chapitre 8 1ere, chapitres 2nde + calcul mental, DST 2nde
authorDenise sur Lya <sekhmet@lya>
Thu, 2 Jun 2016 21:12:25 +0000 (23:12 +0200)
committerDenise sur Lya <sekhmet@lya>
Thu, 2 Jun 2016 21:12:25 +0000 (23:12 +0200)
25 files changed:
1ere/chapitre8_loibino/chap8.pdf
1ere/chapitre8_loibino/chap8.tex
2nde/DST_8/dst8.tex
2nde/DST_8/dst8_A_corrige.pdf
2nde/DST_8/dst8_A_enonce.pdf
2nde/DST_8/dst8_B_corrige.pdf
2nde/DST_8/dst8_B_enonce.pdf
2nde/calcul_mental/probas_unioninter.pdf [new file with mode: 0644]
2nde/calcul_mental/probas_unioninter.tex [new file with mode: 0644]
2nde/chapitre12_fonctionsusuelles/chap12.pdf [new file with mode: 0644]
2nde/chapitre12_fonctionsusuelles/chap12.tex [new file with mode: 0644]
2nde/chapitre12_fonctionsusuelles/demo1.ggb [new file with mode: 0644]
2nde/chapitre13_trigo/cercle.pdf [new file with mode: 0644]
2nde/chapitre13_trigo/cercle.svg [new file with mode: 0644]
2nde/chapitre13_trigo/cercle2.pdf [new file with mode: 0644]
2nde/chapitre13_trigo/cercle2.svg [new file with mode: 0644]
2nde/chapitre13_trigo/cerclesincos.pdf [new file with mode: 0644]
2nde/chapitre13_trigo/cerclesincos.svg [new file with mode: 0644]
2nde/chapitre13_trigo/chap13.pdf [new file with mode: 0644]
2nde/chapitre13_trigo/chap13.tex [new file with mode: 0644]
Droitderéponsedirection.pdf [deleted file]
forum présence enseignants16.docx [deleted file]
header.tex
remisedebulletin2nde1stmg.pdf [deleted file]
surveillanceetchangementdesallesCO10mars.pdf [deleted file]

index 3bd5d08..466aa83 100644 (file)
Binary files a/1ere/chapitre8_loibino/chap8.pdf and b/1ere/chapitre8_loibino/chap8.pdf differ
index 2e8943b..4730a8e 100644 (file)
@@ -200,7 +200,7 @@ $b$ est \dotfill
 
 \bigskip
 
-\includegraphics[width=0.7\textwidth]{graphique_exemple.pdf}
+\includegraphics[width=0.65\textwidth]{graphique_exemple.pdf}
 
 %$P(X \leq 24) = 0,020$
 %$P(X\leq 25) = 0,034$
@@ -215,7 +215,7 @@ On a donc $P(X \in \ldots \ldots \ldots) \geq \upc{95}$, donc la fréquence $f$
 
 \subsection*{Intervalle de fluctuation}
 \begin{prop}
-Si une variable aléatoire $X$ suit une loi binômiale de paramètres $n$ et $p$, alors l'intervalle de fluctuation de la fréquence observée au seuil de \upc{95} est 
+Une variable aléatoire $X$ suit une loi binômiale de paramètres $n$ et $p$. On choisit un seuil d'erreur $\alpha$, c'est-à-dire un seuil de confiance de $1-\alpha$. alors l'intervalle de fluctuation de la fréquence observée au seuil de confiance $1-\alpha$ (ou seuil d'erreur $\alpha$) est 
 \vspace{0.5cm}
 
 où 
index 63af1da..37cd348 100644 (file)
@@ -67,7 +67,7 @@ A(x)B(x) & \ga- & \z & + & \z & - \\
 x & \mI & & -1 & & 2 & & 3 & & \pI \\
 A(x) & \ga- & \z & + & \l & + & \l & \dr+ \\
 C(x) & \ga- & \l & - & \z & + & \z & \dr-\\
-A(x)C(x) & \ga+ & \z & - & \z & + & \z & \dr+\\
+A(x)C(x) & \ga+ & \z & - & \z & + & \z & \dr-\\
 \fin
 
