exo 2nde, chapitre 2nde, + id élèves
authorDenise <dmaurice@phare.normalesup.org>
Mon, 7 Sep 2015 20:00:56 +0000 (22:00 +0200)
committerDenise <dmaurice@phare.normalesup.org>
Mon, 7 Sep 2015 20:00:56 +0000 (22:00 +0200)
2nde/chapitre1_fonctions/18p27.pdf [new file with mode: 0644]
2nde/chapitre1_fonctions/18p27.tex [new file with mode: 0644]
2nde/chapitre1_fonctions/ch1_fonctions.pdf
2nde/chapitre1_fonctions/ch1_fonctions.tex
2nde/chapitre1_fonctions/sequence.txt
2nde/chapitre1_fonctions/support/graphe1.pdf [new file with mode: 0644]
2nde/chapitre1_fonctions/support/graphe1.svg [new file with mode: 0644]
identifiants nouveaux _l_ves.xlsx [new file with mode: 0644]

diff --git a/2nde/chapitre1_fonctions/18p27.pdf b/2nde/chapitre1_fonctions/18p27.pdf
new file mode 100644 (file)
index 0000000..f005704
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diff --git a/2nde/chapitre1_fonctions/18p27.tex b/2nde/chapitre1_fonctions/18p27.tex
new file mode 100644 (file)
index 0000000..70bc335
--- /dev/null
@@ -0,0 +1,29 @@
+\input{../../header_a5.tex}
+
+\begin{document}
+\exo{18p27 -- Corrigé}
+
+\begin{enumerate}
+\item $E$ est placé sur le segment $[AD]$, donc la longueur $AE$ varie entre $6$~: $\cadrem{AE \in [0;6]}$ (ou $0 \leq AE \leq 6$).
+\item 
+\begin{enumerate}[a)]
+  \item $\cadrem{ED = 6 - AE}$. 
+
+Les droites $(EF)$ et $(BD)$ sont parallèles, on peut donc appliquer le théorème de Thalès~:
+\[
+\frac{AE}{AD} = \frac{AF}{AB}
+\]
+\begin{eqnarray*}
+& \equ & \frac{AE}{6} = \frac{AF}{8} \\
+& \equ & AF = \frac{AE}{6} \times 8 = \cadrem{\frac{4 AE}{3}}
+\end{eqnarray*}
+  \item L'aire de $AEF$ s'écrit~:
+\[
+\mathcal{A}_{AEF} = \frac{b \times h}{2} = \frac{AE \times AF}{2} = \frac{AE \times \frac{4 AE}{3}}{2} = \frac{AE^2 \times 4}{3} \times \frac{1}{2}
+\]
+\[
+\cadrem{\mathcal{A}_{AEF} = \frac{2AE^2}{3}}
+\]
+\end{enumerate}
+\end{enumerate}
+\end{document}
index 3942202..9f7a3e0 100644 (file)
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@@ -106,7 +106,9 @@ Une $f$ sur une partie $D$ de $\R$ est un procédé qui associe à tout nombre $
  appelé \emph{image} du nombre $x$. $D$ est appelé \emph{ensemble de définition} de $f$.
 \end{defn}
 
-Vocabulaire~:\\
+Remarque~: l'ensemble de définition est souvent un intervalle.
+
+Vocabulaire~:
 \begin{itemize2}
 \item L'image de $x$ par $f$ s'écrit $f(x)$ et se dit «~$f$ de $x$~».
 \item Si $f(a) = b$, on dit que $a$ est un \emph{antécédent} de $b$ par $f$. 
@@ -118,7 +120,7 @@ On peut définir $f$ par une formule, un graphique, un tableau, un algorithme, \
 Exemples~:
 
 Soit $f$ la fonction définie sur $[0, +\infty [$ par $f(x) = 3x^2 +7$.\\
-L'image de $1$ par $f$ est $10$~: $f(1) = 10$.
+L'image de $1$ par $f$ est $10$~: $f(1) = 3\times 1^2 + 7 = 10$.
 
 Soit $g$ la fonction définie par le tableau suivant~:
 \[
@@ -140,6 +142,22 @@ La \emph{représentation graphique} d'une fonction $f$ est l'ensemble de tous le
 
 Autrement dit, un point $A(x; y)$ appartient à la courbe représentative de la fonction si, et seulement si $y=f(x)$.
 
-Exemple~: 
+Exemple~: Soit la fonction $f$ définie sur $\R$ par $f(x) = 2x^2 -1$.
+Le point $A(-1; 1)$ est sur la courbe car $f(1) = 2\times (-1)^2 -1 = 1$.
+Le point $B(3; 4)$ n'est pas sur la courbe car $f(3) = 2\times 3^2 -1 = 17 \not=4$.
+
+\section{Résolution graphique}
+
+\begin{defn}
+Résoudre une équation (ou une inéquation), c'est donner l'ensemble de \emph{toutes} les valeurs de la variable pour lesquelles l'égalité (ou l'inégalité) est vraie.
+\end{defn}
+
+\subsection{Comparer une fonction à une constante}
+
+Soit $f$ une fonction, et $k$ un réel.
+\begin{itemize2}
+\item Résoudre graphiquement une équation $f(x) = k$ revient à déterminer les abscisses de tous les points dont l'ordonnée est égale à $k$. Ces abscisses sont les solutions de l'équation.
+\item Résoudre graphiquement une inéquation
+\end{itemize2}
 
 \end{document}
index a02621e..330c4e1 100644 (file)
@@ -7,10 +7,10 @@ cours union intersection
 exos : feuille d'exos suite
 
 Fonctions : réactiver les savoirs p 16 livre
-cours base
-vocabulaire ?
-22p27 (vocabulaire)
-19 p 27 (exprimer une fct)
-25 (pas mal de trucs)
+cours base, vocabulaire
+21p27
+22 (vocabulaire)
+23 (vocab)
+25 (tableau - graphique)
 
 Comparer les fcts
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diff --git a/identifiants nouveaux _l_ves.xlsx b/identifiants nouveaux _l_ves.xlsx
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