138 lines
6.6 KiB
TeX
138 lines
6.6 KiB
TeX
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\begin{enumerate}
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\item Compléter les pointillés pour qu'il y est bien égalité.
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\hspace{-1cm}
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\begin{center}
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\Block{set a,b,c = random_str("{a},{b},{b*c}", conditions = ["{a} != {b}", "{a} > 1", "{b}>1","{c}>1"]).split(',')}%
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$\dfrac{\Var{a}}{\Var{b}} = \dfrac{\ldots}{\Var{c}}$
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\hfill
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\Block{set a,b,c = random_str("{a},{b},{b*c}", conditions = ["{a} != {b}", "{a} > 1", "{b}>1","{c}>1"]).split(',')}%
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$\dfrac{\Var{a}}{\Var{b}} = \dfrac{\ldots}{\Var{c}}$
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\hfill
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\Block{set a,b,c = random_str("{a},{b},{b*c}", conditions = ["{a} != {b}", "{a} > 1", "{b}>1","{c}>1"]).split(',')}%
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$\dfrac{\cdots}{\Var{c}} = \dfrac{\Var{a}}{\Var{b}}$
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\hfill
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\Block{set a,b,c = random_str("{a},{b},{a*c}", conditions = ["{a} != {b}", "{a} > 1", "{b}>1","{c}>1"]).split(',')}%
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$\dfrac{\Var{a}}{\Var{b}} = \dfrac{\Var{c}}{\cdots}$
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\end{center}
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\vfill
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\item Faire les calculs suivants en détaillant les étapes (penser à simplifier les fractions quand c'est possible).
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\begin{multicols}{2}
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\begin{enumerate}
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\Block{set e = Expression.random("{a} / {b} + {c} / {b}", ["{b} > 1", "{a} > 0", "{c} > 0"])}
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\item $A = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "A")}
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\end{eqnarray*}
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\end{solution}
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\Block{set e = Expression.random("{a} / {b} + {c} / {b}", ["{b} > 1"])}
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\item $B = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "B")}
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\end{eqnarray*}
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\end{solution}
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\Block{set e = Expression.random("{a} / {b} + {c} / {d*b}", ["{b} > 1", "{c} > 1", "{d} > 1"])}
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\item $C = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "C")}
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\end{eqnarray*}
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\end{solution}
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\Block{set e = Expression.random("{a} / {b} + {c} / {d*b}", ["{b} > 1", "{d} > 1"])}
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\item $D = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "D")}
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\end{eqnarray*}
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\end{solution}
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\Block{set e = Expression.random("{a} / {b} * {c}", ["{b} > 1", "{a} > 0", "{c} > 1", "{c} != {b}"])}
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\item $E = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "E")}
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\end{eqnarray*}
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\end{solution}
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\Block{set e = Expression.random("{a} / {b} * {c} / {d}", ["{b} > 1", "{a} > 0", "{c} > 0", "{d} > 1"])}
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\item $F = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "F")}
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\end{eqnarray*}
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\end{solution}
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\end{enumerate}
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\end{multicols}
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\item Évaluer les expressions suivantes
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\begin{multicols}{2}
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\begin{enumerate}
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\Block{set P = Polynom.random(degree = 1)}
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\Block{set x = Expression.random("{a}")}
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\item $\Var{P}$ en $x = \Var{x}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{P(x).explain()| calculus()}
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\end{eqnarray*}
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\end{solution}
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\Block{set P = Polynom.random(degree = 2)}
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\Block{set x = Expression.random("{a}")}
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\item $\Var{P}$ en $x = \Var{x}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{P(x).explain()| calculus()}
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\end{eqnarray*}
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\end{solution}
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\Block{set P = Expression.random("{a} x * (x - {b})")}
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\Block{set x = Expression.random("{a}")}
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\item $\Var{P}$ en $x = \Var{x}$
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\Block{set P = Expression.random("({a}x + {b})({c} + {d}x)")}
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\Block{set x = Expression.random("{a}")}
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\item $\Var{P}$ en $x = \Var{x}$
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\end{enumerate}
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\end{multicols}
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\item Réduire les expressions suivantes
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\begin{multicols}{2}
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\begin{enumerate}
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\Block{set A = Expression.random("{a}x + {c} + {d}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
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\item A = $\Var{A}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{A.simplify().explain() | calculus()}
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\end{eqnarray*}
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\end{solution}
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\Block{set B = Expression.random("({b} - {a}) + {a}x + {c} + {d}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
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\item B = $\Var{B}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{B.simplify().explain() | calculus()}
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\end{eqnarray*}
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\end{solution}
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\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]"])}
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\item C = $\Var{C}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{C.simplify().explain() | calculus()}
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\end{eqnarray*}
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\end{solution}
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\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]"])}
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\item D = $\Var{D}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{D.simplify().explain() | calculus()}
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\end{eqnarray*}
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\end{solution}
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\end{enumerate}
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\end{multicols}
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\end{enumerate}
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