dst 4 corrigé, chapitre 1ere, calcul mental les deux
authorDenise sur Titasmo <denise.maurice@normalesup.org>
Wed, 6 Jan 2016 16:44:38 +0000 (17:44 +0100)
committerDenise sur Titasmo <denise.maurice@normalesup.org>
Wed, 6 Jan 2016 16:44:38 +0000 (17:44 +0100)
16 files changed:
1ere/DST_4/dst4.tex
1ere/DST_4/dst4_corrige.pdf
1ere/DST_4/dst4_enonce.pdf
1ere/calcul_mental/signe2deg.pdf [new file with mode: 0644]
1ere/calcul_mental/signe2deg.tex [new file with mode: 0644]
1ere/chapitre4_seconddeg/axes.ggb [new file with mode: 0644]
1ere/chapitre4_seconddeg/axes.pdf [new file with mode: 0644]
1ere/chapitre4_seconddeg/chap4.pdf
1ere/chapitre4_seconddeg/chap4.tex
2nde/DST_4/dst4.pdf [new file with mode: 0644]
2nde/calcul_mental/cube_lettres.pdf [new file with mode: 0644]
2nde/calcul_mental/cube_lettres.svg [new file with mode: 0644]
2nde/calcul_mental/cubedebase.svg [new file with mode: 0644]
2nde/calcul_mental/cubedebase_abcdefgh.svg [new file with mode: 0644]
2nde/calcul_mental/geomespace_plan.pdf [new file with mode: 0644]
2nde/calcul_mental/geomespace_plan.tex [new file with mode: 0644]

index 0ea6bf55c46be7c4370ae221270c452dd686ae95..ee589dbc42ee2e6459221e0e631c0d15fd639c08 100644 (file)
@@ -223,7 +223,7 @@ x^3 & \ga- & \z & \dr+ \\
 \fin
 }
 \item $g$ est la fonction définie par $g(x) = 5x$. Quel est son sens de variation~? \bareme{0,5}
-\reponse{$g$ est croissante sur $\R$ (c'est une fonction affine avec un c{\oe}fficient directeur positif).}
+\reponse{$g$ est croissante sur $\R$ (c'est une fonction affine avec un c{\oe}fficient directeur positif). Note : donner le tableau de variations est accepté aussi.}
 \item En utilisant la représentation graphique de ces deux fonctions avec la calculatrice, résoudre graphiquement l'équation $f(x) = g(x)$ (arrondi au dixième). \bareme{1}\reponse{
 Voici un exemple d'affichage calculatrice, avec une fenêtre $Xmin = -5$, $Xmax = 5$, $Ymin = -15$, $Ymax = 15$.
 
@@ -266,7 +266,9 @@ Trouver le taux d'évolution sur la première année.
 \left( 1 + \frac{t}{100} \right) \left( 1 + \frac{3t}{100} \right) = 1 + \frac{50}{100} 
 \]
 
-Et il n'y a plus qu'à résoudre...}
+Et il n'y a plus qu'à résoudre, sans faire d'erreur de calcul !
+% rep : 11,5 %
+}
 
 
 \end{document}
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Binary files a/1ere/DST_4/dst4_corrige.pdf and b/1ere/DST_4/dst4_corrige.pdf differ
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Binary files a/1ere/DST_4/dst4_enonce.pdf and b/1ere/DST_4/dst4_enonce.pdf differ
diff --git a/1ere/calcul_mental/signe2deg.pdf b/1ere/calcul_mental/signe2deg.pdf
new file mode 100644 (file)
index 0000000..5bbbd06
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diff --git a/1ere/calcul_mental/signe2deg.tex b/1ere/calcul_mental/signe2deg.tex
new file mode 100644 (file)
index 0000000..cba9c85
--- /dev/null
@@ -0,0 +1,56 @@
+\input{../../header_beamer.tex}
+
+\begin{document}
+\slide{Signe du trinôme et inéquations du second degré
+
+\bigskip \pause
+
+Pour chaque inéquation, le discriminant et les éventuelles racines du polynôme sont données. Résoudre alors l'inéquation.}
+
+\slide{
+1) \[x^2 -x -2 > 0\]
+\[\Delta = 9 \qquad x_1 = 2 \qquad x_2 = -1 \]
+
+}
+
+\slide{2)
+\[x^2 -1 \leq 0 \]
+\[\Delta = 4 \qquad x_1 = 1 \qquad x_2 = -1 \]
+
+}
+
+\slide{3)
+\[ -x^2 + 2x -3 >0 \]
+\[\Delta = -8 \]
+
+}
+
+\slide{4)
+\[-2x^2 -4 x -2 \leq 0 \]
+\[\Delta = 0 \qquad x_0 = -1 \]
+}
+
+\slide{5)
+\[-25x^2 \geq 0 \]
+\[ \Delta = 0 \qquad x_0 = 0 \]
+
+}
+
+\slide{
+\begin{enumerate}
+\item \[x^2 -x -2 > 0\]
+\[\Delta = 9 \qquad x_1 = 2 \qquad x_2 = -1 \]
+\item \[x^2 -1 \leq 0 \]
+\[\Delta = 4 \qquad x_1 = 1 \qquad x_2 = -1 \]
+\item \[ -x^2 + 2x -3 >0 \]
+\[\Delta = -8 \]
+\item \[-2x^2 -4 x -2 \leq 0 \]
+\[\Delta = 0 \qquad x_0 = -1 \]
+\item \[-25x^2 \geq 0 \]
+\[ \Delta = 0 \qquad x_0 = 0 \]
+\end{enumerate}
+
+}
+
+
+\end{document}
diff --git a/1ere/chapitre4_seconddeg/axes.ggb b/1ere/chapitre4_seconddeg/axes.ggb
new file mode 100644 (file)
index 0000000..4150f4c
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@@ -189,5 +189,69 @@ f(x) &   \\
 
