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% Title Page
\titre{1}
% \seconde \premiereS \PSTMG \TSTMG
\classe{Cinquième}
\date{1 février 2016}
%\duree{1 heure}
\sujet{\Var{infos.num}}
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%\printanswers

\begin{document}

\maketitle

\ifprintanswers
    \begin{center}
        \Large Solution
    \end{center}
    \normalsize
\else
    \textbf{Nom - Prénom}
\fi


\begin{questions}
    \question Completer ces opérations à trous pour qu'il y est égalité.
    \begin{multicols}{2}
        \begin{parts}
            % Facile
            \Block{set a,b,tot,ans,c = random_str("{a},{b},{a+b},{a+b-c},{c}", val_min = 25, val_max = 200).split(',')}
            \part $\Var{a} + \Var{b} = \quad \cdots \quad + \Var{c}$
            \begin{solution}

                $\Var{a} + \Var{b} = \Var{ans} + \Var{c} = \Var{tot}$
            \end{solution}

            % Multiplications
            \Block{set a,b,tot,ans,c = random_str("{a}, {7*b}, {a*7*b}, {b}, {a*7}", val_min=2, val_max=14).split(',')}
            \part $\Var{a} \times \Var{b} = \quad \cdots \quad \times \Var{c}$
            \begin{solution}

                $\Var{a} \times  \Var{b} = \Var{ans} \times \Var{c} = \Var{tot}$
            \end{solution}

            % Trou négatif
            \Block{set a,b,tot,ans,c = random_str("{a},{b},{a+b},{a+b-c},{c}", conditions = ["{a+b-c}<0"], val_min = 25, val_max = 200).split(',')}
            \part $\Var{a} + \Var{b} = \quad \cdots \quad + \Var{c}$
            \begin{solution}

                $\Var{a} + \Var{b} = \Var{ans} + \Var{c} = \Var{tot}$
            \end{solution}

            % Multiplications
            \Block{set a,b,tot,ans,c = random_str("{a}, {b}, {a*b}, {a*b-c}, {c}",conditions=['{a*b-c}>0'], val_min=2, val_max=20).split(',')}
            \part $\Var{a} \times \Var{b} = \quad \cdots \quad + \Var{c}$
            \begin{solution}

                $\Var{a} \times \Var{b} = \Var{ans} + \Var{c} = \Var{tot}$
            \end{solution}
        \end{parts}
        
    \end{multicols}

    \question Répondre aux questions en indiquant les calculs effectués.
    \begin{parts}
        \Block{set a,b = random_str("{a},{b}", conditions=["gcd({a},{b})==1", "gcd({a}, 3)==1", "gcd({a}, 7)==1", "gcd({a}, 11)==1", "{2*a} < {b}"], val_min=2, val_max=25).split(",")}
        \part Quel nombre multiplié par \Var{a} donne \Var{b}?

        \begin{solution}
            Quand on multiple \Var{a} par $\frac{\Var{b}}{\Var{a}} = \Var{int(b)/int(a)}$ on obtient $\Var{b}$. 
            \[ \Var{a} \times \Var{int(b)/int(a)} = \Var{b} \]
        \end{solution}
        \ifprintanswers
        \else
        \begin{minipage}[t]{0.5\textwidth}
            Réponse: \dotfill
            \\[0.2cm]
            .\dotfill
            \\
        \end{minipage}
        \vline
        \begin{minipage}[t]{1.3\textwidth}
            Calculs

        \end{minipage}
        \fi 

        \Block{set a,b = random_str("{a},{b}", conditions=["gcd({a},{b})==1", "gcd({a}, 3)==1", "gcd({a}, 7)==1", "gcd({a}, 11)==1", "{2*a} < {b}"], val_min=2, val_max=25).split(",")}
        \part Par combien faut-il multiplier $\Var{a}$ pour obtenir $\Var{b}$?

        \begin{solution}
            Quand on multiple \Var{a} par $\frac{\Var{b}}{\Var{a}} = \Var{int(b)/int(a)}$ on obtient $\Var{b}$. 
            \[ \Var{a} \times \Var{int(b)/int(a)} = \Var{b} \]
        \end{solution}
        \ifprintanswers
        \else
        \begin{minipage}[t]{0.5\textwidth}
            Réponse: \dotfill
            \\[0.2cm]
            .\dotfill
            \\
        \end{minipage}
        \vline
        \begin{minipage}[t]{1.3\textwidth}
            Calculs

        \end{minipage}
        \fi 

        \Block{set a,b = random_str("{a},{b}", conditions=["gcd({a},{b})==1", "gcd({a}, 10)==1"], val_min=2, val_max=25).split(",")}
        \part Par combien faut-il multiplier $\Var{a}$ pour obtenir $\Var{b}$?

        \begin{solution}
            Quand on multiple \Var{a} par $\frac{\Var{b}}{\Var{a}}$ on obtient $\Var{b}$.

            Multiplier par $\Var{int(a)/int(b)}$ ne convient pas car c'est une valeur approchée. Si on le multiplie par $\Var{a}$, on n'obtiendra pas exactement $\Var{b}$.
        \end{solution}
        \ifprintanswers
        \else
        \begin{minipage}[t]{0.5\textwidth}
            Réponse: \dotfill
            \\[0.2cm]
            .\dotfill
            \\
        \end{minipage}
        \vline
        \begin{minipage}[t]{1.3\textwidth}
            Calculs

        \end{minipage}
        \fi 
    \end{parts}

    \question Faire les calculs suivants en détaillant les étapes.
    \begin{parts}
        \Block{set A = Expression.random("_ + _ * _", val_min = 2)}
        \part $A = \Var{A} = \dotfill$ \\
        \begin{solution}
            $A = \Var{A.simplify().explain() | join(" = ")}$
        \end{solution}
        
        \Block{set B = Expression.random("_ * _ + _", val_min = 2)}
        \part $B = \Var{B} = \dotfill$ \\
        \begin{solution}
            $B = \Var{B.simplify().explain() | join(" = ")}$
        \end{solution}
        
        \Block{set C = Expression.random("(_ + _)*_", val_min = 2)}
        \part $C = \Var{C} = \dotfill$ \\
        \begin{solution}
            $C = \Var{C.simplify().explain() | join(" = ")}$
        \end{solution}
        
        \Block{set D = Expression.random("(_ + _)*_*_ + _", val_min = 2)}
        \part $D = \Var{D} = \dotfill$ \\
        \begin{solution}
            $D = \Var{D.simplify().explain() | join(" = ")}$
        \end{solution}
    \end{parts}

    \question Tracer les symétriques (en codant les traits de constructions)

    \hspace{-1cm}
    \includegraphics[scale=1.0]{./fig/sym}

\end{questions}

\end{document}

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