113 lines
2.5 KiB
TeX
113 lines
2.5 KiB
TeX
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\documentclass[a4paper,10pt]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classDS}
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\usepackage{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/2013_2014}
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% Title Page
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\titre{Calcul littéral et statistiques}
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% \quatreC \quatreD \troisB \troisPro
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\classe{\troisB}
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\date{26 septemble 2013}
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% DS DSCorr DM DMCorr Corr
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\typedoc{DS}
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\duree{1 heure}
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\sujet{}
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\begin{document}
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\maketitle
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\Calc
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Le barème est donné à titre indicatif, il pourra être modifié.
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\begin{Exo}[4.5]
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Développer et réduire les expressions suivantes:
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\begin{eqnarray*}
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A &=& \frac{ 1 }{ 2 } + 2 \\
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P(x) &=& 6 x - 2 \\
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Q(x) &=& 4 x + 11\\
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R(x) &=& ( 6 x - 2 ) \times ( 4 x + 11 )
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\end{eqnarray*}
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Solutions:
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\begin{eqnarray*}
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A & = & \frac{ 1 }{ 2 } + 2 \\
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A & = & \frac{ 1 \times 1 }{ 2 \times 1 } + \frac{ 2 \times 2 }{ 1 \times 2 } \\
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A & = & \frac{ 1 + 4 }{ 2 } \\
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A & = & \frac{ 5 }{ 2 }
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\end{eqnarray*}
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\begin{eqnarray*}
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P(2) & = & 6 \times 2 - 2 \\
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P(2) & = & 12 - 2 \\
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P(2) & = & 10
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\end{eqnarray*}
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\begin{eqnarray*}
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Q(2) & = & 4 \times 2 + 11 \\
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Q(2) & = & 8 + 11 \\
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Q(2) & = & 19
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\end{eqnarray*}
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\begin{eqnarray*}
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P(x) + Q(X) & = & 6 x + 4 x - 2 + 11 \\
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P(x) + Q(X) & = & ( 6 + 4 ) x + ( -2 ) + 11 \\
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P(x) + Q(X) & = & 10 x + 9
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\end{eqnarray*}
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\begin{eqnarray*}
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P(x) + Q(X) & = & 6 x - 2 + 4 x + 11 \\
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P(x) + Q(X) & = & 4 x + 6 x + 11 - 2 \\
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P(x) + Q(X) & = & ( 4 + 6 ) x + 11 + ( -2 ) \\
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P(x) + Q(X) & = & 10 x + 9
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\end{eqnarray*}
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\begin{eqnarray*}
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R(x) & = & ( 6 x - 2 ) \times ( 4 x + 11 ) \\
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R(x) & = & 6 \times 4 x^{ 2 } + ( -2 ) \times 4 x + 6 \times 11 x + ( -2 ) \times 11 \\
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R(x) & = & 6 \times 4 x^{ 2 } + ( ( -2 ) \times 4 + 6 \times 11 ) x + ( -2 ) \times 11 \\
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R(x) & = & 24 x^{ 2 } + ( ( -8 ) + 66 ) x - 22 \\
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R(x) & = & 24 x^{ 2 } + 58 x - 22
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\end{eqnarray*}
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\end{Exo}
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\begin{Exo}
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Résoudre l'équation suivante
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\begin{eqnarray*}
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3 x^{ 2 } + x + 10 & = & 0
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\end{eqnarray*}
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Solution:
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On commence par calculer le discriminant
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\begin{eqnarray*}
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\Delta & = & b^2-4ac
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\end{eqnarray*}
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\begin{eqnarray*}
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\Delta & = & 1^{ 2 } - 4 \times 3 \times 10 \\
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\Delta & = & 1 - 12 \times 10 \\
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\Delta & = & 1 - 120 \\
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\Delta & = & -119
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\end{eqnarray*}
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Alors $\Delta = -119$
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\end{Exo}
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\end{document}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: "master"
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%%% End:
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