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% Title Page
\titre{Technique: calcul et évaluation}
% \seconde \premiereS \PSTMG \TSTMG
\classe{Troisième}
\date{Septembre 2016}
%\duree{1 heure}
\sujet{\Var{infos.num}}
% DS DSCorr DM DMCorr Corr

%\printanswers
\pagestyle{empty}

\newcommand{\lesexos}{%
    \begin{Exo}
        Faire les calculs suivants en détaillant des étapes.
        \begin{multicols}{3}
            \begin{enumerate}
                \Block{set e = Expression.random("{a} + {b}*{c}")}
            \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}")}
            \item $B = \Var{e}$
                \begin{solution}
                    \begin{eqnarray*}
                        \Var{e.simplify().explain() | calculus(name = "A")} 
                    \end{eqnarray*}
                \end{solution}
                \Block{set e = Expression.random("{a} * {b} + {c} * {d}")}
            \item $C = \Var{e}$
                \begin{solution}
                    \begin{eqnarray*}
                        \Var{e.simplify().explain() | calculus(name = "A")} 
                    \end{eqnarray*}
                \end{solution}
                \columnbreak
                \Block{set e = Expression.random("({a} + {b})*{c} + {d}")}
            \item $D = \Var{e}$
                \begin{solution}
                    \begin{eqnarray*}
                        \Var{e.simplify().explain() | calculus(name = "A")} 
                    \end{eqnarray*}
                \end{solution}
                \Block{set e = Expression.random("{a} * ({b} + {c}) * {d}")}
            \item $E = \Var{e}$
                \begin{solution}
                    \begin{eqnarray*}
                        \Var{e.simplify().explain() | calculus(name = "A")} 
                    \end{eqnarray*}
                \end{solution}
                \Block{set e = Expression.random("({a} + {b})({c} - {d})")}
            \item $F = \Var{e}$
                \begin{solution}
                    \begin{eqnarray*}
                        \Var{e.simplify().explain() | calculus(name = "F")} 
                    \end{eqnarray*}
                \end{solution}
                \columnbreak
                \Block{set e = Expression.random("{a}({b}+{c}) + {d}")}
            \item $G = \Var{e}$
                \begin{solution}
                    \begin{eqnarray*}
                        \Var{e.simplify().explain() | calculus(name = "G")} 
                    \end{eqnarray*}
                \end{solution}
                \Block{set e = Expression.random("{a} - ({b} + {c}) * {d}")}
            \item $H = \Var{e}$
                \begin{solution}
                    \begin{eqnarray*}
                        \Var{e.simplify().explain() | calculus(name = "H")} 
                    \end{eqnarray*}
                \end{solution}
                \Block{set e = Expression.random("{c}({a} - {b} * {d})")}
            \item $I = \Var{e}$
                \begin{solution}
                    \begin{eqnarray*}
                        \Var{e.simplify().explain() | calculus(name = "I")} 
                    \end{eqnarray*}
                \end{solution}
            \end{enumerate}
        \end{multicols}
    \end{Exo}

    \begin{Exo}
    Évaluer les expressions suivantes

    \begin{multicols}{3}
        \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 = 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 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 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 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}
    \end{Exo}
}

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