From 3a4ed381bf5f972a1fc4fd6f99cb7598ce3f6496 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Thu, 15 Oct 2020 11:50:34 +0200 Subject: [PATCH 1/5] =?UTF-8?q?Feat:=20d=C3=A9but=20=C3=A9tude=20poly?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- TST/05_Etude_Polynomes/1B.tex | 14 ++++++++++++++ TST/05_Etude_Polynomes/1E.tex | 18 ++++++++++++++++++ TST/05_Etude_Polynomes/exercises.tex | 10 ++++++++++ TST/05_Etude_Polynomes/index.rst | 27 +++++++++++++++++++++++++++ 4 files changed, 69 insertions(+) create mode 100644 TST/05_Etude_Polynomes/1B.tex create mode 100644 TST/05_Etude_Polynomes/1E.tex create mode 100644 TST/05_Etude_Polynomes/exercises.tex create mode 100644 TST/05_Etude_Polynomes/index.rst diff --git a/TST/05_Etude_Polynomes/1B.tex b/TST/05_Etude_Polynomes/1B.tex new file mode 100644 index 0000000..d0f951a --- /dev/null +++ b/TST/05_Etude_Polynomes/1B.tex @@ -0,0 +1,14 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} + +\author{Benjamin Bertrand} +\title{Etude Polynomes - Cours} +\date{octobre 2020} + +\pagestyle{empty} + +\begin{document} + +\maketitle + +\end{document} \ No newline at end of file diff --git a/TST/05_Etude_Polynomes/1E.tex b/TST/05_Etude_Polynomes/1E.tex new file mode 100644 index 0000000..b8ee3a8 --- /dev/null +++ b/TST/05_Etude_Polynomes/1E.tex @@ -0,0 +1,18 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} + +\author{Benjamin Bertrand} +\title{Etude Polynomes - Cours} +\date{octobre 2020} + +\DeclareExerciseCollection{banque} +\xsimsetup{ + step=1, +} + +\begin{document} + +\input{exercises.tex} +\printcollection{banque} + +\end{document} \ No newline at end of file diff --git a/TST/05_Etude_Polynomes/exercises.tex b/TST/05_Etude_Polynomes/exercises.tex new file mode 100644 index 0000000..9dcf5c2 --- /dev/null +++ b/TST/05_Etude_Polynomes/exercises.tex @@ -0,0 +1,10 @@ +\collectexercises{banque} +\begin{exercise}[subtitle={<++>}, step={1}, origin={<++>}, topics={Etude Polynomes}, tags={analyse, fonctions, tableau de variations, dérivation}] + <++> +\end{exercise} + +\begin{solution} + <++> +\end{solution} + +\collectexercisesstop{banque} \ No newline at end of file diff --git a/TST/05_Etude_Polynomes/index.rst b/TST/05_Etude_Polynomes/index.rst new file mode 100644 index 0000000..221ccb8 --- /dev/null +++ b/TST/05_Etude_Polynomes/index.rst @@ -0,0 +1,27 @@ +Etude Polynomes +############### + +:date: 2020-10-15 +:modified: 2020-10-15 +:authors: Benjamin Bertrand +:tags: Analyse, Fonctions, Tableau de variations, Dérivation +:category: TST +:summary: Étude des fonctions polynômes et dérivation + +On fait de l'explicite! Cours avec exemple puis exercices. + +Étape 1: étude des variations d'un polynôme du 3e degré +======================================================= + +Cours avec exemple puis exercices techniques. + +Étape 2: Factorisation d'un polynôme de degré 2 et 3, racines +============================================================= + +Définitions d'une racine et factorisation. + +Étape 3: Étude de signe d'un polynôme de degré 3 +================================================ + +Factorisation puis étude de signe + From f936eada05c857b606156fd608f9c3c3682f6e47 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Thu, 15 Oct 2020 12:11:48 +0200 Subject: [PATCH 2/5] =?UTF-8?q?Feat:=20d=C3=A9but=20du=20prolongement=20g?= =?UTF-8?q?=C3=A9om=C3=A9trique?