadc}{\textrm{c-à-d}} \newcommand{\maxi}{ \textrm{max}} \newcommand{\sgn}{\textrm{sgn}} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Signe associe \newcommand{\associe}{\longmapsto} \newcommand{\asso}{\mapsto} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Angles \renewcommand{\angle}[1]{\widehat{#1}} \newcommand{\anglevec}[2]{(\vec #1\, ,\,\vec #2)} \newcommand{\Anglevec}[2]{(\V{#1}\, ,\,\V{#2})} \newcommand{\anglecouple}[2]{\left( #1\, ,\, #2 \right) } %\newcommand{\anglevecteur0}[3][black]{(\widehat{\vec{#2}\, , \, \textcolor{#1}{\vec{#3}}})} %\newcommand{\anglevecteur}[4][black]{\anglevecteur0{#2}{ \textcolor{#1}{#3} }{#4} } \newcommand{\anglevecteur}[2]{(\widehat{\vec{#1}\, , \, \vec{#2}} ) } %\newcommand{\anglevecteurcouleur}[4]{(\textcolor{#1}{\vec{#3}}\, , \, \textcolor{#2}{\vec{#4}}) } \newcommand{\Anglevecteur}[2]{\(\widehat{\V{#1},\V{#2}}\)} \newcommand{\rad}{ \,\,\textrm{rad} } \newcommand{\mes}{\textrm{mes} } \newcommand{\°}{\degres} \newcommand{°}{\degres} \newcommand{\Mes}[1]{\mes\,\widehat{#1}} \newcommand{\mesvec}[2]{\textrm{mes}\(\vec{#1} \, , \, \vec{#2}\)} \newcommand{\mesvecteur}[2]{\textrm{mes}\anglevecteur{#1}{#2}} \newcommand{\mesVec}[2]{\textrm{mes}\(\V{#1} \, , \, \V{#2}\)} \newcommand{\mesarc}[1]{\textrm{mes}\(\widehat{#1}\)} \newcommand{\mesarco}[1]{\textrm{mes}\(\arcoriente{#1}\)} \newcommand{\ao}[2]{\left(#1\, , \, #2\right)} %\newcommand{\Mes}[1]{% % \ensuremath{% % \mathrm{mes} % \DecalV{\widehat{#1}} % }} %\DeclareTextSymbol{\degree}{T1}{6} %\DeclareTextSymbol{\degre}{OT1}{23} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Vecteurs %\newcommand{\vecteur}[1]{\ovra 0{#1}0} \newcommand{\prodscal}[2]{<#1,#2>} \newcommand{\prodvec}[2]{#1\wedge #2} \newcommand{\vectoriel}[2]{\prodvec{\vec #1}{\vec #2}} \newcommand{\Vectoriel}[2]{\prodvec{\vecteur{#1}}{\vecteur{#2}}} \newcommand{\prodmixte}[3]{\big[#1, #2, #3\big]} \newcommand{\mixte}[3]{\prodmixte{\vec #1}{\vec #2}{\vec #3}} \newcommand{\Mixte}[3]{\prodmixte{\vecteur{#1}}{\vecteur{#2}}{\vecteur{#3}}} \newcommand{\V}[1]{\ovra 0{#1}0} % \newcommand{\test}[2]{#1^2-#2^2} % %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Repères (O,i), (O,i,j), (O,u,v), (O,I,J) et quelconques \newcommand{\Oi}{(O\, ;\,\vec\imath\,)} \newcommand{\Oj}{(O\, ;\,\vec\jmath\,)} \newcommand{\Oij}{(O\, ;\,\vec\imath\, ;\vec\jmath\,)} \newcommand{\Aij}{(A\, ;\,\vec\imath\, ;\vec\jmath\,)} \newcommand{\Omegaij}{(\Omega\, ;\,\vec\imath\, ;\vec\jmath\,)} \newcommand{\Ai}{(A\, ;\,\vec\imath\,)} \newcommand{\Aj}{(A\, ;\,\vec\jmath\,)} \newcommand{\Ojk}{(O\, ;\,\vec\jmath\, ;\vec k\,)} \newcommand{\Oik}{(O\, ;\,\vec\imath\, ;\vec k\,)} \newcommand{\Ouv}{(O\, ;\,\vec u\, ;\vec v\,)} \renewcommand{\ij}{(\vec\imath\, ;\vec\jmath\,)} \newcommand{\ijk}{(\vec\imath\, ;\vec\jmath\, ;\vec k\,)} \newcommand{\Oijk}{\big(O\, ;\,\vec\imath\, ;\vec\jmath\, ;\vec k\,\big)} \newcommand{\oijk}{\big(o\, ;\,\vec\imath\, ;\vec\jmath\, ;\vec k\,\big)} \newcommand{\OIJ}{(O\,;\, I\,;\, J\,)} \newcommand{\repere}[3]{\big(#1\, ;\,\vecteur{#2} ;\vecteur{#3}\big)} \newcommand{\reperesp}[4]{\big(#1\, ;\,\vecteur{#2} ;\vecteur{#3} ;\vecteur{#4}\big)} % \newcommand{\reperepol}[2]{\big(#1\, ;\,\vecteur{#2}\big)} \newcommand{\reperesf}[3]{\big(#1\, ;\,#2 ; #3 \big)} % %Redéfinition de \longrightarrow %\newcommand\longrightarrow{\mathrel{\raise .02em\hbox{$\relbar$}}\joinrel\rightarrow} % % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Aire d'une surface \newcommand{\aire}[1]{% \ensuremath{\mathscr{A}_{#1}}} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Volume d'un volume \newcommand{\volume}[1]{% \ensuremath{\mathscr{V}_{#1}}} % % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% un ; avec un peu d'espace autour \newcommand{\pv}{\ensuremath{\: ; \,}} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Intervalles \newcommand{\interoo}[2]{]#1\, ;\, #2[} \newcommand{\Interoo}[2]{\left]#1\, ;\, #2\right[} \newcommand{\interof}[2]{]#1\, ;\, #2]} \newcommand{\Interof}[2]{\left]#1\, ;\, #2\right]} \newcommand{\interfo}[2]{[#1\, ;\, #2[} \newcommand{\Interfo}[2]{\left[#1\, ;\, #2\right[} \newcommand{\interff}[2]{[#1\, ;\, #2]} \newcommand{\Interff}[2]{\left[#1\, ;\, #2\right]} % \newcommand{\of}[2]{\left] \,#1 \, ; \, #2 \,\right] } \newcommand{\fo}[2]{\left[ \,#1 \, ; \, #2 \,\right[ } \newcommand{\oo}[2]{\left] \,#1 \, ; \, #2 \,\right[ } \newcommand{\ff}[2]{\left[ \,#1 \, ; \, #2 \,\right] } % %\newcommand\interentiers #1#2{[\! [#1\, ;\, #2]\! ]} \newcommand{\interentiers}[2]{\llbracket #1\, ;\, #2\rrbracket} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% autres intervalles \newcommand{\Intff}[2]{\ensuremath{\left[#1\pv #2\right]}} \newcommand{\Intfo}[2]{\ensuremath{\left[#1\pv #2\right[}} \newcommand{\Intof}[2]{\ensuremath{\left]#1\pv #2\right]}} \newcommand{\Intoo}[2]{\ensuremath{\left]#1\pv #2\right[}} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Coordonnées %\newcommand{\coord}[2]{(#1\, ;\, #2)} \newcommand{\bigcoord}[2]{\big(#1\, ;\, #2\big)} \newcommand{\coord}[2]{\left(#1\, ;\, #2\right)} \newcommand{\Coord}[2]{\left(#1\, ;\, #2\right)} \newcommand{\coordesp}[3]{(#1\, ;\, #2\, ;\, #3)} \newcommand{\bigcoordesp}[3]{\big(#1\, ;\, #2\, ;\, #3\big)} \newcommand{\Coordesp}[3]{\left(#1\, ;\, #2\, ;\, #3\right)} \newcommand{\coordpol}[2]{\left[#1\, ;\, #2\right]} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Coordonnées verticales dans le plan \newcommand{\coordp}[2]{% \begin{pmatrix} #1 \\ #2 \end{pmatrix}} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Coordonnées verticales dans l'espace \newcommand{\coordpp}[3]{% \scalebox{.7}{% \begin{pmatrix} #1 \\ #2 \\ #3 \end{pmatrix}}} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Congruences \newcommand{\congru}{\equiv} % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Modulo 2pi ou autre \newcommand{\Mod}[1][2\pi]{\enspace{(#1)}} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Quel que soit \newcommand{\qqsoit}{\forall\,} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Différentielles \renewcommand{\d}{\textrm d} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Intégrale \newcommand{\integ}[4]{\int_{#1}^{#2} #3\,\d #4} % % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Intégration par parties \newcommand{\intpp}[4]{% $\left\{% \begin{matrix} #1 & #3 \\ \stackrel{}{#2} & \stackrel{}{#4} \\ \end{matrix} \right.$} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Somme majuscule \newcommand{\Sum}{\displaystyle{\sum}} % % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Barycentres \newcommand{\bary}{\mathop{\rm Bar}\nolimits} \newcommand{\baryd}[4]{\(#1\, ;\, #2\)\ \textrm{et}\ \(#3\, ;\, #4 \)} \newcommand{\baryt}[6]{(#1\, ;\, #2),\ (#3\, ;\, #4)\ \textrm{et}\ (#5\, ;\, #6)} \newcommand{\baryq}[8]{(#1\, ;\, #2),\ (#3\, ;\, #4),\ (#5\, ;\, #6)\ \textrm{et}\ (#7\, ;\, #8)} \newcommand{\Baryd}[4]{\bary \left\lbrace \(#1\, ;\, #2 \)\, ;\, \(#3\, ;\, #4 \) \right\rbrace } \newcommand{\Baryt}[6]{\bary \left\lbrace \(#1\, ;\, #2\)\, ;\, \(#3\, ;\, #4 \)\, ;\, \(#5\, ;\, #6 \) \right\rbrace } \newcommand{\Baryn}[6]{\bary \left\lbrace \(#1\, ;\, #2\)\, ;\, \(#3\, ;\, #4 \)\, ;\,\ldots\, ;\, \(#5\, ;\, #6\) \right\rbrace } % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Signe inclusion \newcommand{\inclus}{\subset} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Fonctions \newcommand{\fonction}[5]{ \begin{eqnarray*} #1 & \!\!\!\!\! : & \!\!\!\!\! #2\longrightarrow #3\\ & & \!\!\!\!\! #4\longmapsto #5 \end{eqnarray*} } \newcommand{\fonctionligne}[5]{#1:#2\longrightarrow #3,\ #4\longmapsto #5} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Unités de longueur en rm \newcommand{\cm}{\mathop{\rm cm}\nolimits} \newcommand{\mm}{\mathop{\rm mm}\nolimits} \newcommand{\dm}{\mathop{\rm dm}\nolimits} \newcommand{\m}{\mathop{\rm m}\nolimits} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Fonction logarithme intégral [Plt137] \newcommand{\li}{\mathop{\rm li}\nolimits} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Fonction exponentielle \newcommand{\e}{\mathop{\rm e}\nolimits} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Fonction cotangente \newcommand{\cotan}{\mathop{\rm cotan}\nolimits} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Fonctions hyperboliques \newcommand{\ch}{\mathop{\rm ch}\nolimits} \newcommand{\sh}{\mathop{\rm sh}\nolimits} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Parties entière, réelle, imaginaire, nombre i \newcommand{\ent}{\mathop{\rm E}\nolimits} \newcommand{\Int}{\mathop{\rm Int}\nolimits} \renewcommand{\Re}{\mathop{\rm Re}\nolimits} \renewcommand{\Im}{\mathop{\rm Im}\nolimits} \renewcommand{\i}{\textrm{i}} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Comatrice \newcommand{\com}{\mathop{\rm com}\nolimits} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Trace \newcommand{\tr}{\mathop{\rm tr}\nolimits} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Transposée \newcommand{\transposee}[1]{{\vphantom{#1}}^t\negmedspace #1} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Noyau \newcommand{\Ker}{\mathop{\rm Ker}\nolimits} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% PGCD, PPCM \newcommand{\PGCD}{\mathop{\rm PGCD}\nolimits} \newcommand{\PPCM}{\mathop{\rm PPCM}\nolimits} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Matrices \newcommand{\Mn}{\mathcal M_n} \newcommand{\matrice}[4]{ \left( \begin{array}{cc} #1 & #2 \\ #3 & #4 \end{array} \right)} \newcommand{\vect}[2]{ \left(\negmedspace \begin{array}{c} #1\\ #2 \end{array}\negmedspace \right)} \newcommand{\Matrice}[9]{ \left( \begin{array}{ccc} #1 & #2 & #3\\ #4 & #5 & #6\\ #7 & #8 & #9 \end{array} \right)} \newcommand{\Vect}[3]{ \left(\negmedspace \begin{array}{c} #1\\ #2\\ #3 \end{array}\negmedspace \right)} \newcommand{\Ideux}{\matrice{1}{0}{0}{1}} \newcommand{\Itrois}{\Matrice{1}{0}{0}{0}{1}{0}{0}{0}{1}} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Determinants \newcommand{\determinant}[4]{ \left| \begin{array}{cc} #1 & #3 \\ #2 & #4 \end{array} \right|} \newcommand{\Determinant}[9]{ \left| \begin{array}{ccc} #1 & #2 & #3\\ #4 & #5 & #6\\ #7 & #8 & #9 \end{array} \right|} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Systemes \newcommand{\sysu}[1]{ \left\lbrace \begin{array}{l} #1\\ \end{array} \right.} \newcommand{\sys}[2]{ \left\lbrace \begin{array}{l} \negthickspace\negthickspace #1\\ \negthickspace\negthickspace #2\\ \end{array} \right.\negthickspace\negthickspace} \newcommand{\sysd}[2]{ %\left\lbrace \left\{ \begin{array}{l} #1\\ #2 \end{array} \right.} %%%%%%%%%%%%%%%%%%%%%%%% %\left\{\begin{array}{l c l} %v_{0} &=& 1\\ %v_{n + 1}&=& \dfrac{9}{6 - v_{n}} %\end{array}\right. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \newcommand{\syst}[3]{ \left\lbrace \begin{array}{l} #1\\ #2\\ #3\\ \end{array} \right.} \newcommand{\sysq}[4]{ \left\lbrace \begin{array}{l} #1\\ #2\\ #3\\ #4\\ \end{array} \right.} \newcommand{\sysc}[5]{ \left\lbrace \begin{array}{l} #1\\ #2\\ #3\\ #4\\ #5\\ \end{array} \right.} \newcommand{\sisi}[4]{ \left\lbrace \begin{array}{rm{0.2cm}l} #1 & & \text{#2}\\ #3 & & \text{#4} \end{array} \right.} % %\newcommand{\accod}[4]{\begin{cases} #1 & #2 \\ #3 & #4 \end{cases} } % \newcommand{\accot}[6]{\begin{cases} #1 & #2 \\ #3 & #4 \\ #5 & #6 \end{cases} } %% %\newcommand{\accod}[2]{ \left\{ % \begin{split} % #1 \\ % #2 % \end{split} % \right. } % \newcommand{\accott}[3]{ \begin{equation} \left\{ \begin{split} #1 \\ #2 \\ #3 \end{split} \right. \end{equation} } \newcommand{\Syst}[2]{\left\{\begin{array}{ccccc} #1\\ #2 \end{array}\right.} % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Covariance \newcommand{\cov}{\mathop{\rm cov}\nolimits} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Symboles entre droites %\newcommand{\paral}{\sslash} \newcommand{\paral}{\mathop{/\!\! /}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% jours heures minutes secondes \newcommand{\jour}{\ \textrm{j} \ } \newcommand{\heure}{\ \textrm{h} \ } \newcommand{\minute}{\ \textrm{min} \ } \newcommand{\seconde}{\ \textrm{s} \ } \newcommand{\algobox}{\texttt{AlgoBox}} \newcommand{\xcas}{\texttt{Xcas}} \newcommand{\excel}{\texttt{Excel}\ } \newcommand{\calc}{\texttt{Calc}} \newcommand{\geogebra}{\texttt{GeoGebra}} \newcommand{\python}{\texttt{Python}\ } \newcommand{\ou}{ \quad \text{ ou } \quad } \newcommand{\et}{ \quad \text{ et } \quad } \newcommand{\btr}{\ensuremath{\blacktriangleright\ }} \newcommand{\wtr}{\ensuremath{\triangleright\ }} \newcommand{\bp}{\ensuremath{\bullet\ }} %%%%%%%%%%%%%%%%%%%%% B(n;p) - Loi binomiale %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \newcommand{\bnp}[2][n]{\ensuremath{\mathscr B\(#1 \pv #2 \)}} $

CH03 - Fractions
Corrigé de l'IE
Pour s'entraîner en ligne :  
Questions flash & corrections des exercices
Carte mentale du chapitre :

Voici des vidéos qui reviennent sur des compétences du chapitre.
 
CH02 - Triangles, hauteurs & médiatrices
Corrigé du DS
Questions flash & corrections des exercices
Animation Geogebra : Concourance des 3 hauteurs d'un triangle.
Vous pouvez déplacer les sommets du triangle ci-dessous :

Animation Geogebra : Concourance des 3 médiatrices d'un triangle.
Vous pouvez déplacer les sommets du triangle ci-dessous :

Carte mentale du chapitre :

Voici les vidéos des constructions de la leçon :
Trois rappels indispensables de Cycle 3.
Quelques vidéos rappelant des méthodes de constructions vues en classe.
 
CH01 - Enchaînements d'opérations
Corrigé du DS
Corrigé de l'IE (A)  -  Corrigé de l'IE (B)
Questions flash & corrections des exercices
Des vidéos qui pourraient vous aider :
 
Initiation à l'algorithmique avec Scratch
Développé par le groupe de recherche Lifelong Kindergarten auprès du laboratoire Média du MIT (Massachusetts Institute of Technology), Scratch est un nouveau langage de programmation qui facilite la création d’histoires interactives, de dessins animés, de jeux, de compositions musicales et de simulations numériques.
Scratch est un logiciel libre conçu pour initier les élèves dès l’âge de 8 ans à des concepts fondamentaux en mathématiques et en informatique. Il repose sur une approche ludique de l’algorithmique, pour les aider à créer, à raisonner et à coopérer. Il favorise également leur partage sur le Web. À partir de 2007, le site Web a été ouvert afin de permettre à tous d'une part, de publier, donc de faire partager, ses projets sur le Web et d'autre part d'apporter une aide à la mise en œuvre de Scratch.
Pour découvrir et utiliser Scratch, cliquez sur
 
Généralités
Présentation & fonctionnement des cours