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DM de noel pour les 302

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Bertrand Benjamin 2017-12-06 11:34:44 +03:00
parent 920999f766
commit b3df2a974d
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3e/DM/DM noel/all_DM_noel.pdf Normal file
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3e/DM/DM noel/exo_calculs.tex Normal file
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\begin{enumerate}
\item Compléter les pointillés pour qu'il y est bien égalité.
\hspace{-1cm}
\begin{center}
\Block{set a,b,c = random_str("{a},{b},{b*c}", conditions = ["{a} != {b}", "{a} > 1", "{b}>1","{c}>1"]).split(',')}%
$\dfrac{\Var{a}}{\Var{b}} = \dfrac{\ldots}{\Var{c}}$
\hfill
\Block{set a,b,c = random_str("{a},{b},{b*c}", conditions = ["{a} != {b}", "{a} > 1", "{b}>1","{c}>1"]).split(',')}%
$\dfrac{\Var{a}}{\Var{b}} = \dfrac{\ldots}{\Var{c}}$
\hfill
\Block{set a,b,c = random_str("{a},{b},{b*c}", conditions = ["{a} != {b}", "{a} > 1", "{b}>1","{c}>1"]).split(',')}%
$\dfrac{\cdots}{\Var{c}} = \dfrac{\Var{a}}{\Var{b}}$
\hfill
\Block{set a,b,c = random_str("{a},{b},{a*c}", conditions = ["{a} != {b}", "{a} > 1", "{b}>1","{c}>1"]).split(',')}%
$\dfrac{\Var{a}}{\Var{b}} = \dfrac{\Var{c}}{\cdots}$
\end{center}
\vfill
\item Faire les calculs suivants en détaillant les étapes (penser à simplifier les fractions quand c'est possible).
\begin{multicols}{2}
\begin{enumerate}
\Block{set e = Expression.random("{a} / {b} + {c} / {b}", ["{b} > 1", "{a} > 0", "{c} > 0"])}
\item $A = \Var{e}$
\begin{solution}
\begin{eqnarray*}
\Var{e.simplify().explain() | calculus(name = "A")}
\end{eqnarray*}
\end{solution}
\Block{set e = Expression.random("{a} / {b} + {c} / {b}", ["{b} > 1"])}
\item $B = \Var{e}$
\begin{solution}
\begin{eqnarray*}
\Var{e.simplify().explain() | calculus(name = "B")}
\end{eqnarray*}
\end{solution}
\Block{set e = Expression.random("{a} / {b} + {c} / {d*b}", ["{b} > 1", "{c} > 1", "{d} > 1"])}
\item $C = \Var{e}$
\begin{solution}
\begin{eqnarray*}
\Var{e.simplify().explain() | calculus(name = "C")}
\end{eqnarray*}
\end{solution}
\Block{set e = Expression.random("{a} / {b} + {c} / {d*b}", ["{b} > 1", "{d} > 1"])}
\item $D = \Var{e}$
\begin{solution}
\begin{eqnarray*}
\Var{e.simplify().explain() | calculus(name = "D")}
\end{eqnarray*}
\end{solution}
\Block{set e = Expression.random("{a} / {b} * {c}", ["{b} > 1", "{a} > 0", "{c} > 1", "{c} != {b}"])}
\item $E = \Var{e}$
\begin{solution}
\begin{eqnarray*}
\Var{e.simplify().explain() | calculus(name = "E")}
\end{eqnarray*}
\end{solution}
\Block{set e = Expression.random("{a} / {b} * {c} / {d}", ["{b} > 1", "{a} > 0", "{c} > 0", "{d} > 1"])}
\item $F = \Var{e}$
\begin{solution}
\begin{eqnarray*}
\Var{e.simplify().explain() | calculus(name = "F")}
\end{eqnarray*}
\end{solution}
\end{enumerate}
\end{multicols}
\item Évaluer les expressions suivantes
\begin{multicols}{2}
\begin{enumerate}
\Block{set P = Polynom.random(degree = 1)}
\Block{set x = Expression.random("{a}")}
\item $\Var{P}$ en $x = \Var{x}$
\begin{solution}
\begin{eqnarray*}
\Var{P(x).explain()| calculus()}
\end{eqnarray*}
\end{solution}
\Block{set P = Polynom.random(degree = 2)}
\Block{set x = Expression.random("{a}")}
\item $\Var{P}$ en $x = \Var{x}$
\begin{solution}
\begin{eqnarray*}
\Var{P(x).explain()| calculus()}
\end{eqnarray*}
\end{solution}
\Block{set P = Expression.random("{a} x * (x - {b})")}
\Block{set x = Expression.random("{a}")}
\item $\Var{P}$ en $x = \Var{x}$
\Block{set P = Expression.random("({a}x + {b})({c} + {d}x)")}
\Block{set x = Expression.random("{a}")}
\item $\Var{P}$ en $x = \Var{x}$
\end{enumerate}
\end{multicols}
\item Réduire les expressions suivantes
\begin{multicols}{2}
\begin{enumerate}
\Block{set A = Expression.random("{a}x + {c} + {d}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
\item A = $\Var{A}$
\begin{solution}
\begin{eqnarray*}
\Var{A.simplify().explain() | calculus()}
\end{eqnarray*}
\end{solution}
\Block{set B = Expression.random("({b} - {a}) + {a}x + {c} + {d}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
\item B = $\Var{B}$
\begin{solution}
\begin{eqnarray*}
\Var{B.simplify().explain() | calculus()}
\end{eqnarray*}
\end{solution}
\Block{set C = Expression.random("{a}x^2 + {c} + {d}x + {d} + {a}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
\item C = $\Var{C}$
\begin{solution}
\begin{eqnarray*}
\Var{C.simplify().explain() | calculus()}
\end{eqnarray*}
\end{solution}
\Block{set D = Expression.random("{a}x^2 + {c}x^2 + {d}x + {d} + {a}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
\item D = $\Var{D}$
\begin{solution}
\begin{eqnarray*}
\Var{D.simplify().explain() | calculus()}
\end{eqnarray*}
\end{solution}
\end{enumerate}
\end{multicols}
\end{enumerate}

