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