From b003547168d30cb24da88f8cbd975aa450fb9cd2 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Thu, 16 Mar 2023 09:57:38 +0100 Subject: [PATCH] Feat(2nd): DM2 --- .../DM_2023-04-24/bopytex_config.py | 22 ++ .../DM_2023-04-24/corr_joined_DM2.pdf | Bin 0 -> 1195114 bytes 2nd/Evaluations/DM_2023-04-24/joined_DM2.pdf | Bin 0 -> 929204 bytes 2nd/Evaluations/DM_2023-04-24/tpl_DM2.tex | 228 ++++++++++++++++++ 4 files changed, 250 insertions(+) create mode 100644 2nd/Evaluations/DM_2023-04-24/bopytex_config.py create mode 100644 2nd/Evaluations/DM_2023-04-24/corr_joined_DM2.pdf create mode 100644 2nd/Evaluations/DM_2023-04-24/joined_DM2.pdf create mode 100644 2nd/Evaluations/DM_2023-04-24/tpl_DM2.tex diff --git a/2nd/Evaluations/DM_2023-04-24/bopytex_config.py b/2nd/Evaluations/DM_2023-04-24/bopytex_config.py new file mode 100644 index 0000000..a4654ef --- /dev/null +++ b/2nd/Evaluations/DM_2023-04-24/bopytex_config.py @@ -0,0 +1,22 @@ +# bopytex_config.py +from math import ceil +from mapytex.calculus.random import expression as random_expression +from mapytex.calculus.random import list as random_list +from mapytex import stat +from mapytex import render +import random + +random.seed(0) # Controlling the seed allows to make subject reproductible + +render.set_render("tex") + +direct_access = { + "random_expression": random_expression, + "random_list": random_list, + "stat": stat, + "random": random, + "min": min, + "max": max, + "int": int, + "ceil": ceil, +} diff --git a/2nd/Evaluations/DM_2023-04-24/corr_joined_DM2.pdf b/2nd/Evaluations/DM_2023-04-24/corr_joined_DM2.pdf new file mode 100644 index 0000000000000000000000000000000000000000..36875722d288cc613b28768676d960e89846de8a GIT binary patch literal 1195114 zcmbrm18^r_^FEr5^NDTSwr$(CZQHhOXX9jJ+s4Mu#?IaEPxX6my>;)u?wzSK)qQH_ zoSr^U%}hVtHKYn6Vzi8OtN_xvrQtOIBLgP^1A)Df6@Z5aKrdrzXYOJ_z{W!GUmJj4 z%+kii)QNyz%*N2gRK(QS-ozBZ#|LnBaWXZu1$b;Qt1tiw34`f^@PY^%Lz)&QoL 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+\usetikzlibrary{decorations.markings} +\pgfplotsset{compat=1.18} + +\title{ DM1 \hfill \Var{ subject.Nom }} +\tribe{2nd} +\date{A rendre pour le 2 décembre 2022} +\duree{} + +\xsimsetup{ + solution/print = false +} + + +\pagestyle{empty} + +\begin{document} +\maketitle + +Le barème est donné à titre indicatif, il pourra être modifié. + +\begin{exercise}[subtitle={Calculs avec des fractions}, points=5] + Détailler les calculs suivants et donner le résultat sous la forme d'une fraction irréductible. + \Block{ + set fractions = { + "A": random_expression("{a} / {b} + {c} / {d}", ["a!=b", "c!=d", "b > 1", "d > 1"], global_config={"min_max": (0, 10)}), + "B": random_expression("{a} / {b} + {c}", ["a!=b", "b > 1"], global_config={"min_max": (1, 10)}), + "C": random_expression("{a} / {b} * {c}", ["a!=b", "b > 1"], global_config={"min_max": (1, 10)}), + "D": random_expression("{a} / {b} * {c} / {b}", ["a!=b", "c!=b", "b > 1"], global_config={"min_max": (1, 10)}), + "E": random_expression("{a} / {b} / ({c} / {b})", ["a!=b", "c!=b", "b > 1"], global_config={"min_max": (1, 10)}), + } + } + \begin{multicols}{3} + \begin{enumerate} + %- for (l, e) in fractions.items() + \item $\Var{l} = \Var{e}$ + %- endfor + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{solution} + \begin{multicols}{3} + \begin{enumerate} + %- for (l, e) in fractions.items() + \item + \begin{align*} + \Var{l} & = \Var{e.simplify().explain() | join(' \\\\ & = ')} \\ + & = \Var{e.simplify().simplified} + \end{align*} + %- endfor + \end{enumerate} + \end{multicols} +\end{solution} + +\begin{exercise}[subtitle={Inéquation et tableaux}, points=3] + Tracer