2016-2017/3e/Expression_litterale/Periode1/01_entrainement_eval.tex

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\titre{Technique: calcul et évaluation}
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\classe{Troisième}
\date{Septembre 2016}
%\duree{1 heure}
\sujet{01}
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    \begin{Exo}
        Faire les calculs suivants en détaillant des étapes.
        \begin{multicols}{3}
            \begin{enumerate}
                
            \item $A = -2 - 2 \times ( -3 )$
                \begin{solution}
                    \begin{eqnarray*}
                        A & = & -2 - 2 \times ( -3 ) \\ 
A & = & -2 + 6 \\ 
A & = & 4 
                    \end{eqnarray*}
                \end{solution}
                
            \item $B = 1 - ( -4 \times 3 )$
                \begin{solution}
                    \begin{eqnarray*}
                        A & = & 1 - ( -4 \times 3 ) \\ 
A & = & 1 - ( -12 ) \\ 
A & = & 13 
                    \end{eqnarray*}
                \end{solution}
                
            \item $C = -10 \times ( -7 ) - 8 \times ( -3 )$
                \begin{solution}
                    \begin{eqnarray*}
                        A & = & -10 \times ( -7 ) - 8 \times ( -3 ) \\ 
A & = & 70 + 24 \\ 
A & = & 94 
                    \end{eqnarray*}
                \end{solution}
                \columnbreak
                
            \item $D = ( 2 - 8 ) \times 7 - 2$
                \begin{solution}
                    \begin{eqnarray*}
                        A & = & ( 2 - 8 ) \times 7 - 2 \\ 
A & = & -6 \times 7 - 2 \\ 
A & = & -42 - 2 \\ 
A & = & -44 
                    \end{eqnarray*}
                \end{solution}
                
            \item $E = 8 ( 9 - 10 ) \times ( -2 )$
                \begin{solution}
                    \begin{eqnarray*}
                        A & = & 8 ( 9 - 10 ) \times ( -2 ) \\ 
A & = & 8 \times ( -1 ) \times ( -2 ) \\ 
A & = & -8 \times ( -2 ) \\ 
A & = & 16 
                    \end{eqnarray*}
                \end{solution}
                
            \item $F = ( -10 - 2 ) ( 10 - 6 )$
                \begin{solution}
                    \begin{eqnarray*}
                        F & = & ( -10 - 2 ) ( 10 - 6 ) \\ 
F & = & -12 \times 4 \\ 
F & = & -48 
                    \end{eqnarray*}
                \end{solution}
                \columnbreak
                
            \item $G = 5 ( -3 - 8 ) + 3$
                \begin{solution}
                    \begin{eqnarray*}
                        G & = & 5 ( -3 - 8 ) + 3 \\ 
G & = & 5 \times ( -11 ) + 3 \\ 
G & = & -55 + 3 \\ 
G & = & -52 
                    \end{eqnarray*}
                \end{solution}
                
            \item $H = 1 - ( -2 - 8 ) \times ( -6 )$
                \begin{solution}
                    \begin{eqnarray*}
                        H & = & 1 - ( -2 - 8 ) \times ( -6 ) \\ 
H & = & 1 - ( -10 \times ( -6 ) ) \\ 
H & = & 1 - 60 \\ 
H & = & -59 
                    \end{eqnarray*}
                \end{solution}
                
            \item $I = 5 ( 10 - ( -8 \times 3 ) )$
                \begin{solution}
                    \begin{eqnarray*}
                        I & = & 5 ( 10 - ( -8 \times 3 ) ) \\ 
I & = & 5 ( 10 - ( -24 ) ) \\ 
I & = & 5 \times 34 \\ 
I & = & 170 
                    \end{eqnarray*}
                \end{solution}
            \end{enumerate}
        \end{multicols}
    \end{Exo}

    \begin{Exo}
    Évaluer les expressions suivantes

    \begin{multicols}{3}
        \begin{enumerate}
            
            
        \item $10 x - 7$ en $x = 3$
            \begin{solution}
                \begin{eqnarray*}
                    A & = & 10 \times 3 - 7 \\ 
A & = & 30 - 7 \\ 
A & = & 23
                \end{eqnarray*}
            \end{solution}
            
            
        \item $-3 x - 8$ en $x = -5$
            \begin{solution}
                \begin{eqnarray*}
                    A & = & -3 \times ( -5 ) - 8 \\ 
A & = & 15 - 8 \\ 
A & = & 7
                \end{eqnarray*}
            \end{solution}
            
        \item $-3 x - 8$ en $x = 2$
            \begin{solution}
                \begin{eqnarray*}
                    A & = & -3 \times 2 - 8 \\ 
A & = & -6 - 8 \\ 
A & = & -14
                \end{eqnarray*}
            \end{solution}

            
            
        \item $2 x^{  2 } + 2 x - 4$ en $x = 4$
            \begin{solution}
                \begin{eqnarray*}
                    A & = & 2 \times 4^{  2 } + 2 \times 4 - 4 \\ 
A & = & 2 \times 16 + 8 - 4 \\ 
A & = & 32 + 8 - 4 \\ 
A & = & 40 - 4 \\ 
A & = & 36
                \end{eqnarray*}
            \end{solution}
            
        \item $2 x^{  2 } + 2 x - 4$ en $x = 4$
            \begin{solution}
                \begin{eqnarray*}
                    A & = & 2 \times 4^{  2 } + 2 \times 4 - 4 \\ 
A & = & 2 \times 16 + 8 - 4 \\ 
A & = & 32 + 8 - 4 \\ 
A & = & 40 - 4 \\ 
A & = & 36
                \end{eqnarray*}
            \end{solution}
        
        
        \item $-8 x^{  2 } + 9 x + 8$ en $x = -7$
            \begin{solution}
                \begin{eqnarray*}
                    A & = & -8 \times ( -7 )^{  2 } + 9 \times ( -7 ) + 8 \\ 
A & = & -8 \times 49 - 63 + 8 \\ 
A & = & -392 - 63 + 8 \\ 
A & = & -455 + 8 \\ 
A & = & -447
                \end{eqnarray*}
            \end{solution}
            
        
        \item $-3 x ( x - ( -7 ) )$ en $x = 8$
            
        \item $-3 x ( x - ( -7 ) )$ en $x = -10$
            
            
        \item $( -4 x + 5 ) ( -4 - 10 x )$ en $x = 1$
        \end{enumerate}
    \end{multicols}
    \end{Exo}
}

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