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file mode 100644 index 0000000..6759806 --- /dev/null +++ b/1ST/Evaluations/DS_2023-01-16/automatismes.tex @@ -0,0 +1,36 @@ +\documentclass[a4paper, twocolumn, landscape, 10pt, fleqn]{article} +\usepackage{myXsim} +\usepackage{tkz-fct} +\usepackage{pgfplots} +\usetikzlibrary{decorations.markings} +\pgfplotsset{compat=1.18} + +% Title Page +\title{ DS3 \hfill Automatismes} +\tribe{1ST} +\date{16 janvier 2023} +\duree{1h} + +\DeclareExerciseCollection[step=1]{banque} +\xsimsetup{collect} + +\pagestyle{empty} + +\begin{document} +\input{exercises.tex} + +\maketitle + +\printcollection{banque} + +\newpage + +\maketitle + +\printcollection{banque} +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: diff --git a/1ST/Evaluations/DS_2023-01-16/exercises.tex b/1ST/Evaluations/DS_2023-01-16/exercises.tex new file mode 100644 index 0000000..49b8a43 --- /dev/null +++ b/1ST/Evaluations/DS_2023-01-16/exercises.tex @@ -0,0 +1,99 @@ +\begin{exercise}[subtitle={Automatismes}, step={1}, origin={Ma tête}, topics={ }, tags={ }] + \begin{enumerate} + \item Par combien faut-il multiplier une quantité positive pour la faire diminuer de 20\%? + \vspace{0.2cm} + \item Une quantité passe de 5 à 7, calculer le taux d'évolution de cette transformation. Vous donnerez le résultat sous forme de pourcentage. + \vspace{1cm} + + \item Résoudre l'équation suivante (simplifier le résultat le plus possible) + \[ + 5x + 20 = 0 + \] + \vfill + \item Résoudre l'équation suivante (simplifier le résultat le plus possible) + \[ + 8 - 12x = 0 + \] + \vfill + \item Résoudre l'équation suivante (simplifier le résultat le plus possible) + \item Soit $(u_n)$ la suite arithmétique de premier terme $u_0 = 10$ et de raison $r = 5$. Calculer $u_4$. + \vspace{1cm} + \item Le nombre d'élèves d'un établissement augment de 10\% chaque année. En 2010, il était de 500élèves. + + On modélise le nombre d'élèves par la suite $(u_n)$. + + Quelle est la nature de la suite. Préciser les paramètres. + \vspace{1cm} + + \item Déterminer l'équation de la droite. + + \begin{tikzpicture} + \begin{axis}[ + height = 3cm, + width = 6cm, + axis lines = center, + grid = both, + xlabel = {x}, + xtick distance=1, + ylabel = {$f(x)$}, + ytick distance=1, + ymin = 0, + ] + \addplot[domain=-3:5,samples=2, color=red, very thick]{-1/3*x + 2}; + \end{axis} + \end{tikzpicture} + + \item Soit $f(x) = 3x - 1$ calculer le taux de variation de $f$ entre $x=3$ et $x=5$. + \vspace{1cm} + + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Tangente et dérivée}, step={2}, origin={Création}, topics={Dérivée}, tags={Dérivée, tangente}, points={6}] + Cet exercice comporte + \begin{enumerate} + \item On définit la fonction $g(x) = 4x^2 - 5x + 1$ et on donne sa fonction dérivée $g'(x) = 8x - 5$. + \begin{enumerate} + \item Calculer le nombre dérivé de la fonction $g$ au point d'abscisse $x=2$. + \item Que peut-on en déduire sur la croissance de la fonction $g$ autour du point d'abscisse $x=2$? + \end{enumerate} + \item Déterminer la fonction dérivée des fonctions suivantes + \begin{multicols}{3} + \begin{enumerate} + \item $l(x) = 5$ + \item $m(x) = -3x + 10$ + \item $o(x) = 5x^2 - x + 1$ + \end{enumerate} + \end{multicols} + + \item