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../1B.tex | 14 +++++++++++ .../1E.tex | 18 ++++++++++++++ .../exercises.tex | 10 ++++++++ .../index.rst | 24 +++++++++++++++++++ 4 files changed, 66 insertions(+) create mode 100644 TST/06_Prolongement_geometrique_vers_exponentiel/1B.tex create mode 100644 TST/06_Prolongement_geometrique_vers_exponentiel/1E.tex create mode 100644 TST/06_Prolongement_geometrique_vers_exponentiel/exercises.tex create mode 100644 TST/06_Prolongement_geometrique_vers_exponentiel/index.rst diff --git a/TST/06_Prolongement_geometrique_vers_exponentiel/1B.tex b/TST/06_Prolongement_geometrique_vers_exponentiel/1B.tex new file mode 100644 index 0000000..ae1093d --- /dev/null +++ b/TST/06_Prolongement_geometrique_vers_exponentiel/1B.tex @@ -0,0 +1,14 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} + +\author{Benjamin Bertrand} +\title{Prolongement géométrique vers exponentiel - Cours} +\date{octobre 2020} + +\pagestyle{empty} + +\begin{document} + +\maketitle + +\end{document} \ No newline at end of file diff --git a/TST/06_Prolongement_geometrique_vers_exponentiel/1E.tex b/TST/06_Prolongement_geometrique_vers_exponentiel/1E.tex new file mode 100644 index 0000000..5bba213 --- /dev/null +++ b/TST/06_Prolongement_geometrique_vers_exponentiel/1E.tex @@ -0,0 +1,18 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} + +\author{Benjamin Bertrand} +\title{Prolongement géométrique vers exponentiel - Cours} +\date{octobre 2020} + +\DeclareExerciseCollection{banque} +\xsimsetup{ + step=1, +} + +\begin{document} + +\input{exercises.tex} +\printcollection{banque} + +\end{document} \ No newline at end of file diff --git a/TST/06_Prolongement_geometrique_vers_exponentiel/exercises.tex b/TST/06_Prolongement_geometrique_vers_exponentiel/exercises.tex new file mode 100644 index 0000000..b274b7b --- /dev/null +++ b/TST/06_Prolongement_geometrique_vers_exponentiel/exercises.tex @@ -0,0 +1,10 @@ +\collectexercises{banque} +\begin{exercise}[subtitle={<++>}, step={1}, origin={<++>}, topics={Prolongement géométrique vers exponentiel}, tags={exponentiel, suite, programmation}] + <++> +\end{exercise} + +\begin{solution} + <++> +\end{solution} + +\collectexercisesstop{banque} \ No newline at end of file diff --git a/TST/06_Prolongement_geometrique_vers_exponentiel/index.rst b/TST/06_Prolongement_geometrique_vers_exponentiel/index.rst new file mode 100644 index 0000000..137b360 --- /dev/null +++ b/TST/06_Prolongement_geometrique_vers_exponentiel/index.rst @@ -0,0 +1,24 @@ +Prolongement géométrique vers exponentiel +######################################### + +:date: 2020-10-15 +:modified: 2020-10-15 +:authors: Benjamin Bertrand +:tags: Exponentiel, Suite, Programmation +:category: TST +:summary: Prolongement d'une suite géométrique pour aller vers la découverte de l'exponentielle. + +Étape 1: Prolongement +===================== + +Compléter les trous d'une suite géométrique et revenir en arrière. + +Étape 2: Tracer les courbes +=========================== + +Tracer les courbes de fonctions exponentielle. C'est l'occasion d'utiliser la calculatrice pour calculer des valeurs. Le but étant de conclure sur la croissance des exponentielles en fonction de la forme de la formule. + +Étape 3: programmation combler les trous +======================================== + +Calculer les valeurs décimales d'une exponentielle à partie d'un algo et de programmation. From c8fc6b10b52ef2014f5811ef1b70ef13df590bbf Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Thu, 15 Oct 2020 12:12:06 +0200 Subject: [PATCH 3/5] =?UTF-8?q?Feat:=20mise=20=C3=A0=20jour=20des=20liens?