 }
@@ -96,7 +96,7 @@ A(x)B(x) & \ga- & \z & + & \z & - \\
 x & \mI & & -1 & & 2 & & 3 & & \pI \\
 A(x) & \ga- & \z & + & \l & + & \l & \dr+ \\
 C(x) & \ga- & \l & - & \z & + & \z & \dr-\\
-\frac{A(x)}{C(x)} & \ga+ & \z & - & \bb & + & \bb & \dr+\\
+\frac{A(x)}{C(x)} & \ga+ & \z & - & \bb & + & \bb & \dr-\\
 \fin
 }{
 
@@ -241,13 +241,13 @@ Les coordonnées ne sont pas proportionnelles, donc $\ve{LU}$ et $\ve{UR}$ ne so
 
   \item Trouver les coordonnées d'un point $S$, de même abscisse que $L$, tel que $(LU) // (RS)$ \bareme{1}
 \reponse{On cherche $S(\version{3}{2}; a)$, de telle sorte que les vecteurs $\ve{LU}$ et $\ve{RS}$ soient colinéaires.
-\[\ve{LU} (-2; 2) \]
+\[\ve{LU} (-2; -2) \]
 \[\ve{RS} (\version{3 - 6}{2 - 5}; \version{a-0}{a-1}) = (-3; \version{a}{a-1}) \]
 Avec le produit en croix, on obtient :
-\[\version{-2 \times a = -3 \times 2 \equi a = \frac{-6}{-2} = 3}
-{ -2 \times (a-1) = -3 \times 2 \equi -2a = -6 -2 \equi a = \frac{-8}{-2} = 4
+\[\version{-2 \times a = -3 \times -2 \equi a = \frac{6}{-2} = -3}
+{ -2 \times (a-1) = -3 \times -2 \equi -2a = 6 -2 \equi a = \frac{4}{-2} = -2
 \]
-D'où \cadrem{S(\version{3; 3}{2; 4})}
+D'où \cadrem{S(\version{3; -3}{2; -2})}
 }
 
