82 lines
3.9 KiB
TeX
82 lines
3.9 KiB
TeX
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\begin{exercise}[subtitle={Automatismes}]
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\begin{enumerate}
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\item Développer puis réduire les expressions suivantes
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\begin{multicols}{3}
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\begin{enumerate}
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%- set A = Expression.random("{a}*x^2 + {b}*x + {c}*x + {d}")
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\item $A = \Var{A}$
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%- set B = Expression.random("{a}*x^2 + {b}*x^2 + {c}*x + {d} + {e}*x")
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\item $B = \Var{B}$
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%- set C = Expression.random("{a}*({b}*x + {d})")
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\item $C = \Var{C}$
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%- set D = Expression.random("{a}*x*({b}x + {d})")
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\item $D = \Var{D}$
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%- set E = Expression.random("({a}x+{b})({c}x+{d})")
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\item $E = \Var{E}$
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%- set F = Expression.random("({a}x+{b})^2")
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\item $F = \Var{F}$
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\end{enumerate}
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\end{multicols}
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\item Faire les calculs en détaillant les étapes
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\begin{multicols}{2}
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\begin{enumerate}
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%- set fA = Expression.random("{a}/{b} + {c}/{b}", min_max=[2, 10])
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\item $\Var{fA}$
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%- set fB = Expression.random("{a}/{b} + {c}/{k*b}", min_max=[2, 10], conditions=["a!=b"])
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\item $\Var{fB}$
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%- set fC = Expression.random("{a}/{b} + {c}/{d}", min_max=[2, 10], conditions=["b%d!=0", "a!=b", "c!=d" ])
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\item $\Var{fC}$
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%- set fD = Expression.random("{a}/{b} * {c}/{d}", min_max=[2, 10], conditions=["b%d!=0", "a!=b", "c!=d" ])
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\item $\Var{fD}$
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\end{enumerate}
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\end{multicols}
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\item Résoudre les équations et l'inéquation suivantes
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\begin{multicols}{3}
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\begin{enumerate}
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%- set eA = Expression.random("{a}*x + {d}")
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\item $\Var{eA} = 0$
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%- set eB_l = Expression.random("{a}*x+ {d}")
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%- set eB_r = Expression.random("{a}*x + {d}")
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\item $\Var{eB_l} = \Var{eB_r}$
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%- set eC = Expression.random("{a}*x+ {d}")
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\item $\Var{eC} \leq 0$
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\end{enumerate}
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\end{multicols}
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\end{enumerate}
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\end{exercise}
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\begin{solution}
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\begin{enumerate}
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\item Pas de correction disponible...
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%#\begin{enumerate}
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%# \item \[A = \Var{A} = \Var{A.simplify()}\]
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%# \item \[B = \Var{B} = \Var{B.simplify()}\]
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%# \item \[C = \Var{C} = \Var{C.simplify()}\]
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%# \item \[D = \Var{D} = \Var{D.simplify()}\]
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%# \item \[E = \Var{E} = \Var{E.simplify()}\]
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%# \item \[F = \Var{F} = \Var{F.simplify()}\]
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%#\end{enumerate}
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\item Faire les calculs en détaillant les étapes
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\begin{multicols}{2}
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\begin{enumerate}
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\item $\Var{fA} = \Var{fA.simplify()}$
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\item $\Var{fB} = \Var{fB.simplify()}$
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\item $\Var{fC} = \Var{fC.simplify()}$
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\item $\Var{fD} = \Var{fD.simplify()}$
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\end{enumerate}
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\end{multicols}
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\item Résoudre les équations et l'inéquation suivantes
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\begin{multicols}{3}
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\begin{enumerate}
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\item $x = -\dfrac{\Var{-eA[0]}}{\Var{eA[1]}}}$
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\item $x = \frac{\Var{eB_l[0] - eB_r[0]}}{\Var{eB_l[1] - eB_r[1]}}$
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\item
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%- if eC[1] > 0
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$x \leq -\dfrac{\Var{-eC[0]}}{\Var{eC[1]}}}$
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%- else
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$x \geq -\dfrac{\Var{-eC[0]}}{\Var{eC[1]}}}$
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%- endif
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\end{enumerate}
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\end{multicols}
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\end{enumerate}
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\end{solution}
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