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ycm)o3()kYKUbJHR7hEq$BQ?Q9|Mw#T0-gN>L;X?i)N(X1m@Jf9SXkFYkNQ87ld)+4 diff --git a/SNT/DS/210115_img/exercises.tex b/SNT/DS/210115_img/exercises.tex index cbae756..fe81a6d 100644 --- a/SNT/DS/210115_img/exercises.tex +++ b/SNT/DS/210115_img/exercises.tex @@ -1,4 +1,14 @@ \collectexercises{banque} +\begin{exercise}[subtitle={Couleurs}, points=4, tribe={1}] + Compléter les phrases suivantes + \begin{enumerate} + \item Le code couleur RGB \texttt{0 255 0} décrit la couleur \dotfill + \item Le code couleur RGB \texttt{0 255 255} décrit la couleur \dotfill + \item Le code couleur RGB \texttt{255 255 255} décrit la couleur \dotfill + \item Pour coder la couleur rouge, on peut utiliser le code RGB \dotfill + \end{enumerate} +\end{exercise} + \begin{exercise}[subtitle={Couleurs}, points=4, tribe={2}] Compléter les phrases suivantes \begin{enumerate} @@ -9,6 +19,51 @@ \end{enumerate} \end{exercise} +\begin{exercise}[subtitle={Image bitmap}, points=4, tribe={1}] + \begin{enumerate} + \item Décrire sur la grille l'image codée en noir et blanc ci-dessous + + \begin{minipage}{0.6\textwidth} + \texttt + P1 \\ + 5 8 \\ + 1 0 0 0 1 + 0 1 0 1 0 + 0 0 1 0 0 + 0 1 0 1 0 + 1 1 0 0 1 + 0 1 1 1 0 + 0 1 1 1 0 + \end{minipage} + \begin{minipage}{0.4\textwidth} + \begin{tikzpicture}[baseline=(a.north), xscale=0.5, yscale=0.5] + \tkzInit[xmin=-5,xmax=5,xstep=1, + ymin=-5,ymax=5,ystep=1] + \tkzGrid + \end{tikzpicture} + \end{minipage} + \item Écrire le code pour décrire l'image suivante + + \begin{minipage}{0.4\linewidth} + \begin{tikzpicture}[baseline=(a.north), xscale=1, yscale=1] + \tkzInit[xmin=0,xmax=5,xstep=1, + ymin=0,ymax=4,ystep=1] + \tkzGrid + \draw [fill] (0,3) rectangle (1, 4); + \draw [fill] (1,2) rectangle (2, 3); + \draw [fill] (2,0) rectangle (3, 1); + \draw [fill] (3,0) rectangle (4, 1); + \draw [fill] (2,1) rectangle (3, 2); + \draw [fill] (3,2) rectangle (4, 3); + \draw [fill] (4,3) rectangle (5, 4); + \end{tikzpicture} + \end{minipage} + \begin{minipage}{0.6\linewidth} + \reponse{3cm} + \end{minipage} + \end{enumerate} +\end{exercise} + \begin{exercise}[subtitle={Image bitmap}, points=4, tribe={2}] \begin{enumerate} \item Décrire sur la grille l'image codée en noir et blanc ci-dessous @@ -52,6 +107,20 @@ \end{enumerate} \end{exercise} +\begin{exercise}[subtitle={Avec l'ordinateur}, points=3, tribe={1}] + \begin{enumerate} + \item Comment s'appelle les données qui décrive une imagez? + \reponse{1cm} + \item Ouvrir l'image \texttt{image1.jpg} et compléter les informations suivantes la concernant: + \begin{itemize} + \item Date de la prise d'image: \dotfill + \item Définition: \dotfill + \item Nom de l'appareil \dotfill + \end{itemize} + \end{enumerate} + \pagebreak +\end{exercise} + \begin{exercise}[subtitle={Avec l'ordinateur}, points=3, tribe={2}] \begin{enumerate} \item Comment s'appelle les données qui décrive une image? @@ -66,11 +135,26 @@ \pagebreak \end{exercise} -\begin{exercise}[subtitle={Cours}, points=3, tribe={2}] +\begin{exercise}[subtitle={Cours}, points=4, tribe={1}] \begin{enumerate} + \item Quel est le poids d'une image en noir et blanc de définition $\np{1440}\times\np{900}$. + \reponse{1cm} \item Combien d'octet faut-il pour coder une couleur en RGB? \reponse{1cm} - \item Combien de niveau de gris différent peut-on coder avec 2bits? + \item Combien de niveau de gris différent peut-on coder avec 8bits? + \reponse{1cm} + \item Est-ce qu'un ficher numérique image ne contient que des données concernant les pixels? Si non, donner des exemples de données stockées. + \reponse{1cm} + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Cours}, points=4, tribe={2}] + \begin{enumerate} + \item Quel est le poids d'une