le tableau de signe de la fonction suivante en le démontrant à l'aide de la résolution d'une inéquation. + %- set f = random_expression("{a}x + {b}", global_config={"min_max":(-20, 20), "rejected":[0, 1]}) + $$f(x) = \Var{f}$$ +\end{exercise} + +\begin{solution} + Pour déterminer les valeurs de $x$ pour lesquelles $f(x)$ est positive, il faut résoudre l'inéquation + + %- set cst = -f[0] + %- set coef = f[1] + %- set racine = cst / coef + \begin{align*} + f(x) & \geq 0 \\ + \Var{f} & \geq 0 \\ + \Var{f + cst} &\geq \Var{0 + cst} \\ + %- if coef > 0 + \frac{\Var{f + cst}}{\Var{coef}} &\geq \frac{\Var{cst}}{\Var{coef}} \\ + x &\geq \Var{racine.simplify()} \\ + \end{align*} + + Donc $f(x)$ est positif quand $x$ est supérieur à $\Var{racine}$. On en déduit le tableau de signe + %- else + \frac{\Var{f + cst}}{\Var{coef}} &\leq \frac{\Var{cst}}{\Var{coef}} \\ + x &\leq \Var{racine.simplify()} \\ + \end{align*} + + Donc $f(x)$ est positif quand $x$ est inférieur à $\Var{racine}$. On en déduit le tableau de signe + %- endif + + \begin{center} + \begin{tikzpicture} + \tkzTabInit[lgt=2,espcl=1]{$ t $/1,$ f(t) $/1}{, $\Var{racine}$ ,} + %- if coef > 0 + \tkzTabLine{, -, z, +, } + %- else + \tkzTabLine{, +, z, -, } + %- endif + \end{tikzpicture} + \end{center} +\end{solution} + +\begin{exercise}[subtitle={Vecteurs}, points=3] + \begin{multicols}{2} + \begin{enumerate} + \item Tracer les vecteurs $\vect{z} = \vect{u} + \vect{v}$ et $\vect{y} = 2\vect{u} - \vect{v}$ (le vecteur peut sortir du cadre) + %- set xa1, ya1 = random_list(["x", "y"], global_config={"min_max": (-5, 5), "rejected":[-2, -1, 0, 1, 2]}) + %- set xa2, ya2 = -xa1, ya1 + + %- set aminx = min(0, xa1, xa2, xa1+xa2, 2*xa1-xa2) + %- set amaxx = max(0, xa1, xa2, xa1+xa2, 2*xa1-xa2) + %- set aminy = min(0, ya1, ya2, ya1+ya2, 2*ya1-ya2) + %- set amaxy = max(0, ya1, ya2, ya1+ya2, 2*ya1-ya2) + + \begin{center} + \begin{tikzpicture}[scale=0.4] + \draw (\Var{aminx-1}, \Var{aminy-1}) rectangle (\Var{amaxx+1}, \Var{amaxy+1}); + \draw[very thick, ->] (0, 0) -- node [midway, sloped, above] {$\vect{u}$} (\Var{xa1}, \Var{ya1}); + \draw[very thick, -> ] (0, 0) -- node [midway, sloped, above] {$\vect{v}$} (\Var{xa2}, \Var{ya2}); + \end{tikzpicture} + \end{center} + \item Tracer la force résultat de la somme des 3 forces exercées sur le point $0$ représenté ci-dessous. + %- set x1, y1 = random_list(["x", "y"], global_config={"min_max": (-5, 5), "rejected":[-2, -1, 0, 1, 2]}) + %- set x2, y2 = -x1, y1 + %- set x3, y3 = x2, 0 + + %- set minx = min(0, x1, x2, x3, x1+x2, x2+x3, x1+x3, x1+x2+x3 ) + %- set maxx = max(0, x1, x2, x3, x1+x2, x2+x3, x1+x3, x1+x2+x3 ) + %- set miny = min(0, y1, y2, y3, y1+y2, y2+y3, y1+y3, y1+y2+y3 ) + %- set maxy = max(0, y1, y2, y3, y1+y2, y2+y3, y1+y3, y1+y2+y3 ) + + \begin{center} + \begin{tikzpicture}[scale=0.4] + \draw (\Var{minx-1}, \Var{miny-1}) rectangle (\Var{maxx+1}, \Var{maxy+1}); + \draw[very thick, ->] (0, 0) -- node [midway, sloped, above] {$\vect{F_1}$} (\Var{x1}, \Var{y1}); + \draw[very thick, -> ] (0, 0) -- node [midway, sloped, above] {$\vect{F_2}$} (\Var{x2}, \Var{y2}); + \draw[very thick, -> ] (0, 0) -- node [midway, sloped, above] {$\vect{F_3}$} (\Var{x3}, \Var{y3}); + \end{tikzpicture} + \end{center} + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{solution} + \begin{multicols}{2} + \begin{enumerate} + \item + \begin{center} + \begin{tikzpicture}[scale=0.4] + \draw (\Var{aminx-1}, \Var{aminy-1}) rectangle (\Var{amaxx+1}, \Var{amaxy+1}); + \draw[very thick, ->] (0, 0) -- node [midway, sloped, above] {$\vect{u}$} (\Var{xa1}, \Var{ya1}); + \draw[very thick, -> ] (0, 0) -- node [midway, sloped, above] {$\vect{v}$} (\Var{xa2}, \Var{ya2}); + + + \draw[very thick, ->, color=blue] (0, 0) + -- ++ (\Var{xa1}, \Var{ya1}) node [midway, sloped, above] {$\vect{u}$} + -- ++ (\Var{xa2}, \Var{ya2}) node [midway, sloped, above] {$\vect{v}$} ; + \draw[very thick, ->, color=blue] (0, 0) -- node [midway, sloped, left] {$\vect{z}$} (\Var{xa2+xa1}, \Var{ya2+ya1}); + \draw[very thick, ->, color=green] (0, 0) + -- ++ (\Var{xa1}, \Var{ya1}) node [midway, sloped, above] {$\vect{u}$} + -- ++ (\Var{xa1}, \Var{ya1}) node [midway, sloped, above] {$\vect{u}$} + -- ++ (-\Var{xa2}, -\Var{ya2}) node [midway, sloped, above] {$-\vect{v}$} ; + \draw[very thick, ->, color=green] (0, 0) -- node [midway, sloped, above] {$\vect{y}$} (\Var{2*xa1 - xa2}, \Var{2*ya1 - ya2}); + \end{tikzpicture} + \end{center} + + \item + \begin{center} + \begin{tikzpicture}[scale=0.4] + \draw (\Var{minx-1}, \Var{miny-1}) rectangle (\Var{maxx+1}, \Var{maxy+1}); + \draw[very thick, ->] (0, 0) -- node [midway, sloped, above] {$\vect{F_1}$} (\Var{x1}, \Var{y1}); + \draw[very thick, -> ] (0, 0) -- node [midway, sloped, above] {$\vect{F_2}$} (\Var{x2}, \Var{y2}); + \draw[very thick, -> ] (0, 0) -- node [midway, sloped, above] {$\vect{F_3}$} (\Var{x3}, \Var{y3}); + + \draw[very thick, ->, color=blue] (0, 0) + --++ (\Var{x1}, \Var{y1}) node [midway, sloped, above] {$\vect{F_1}$} + --++ (\Var{x2}, \Var{y2}) node [midway, sloped, above] {$\vect{F_2}$} + --++ (\Var{x3}, \Var{y3}) node [midway, sloped, above] {$\vect{F_3}$} + ; + \draw[very thick, ->, color=blue] (0, 0) -- (\Var{x1+x2+x3}, \Var{y1+y2+y3}) node [midway, sloped, above] {$\vect{F_1}+\vect{F_2}+\vect{F_3}$}; + \end{tikzpicture} + \end{center} + \end{enumerate} + \end{multicols} +\end{solution} + +\begin{exercise}[subtitle={Statistiques}, points=5] + %- set center = random.randint(30, 50) + %- set qty = random.randint(20, 40) + %- set dataset = stat.Dataset.random(qty, rd_args=(center, 1.5), nbr_format=int) + Ci-dessous la taille des poissons péchés lors du dernier challenge PêcheParty. + \begin{center} + \Var{dataset.tabular_latex(ceil(qty/15))} + \end{center} + \begin{enumerate} + \item Décrire la série statistique et donner l'effectif total. + \item Calculer la moyenne, les quartiles, l'écart interquartile et la médiane de cette série statistique. + \item Quelle est la valeur de l'écart-type de cette série statistique? + \end{enumerate} +\end{exercise} + +\begin{solution} + Dans cette correction les étapes de construction des indicateurs ne sont pas détaillés. + + Tableau des effectifs + %- set wdataset = stat.WeightedDataset(dataset) + \begin{center} + \Var{wdataset.tabular_latex()} + \end{center} + La population sont les poissons péchés lors du dernier challenge PêcheParty. Les individus sont les poissons. Le caractère est la taille des poissons. + \begin{multicols}{2} + \begin{itemize} + \item Effectif total : $\Var{dataset.effectif_total()}$ + \item Premier quartile $ Q_1 = \Var{dataset.quartile(1)}$ (position $\Var{dataset.posi_quartile(1)}$) + \item Médiane $ Me = \Var{dataset.quartile(2)}$ (position $\Var{dataset.posi_quartile(2)}$) + \item Troisième quartile $ Q_3 = \Var{dataset.quartile(3)}$ (position $\Var{dataset.posi_quartile(3)}$) + \item interquartile: $Q_3 - Q_1 = \Var{dataset.quartile(3)} - \Var{dataset.quartile(1)} = \Var{dataset.quartile(3) - dataset.quartile(1) }$ + + \item Moyenne: $\overline{x} = \Var{dataset.mean()}$ + \item Écart-type: $\sigma = \Var{dataset.sd()}$ + \end{itemize} + \end{multicols} +\end{solution} + + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End:

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