204 lines
6.7 KiB
TeX
204 lines
6.7 KiB
TeX
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\documentclass[a4paper,12pt, table]{/media/documents/Cours/Prof/Enseignements/2014-2015/tools/style/classDS}
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\usepackage{/media/documents/Cours/Prof/Enseignements/2014-2015/2014_2015}
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%\geometry{left=10mm,right=10mm, top=10mm, bottom=10mm}
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% Title Page
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\titre{4}
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% \seconde \premiereS \PSTMG \TSTMG
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\classe{\seconde}
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\date{6 mai 2015}
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%\duree{1 heure}
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\sujet{28}
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% DS DSCorr DM DMCorr Corr
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\typedoc{DM}
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%\printanswers
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\begin{document}
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\maketitle
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Vous devez rendre le sujet avec la copie.
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\begin{questions}
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\question
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\begin{parts}
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\part Développer et simplifier les expressions suivantes
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\begin{subparts}
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\begin{multicols}{2}
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\subpart $A = ( -4 x + 10 ) ( -4 - ( -10 x ) )$
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\begin{solution}
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\begin{eqnarray*}
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A & = & ( -4 x + 10 ) ( -4 - ( -10 x ) ) \\
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A & = & ( - 4 x + 10 ) ( -4 - ( - 10 x ) ) \\
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A & = & ( - 4 x + 10 ) ( - 4 - ( - 10 x ) ) \\
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A & = & ( - 4 x + 10 ) ( - 4 + 10 x ) \\
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A & = & - 40 x^{ 2 } + 116 x - 40
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\end{eqnarray*}
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\end{solution}
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\subpart $B = ( -6 x - 1 )^{ 2 } + 6$
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\begin{solution}
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\begin{eqnarray*}
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A & = & ( -6 x - 1 )^{ 2 } + 6 \\
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A & = & ( - 6 x - 1 )^{ 2 } + 6 \\
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A & = & ( - 6 x - 1 )^{ 2 } + 6 \\
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A & = & - 6 x - 1^{ 2 } + 6 \\
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A & = & - 6 x - 1 ( - 6 x - 1 ) + 6 \\
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A & = & -6 \times ( -6 ) x^{ 2 } + ( -1 \times ( -6 ) - 6 \times ( -1 ) ) x - 1 \times ( -1 ) + 6 \\
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A & = & 36 x^{ 2 } + ( 6 + 6 ) x + 1 + 6 \\
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A & = & 36 x^{ 2 } + 12 x + 7
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\end{eqnarray*}
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\end{solution}
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\subpart $C = 5 x + 2 + 4 ( -2 x + 2 )^{ 2 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & 5 x + 2 + 4 ( -2 x + 2 )^{ 2 } \\
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A & = & 5 x + 2 + 4 ( - 2 x + 2 )^{ 2 } \\
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A & = & 5 x + 2 + 4 ( - 2 x + 2 ) ( - 2 x + 2 ) \\
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A & = & 5 x + 2 + 4 ( -2 \times ( -2 ) x^{ 2 } + ( 2 \times ( -2 ) - 2 \times 2 ) x + 2 \times 2 ) \\
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A & = & 5 x + 2 + 4 ( 4 x^{ 2 } + ( -4 - 4 ) x + 4 ) \\
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A & = & 5 x + 2 + 4 ( 4 x^{ 2 } - 8 x + 4 ) \\
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A & = & 5 x + 2 + 4 \times 4 x^{ 2 } + 4 \times ( -8 ) x + 4 \times 4 \\
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A & = & 16 x^{ 2 } - 27 x + 18
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\end{eqnarray*}
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\end{solution}
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\end{multicols}
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\end{subparts}
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\part Factoriser les expressions suivantes
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\begin{subparts}
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\begin{multicols}{2}
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\subpart $A = -3 x^{ 2 } - x$
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\subpart $B = 100 x^{ 2 } + 36 + 120 x$
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\subpart $C = 49 x^{ 2 } - 49$
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\subpart $D = 36 x^{ 2 } - 12 x + 1$
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\end{multicols}
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\end{subparts}
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\part Résoudre les équations suivantes
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\begin{subparts}
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\begin{multicols}{2}
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\subpart $10 x - 10 = 0$
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\subpart $9 x + 5 = - 6 x + 4$
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\columnbreak
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\subpart $- 5 x^{ 2 } - 4 x - 9 = -5x^2$
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\subpart $( -6 x + 7 ) ( -5 x - 1 ) = 0$
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\end{multicols}
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\end{subparts}
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\end{parts}
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\question
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\begin{parts}
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\part Soit $A(-9 ; -3)$, $B(-9 ; -3)$, $C(8 ; -3)$ et $D(-3 ; -9)$. Est-ce que les vecteurs $\vec{AB}$ et $\vec{CD}$ sont colinéaires?