 \end{enumerate}
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diff --git a/2nde/calcul_mental/probas_unioninter.pdf b/2nde/calcul_mental/probas_unioninter.pdf
new file mode 100644 (file)
index 0000000..8fe4638
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diff --git a/2nde/calcul_mental/probas_unioninter.tex b/2nde/calcul_mental/probas_unioninter.tex
new file mode 100644 (file)
index 0000000..45663fa
--- /dev/null
@@ -0,0 +1,78 @@
+\input{../../header_beamer.tex}
+%%%%%%%%%%%% partie à modifier
+
+\newcommand\titre{Union et intersection}
+
+\newcommand\consigne{$\Omega = \{1; 2; 3; 4; 5; 6; 7; 8 \}$
+
+\bigskip}
+\newcommand\qa{$A = \{ 2; 5; 7; 8 \}$. $\bar{A} = $ ? }
+\newcommand\ra{$\bar{A} = \{1; 3; 4; 6 \}$}
+\newcommand\qb{$A = \{ 2; 5; 7; 8 \}$, $B = \{ 1; 2; 3 \}$. $A \cap B$ ?}
+\newcommand\rb{$A \cap B  = \{ 2 \}$}
+\newcommand\qc{$A = \{ 2; 5; 7; 8 \}$, $B = \{ 1; 2; 3 \}$. $A \cup B$ ?}
+\newcommand\rc{$A \cup B = \{1; 2; 3; 5; 7; 8 \}$}
+\newcommand\qd{$A = \{ 2; 5; 7; 8 \}$,  $C = \{ 3; 4 \}$. $A \cap C$ ?}
+\newcommand\rd{$A \cap C = \emptyset$}
+\newcommand\qe{$A = \{ 2; 5; 7; 8 \}$,  $C = \{ 3; 4 \}$. $A \cup C$ ?}
+\newcommand\re{$A \cup C = \{2; 3; 4; 5; 7; 8 \}$}
+
+%%%%%%%%%%%%%%%
+
+
+\begin{document}
+\slide{\titre
+
+\bigskip \pause
+
+\consigne}
+
+\slide{\consigne
+
+\begin{enumerate}[1)]
+\item \qa
+\end{enumerate}
+}
+
+\slide{\consigne
+
+\begin{enumerate}[1)]
+\setcounter{enumi}{1}
+\item \qb
+\end{enumerate}
+}
+\slide{\consigne
+
+\begin{enumerate}[1)]
+\setcounter{enumi}{2}
+\item \qc
+\end{enumerate}
+}
+
+\slide{\consigne
+
+\begin{enumerate}[1)]
+\setcounter{enumi}{3}
+\item \qd
+\end{enumerate}
+}
+\slide{\consigne
+
+\begin{enumerate}[1)]
+\setcounter{enumi}{4}
+\item \qe
+\end{enumerate}
+}
+
+\slide{\consigne
+\begin{enumerate}[1)]
+\item \qa~\reponse{2}{\ra}
+\item \qb~\reponse{3}{\rb}
+\item \qc~\reponse{4}{\rc}
+\item \qd~\reponse{5}{\rd}
+\item \qe~\reponse{6}{\re}
+\end{enumerate}
+
+
+}
+\end{document}
diff --git a/2nde/chapitre12_fonctionsusuelles/chap12.pdf b/2nde/chapitre12_fonctionsusuelles/chap12.pdf
new file mode 100644 (file)
index 0000000..31a7c61
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diff --git a/2nde/chapitre12_fonctionsusuelles/chap12.tex b/2nde/chapitre12_fonctionsusuelles/chap12.tex
new file mode 100644 (file)
index 0000000..80270fc
--- /dev/null
@@ -0,0 +1,124 @@
+\input{../../header.tex}
+
+
+\title{\vspace{-1cm}Chapitre 12 -- Fonction usuelles \vspace{-1.5cm}}
+\date{}
+
+\begin{document}
+\maketitle
+
+\section{Fonctions du second degré}
+\subsection{Fonction carré}
+
+\begin{defn} La \souligne{fonction carré} est la fonction définie sur $\R$ par $f(x) = x^2$.
+\end{defn}
+
+
+Dans un repère, la courbe représentative de la fonction carré s'appelle \dotfill \lignepoint
+
+
+\subsubsection*{Variations et signe}
+
+\begin{minipage}{0.45\textwidth}
+\begin{tabular}{|c|p{5cm}|}
+\hline
+$x$ &  \\
+\hline
+$x^2$ & ~\vspace{0.5cm}\\
+\hline
+\end{tabular}
+\end{minipage}\begin{minipage}{0.45\textwidth}
+\variations
+x & \hspace{5cm} \\
+x^2 & \\
+\fin
+\end{minipage}
+
+
+\begin{prop}[Équation $x^2 = a$]
+L'équation $x^2 = a$ admet :
+\begin{itemize2}
+  \item \dotfill
+  \item \dotfill
+  \item \dotfill
+\end{itemize2}
+\end{prop}
+
+\subsection{Fonction polynôme de degré 2}
+\begin{defn}
+Soient $a$, $b$ et $c$ trois réels tels que $a \not=0$. La fonction définie sur $\R$ par $f(x) = ax^2 + bx + c$ est appelée \souligne{fonction polynôme de degré 2}.
+
+Cette écriture est la {forme développée} de $f$.
+\end{defn}
+
+Exemples : $f(x) = 2x^2 -7x + 1$ \dotfill
+
+$g(x) = 3 - x^2 $ \dotfill
+
+%$h(x) = 7x + 1$ \dotfill
+
+\subsubsection*{Variations}
+
+\begin{defn}
+Si $f : x \mapsto ax^2 + bx + c$ est une fonction polynôme de degré 2, il existe des réels $\alpha$ et $\beta$ tels que 
+\[ f(x) = a (x-\alpha)^2 + \beta \]
+Cette forme est appelée la \souligne{forme canonique} de $f$.
+\end{defn}
+
+Dans un repère, la courbe représentative de $f : x \mapsto  a (x-\alpha)^2 + \beta$ est \dotfill \lignepoint
+
+\bigskip
+
+\begin{minipage}{0.45\textwidth}
+Si $a>0$ : 
+
+\begin{tabular}{|c|p{5cm}|}
+\hline
+$x$ &  \\
+\hline
+$f$ & ~\vspace{0.5cm}\\
+\hline
+\end{tabular}
+\end{minipage}
+\begin{minipage}{0.45\textwidth}
+Si $a<0$ : 
+
+\begin{tabular}{|c|p{5cm}|}
+\hline
+$x$ &  \\
+\hline
+$f$ & ~\vspace{0.5cm}\\
+\hline
+\end{tabular}
+\end{minipage}
+
+Exemple : $f(x) = 2x^2 + 4x -6$. Montrer que $f(x) = 2(x+1)^2 -8$, et en déduire le tableau de variations de $f$.
+
+\newpage
+\subsubsection*{Signe}
+Si on peut factoriser l'expression de $f$, alors on peut étudier son signe (voir chapitre 9).
+
+\smallskip
+
+Exemple : montrer que $f(x) = 2(x+3)(x-1)$, et en déduire son signe.
+\smallskip
+\lignepoint
+\smallskip
+\lignepoint
+\smallskip
+\lignepoint
+\smallskip
+\lignepoint
+\smallskip
+\lignepoint
+\smallskip
+\lignepoint
+\smallskip
+
+\section{Fonction inverse et fonctions homographiques}
+
+\subsection{Fonction inverse}
+
+\subsection{Fonctions homographiques}
+
+\end{document}
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diff --git a/2nde/chapitre13_trigo/cerclesincos.pdf b/2nde/chapitre13_trigo/cerclesincos.pdf
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diff --git a/2nde/chapitre13_trigo/chap13.pdf b/2nde/chapitre13_trigo/chap13.pdf
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diff --git a/2nde/chapitre13_trigo/chap13.tex b/2nde/chapitre13_trigo/chap13.tex
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index 0000000..507ce30
--- /dev/null
@@ -0,0 +1,198 @@
+\input{../../header.tex}
+
+
+\title{\vspace{-1cm}Chapitre 13 -- Trigonométrie \vspace{-1.5cm}}
+\date{}
+
+\begin{document}
+\maketitle
+
+\section{Enroulement de la droite numérique sur le cercle trigonométrique}
+\begin{minipage}{4cm}
+\includegraphics[width=4cm]{cercle.pdf}
+\end{minipage}
+\begin{minipage}{13cm}
+Dans le repère orthonormé $(0; I; J)$, on appelle \souligne{cercle trigonométrique} le cercle de centre $0$ et de rayon $1$. On l'oriente dans le sens \souligne{direct} : le sens inverse des aiguilles d'une montre.
+
+\bigskip
+
+ On trace la tangente à ce cercle au point $I(1; 0)$, et on imagine que cette droite s'\og enroule \fg autour du cercle trigonométrique.
+
+\smallskip
+
+
+À chaque nombre réel, on associe un point sur cette droite, et donc un unique point sur le cercle trigonométrique. 
+
+\smallskip
+
+
+\end{minipage}
+
+Sur le dessin, on a $x$ associé au point $M$ et $y$ au point $N$.
+
+\begin{itemize2}
+\item Donner le périmètre du cercle trigonométrique (en valeur exacte) : \dotfill
+\item Le réel $\frac{\pi}{2}$ est associé au point $J$ : expliquer pourquoi \dotfill 
+
+\smallskip
+\lignepoint
+\end{itemize2}
+
+\bigskip
+
+\begin{minipage}{13cm}
+\begin{itemize2}
+\item Dans le cercle trigonométrique ci-contre, placer les points $A$, $B$, $C$, $D$, $E$ associés aux réels $0$, $\pi$, $-\frac{\pi}{2}$, $-\frac{3\pi}{2}$, $2\pi$.
+
+\item À l'inverse, donner 4 réels différents associés au point $J$ : \dotfill
+