Dans le plan muni d'un repère orthonormé, $\mathcal{C_f}$ est la courbe représentative d'une fonction $f$, définie et dérivable sur l'ensemble $\R$ des réels. + + Dans la figure ci-dessous, on a tracé la courbe $\mathcal{C_f}$. Les points $A$ et $B$ sont les points d'abscisse respectives $-1$ et $3$ et on a tracé les tangentes à $\mathcal{C_f}$ en ces points. + + \begin{center} + \includegraphics[scale=0.3]{./fig/graph} + \end{center} + + Les questions suivantes se répondent par une lecture graphique. + \begin{enumerate} + \item Déterminer la valeur du nombre dérivée de la fonction $f$ au point d'abscisse $x=-1$. + \item Déterminer la valeur de $f'(3)$. + \item Déterminer le taux d'accroissement de la fonction $f$ entre $x=-3$ et $x=12$. + \end{enumerate} + + \end{enumerate} + +\end{exercise} + +\begin{exercise}[subtitle={Plat cuisiné}, step={2}, origin={E3C 77 mai 2020}, topics={Répétition d'expérience}, tags={}, points={6}] + Des plats cuisinés d’un certain type sont fabriqués en grandes quantités. + + On prélève au hasard un plat d’un lot dans lequel 97\% des plats sont conformes au cahier des charges. On remet le plat dans le lot et on effectue un deuxième prélèvement d’un plat. On refait un troisième prélèvement dans les mêmes conditions. + + \begin{enumerate} + \item Faire un arbre pour représenter la situation. + \item A-t-on une situation d'équiprobabilité ? + \item Calculer la probabilité que les trois plats prélevés soient conformes. + \item Calculer la probabilité de l’évènement C : « seul un plat prélevé est conforme au cahier des charges ». On donnera une valeur approchée du résultat au millième. + \end{enumerate} +\end{exercise} diff --git a/1ST/Evaluations/DS_2023-01-16/fig/graph.png b/1ST/Evaluations/DS_2023-01-16/fig/graph.png new file mode 100644 index 0000000000000000000000000000000000000000..cb18a03703261cc5e4411aea49658b3c58b53c85 GIT binary patch literal 162496 zcmZs@2{@Gf+di(MgivG&MNOzC29uB_2~8Oy%E;2hlwI~EOA*45MwYBu%f3B!kzIzQ zNywI+>?!;5zedmZ`@Zk*_}_=aF*9y+FQ02Y&-1ziZmO#uVmQV?Lql^2bM2}Y4GkS5 z4b8rD^n2kGeE+Q|8XA5Y%vD8gm)My&+zS&`z3uj@vH0*JXJ^NX*+r%w`LE;l>{lT^ zVMJef&hu=Q*_}40Ov#=8GXI|YNB62AlY5vXj2~D2(?6G5UQwLY_vvGy=uVKoeArIk z*>mU4En!zSD)PSTIEs&W497m72!75c@Bk->VygT1rMlRvkw<>BlSy0kc3~;ixbsLpDx8u9A%)>(Ya#~yC@Z6zq7ryu`(Z& zq$?5$pNPr2{u&ihSi@8gUc}y_{G-G9P&Q|JpxSF^;QeD00J5>J`}F?t3Ns6fSxeN?=*KYU0oS*K^LHbZKi_ev=zk%mL_|F^wC`lYbEBzQ0+$q%dXt^U}A6{3mXHFOb0R@%33-?qogg%Mo6ysB?!PL+R}&fGP_HIonVRC6q& zRb-8gjs1}oC#xj*_`{LE=aZ_d$57oVySu(*jVp3iakm1+s z39k?z(QOC}{qckJXsi$MRS6x3atDg2m45YhV-bJk%O4*DeSXwyYqBeA{+68|9UWa= zT^(h42V 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b/1ST/Evaluations/DS_2023-01-16/sujet.tex new file mode 100644 index 0000000..d83b03c --- /dev/null +++ b/1ST/Evaluations/DS_2023-01-16/sujet.tex @@ -0,0 +1,28 @@ +\documentclass[a4paper,12pt]{article} +\usepackage{myXsim} + +% Title Page +\title{ DS3 \hfill } +\tribe{1ST} +\date{16 janvier 2023} +\duree{1h} + + +\DeclareExerciseCollection[step=2]{banque} +\xsimsetup{collect} + +\pagestyle{empty} + +\begin{document} +\maketitle + +Le barème est donné à titre indicatif, il pourra être modifié. + +\input{exercises.tex} +\printcollection{banque} +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: