85 lines
4.3 KiB
TeX
85 lines
4.3 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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\item Calculer les quantités suivantes
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\begin{multicols}{3}
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\begin{enumerate}
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\Block{set a, b = random_str("{a},{b*a}", val_min=2, val_max = 5).split(',')}
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\item $\dfrac{1}{\Var{a}}$ de \Var{b}m
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\Block{set a, b, c = random_str("{a},{b*a}, {a+1}", val_min=2, val_max = 5).split(',')}
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\item $\dfrac{\Var{c}}{\Var{a}}$ de \Var{b}\euro
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\Block{set a, b = random_str("{a},{b*a}", val_min=2, val_max = 10).split(',')}
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\item $\dfrac{1}{\Var{a}}$ de \Var{b}élèves
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\Block{set a = random_str("{a*3}", val_min=2, val_max = 10)}
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\item Un tiers de \Var{a}m
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\Block{set a, b = random_str("{a*10},{b*10}", val_min=2, val_max = 10).split(',')}
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\item \Var{a}\% de \Var{b} \euro
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\Block{set a, b = random_str("{a*10},{b*a}", val_min=2, val_max = 9).split(',')}
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\item \Var{a}\% de \Var{b} \euro
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\end{enumerate}
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\end{multicols}
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\item Faire les calculs suivants en détaillant des étapes.
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\begin{multicols}{3}
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\begin{enumerate}
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\Block{set e = Expression.random("({a} + {b})*{c} + {d}")}
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\item $\Var{e}$
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\Block{set e = Expression.random("{a} * ({b} + {c}) * {d}")}
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\item $\Var{e}$
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\Block{set e = Expression.random("{c}({a} - {b}) + {d}")}
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\item $\Var{e}$
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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", val_min=2, 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", val_min=2, 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("({b} - {a}) + {a}x + {c} + {d}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", val_min=2, 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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