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\part Soit $A(-9 ; 6)$, $B(-10 ; -8)$, $C(9 ; -4)$ et $D(5 ; -9)$. Est-ce que les vecteurs $\vec{AB}$ et $\vec{CD}$ sont colinéaires?
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\part Soit $A(-3 ; -2)$, $B(-6 ; 8)$, $C(-5 ; 7)$ et $D(-2 ; -3)$. Est-ce que les droites $(AC)$ et $(BD)$ sont colinéaires?
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\end{parts}
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\question
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\begin{parts}
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\part Faire les calculs suivants en \textbf{détaillant les étapes} et en simplifiant les fractions.
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\begin{multicols}{2}
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\begin{subparts}
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\subpart $\displaystyle A = \frac{ 6 }{ 6 } \times 1$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ 6 }{ 6 } \times 1 \\
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A & = & 1
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle B = \frac{ -3 }{ 9 } + \frac{ 4 }{ 90 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ -3 }{ 9 } + \frac{ 4 }{ 90 } \\
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A & = & \frac{ -3 \times 10 }{ 9 \times 10 } + \frac{ 4 \times 1 }{ 90 \times 1 } \\
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A & = & \frac{ -30 }{ 90 } + \frac{ 4 }{ 90 } \\
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A & = & \frac{ -30 + 4 }{ 90 } \\
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A & = & \frac{ -26 }{ 90 } \\
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A & = & \frac{ -13 \times 2 }{ 45 \times 2 } \\
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A & = & \frac{ -13 }{ 45 }
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle C = \frac{ -3 }{ 7 } + \frac{ 1 }{ -2 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ -3 }{ 7 } + \frac{ 1 }{ -2 } \\
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A & = & \frac{ -3 \times ( -2 ) }{ 7 \times ( -2 ) } + \frac{ 1 \times 7 }{ -2 \times 7 } \\
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A & = & \frac{ 6 }{ -14 } + \frac{ 7 }{ -14 } \\
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A & = & \frac{ 6 + 7 }{ -14 } \\
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A & = & \frac{ 13 }{ -14 } \\
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A & = & \frac{ -13 }{ 14 }
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle D = \frac{ 4 }{ -6 } - 2$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ 4 }{ -6 } - 2 \\
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A & = & \frac{ 4 \times 1 }{ -6 \times 1 } + \frac{ -2 \times ( -6 ) }{ 1 \times ( -6 ) } \\
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A & = & \frac{ 4 }{ -6 } + \frac{ 12 }{ -6 } \\
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A & = & \frac{ 4 + 12 }{ -6 } \\
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A & = & \frac{ 16 }{ -6 } \\
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A & = & \frac{ -16 }{ 6 } \\
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A & = & \frac{ -8 \times 2 }{ 3 \times 2 } \\
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A & = & \frac{ -8 }{ 3 }
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\end{eqnarray*}
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\end{solution}
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\end{subparts}
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\end{multicols}
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\part Mettre les expressions suivantes sur le même dénominateur
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\begin{multicols}{2}
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\begin{subparts}
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\subpart $\displaystyle A = \frac{ 7 }{ -8 x } \times 8$
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\subpart $\displaystyle B = \frac{ 5 }{ -6 } + \frac{ -4 x }{ 36 }$
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\subpart $\displaystyle C = \frac{ 7 x }{ 9 } + \frac{ 1 }{ 4 x }$
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\subpart $\displaystyle D = \frac{ -9 }{ 4 x } + 6$
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\end{subparts}
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\end{multicols}
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\end{parts}
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\end{questions}
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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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