Feat: dessins à compléter

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+</svg>

TST/DS/DS_20_12_11/DS_20_12_11.tex

@@ -0,0 +1,31 @@
+\documentclass[a5paper,10pt]{article}
+\usepackage{myXsim}
+\usepackage{tasks}
+
+% Title Page
+\title{DS 4 }
+\tribe{TST}
+\date{11 décembre 2020}
+\duree{1h}
+
+\DeclareExerciseCollection{banque}
+\xsimsetup{
+    %tribe=TST1,
+    type=Exercise,
+}
+
+
+\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:
+

TST/DS/DS_20_12_11/DS_20_12_11_QF.tex

@@ -0,0 +1,51 @@
+\documentclass[a4paper,10pt, landscape, twocolumn]{article}
+\usepackage{myXsim}
+
+% Title Page
+\title{DS 4}
+\tribe{TST}
+\date{11 décembre 2020}
+\duree{15 minutes}
+
+\pagestyle{empty}
+
+\DeclareExerciseCollection{banque}
+\xsimsetup{
+    %tribe=TST1,
+    type=automatismes,
+}
+
+\begin{document}
+\input{exercises.tex}
+
+\maketitle
+
+\medskip
+{\Large Nom - Prénom: \dotfill}
+
+\medskip
+Calculatrice non autorisée
+
+\printcollection{banque}
+
+\vfill
+
+\pagebreak
+
+\maketitle
+
+\medskip
+{\Large Nom - Prénom: \dotfill}
+
+\medskip
+Calculatrice non autorisée
+
+\printcollection{banque}
+
+\end{document}
+
+%%% Local Variables: 
+%%% mode: latex
+%%% TeX-master: "master"
+%%% End:
+

TST/DS/DS_20_12_11/exercises.tex

@@ -0,0 +1,78 @@
+\collectexercises{banque}
+\begin{exercise}[subtitle={Automatismes}, points=6, tribe={TST1}, type={automatismes}]
+    \begin{enumerate}
+        \item Un article de mode est vendu en solde 135\euro. Les vendeurs expliquent qu'il est soldé à 20\%. Quel était son prix avant les soldes?
+            \vfill
+        \item Simplifier le calcul suivant
+            \[
+                \frac{5^4 \times 5^{-3}}{5^2 \times 5^6} &=
+            \]
+            \vfill
+        \item Soit $X$ la variable aléatoire dont la loi de probabilité est résumé pas le tableau suivant
+            \begin{center}
+                \begin{tabular}{|c|*{3}{p{2cm}|}}
+                    \hline
+                    $x_i$ & -3 & 2 & 5 \\
+                    \hline
+                    $p_i$ & 0.4 & 0.1 & 0.5 \\
+                    \hline
+                \end{tabular}
+            \end{center}
+            Calculer la valeur de $P(X > 0)$.
+            \vfill
+        \item Calculer la moyenne géométrique de $a=3$ et $b=9$.
+            \vfill
+        \item Soit $(d)$ la droite d'équation $y = 4x + 1$. Est-ce que le point $A(3; 11)$ appartient à la droite?
+            \vfill
+    \end{enumerate}
+\end{exercise}
+
+\begin{exercise}[subtitle={Fonctions polynômes}, points=8, tribe={TST1}, type={Exercise}]
+    Soit $f$ la fonction définie sur $\intFF{0}{5}$ par 
+    \[
+        f(x) = x^3 - 7,5x^2 + 18x - 11,5
+    \]
+    \begin{enumerate}
+        \item Calculer $f(1)$ puis interpréter.
+        \item 
+            \begin{enumerate}
+                \item Calculer $f'(x)$ la dérivée de $f(x)$.
+                \item Démontrer que $x=3$ et $x=2$ sont des racines de $f'(x)$.
+            \end{enumerate}
+            Dans la suite, on supposera que l'on a $f'(x) = 3(x-3)(x-2)$.
+            \begin{enumerate}
+                \setcounter{enumii}{2}
+                \item Tracer le tableau de signe de $f'(x)$ et en déduire les variations de $f$ sur $\intFF{0}{5}$.
+            \end{enumerate}
+        \item (Vrai/faux) Les phrases suivantes sont-elles vraies ou fausses. Vous justifierez vos réponses.
+            \begin{enumerate}
+                \item $f$ est croissante sur l'intervalle $\intFF{0}{2}$ et décroissante sur l'intervalle $\intFF{2}{3}$.
+                \item $f$ est une fonction polynôme de degré 2.
+                \item $f(x)$ a pour maximum 2,5.
+            \end{enumerate}
+    \end{enumerate}
+\end{exercise}
+
+\begin{exercise}[subtitle={Placements}, points=7, tribe={TST1}, type={Exercise}]
+    \begin{enumerate}
+        \item Bob a placé, en 2015, \np{2000}\euro sur un compte avec un rendement de 2,5\% par ans.
+            \begin{enumerate}
+                \item Quel sera le solde du compte en 2016, et 2020?
+                \item Si on modélise le solde du compte par la suite $(u_n)$. Quelle est la nature de la suite? Préciser les paramètres.
+                \item Exprimer $u_n$ en fonction de $n$.
+            \end{enumerate}
+        \item Sa copine Sarah a fait un placement similaire qui a débuté en 2015. On note $v_n$ la suite qui modélise le solde de son compte. On supposera qu'elle est géométrique et on a les valeurs suivantes
+            \[
+                u_1 = 2500 \qquad \qquad u_3 = 2700
+            \]
+            \begin{enumerate}
+                \item Calculer la moyenne géométrique de $u_1$ et de $u_3$ pour démontrer que  la valeur de $u_2$ est d'environ \np{2598}.
+                \item Démontrer que la raison de la suite est $q=1,39$.
+                \item En déduire le rendement du placement de Sarah.
+                \item Quelle était la somme que Sarah a placé sur son compte en 2015?
+            \end{enumerate}
+    \end{enumerate}
+\end{exercise}
+
+
+\collectexercisesstop{banque}