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z+_zm@>LqH;9he-GwLdg;vXQBq(PHsd_Ozv6vo5Al@Ur*(X7CKK@>97f9!tY+bnF?V vIt&N11ZABKBOAY*VRL1&B>dOC?+P&mLp)&-I~q4Pkb@tMo?c2t8ts1oH)9r~ literal 0 HcmV?d00001 diff --git a/2nd/15_Intervalles_et_nombres_reels/4E_sol_ineq.tex b/2nd/15_Intervalles_et_nombres_reels/4E_sol_ineq.tex new file mode 100644 index 0000000..97fbfd6 --- /dev/null +++ b/2nd/15_Intervalles_et_nombres_reels/4E_sol_ineq.tex @@ -0,0 +1,22 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} + +\author{Benjamin Bertrand} +\title{Intervalles - Exercices} +\date{Mai 2023} + +\DeclareExerciseCollection[step=4]{banque} +\xsimsetup{collect} + +\pagestyle{empty} + +\begin{document} +\input{exercises.tex} + +\setcounter{exercise}{7} +\printcollection{banque} +\vfill +\printcollection{banque} +\vfill + +\end{document} diff --git a/2nd/15_Intervalles_et_nombres_reels/exercises.tex b/2nd/15_Intervalles_et_nombres_reels/exercises.tex index dcb4b07..a45acdf 100644 --- a/2nd/15_Intervalles_et_nombres_reels/exercises.tex +++ b/2nd/15_Intervalles_et_nombres_reels/exercises.tex @@ -177,5 +177,67 @@ \item $\dfrac{-3}{3} \ldots \intFF{-1}{3}$ \end{enumerate} \end{multicols} - +\pagebreak +\end{exercise} + + +\begin{exercise}[subtitle={Équations graphiques}, step={4}, origin={Ma tête}, topics={ Intervalles et nombres réels }, tags={ Inéquation, Intervalle, Nombres }, mode={\trainMode}] + Résoudre les inéquations en utilisant les tableaux de signes + \begin{multicols}{2} + \begin{enumerate} + \item $f(x) \leq 0$ + \begin{tikzpicture}[baseline=(a.north)] + \tkzTabInit[lgt=2,espcl=1]{$ x $/1,$ f(f) $/1}{-5, 1, 2, $+\infty$} + \tkzTabLine{, +, z, -, z, + , } + \end{tikzpicture} + \item $g(x) < 0$ + \begin{tikzpicture}[baseline=(a.north)] + \tkzTabInit[lgt=2,espcl=1]{$ x $/1,$ g(f) $/1}{$-\infty$, 0, 10, $+\infty$} + \tkzTabLine{, -, z, +, z, - , } + \end{tikzpicture} + \item $z(t) > 0$ + \begin{tikzpicture}[baseline=(a.north)] + \tkzTabInit[lgt=2,espcl=1]{$ t $/1,$ z(t) $/1}{-5, -1, 3, 4, 5} + \tkzTabLine{, +, z, -, z, +, z, - , } + \end{tikzpicture} + \item $z(t) \leq 0$ + \begin{tikzpicture}[baseline=(a.north)] + \tkzTabInit[lgt=2,espcl=1]{$ t $/1,$ z(t) $/1}{0, 1, 2, 3, 4} + \tkzTabLine{, -, z, +, z, -, z, + , } + \end{tikzpicture} + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{exercise}[subtitle={Équations et tableau de signes}, step={4}, origin={Ma tête}, topics={ Intervalles et nombres réels }, tags={ Inéquation, Intervalle, Nombres }, mode={\trainMode}] + \begin{minipage}{0.4\linewidth} + Sur le graphique ci-contre, on a tracé les représentations de 3 fonctions $f$, $g$ et $h$. + + Résoudre les inéquations suivantes en utilisant le graphique, vous donnerez les solutions sous forme d'intervalles. + \begin{enumerate} + \item $f(x) < 1$ + \item $f(x) \geq 0$ + \item $g(x) \leq 1$ + \item $g(x) > 0$ + \item $h(x) < g(x)$ + \item $h(x) \geq 0$ + \end{enumerate} + \end{minipage} + \hfill + \begin{minipage}{0.5\linewidth} + \begin{tikzpicture}[xscale=1.5, yscale=0.8] + \tkzInit[xmin=-3,xmax=3,xstep=1, + ymin=-3,ymax=4,ystep=1] + \tkzGrid + \tkzAxeXY + \tkzFct[domain = -3:3,color=red,very thick]{-2*x**2 + 3}; + \tkzText(1.8, -2.2){$\mathcal{C}_f$}; + + \tkzFct[domain = -3:3,color=green,very thick]{-0.5*x+1}; + \tkzText(-2.5, 1.8){$\mathcal{C}_g$}; + + \tkzFct[domain = -3:3,color=blue,very thick]{1/x}; + \tkzText(-2.5, -1.5){$\mathcal{C}_h$}; + \end{tikzpicture} + \end{minipage} \end{exercise} diff --git a/2nd/15_Intervalles_et_nombres_reels/plan_de_travail.pdf b/2nd/15_Intervalles_et_nombres_reels/plan_de_travail.pdf index adbbf7c56262ed35e652ba4887d2daeb4f30f369..ba98fa1d8729f24dd42b7544e919dc434d21cf5a 100644 GIT binary patch delta 49861 zcmV)XK&`+1k^`vf1F&BP0yH#}VFoAzGdDAnVN(=;?On-^Bu8?+*H^?*bBGw<7obr< z_4ESp*3$&$K=H&GN)WmQ3@`e9J@YNxBP}u`v$`dU3X;Xj@-$z}+}!N>W-g|Go5b|- zNo;>F(nO&ru~=gzeg&nio_@o({5OC7`1JP2r$2x2Zc<`#PFXem`0Eo0@UNUyShR6d z5ON8B+D<=yoql>FgnALed=SFgXDRTvarmt9<MCPH=Uw@sbn`qblc+4Ew7)37!0-3? 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