208 lines
6.8 KiB
TeX
208 lines
6.8 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{5}
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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 $A = ( 1 x + 7 ) ( 1 - ( -2 x ) )$
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\begin{solution}
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\begin{eqnarray*}
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A & = & ( 1 x + 7 ) ( 1 - ( -2 x ) ) \\
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A & = & ( 1 x + 7 ) ( 1 - ( - 2 x ) ) \\
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A & = & ( x + 7 ) ( 1 - ( - 2 x ) ) \\
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A & = & ( x + 7 ) ( 1 + 2 x ) \\
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A & = & 2 x^{ 2 } + 15 x + 7
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\end{eqnarray*}
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\end{solution}
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\subpart $B = ( 7 x - 4 )^{ 2 } + 4$
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\begin{solution}
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\begin{eqnarray*}
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A & = & ( 7 x - 4 )^{ 2 } + 4 \\
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A & = & ( 7 x - 4 )^{ 2 } + 4 \\
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A & = & 7 x - 4^{ 2 } + 4 \\
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A & = & 7 x - 4 ( 7 x - 4 ) + 4 \\
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A & = & 7 \times 7 x^{ 2 } + ( -4 \times 7 + 7 \times ( -4 ) ) x - 4 \times ( -4 ) + 4 \\
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A & = & 49 x^{ 2 } + ( -28 - 28 ) x + 16 + 4 \\
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A & = & 49 x^{ 2 } - 56 x + 20
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\end{eqnarray*}
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\end{solution}
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\subpart $C = -2 x + 5 + 4 ( 2 x - 1 )^{ 2 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & -2 x + 5 + 4 ( 2 x - 1 )^{ 2 } \\
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A & = & - 2 x + 5 + 4 ( 2 x - 1 )^{ 2 } \\
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A & = & - 2 x + 5 + 4 ( 2 x - 1 )^{ 2 } \\
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A & = & - 2 x + 5 + 4 \times 2 x - 1^{ 2 } \\
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A & = & - 2 x + 5 + 4 \times 2 x - 1 ( 2 x - 1 ) \\
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A & = & - 2 x + 5 + 4 ( 2 \times 2 x^{ 2 } + ( -1 \times 2 + 2 \times ( -1 ) ) x - 1 \times ( -1 ) ) \\
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A & = & - 2 x + 5 + 4 ( 4 x^{ 2 } + ( -2 - 2 ) x + 1 ) \\
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A & = & - 2 x + 5 + 4 ( 4 x^{ 2 } - 4 x + 1 ) \\
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A & = & - 2 x + 5 + 4 \times 4 x^{ 2 } + 4 \times ( -4 ) x + 4 \\
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A & = & 16 x^{ 2 } - 18 x + 9
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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 $A = 10 x^{ 2 } - x$
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\subpart $B = 1 x^{ 2 } + 49 + 14 x$
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\subpart $C = 16 x^{ 2 } - 9$
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\subpart $D = 1 x^{ 2 } - 12 x + 36$
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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 $- 8 x + 10 = 0$
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\subpart $- 10 x - 7 = x + 7$
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\columnbreak
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\subpart $3 x^{ 2 } - 6 x + 7 = 3x^2$
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\subpart $( 2 x + 8 ) ( -1 x - 7 ) = 0$
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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 $A(7 ; 6)$, $B(3 ; 10)$, $C(10 ; 3)$ et $D(3 ; 10)$. Est-ce que les vecteurs $\vec{AB}$ et $\vec{CD}$ sont colinéaires?
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\part Soit $A(3 ; -6)$, $B(2 ; 2)$, $C(-10 ; 1)$ et $D(4 ; -5)$. Est-ce que les vecteurs $\vec{AB}$ et $\vec{CD}$ sont colinéaires?
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\part Soit $A(-10 ; -2)$, $B(-10 ; -2)$, $C(7 ; 6)$ et $D(-3 ; -5)$. 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 $\displaystyle A = \frac{ -2 }{ 8 } \times ( -9 )$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ -2 }{ 8 } \times ( -9 ) \\
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A & = & \frac{ -2 \times ( -9 ) }{ 8 } \\
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A & = & \frac{ 18 }{ 8 } \\
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A & = & \frac{ 9 \times 2 }{ 4 \times 2 } \\
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A & = & \frac{ 9 }{ 4 }
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle B = \frac{ 4 }{ 10 } + \frac{ -4 }{ 70 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ 4 }{ 10 } + \frac{ -4 }{ 70 } \\
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A & = & \frac{ 4 \times 7 }{ 10 \times 7 } + \frac{ -4 \times 1 }{ 70 \times 1 } \\
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A & = & \frac{ 28 }{ 70 } + \frac{ -4 }{ 70 } \\
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A & = & \frac{ 28 - 4 }{ 70 } \\
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A & = & \frac{ 24 }{ 70 } \\
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A & = & \frac{ 12 \times 2 }{ 35 \times 2 } \\
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A & = & \frac{ 12 }{ 35 }
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle C = \frac{ 1 }{ 8 } + \frac{ 7 }{ -7 }$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ 1 }{ 8 } + \frac{ 7 }{ -7 } \\
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A & = & \frac{ 1 \times ( -7 ) }{ 8 \times ( -7 ) } + \frac{ 7 \times 8 }{ -7 \times 8 } \\
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A & = & \frac{ -7 }{ -56 } + \frac{ 56 }{ -56 } \\
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A & = & \frac{ -7 + 56 }{ -56 } \\
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A & = & \frac{ 49 }{ -56 } \\
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A & = & \frac{ -49 }{ 56 } \\
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A & = & \frac{ -7 \times 7 }{ 8 \times 7 } \\
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A & = & \frac{ -7 }{ 8 }
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\end{eqnarray*}
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\end{solution}
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\subpart $\displaystyle D = \frac{ 1 }{ -9 } - 2$
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\begin{solution}
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\begin{eqnarray*}
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A & = & \frac{ 1 }{ -9 } - 2 \\
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A & = & \frac{ 1 \times 1 }{ -9 \times 1 } + \frac{ -2 \times ( -9 ) }{ 1 \times ( -9 ) } \\
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A & = & \frac{ 1 }{ -9 } + \frac{ 18 }{ -9 } \\
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A & = & \frac{ 1 + 18 }{ -9 } \\
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A & = & \frac{ 19 }{ -9 } \\
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A & = & \frac{ -19 }{ 9 }
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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 $\displaystyle A = \frac{ 7 }{ -5 x } \times 5$
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\subpart $\displaystyle B = \frac{ 8 }{ -3 } + \frac{ 5 x }{ -18 }$
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\subpart $\displaystyle C = \frac{ 3 x }{ 4 } + \frac{ 7 }{ -9 x }$
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\subpart $\displaystyle D = \frac{ 7 }{ 9 x } - 7$
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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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