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+\input{exercises.tex} +\printcollection{banque} + +\end{document} diff --git a/TST/04_Formalisation_des_suites/exercises.tex b/TST/04_Formalisation_des_suites/exercises.tex index f7a448a..5ea97c5 100644 --- a/TST/04_Formalisation_des_suites/exercises.tex +++ b/TST/04_Formalisation_des_suites/exercises.tex @@ -112,5 +112,75 @@ \end{multicols} \end{exercise} +\begin{exercise}[subtitle={TYPE E3C}, step={4}, origin={T1CMATH03609}, topics={Formalisation des suites}, tags={Suites, Analyse}] + \noindent + \begin{minipage}{0.5\textwidth} + Le nuage de point ci-contre représente les 6 premières valeurs de la suite $u$. + \begin{enumerate} + \item Lire graphiquement la valeur de $u(3)$ + \item La suite $u$ peut-elle être arithmétique? Justifier + \item Dans la suite, on admet que $u(4) = 2$ et $u(5) = 4$. On suppose que la suite est géométrique. + \begin{enumerate} + \item Calculer la raison de la suite $u$. + \item Exprimer, pour tout $n$ positif ou nul, $u(n+1)$ en fonction de $u(n)$. + \item Donner par le calcul la valeur exacte de $u(7)$. + \end{enumerate} + \end{enumerate} + \end{minipage} + \begin{minipage}{0.5\textwidth} + \includegraphics[scale=0.3]{./fig/T1CMATH03609_graph} + \end{minipage} +\end{exercise} +\begin{exercise}[subtitle={TYPE E3C}, step={4}, origin={T1CMATH03610}, topics={Formalisation des suites}, tags={Suites, Analyse}] + En 2019, une entreprise souhaite réaliser une campagne de publicité pour promouvoir ses produits. + + Elle prend alors contact avec une agence de publicité, nommée A, qui lui indique qu’en 2019, selon ses tarifs, le coût d’une campagne de publicité s’élève à 10000euros pour 2019 mais que celui-ci augmentera ensuite de 750€ par an. + + On note $u_n$le coût d’une campagne publicitaire pour l’entreprise suivant les tarifs de l’agence A pour l’année $(2019+n)$.Ainsi $u_0$=10000. + + \begin{enumerate} + \item Quel sera le coût d’une campagne de publicité pour l’entreprise en 2025 si elle choisit l’agence A? + \item Quelle est la nature de la suite $(u_n)$? Argumenter la réponse. + \item Déterminer le sens de variation de la suite $(u_n)$. Justifier la réponse. + \item L’entreprise contacte une agence de publicité B qui lui dit que le coût d’une campagne de publicité pour l’année $(2019+n)$ est donné par: $v_n = n^2+200n+\np{10000}$ + \begin{enumerate} + \item Déterminer la valeur de $v_2$. + \item Quel sera le coût d’une campagne de publicité pour l’entreprise en 2025 si elle choisit l’agence B? + \end{enumerate} + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={TYPE E3C}, step={4}, origin={T1CMATH03614}, topics={Formalisation des suites}, tags={Suites, Analyse}] + \noindent + \begin{minipage}{0.6\textwidth} + On considère la suite $u$ de premier terme $u(0) = 200$ et telle que pour tout entier positif $n$: + \[ + u(n+1) = u(n) + 20 + \] + \begin{enumerate} + \item Calculer $u(1)$. + \item + \begin{enumerate} + \item Quelle est la nature de la suite $u$? Argumenter la réponse. + \item Quel est le sens de variation de la suite $u$? Justifier la réponse. + \end{enumerate} + \item Compléter le repère ci-contre, en y représentant le terme $u(2)$ de la suite. + \end{enumerate} + \end{minipage} + \hfill + \begin{minipage}{0.3\textwidth} + \includegraphics[scale=0.3]{./fig/T1CMATH03614_graph} + \end{minipage} + + \begin{enumerate} + \setcounter{enumi}{3} + \item Parmi les situations suivantes, laquelle pourrait être modélisée grâce à la suite $u$? Justifier votre réponse. + \begin{itemize} + \item Situation A : une entreprise a vendu 200 unités d'un nouveau produit la première année. Chaque année elle en vend 10\% de plus que l'année précédente. + \item Situation B : une entreprise a vendu 200 unités d'un nouveau produit la première année. Chaque année elle en vend 20\% de plus que l'année précédente + \item Situation C : une entreprise a vendu 200 unités d'un nouveau produit la première année. Chaque année elle en vend 20 de plus que l'année précédente. + \end{itemize} + \end{enumerate} +\end{exercise} \collectexercisesstop{banque} diff --git a/TST/04_Formalisation_des_suites/fig/T1CMATH03609_graph.png b/TST/04_Formalisation_des_suites/fig/T1CMATH03609_graph.png new file mode 100644 index 0000000000000000000000000000000000000000..995aabd1f44421a0531bb5d9dbb442c23cc44c09 GIT binary patch literal 16750 zcmdUXcT`jPw{NUC%7Bgql&YhM4G@qTh*)SUC>l^o0I34f4LzugA}WL;Abk`O0RibH z1Vp4a0U`9z5$S;t0wj6+IQPE0)?M$d_5QfOci&^NW`-o^YK#?8Xj%F5Br*2#T-ONA;5C5qCzq;|_Qer8}Q!kFPlUDwU-$m3m! zMDaQAKM^K(rvBDxqr$8Nh4EV>Tqg`tPICJELeZ{~HzTzj2Yf89MD6P_cy~JNm6pqv z^9~oeA6CwEte5a=zSIiZw`s>`CsY{@n|$HT`lpJ`Jf*FqR{f0hbYuzr7WDQl@b3lZ zKVTK8eQjlt$0g64v9h;6#UgMVo8i6Be(9ZdDIHT|bzy(X(>IKIFP0V*L=HQ98U<{E z1I+}2)u-?zc^2}Hw?(UMa+_vqM@d0FoX*qi0cqf+dh*NK(Ky^h)Z^u+I;jyBwIKs7 zZ{c0^LkV2j>*nTWBg2}@!SI6kh0x6?)b+nax1msf?@)v5JHO}gJ{0QVk*z1-?aMo0 zvr*4?|GLn_n(*cSB?mOOZ@Gnq^}No^%ye*cBn&V0&f*UoIM8k@tC!I^H~bfTY5(ul 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