From db0035da4da031a4c3e30ed349f0d8efc434a1f0 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Tue, 29 Sep 2020 11:21:23 +0200 Subject: [PATCH] Feat: DS2 pour les TST1 --- TST/DS/DS_20_10_30/DS_20_09_30.pdf | Bin 0 -> 79758 bytes TST/DS/DS_20_10_30/DS_20_09_30.tex | 31 +++++++ TST/DS/DS_20_10_30/DS_20_09_30_QF.pdf | Bin 0 -> 56210 bytes TST/DS/DS_20_10_30/DS_20_09_30_QF.tex | 48 +++++++++++ TST/DS/DS_20_10_30/exercises.tex | 113 ++++++++++++++++++++++++++ tools/style/myXsim.sty | 1 + 6 files changed, 193 insertions(+) create mode 100644 TST/DS/DS_20_10_30/DS_20_09_30.pdf create mode 100644 TST/DS/DS_20_10_30/DS_20_09_30.tex create mode 100644 TST/DS/DS_20_10_30/DS_20_09_30_QF.pdf create mode 100644 TST/DS/DS_20_10_30/DS_20_09_30_QF.tex create mode 100644 TST/DS/DS_20_10_30/exercises.tex diff --git a/TST/DS/DS_20_10_30/DS_20_09_30.pdf b/TST/DS/DS_20_10_30/DS_20_09_30.pdf new file mode 100644 index 0000000000000000000000000000000000000000..9b87a366b2bd341979c22188745328c53a27c188 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+\input{exercises.tex} +\printcollection{banque} +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: + diff --git a/TST/DS/DS_20_10_30/DS_20_09_30_QF.pdf b/TST/DS/DS_20_10_30/DS_20_09_30_QF.pdf new file mode 100644 index 0000000000000000000000000000000000000000..455305ba90b8d46cc49201ff388b1a3c9ccf16de GIT binary patch literal 56210 zcmce6bBt)u)@9qaZQHhO+qQArwr%^it=qP3+wPwG`(|F|OJwP5^f@pt{7_g@PoQ)hcu zCu37*0@lAXN>KDNrgr8o76go}1pll3-Nn+z#ng#_Ud+bO#Z<)9*xtkxijNP<*~Q7! z&=$&LeF1)2fns_W2mt&G@D|F{&g6fs{O$eo>+F9w{?9<*_;*3z{EtCk{D+)>3k{6_ zQ2w9cfsyIo2I4<=m>BSKN%r zc(PD}xyIiQUsQ^CEb@ia&af}Jz3a(4?sIY!)bQ{i7*>3|#8?1BRml;j8UVC-Xz4Cx zhhNSwTQ=5DEgC|s87*>hI-(w>m`n=Ns+qJ2lv6fVe!hZ%2l4D=tt?i^^!INHd0_CZ z*ycZXq$+QQY;R10#J6Fs<0M6~z!`Pqet6LZT9QN+Lt{+jCrLY8S{V#V1rq)3cZDI1 zY9KWS(zxQdu38p1w|f2?NRxdIgHf_z6w zE=JzUY*=^d8W%}AojB!PbC_Xn%{n3R*Zk5dO|6|fg_!R<0_r`p2!U6 z5fumS3?{=SR0I-<-DH^TYXm{=%Afm5hcFe)8Z>_2KRLf=B!JTS3;^%ayp?UYkZnqx 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Interpréter votre réponse. + \end{enumerate} + \item Recherche par le calcul + \begin{enumerate} + \item Calculer $f'$ la dérivée de $f$. + \item Étudier le signe de $f'$ et en déduire les variations de $f$. + \item En déduire la valeur du maximum de $f$ ainsi que la valeur de $x$ pour laquel il est atteind. + \end{enumerate} + \end{enumerate} + \end{minipage} + \hfill + \begin{minipage}{0.4\textwidth} + \begin{tikzpicture}[xscale=0.6, yscale=0.7] + \tkzInit[xmin=0,xmax=55,xstep=5, + ymin=-5,ymax=45,ystep=5] + \tkzGrid + \tkzGrid[sub, subxstep=1, subystep=1] + \tkzDrawX[label={Production}, below=-20pt] + \tkzLabelX + \tkzDrawY[label={Recettes}, left=-50pt] + \tkzLabelY + \tkzFct[domain=0:55,color=red,very thick]% + { -0.1*\x**2+6*\x-50 }; + \end{tikzpicture} + \end{minipage} + \begin{enumerate} + \setcounter{enumi}{2} + \item (*) Soit $g$ la fonction définie par $g(x)=-0,1x^2+7,5x+90$ qui représente les coûts de production en fonction de $x$. + \begin{enumerate} + \item Simplifier l'expression des bénéfices $b(x) = f(x) - g(x)$. + \item Déterminer pour quelle valeur de $x$ les bénéfices sont positifs. + \end{enumerate} + \end{enumerate} + +\end{exercise} + +\begin{exercise}[subtitle={Suites}, points=7, step=1, type={Exercise}] + + \noindent + \begin{minipage}{0.6\textwidth} + \begin{enumerate} + \item On s'intéresse à une ruche qui n'est soumise ni au bruit ni à la pollution. Le graphique ci-contre représente l'évolution de la population en fonction des années. + + On note $n$ le numéro de l'année et $u_n$ le nombre d'abeilles à l'année $n$. + \bigskip + + \begin{enumerate} + \item Pourquoi peut-on estimer que la suite $(u_n)$ est arithmétique? Quelle est sa raison et son premier terme? + \item Quelle sera la population de cette ruche l'année 6? L'année 10? + \end{enumerate} + \end{enumerate} + \end{minipage} + \begin{minipage}{0.4\textwidth} + \begin{tikzpicture}[baseline=(a.north), xscale=0.7, yscale=0.7] + \tkzInit[xmin=0,xmax=6,xstep=1, + ymin=6500,ymax=9000,ystep=500] + \tkzGrid + \tkzGrid[sub, subystep=100, subxstep=1] + \tkzDrawX[label={année}, below=-20pt] + \tkzLabelX + \tkzDrawY[label={Nombre}, left=-30pt] + \tkzLabelY + \global\edef\tkzFctLast{7100+x*350} + \foreach \va in {0, 1, ...,5}{% + \tkzDefPointByFct[draw](\va)% + } + \end{tikzpicture} + \end{minipage} + + \begin{enumerate} + \setcounter{enumi}{1} + \item On s'intéresse à une riche perturbée par la pollution et le bruit. Elle est composée initialement de \np{50000} abeilles dont la reine mais sa population diminue de 8\% par an. + \begin{enumerate} + \item Quelle est la population de cette ruche après un an de perturbation? + \item Expliquer pourquoi la population de cette ruche est multipliée par 0.92 chaque année. + \end{enumerate} + On modélise la population de cette ruche par la suite géométrique $(v_n)$ de premier terme $v_0 = \np{50000}$ et de raison $q = 0.92$ + \begin{enumerate} + \setcounter{enumii}{2} + \item Calculer $v_1$, $v_2$ et $v_3$. + \item Écrire une programme python qui permettrait de calculer $v_{10}$. + \end{enumerate} + \end{enumerate} + +\end{exercise} + + +\collectexercisesstop{banque} diff --git a/tools/style/myXsim.sty b/tools/style/myXsim.sty index d9d9905..f9ccbd8 100644 --- a/tools/style/myXsim.sty +++ b/tools/style/myXsim.sty @@ -8,6 +8,7 @@ \RequirePackage[no-files]{xsim} \DeclareExerciseTagging{step} +\DeclareExerciseTagging{type} \DeclareExerciseTagging{difficulty} \DeclareExerciseTagging{origin}