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- TST/index.rst | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/TST/index.rst b/TST/index.rst index bbcda6e..29d9ec6 100644 --- a/TST/index.rst +++ b/TST/index.rst @@ -2,7 +2,7 @@ Terminale technologique ####################### :date: 2020-08-21 -:modified: 2020-09-01 +:modified: 2020-10-15 :authors: Bertrand Benjamin :category: TST :tags: Progression @@ -32,8 +32,8 @@ Période 1 (septembre octobre - 7 semaines) Période 2 (novembre décembre - 7 semaines) ========================================== -- Étude de polynômes de degré 2 et 3 -- Prolongement des suites géométrique vers l'exponentielle +- `Étude de polynômes de degré 2 et 3 <./05_Etude_Polynomes>`_ +- `Prolongement des suites géométrique vers l'exponentielle <./06_Prolongement_geometrique_vers_exponentiel>`_ - Loi binomiale - Manipulation de l'exponentielle From ddb02935d0582dcf38e7452eb60a1552f5790208 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Thu, 15 Oct 2020 13:36:25 +0200 Subject: [PATCH 4/5] Feat: quelques infos en plus --- EnsSci/02_Biodiversite_et_evolution/index.rst | 10 ++++++++-- 1 file changed, 8 insertions(+), 2 deletions(-) diff --git a/EnsSci/02_Biodiversite_et_evolution/index.rst b/EnsSci/02_Biodiversite_et_evolution/index.rst index c2d03b5..9095e5c 100644 --- a/EnsSci/02_Biodiversite_et_evolution/index.rst +++ b/EnsSci/02_Biodiversite_et_evolution/index.rst @@ -2,7 +2,7 @@ Biodiversité et évolution ######################### :date: 2020-08-27 -:modified: 2020-09-18 +:modified: 2020-10-15 :authors: Benjamin Bertrand :tags: Échantillonnage, Statistique :category: EnsSci @@ -16,14 +16,20 @@ Zoologie de ce qu'il y a dans un océan. Étape 2: (MATH) Évaluer la taille des populations: CMR ====================================================== +(Camille) + Calculs de proportion avec la méthode de Capture-Marquage-Recapture. +On récupère doc 2 p174 avec ajout de la formule. Refonte des docs pour plus de clarté. + + Étape 3: (MATH) Évaluer la taille des populations: échantillonnage ================================================================== Estimation d'une proportion d'une population avec l'échantillonnage. -Penser à rapprocher les 2 méthodes. +Étape 4: Hardy-Weinberg +======================= Étape 4: (SVT) Notion de génétique ================================== From d5c49aa07ab677790561871291e9b72943285865 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Thu, 15 Oct 2020 14:09:11 +0200 Subject: [PATCH 5/5] =?UTF-8?q?Feat:=204e=20=C3=A9tape=20sur=20les=20suite?= =?UTF-8?q?s=20pour=20les=20TST?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- TST/04_Formalisation_des_suites/4E_typeEC.pdf | Bin 0 -> 109217 bytes TST/04_Formalisation_des_suites/4E_typeEC.tex | 20 +++++ TST/04_Formalisation_des_suites/exercises.tex | 70 ++++++++++++++++++ .../fig/T1CMATH03609_graph.png | Bin 0 -> 16750 bytes 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a/TST/04_Formalisation_des_suites/exercises.tex +++ b/TST/04_Formalisation_des_suites/exercises.tex @@ -112,5 +112,75 @@ \end{multicols} \end{exercise} +\begin{exercise}[subtitle={TYPE E3C}, step={4}, origin={T1CMATH03609}, topics={Formalisation des suites}, tags={Suites, Analyse}] + \noindent + \begin{minipage}{0.5\textwidth} + Le nuage de point ci-contre représente les 6 premières valeurs de la suite $u$. + \begin{enumerate} + \item Lire graphiquement la valeur de $u(3)$ + \item La suite $u$ peut-elle être arithmétique? Justifier + \item Dans la suite, on admet que $u(4) = 2$ et $u(5) = 4$. On suppose que la suite est