+\smallskip
+
+\lignepoint
+
+\item Si $x$ est associé à un point $M$, quels sont tous les réels également associés à $M$ ? \dotfill
+
+\lignepoint
+\end{itemize2}
+\end{minipage}
+\begin{minipage}{4cm}
+~~~\includegraphics[width=4cm]{cercle2.pdf}
+\end{minipage}
+
+\bigskip
+
+Pour trouver un point associé à un réel $x$, on peut utiliser la propriété suivante : dans le cercle trigonométrique, la longueur de l'arc $\arc{IM}$ est proportionnelle à l'angle $\widehat{IOM}$.
+
+Placer, à l'aide du rapporteur, le point $F$ associé au réel $\frac{3\pi}{4}$. 
+
+\smallskip
+\lignepoint
+\smallskip
+
+\lignepoint
+\smallskip
+
+\lignepoint
+
+\bigskip
+
+Faire de même avec le point $G$ associé au réel $\frac{11\pi}{10}$.
+
+
+\smallskip
+
+\lignepoint
+
+\smallskip
+
+\lignepoint
+\smallskip
+
+\lignepoint
+
+\bigskip
+
+Faire de même avec le point $H$ associé au réel $-\frac{25\pi}{3}$.
+
+
+\smallskip
+
+\lignepoint
+
+\smallskip
+
+\lignepoint
+\smallskip
+
+\lignepoint
+
+\newpage
+%%%%%%%%%%%%%%%%
+\section{Cosinus et sinus d'un nombre réel}
+\begin{minipage}{4cm}
+\includegraphics[width=4cm]{cerclesincos.pdf}
+\end{minipage}
+\begin{minipage}{13cm}
+\begin{defn}
+Si un point $x$ est associé à un réel $M$, on définit :
+\begin{itemize2}
+  \item Le cosinus de $x$ $\cos(x)$ : l'abscisse du point $M$
+  \item Le sinus de $x$ $\sin(x)$: l'ordonnée du point $M$
+\end{itemize2}
+\end{defn}
+\end{minipage}
+
+\bigskip
+
+À l'aide de la figure de la page précédente, déterminer approximativement (en mesurant) le cosinus et le sinus de $\frac{3\pi}{4}$, $\frac{11\pi}{10}$, $-\frac{25\pi}{3}$.
+
+\smallskip
+\lignepoint
+
+
+\smallskip
+\lignepoint
+
+
+\bigskip
+
+Déterminer le sinus et le cosinus des nombres $0$, $\frac{\pi}{2}$, $\pi$, $\frac{3\pi}{2}$.
+
+\smallskip
+\lignepoint
+
+
+\smallskip
+\lignepoint
+
+
+\bigskip
+
+Vérifier les réponses ci-dessus avec l'aide de la calculatrice. Pour cela, régler d'abord la calculatrice en "radians".
+
+\bigskip
+
+\begin{prop}
+Pour tout réel $x$, on a les propriétés suivantes :
+\begin{itemize2}
+  \item $-1\leq \cos x \leq 1$
+  \item $-1\leq \cos x \leq 1$
+  \item $(\cos x)^2 + (\sin x)^2 = 1$
+\end{itemize2}
+\end{prop}
+\bigskip
+
+Expliquer les deux premières propriétés à l'aide de la définition et du cercle trigonométrique : \dotfill
+\smallskip
+\lignepoint
+
+\bigskip
+
+Expliquer la troisième propriété à l'aide d'un théorème bien connu du collège (indication : introduire un triangle rectangle adéquat) : \dotfill
+
+\smallskip
+\lignepoint
+
+
+\smallskip
+\lignepoint
+\bigskip
+
+\subsubsection*{Quelques calculs de sinus et cosinus}
+
+\begin{tabular}{|c|p{4.5cm}|p{4.5cm}|p{4.5cm}|}
+\hline
+$x$ & $\frac{\pi}{6}$ & $\frac{\pi}{4}$ & $\frac{\pi}{3}$ \\
+\hline
+Angle en  ° & & &  \\
+\hline
+Figure & \includegraphics[width=2.7cm]{cercle2.pdf} & \includegraphics[width=2.7cm]{cercle2.pdf} &\includegraphics[width=2.7cm]{cercle2.pdf} \\
+\hline
+$M$ & $M$ est placé tel quel $OJM$ est un triangle équilatéral. & & \vspace{1,5cm} \\
+\hline
+$\cos x$ & & & \\
+$\sin x$ & & & \vspace{0.5cm}\\
+\hline
+\end{tabular}
+
+\end{document}
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@@ -17,6 +17,7 @@
 \usepackage{tikz}
 \usepackage{wrapfig}
 \usepackage{multirow}
+\usepackage{fourier}
 
 \newcommand\eur{\text{\,\euro\xspace}}
 
 
 \newcommand\xb{{\bar{x}}}
 
+\newcommand\arc[1]{{\wideparen{#1}}}
+
 %%%%%%%%%%%%%%%%%%%%%%%%% Pour les corrigés
 
 \newcommand\reponse[1]{
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