image en noir et blanc de définition $\np{1024}\times\np{740}$. + \reponse{1cm} + \item Combien d'octet faut-il pour coder une couleur en RGB? + \reponse{1cm} + \item Combien de niveau de gris différent peut-on coder avec 3bits? \reponse{1cm} \item Est-ce qu'un ficher numérique image ne contient que des données concernant les pixels? Si non, donner des exemples de données stockées. \reponse{1cm} From a1d73135b85b3373b9d56c40cf9a44987bf5fb64 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Thu, 14 Jan 2021 11:21:51 +0100 Subject: [PATCH 3/6] =?UTF-8?q?Feat:=20pr=C3=A9sentation=20de=20la=20s?= =?UTF-8?q?=C3=A9ance=20protocole?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- SNT/03_Internet/1B_niveau_internet.pdf | Bin 341211 -> 340997 bytes SNT/03_Internet/1B_niveau_internet.tex | 5 +- SNT/03_Internet/2B_protocoles.tex | 43 +++++++ SNT/03_Internet/2P_Protocole.pdf | Bin 0 -> 307174 bytes SNT/03_Internet/2P_Protocole.tex | 148 +++++++++++++++++++++++++ SNT/03_Internet/fig/lampe_allumee.png | Bin 0 -> 105563 bytes SNT/03_Internet/fig/lampe_eteind.png | Bin 0 -> 70528 bytes 7 files changed, 192 insertions(+), 4 deletions(-) create mode 100644 SNT/03_Internet/2B_protocoles.tex create mode 100644 SNT/03_Internet/2P_Protocole.pdf create mode 100755 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STI2D} +\date{18 janvier 2021} +\duree{30min} + +\pagestyle{empty} +\newcommand{\reponse}[1]{% + \begin{bclogo}[barre=none, logo=]{Réponse} + \vspace{#1} + \end{bclogo} +} + +\begin{document} +\maketitle + +Le barème est donné à titre indicatif, il pourra être modifié. + + +\begin{exercise}[subtitle={Questions diverses}, points=5] + Dans cet exercice les questions sont indépendantes les unes des autres. + \begin{enumerate} + \item Calculer la dérivée de $f(x) = (2x+1)e^{4x}$ + \reponse{1cm} + \item Calculer une primitive de $g(x) = 10e^{5x}$. + \reponse{1cm} + \item Soit $h(t) = e^{-0.5t}$ et $H(t) = -2e^{-0.5t}$ une primitive de $h(t)$. Calculer la quantité $\ds \int_0^{10} e^{-0.5t} \; dt$. + \reponse{1cm} + \item Soit $z = \sqrt{2} - \sqrt{2}i$. Calculer le module et l'argument de $z$. + \reponse{2cm} + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Ciment}, points=5] + Le clinker est un constituant du ciment qui résulte de la cuisson d'un mélange composé de calcaire et d'argile. La fabrication du clinker nécessite des fours à très haute température qui libèrent dans l'air une grande quantité de dioxyde de carbone (CO$_2$). + + Dans une cimenterie, la fabrication du clinker s'effectue de 7 h 30 à 20 h, dans une pièce de volume \np{900000}~dm$^3$. + + À 20 h, après une journée de travail, le taux volumique de CO$_2$ dans la pièce est de 0,6\,\%. + \begin{enumerate} + \item Justifier que le volume de CO$_2$ présent dans cette pièce à 20 h est de \np{5400}~dm$^3$ . + \item On modélise le volume de CO$_2$ présent dans la pièce par une fonction du temps $t$ écoulé après 20h (exprimé en minutes) qui pour formule $f(t) = V_0e^{-0.01t} + 450$ + \begin{enumerate} + \item Démontrer que $V_0$ est égale à \np{4950}. + \item Quel sera, au dm$^3$ près, le volume de CO$_2$ dans cette pièce à 21 h ? + \item Démontrer que $V'(t) = -49,5e^{-0.01t}$. + \item Étudier le signe de $V'(t)$ puis en déduire le sens de variation de $V(t)$. + \end{enumerate} + \end{enumerate} +\end{exercise} + + + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: + From ad10f9a12d0f26fb141f6f028a77480d1cb550db Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Thu, 14 Jan 2021 13:53:40 +0100 Subject: [PATCH 6/6] =?UTF-8?q?Feat:=20D=C3=A9but=20du=20chapitre=20sur=20?= =?UTF-8?q?l'exponentielle=20complexe?