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3e/DM/DM noel/exo_proba.tex Normal file
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\Block{set a,b,c = random_str("{a*d},{b*d},{c}", conditions = ["{a} != {b}", "{a} > 1", "{b}>1", "{c} > 1", "{d}>1"]).split(',')}
\Block{set total = int(a) + int(b) + int(c)}
Dans un sac, il y a \Var{a} bonbons à la menthe, \Var{b} bonbons à la fraise et \Var{c} au chocolat. On choisit un bonbon au hasard dans ce sac.
\begin{enumerate}
\item Combien y a-t-il d'issues en tout?
\begin{solution}
Il y a \Var{total} bonbons.
\end{solution}
\item Calculer la probabilité de tirer un bonbon à la fraise.
\begin{solution}
$T($ tirer un bonbon à la fraise $) = \dfrac{\Var{a}}{\Var{total}}$
\end{solution}
\item Calculer la probabilité de tirer un bonbon qui n'est pas au chocolat.
\begin{solution}
\Block{set nonChoco = int(a) + int(b)}
$T($ tirer un bonbon à la fraise $) = \dfrac{\Var{nonChoco}}{\Var{total}}$
\end{solution}
\item Calculer la probabilité de tirer un bonbon au réglisse.
\begin{solution}
$T($ tirer un bonbon au réglisse $) = \dfrac{0}{\Var{total}} = 0$
\end{solution}
\item Dans un autre sac, on place 25 bonbons à la menthe et 34 bonbons à la fraise. Lise préfère les bonbons à la menthe. Dans quel sac doit-elle tirer un bonbon pour avoir le plus de chance d'avoir un bonbon qu'elle préfère?
\end{enumerate}

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3e/DM/DM noel/exo_tech_thales.tex Normal file
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\Block{set AO, OD, CD, OB = random_str("{a},{b},{c},{d}", ["{a} < {b}", "{c} != {d}"], 2, 20).split(',')}
Dans la figure suivante, $(AB)$ et $(CD)$ sont parallèles, $AO = \Var{AO}$, $OD = \Var{OD}$, $CD = \Var{CD}$ et $OB = \Var{OB}$.
\Block{set fig = random_str("{a}", [], 1, 2)}
\begin{minipage}{0.5\textwidth}
\includegraphics[scale=0.4]{./fig/thales\Var{fig}}
\end{minipage}
\begin{minipage}{0.5\textwidth}
Calculer les longueurs $AB$ et $BC$.
\end{minipage}

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3e/DM/DM noel/tpl_DM_noel.tex Normal file
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\documentclass[a4paper,12pt]{article}
\usepackage{myXsim}
\usepackage{wrapfig}
\title{DM de noël}
\tribe{302}
\date{Mardi de ma rentrée}
\sujet{\Var{infos.num}}
\xsimsetup{
solution/print = false
}
\begin{document}
\maketitle
Vous devez rendre le sujet avec la copie.
\begin{exercise}[subtitle={Techniques de calculs \Cal}]
\Block{include "./exo_calculs.tex"}
\end{exercise}
\begin{exercise}[subtitle={Thalès \Com \Rai}]
\Block{include "./exo_tech_thales.tex"}
\end{exercise}
\begin{exercise}[subtitle={Mes bonbons préférés \Rep \Com}]
\Block{include "./exo_proba.tex"}
\end{exercise}
\end{questions}
\end{document}
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