 \newpage
 \section{Représentation graphique}
+Soit $f$ la fonction définie sur $\R$ par $f(x) = ax^2 + bx +c$, avec $a\not=0$.
+\begin{prop}
+La courbe représentative de $f$ dans un repère est une \ldots \ldots\ldots\ldots\ldots\ldots\ldots, dont le sommet $S$ a pour coordonnées
+\vspace{2cm}
+
+Elle admet un axe de symétrie~: \dotfill 
+\end{prop}
+\begin{itemize2}
+\item Si $a>0$,
+
+\bigskip
+
+\variations
+x & \mI & \hspace{2cm} & \pI \\
+f(x) & & \\
+\fin
+
+\bigskip
+
+
+\item Si $a<0$,
+
+\bigskip
+
+
+\variations
+x & \mI & \hspace{2cm} & \pI \\
+f(x) & & \\
+\fin
+
+\bigskip
+
+
+\item Si $\Delta >0$, \dotfill
+\lignepoint
+
+\bigskip
+
+
+\item Si $\Delta =0$, \dotfill
+\lignepoint
+
+\bigskip
+
+
+\item Si $\Delta <0$, \dotfill
+
+\end{itemize2}
+
+\bigskip
+
+Exemples :
+
+\newcommand\axes{\includegraphics[width=4cm]{axes.pdf}}
+
+\begin{tabular}{|p{1.5cm}|p{4cm}|p{4cm}|p{4cm}|}
+\hline
+& $\Delta >0$ & $\Delta = 0$ & $\Delta <0$ \\
+\hline
+$a>0$ & \axes & \axes & \axes \\
+\hline
+$a<0$ & \axes & \axes & \axes \\
+\hline 
+\end{tabular}
 
 \end{document}
diff --git a/2nde/DST_4/dst4.pdf b/2nde/DST_4/dst4.pdf
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diff --git a/2nde/calcul_mental/cube_lettres.pdf b/2nde/calcul_mental/cube_lettres.pdf
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diff --git a/2nde/calcul_mental/geomespace_plan.pdf b/2nde/calcul_mental/geomespace_plan.pdf
new file mode 100644 (file)
index 0000000..e42d159
Binary files /dev/null and b/2nde/calcul_mental/geomespace_plan.pdf differ
diff --git a/2nde/calcul_mental/geomespace_plan.tex b/2nde/calcul_mental/geomespace_plan.tex
new file mode 100644 (file)
index 0000000..dc5bb60
--- /dev/null
@@ -0,0 +1,56 @@
+\input{../../header_beamer.tex}
+
+
+\newcommand\cube{\includegraphics[width=5.5cm]{cube_lettres.pdf}
+}
+\begin{document}
+\slide{Geométrie dans l'espace : qu'est-ce qu'un plan~?}
+
+\slide{$ABCDEFGH$ est un cube de l'espace, et $I, J, K, L$ sont des points sur les arêtes $[DA]$,  $[AB]$, $[BC]$, $[CD]$.
+
+\cube
+
+}
+
+\slide{
+\cube
+
+1) Est-ce que les points $A$, $B$, $C$, $D$ permettent de définir un plan~?
+}
+
+\slide{
+\cube
+
+2) Les points $A$, $B$, $L$~?
+}
+
+\slide{
+\cube
+
+3) Les points $A$, $D$, $I$~?
+}
+
+\slide{
+\cube
+
+4) Les points $I$, $J$, $K$, $L$~?
+}
+
+\slide{
+\cube
+
+5) Les points $A$, $B$, $C$, $F$~?
+}
+
+\slide{
+\cube
+\begin{enumerate}
+\item Est-ce que les points $A$, $B$, $C$, $D$ permettent de définir un plan~?
+\item Les points $A$, $B$, $L$~?
+\item Les points $A$, $D$, $I$~?
+\item Les points $I$, $J$, $K$, $L$~?
+\item Les points $A$, $B$, $C$, $F$~?
+\end{enumerate}
+}
+
+\end{document}