Source Latex
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% Raccourcis diverses:
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\newcommand{\TITLE}{R�visions - Calcul alg�brique}
\author{Y. Morel}
\date{}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\hfill{\LARGE \bf \TITLE}
\hfill $1^{\mbox{\scriptsize{�re}}}\ STG$
\vspace{1cm}
\bgex Simplifier les nombres ou expressions suivants:
\[ A=\frac{5}{2}+\frac{8}{3} \ ;\ \
B=\frac{7}{12}-\frac{2}{3}\ ;\ \
C=2+\frac{5}{7}\ ;\ \
D=4+\frac{3}{9}\ ; \]
\vspd
\[
E=\frac{5}{7}\tm\frac{4}{15}\ ;\ \
F=\frac{\dsp\frac{8}{9}}{\dsp\frac{3}{5}}\ ;\ \
G=\frac{\dsp\frac{5}{3}}{\dsp\frac{2}{6}}\ ;\ \
H=\frac{\dsp\frac{8}{3}}{6}
\]
%\vspd
%\[
%H=\frac{1}{x}+\frac{3}{x+2}\ ;\ \
%I=\frac{3x}{x+1}+\frac{2}{5x}\ ;\ \
%J=5+\frac{3}{2+x}\ ;\ \
%K=\frac{1}{2-3x}-\frac{1}{2+3x}
%\]
\enex
\vspace{0.5cm}
\bgex R�soudre les �quations suivantes: \vspt
\begin{tabular}{*3{p{4cm}}}
$\bullet\dsp\ 2x+3=7$
& $\bullet\dsp\ -5x+\frac{4}{3}=8$
& $\bullet\dsp\ \frac{3x}{2}-4=\frac{5}{4}$ \vspace{0.8cm}\\
$\bullet\dsp\ \frac{3}{2}x+\frac{5}{3}=3$
& $\bullet\dsp\ \frac{2x-5}{7}=\frac{3}{4}$
& $\bullet\dsp\ \frac{-2x-5}{8}=\frac{3x-7}{2}$
\end{tabular}
\enex
\vspace{0.8cm}
\bgex
\bgit
\vspt
\item[1)] D�velopper les expressions suivantes: \vspt
\begin{tabular}{ll}
$\bullet\ A(x)=(x+2)(2x-3)$
& $\bullet\ B(x)=(x+2)(2x-3)(-3x+1)$ \vspace{0.8cm}\\
$\bullet\ C(x)=(x+3)^2$
& $\bullet\ D(x)=(3x-4)^2$ \hspace{1cm}
$\bullet\ E(x)=(2x+1)^2$
\end{tabular}
\vspace{0.8cm}
\item[2)] Factoriser les expressions suivantes: \vspt
\begin{tabular}{p{9cm}l}
$\bullet\ F(x)=(2x-3)(x-2)-(2x-3)(x+4)$
& $\bullet\ G(x)=(-2x+5)^2+(-2x+5)(3x-4)$ \vspace{0.8cm}\\
$\bullet\ H(x)=(3x^2+2x)(x-6)-(x+7)(3x^2+2x)$
& $\bullet\ I(x)=(x-2)(x^2-9)-(x-2)(x-3)$
\end{tabular}
\vspace{0.8cm}
\item[3)] Compl�ter: \vspt
\begin{tabular}{*3{p{5cm}}}
$\bullet\ A(1)=\ \dots$
& $\bullet\ A(-2)=\ \dots$
& $\bullet\ B(2)=\ \dots$ \vspace{0.6cm}\\
$\bullet\ B\lp\dsp\frac{1}{3}\rp=\ \dots$
& $\bullet\ D(-1)=\ \dots$
& $\bullet\ E(-2)=\ \dots$
\end{tabular}
\vspace{0.8cm}
\item[4)] R�soudre les �quations suivantes: \vspd
$\bullet\ A(x)=0$ \hspace{2.5cm}
% $\bullet\ B(x)=0$ \hspace{1.5cm}
$\bullet\ H(x)=0$ \hspace{2.5cm}
% $\bullet\ I(x)=0$ \hspace{1.5cm}
$\bullet\ A(x)=B(x)$
\enit
\enex
\end{document}
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