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../1B_forme_expo.pdf | Bin 0 -> 92158 bytes .../1B_forme_expo.tex | 63 +++++++++++++++++ .../1E_multiplication.pdf | Bin 0 -> 71971 bytes .../1E_multiplication.tex | 23 ++++++ .../06_Exponentielle_complexe/exercises.tex | 66 ++++++++++++++++++ TST_sti2d/06_Exponentielle_complexe/index.rst | 25 +++++++ TST_sti2d/index.rst | 8 +-- 7 files changed, 181 insertions(+), 4 deletions(-) create mode 100644 TST_sti2d/06_Exponentielle_complexe/1B_forme_expo.pdf create mode 100644 TST_sti2d/06_Exponentielle_complexe/1B_forme_expo.tex create mode 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+\author{Benjamin Bertrand} +\title{Exponentielle complexe - Cours} +\date{janvier 2021} + +\pagestyle{empty} + +\begin{document} + +\maketitle + +\section{Multiplication des nombres complexes} + +En exercice, nous avons conjecturé la propriété suivante + +\begin{propriete} + Soit $z$ et $z'$ deux nombres complexes, quand on multiplie ces deux nombres, + \begin{itemize} + \item les modules se multiplient: $|z\times z'| = |z| \times |z'|$ + \item les modules s'ajoutent: $arg(z\times z') = arg(z) + arg(z')$ + \end{itemize} +\end{propriete} + +\section{Forme trigonométrique} + +\begin{definition} + +La forme exponentielle d'une nombre complexe de module $r$ (avec $r>0$) et d'argument $\theta$ est +\[ + z = re^{i\theta} +\] + +\end{definition} + +\begin{propriete} + Soit $z$ un nombre complexe, $r$ son module et $\theta$ son argument, alors + \[ + z = r(\cos(\theta) + i\sin(\theta)) = re^{i\theta} + \] +\end{propriete} + +\subsection*{Exemple} +Forme exponentielle de $z = \sqrt{3} - i$ +\afaire{} + +\begin{propriete} +Soient $z = re^{i\theta}$ et $z' = r'e^{i\theta'}$ deux nombres complexes écrits sous forme exponentielle. Alors +\[ + z\times z' = re^{i\theta} \times r'e^{i\theta'} = rr'e^{i(\theta+\theta')} +\] +\end{propriete} + +\subsection*{Exemple} +Soient $z = 2e^{i\frac{\pi}{3}}$ et $z' = \sqrt{3}e^{i\frac{\pi}{2}}$. La forme exponentielle de $zz'$ est +\[ + z\times z' = +\] +\afaire{} + + +\end{document} diff --git a/TST_sti2d/06_Exponentielle_complexe/1E_multiplication.pdf b/TST_sti2d/06_Exponentielle_complexe/1E_multiplication.pdf new file mode 100644 index 0000000000000000000000000000000000000000..142e6d41173f6e4c403e30016806dc3a7df9ecc4 GIT binary patch literal 71971 zcmce+bFe5)_APjAvkAzMJ4ZoKT7f>>#bzCxJEMSQ%xkF@CJ} zYF3LiE6aukcUpHGIq~pu9e#~lZClObOeAqr14q&2?E8?G^Hq=RV(;kcyxpax?ZYE4 z;?>^q`c#MW!?x3RuV~t7EWtdImy)b4`Yl!^WT%-!0%eM?NlYCHqd{G zwNlCQ?wJJyM~N#*f#xgSYjQ<3&v4O8b6j-O?YJSMkn6vj+}v!xoY&xh2FmhF2N|f@ z=-j!EPai6YEnA#rHx+u3wY3+3{Uoru4?+O`_f99yV{~%+P3Flq{BE4x+Bu{Y?BgT@ z8byZZ^JbDhsyrbJx`T&TiHH|%l?ftI7>7e|QPSj{nAS|^hPeVcDMF3wYEp`OAmp5X z6GQW=Rge&JB<{=Yg9;D<`!6JsF60i23U&&D=(kZlnS)k~*HN=qF6dXYz{cJ9eol>t zRkOxZgx4>8f5BN`eCWDCY%s(mJ@M zQKBbI}{z8k=d{ zhlhvGjUQw4I_Vb3&65!-Bf6~*({k<1`6+P-*7t!vR=L4aW7rK*I&6UH)F#@x@TINVv!*KE| z`q|@VXCN=9yEvZquC|_@S0&6wo`DThgl~O{-Jy<($cu-?stKc>R`)Baxv2u@244rq 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+\DeclareExerciseCollection{banque} +\xsimsetup{ + step=1, +} + +\pagestyle{empty} + +\begin{document} + +\input{exercises.tex} +\printcollection{banque} +\vfill +\printcollection{banque} +\vfill + +\end{document} diff --git a/TST_sti2d/06_Exponentielle_complexe/exercises.tex b/TST_sti2d/06_Exponentielle_complexe/exercises.tex new file mode 100644 index 0000000..0457b2b --- /dev/null +++ b/TST_sti2d/06_Exponentielle_complexe/exercises.tex @@ -0,0 +1,66 @@ +\collectexercises{banque} +\begin{exercise}[subtitle={Multiplication entre complexe}, step={1}, origin={Création}, topics={Exponentielle complexe}, tags={Complexe}] + Soit les 4 nombres complexes sous forme algébrique + \[ + z_A = 1 + \sqrt{3}i \qquad + z_B = -i + \sqrt{3} \qquad + z_C = -\frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}i \qquad + z_D = 3\sqrt{2} + 3\sqrt{2}i + \] + \begin{enumerate} + \item Calculer le module et l'argument de ces 4 nombres complexes. + \item À partir de la forme algébrique, calculer tous les produits possibles et déterminer le module et l'argument des résultats. Vous reporterez vos résultats dans les tableaux suivants + + \begin{tabular}{|c|*{6}{p{3cm}|}} + \hline + Algébrique & A & B & C & D \\ + \hline + A & & & & \\ + \hline + B & & & & \\ + \hline + C & & & & \\ + \hline + D & & & & \\ + \hline + \end{tabular} + + {\small + \hspace{-1cm} + \begin{tabular}{|c|*{6}{p{1.5cm}|}} + \hline + Module & A($r= \cdots$) & B($r= \cdots$) & C ($r= \cdots$)& D($r= \cdots$) \\ + \hline + A ($r= \cdots$) & & & &\\ + \hline + B ($r= \cdots$) & & & &\\ + \hline + C ($r= \cdots$) & & & &\\ + \hline + D ($r= \cdots$) & & & &\\ + \hline + \end{tabular} + \hfill + \begin{tabular}{|c|*{6}{p{1.5cm}|}} + \hline + Argument & A($\theta= \cdots$) & B($\theta= \cdots$) & C($\theta= \cdots$) & D($\theta= \cdots$) \\ + \hline + A ($\theta= \cdots$) & & & &\\ + \hline + B ($\theta= \cdots$) & & & &\\ + \hline + C ($\theta= \cdots$) & & & &\\ + \hline + D ($\theta= \cdots$) & & & &\\ + \hline + \end{tabular} + } + \item Compléter les phrases suivantes à partir de vos résultats + \begin{itemize} + \item Quand on multiplie 2 nombres complexes alors les modules sont \dotfill + \item Quand on multiplie 2 nombres complexes alors les arguments sont \dotfill + \end{itemize} + \end{enumerate} +\end{exercise} + +\collectexercisesstop{banque} diff --git a/TST_sti2d/06_Exponentielle_complexe/index.rst b/TST_sti2d/06_Exponentielle_complexe/index.rst new file mode 100644 index 0000000..12e2e4b --- /dev/null +++ b/TST_sti2d/06_Exponentielle_complexe/index.rst @@ -0,0 +1,25 @@ +Exponentielle complexe +###################### + +:date: 2021-01-14 +:modified: 2021-01-14 +:authors: Benjamin Bertrand +:tags: Complexe +:category: TST_sti2d +:summary: Forme exponentielle des nombres complexes + +Étape 1: Multiplication des nombres complexes +============================================= + +Par groupe, les élèves cherchent le module et l'argument de 4 nombres complexes. Ensuite, ils les multiplient entre eux et cherchent le module et l'argument du produit. Le but est de trouver quel est l'effet sur le module et l'argument de la multiplication entre complexes. Dès qu'ils conjecturent un résultat, on le communique à la classe qui a chercher à la conforter ou la contredire. + +.. image:: ./1E_multiplication.pdf + :height: 200px + :alt: Multiplier des nombres complexes et trouver une relation sur le module et l'argument. + +Bilan + +.. image:: ./1B_forme_expo.pdf + :height: 200px + :alt: Bilan sur la forme complexe + diff --git a/TST_sti2d/index.rst b/TST_sti2d/index.rst index 6e002c8..02d9de5 100644 --- a/TST_sti2d/index.rst +++ b/TST_sti2d/index.rst @@ -2,7 +2,7 @@ Terminale technologique spécialité sti2d ######################################## :date: 2020-08-21 -:modified: 2021-01-07 +:modified: 2021-01-14 :authors: Bertrand Benjamin :category: TST_sti2d :tags: Progression @@ -25,13 +25,13 @@ Période 1 (septembre octobre - 7 semaines) Période 2 (novembre décembre - 7 semaines) ========================================== -- `Primitives et intégrales <./04_Integrale_et_Primitives>`_ -- `Fonction exponentielle <./05_Fonction_Expronentielle>`_ +- `Primitives et intégrales <./04_Integrale_et_Primitives/>`_ +- `Fonction exponentielle <./05_Fonction_Exponentielle/>`_ Période 3 (Janvier - 5 semaines) ================================ -- Forme exponentielle des complexes +- `Forme exponentielle des complexes <./06_Exponentielle_complexe>`_ - Équation différentielle linéaire et affine Période 4 (Février mars avril - 7 semaines)