208 lines
7.0 KiB
TeX
208 lines
7.0 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{12}
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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 $A = ( 5 x - 8 ) ( 5 - ( -5 x ) )$
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\begin{solution}
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\begin{eqnarray*}
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A & = & ( 5 x - 8 ) ( 5 - ( -5 x ) ) \\
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A & = & ( 5 x - 8 ) ( 5 - ( - 5 x ) ) \\
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A & = & ( 5 x - 8 ) ( 5 - ( - 5 x ) ) \\
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A & = & 5 x - 8 ( 5 + 5 x ) \\
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A & = & 25 x^{ 2 } - 15 x - 40
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\end{eqnarray*}
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\end{solution}
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\subpart $B = ( -3 x + 5 )^{ 2 } - 5$
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\begin{solution}
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\begin{eqnarray*}
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A & = & ( -3 x + 5 )^{ 2 } - 5 \\
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A & = & ( - 3 x + 5 )^{ 2 } - 5 \\
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A & = & ( - 3 x + 5 ) ( - 3 x + 5 ) - 5 \\
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A & = & -3 \times ( -3 ) x^{ 2 } + ( 5 \times ( -3 ) - 3 \times 5 ) x + 5 \times 5 - 5 \\
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A & = & 9 x^{ 2 } + ( -15 - 15 ) x + 25 - 5 \\
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A & = & 9 x^{ 2 } - 30 x + 20
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\end{eqnarray*}
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\end{solution}
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\subpart $C = -8 x - 4 + 4 ( 7 x - 2 )^{ 2 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & -8 x - 4 + 4 ( 7 x - 2 )^{ 2 } \\
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A & = & - 8 x - 4 + 4 ( 7 x - 2 )^{ 2 } \\
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A & = & - 8 x - 4 + 4 ( 7 x - 2 )^{ 2 } \\
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A & = & - 8 x - 4 + 4 \times 7 x - 2^{ 2 } \\
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A & = & - 8 x - 4 + 4 \times 7 x - 2^{ 2 } \\
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A & = & - 8 x - 4 + 4 \times 7 x - 2 ( 7 x - 2 ) \\
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A & = & - 8 x - 4 + 4 ( 7 \times 7 x^{ 2 } + ( -2 \times 7 + 7 \times ( -2 ) ) x - 2 \times ( -2 ) ) \\
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A & = & - 8 x - 4 + 4 ( 49 x^{ 2 } + ( -14 - 14 ) x + 4 ) \\
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A & = & - 8 x - 4 + 4 ( 49 x^{ 2 } - 28 x + 4 ) \\
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A & = & - 8 x - 4 + 4 ( 49 x^{ 2 } - 28 x + 4 ) \\
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A & = & - 8 x - 4 + 4 \times 49 x^{ 2 } + 4 \times ( -28 ) x + 4 \times 4 \\
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A & = & 196 x^{ 2 } - 120 x + 12
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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 $A = 1 x^{ 2 } - x$
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\subpart $B = 25 x^{ 2 } + 25 + 50 x$
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\subpart $C = 49 x^{ 2 } - 81$
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\subpart $D = 64 x^{ 2 } - 112 x + 49$
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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 $9 x - 1 = 0$
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\subpart $- 9 x + 1 = - 7 x - 6$
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\columnbreak
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\subpart $6 x^{ 2 } - 10 x + 2 = 6x^2$
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\subpart $( -8 x + 6 ) ( 10 x - 1 ) = 0$
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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 $A(8 ; -2)$, $B(8 ; -2)$, $C(1 ; 2)$ et $D(-6 ; -7)$. Est-ce que les vecteurs $\vec{AB}$ et $\vec{CD}$ sont colinéaires?
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\part Soit $A(4 ; -8)$, $B(-4 ; -10)$, $C(8 ; -7)$ et $D(2 ; 5)$. Est-ce que les vecteurs $\vec{AB}$ et $\vec{CD}$ sont colinéaires?
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\part Soit $A(5 ; -4)$, $B(5 ; -4)$, $C(10 ; -1)$ et $D(7 ; 6)$. 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 $\displaystyle A = \frac{ -7 }{ -10 } \times ( -7 )$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ -7 }{ -10 } \times ( -7 ) \\
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A & = & \frac{ -7 \times 7 \times ( -1 ) }{ 10 \times ( -1 ) } \\
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A & = & \frac{ -49 \times ( -1 ) }{ -10 } \\
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A & = & \frac{ 49 }{ -10 } \\
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A & = & \frac{ -49 }{ 10 }
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle B = \frac{ 5 }{ -2 } + \frac{ -1 }{ 14 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ 5 }{ -2 } + \frac{ -1 }{ 14 } \\
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A & = & \frac{ 5 \times 7 }{ -2 \times 7 } + \frac{ -1 \times ( -1 ) }{ 14 \times ( -1 ) } \\
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A & = & \frac{ 35 }{ -14 } + \frac{ 1 }{ -14 } \\
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A & = & \frac{ 35 + 1 }{ -14 } \\
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A & = & \frac{ 36 }{ -14 } \\
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A & = & \frac{ -36 }{ 14 } \\
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A & = & \frac{ -18 \times 2 }{ 7 \times 2 } \\
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A & = & \frac{ -18 }{ 7 }
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle C = \frac{ 10 }{ -3 } + \frac{ 9 }{ 5 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ 10 }{ -3 } + \frac{ 9 }{ 5 } \\
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A & = & \frac{ 10 \times 5 }{ -3 \times 5 } + \frac{ 9 \times ( -3 ) }{ 5 \times ( -3 ) } \\
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A & = & \frac{ 50 }{ -15 } + \frac{ -27 }{ -15 } \\
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A & = & \frac{ 50 - 27 }{ -15 } \\
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A & = & \frac{ 23 }{ -15 } \\
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A & = & \frac{ -23 }{ 15 }
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle D = \frac{ 4 }{ -5 } - 1$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ 4 }{ -5 } - 1 \\
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A & = & \frac{ 4 \times 1 }{ -5 \times 1 } + \frac{ -1 \times ( -5 ) }{ 1 \times ( -5 ) } \\
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A & = & \frac{ 4 }{ -5 } + \frac{ 5 }{ -5 } \\
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A & = & \frac{ 4 + 5 }{ -5 } \\
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A & = & \frac{ 9 }{ -5 } \\
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A & = & \frac{ -9 }{ 5 }
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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 $\displaystyle A = \frac{ -7 }{ 9 x } \times ( -3 )$
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\subpart $\displaystyle B = \frac{ -6 }{ 5 } + \frac{ 3 x }{ 25 }$
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\subpart $\displaystyle C = \frac{ 7 x }{ 7 } + \frac{ -5 }{ 5 x }$
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\subpart $\displaystyle D = \frac{ -8 }{ -4 x } - 1$
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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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