géométrique. + \begin{enumerate} + \item Calculer la raison de la suite $u$. + \item Exprimer, pour tout $n$ positif ou nul, $u(n+1)$ en fonction de $u(n)$. + \item Donner par le calcul la valeur exacte de $u(7)$. + \end{enumerate} + \end{enumerate} + \end{minipage} + \begin{minipage}{0.5\textwidth} + \includegraphics[scale=0.3]{./fig/T1CMATH03609_graph} + \end{minipage} +\end{exercise} +\begin{exercise}[subtitle={TYPE E3C}, step={4}, origin={T1CMATH03610}, topics={Formalisation des suites}, tags={Suites, Analyse}] + En 2019, une entreprise souhaite réaliser une campagne de publicité pour promouvoir ses produits. + + Elle prend alors contact avec une agence de publicité, nommée A, qui lui indique qu’en 2019, selon ses tarifs, le coût d’une campagne de publicité s’élève à 10000euros pour 2019 mais que celui-ci augmentera ensuite de 750€ par an. + + On note $u_n$le coût d’une campagne publicitaire pour l’entreprise suivant les tarifs de l’agence A pour l’année $(2019+n)$.Ainsi $u_0$=10000. + + \begin{enumerate} + \item Quel sera le coût d’une campagne de publicité pour l’entreprise en 2025 si elle choisit l’agence A? + \item Quelle est la nature de la suite $(u_n)$? Argumenter la réponse. + \item Déterminer le sens de variation de la suite $(u_n)$. Justifier la réponse. + \item L’entreprise contacte une agence de publicité B qui lui dit que le coût d’une campagne de publicité pour l’année $(2019+n)$ est donné par: $v_n = n^2+200n+\np{10000}$ + \begin{enumerate} + \item Déterminer la valeur de $v_2$. + \item Quel sera le coût d’une campagne de publicité pour l’entreprise en 2025 si elle choisit l’agence B? + \end{enumerate} + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={TYPE E3C}, step={4}, origin={T1CMATH03614}, topics={Formalisation des suites}, tags={Suites, Analyse}] + \noindent + \begin{minipage}{0.6\textwidth} + On considère la suite $u$ de premier terme $u(0) = 200$ et telle que pour tout entier positif $n$: + \[ + u(n+1) = u(n) + 20 + \] + \begin{enumerate} + \item Calculer $u(1)$. + \item + \begin{enumerate} + \item Quelle est la nature de la suite $u$? Argumenter la réponse. + \item Quel est le sens de variation de la suite $u$? Justifier la réponse. + \end{enumerate} + \item Compléter le repère ci-contre, en y représentant le terme $u(2)$ de la suite. + \end{enumerate} + \end{minipage} + \hfill + \begin{minipage}{0.3\textwidth} + \includegraphics[scale=0.3]{./fig/T1CMATH03614_graph} + \end{minipage} + + \begin{enumerate} + \setcounter{enumi}{3} + \item Parmi les situations suivantes, laquelle pourrait être modélisée grâce à la suite $u$? Justifier votre réponse. + \begin{itemize} + \item Situation A : une entreprise a vendu 200 unités d'un nouveau produit la première année. Chaque année elle en vend 10\% de plus que l'année précédente. + \item Situation B : une entreprise a vendu 200 unités d'un nouveau produit la première année. Chaque année elle en vend 20\% de plus que l'année précédente + \item Situation C : une entreprise a vendu 200 unités d'un nouveau produit la première année. Chaque année elle en vend 20 de plus que l'année précédente. + \end{itemize} + \end{enumerate} +\end{exercise} \collectexercisesstop{banque} diff --git a/TST/04_Formalisation_des_suites/fig/T1CMATH03609_graph.png b/TST/04_Formalisation_des_suites/fig/T1CMATH03609_graph.png new file mode 100644 index 0000000000000000000000000000000000000000..995aabd1f44421a0531bb5d9dbb442c23cc44c09 GIT binary patch literal 16750 zcmdUXcT`jPw{NUC%7Bgql&YhM4G@qTh*)SUC>l^o0I34f4LzugA}WL;Abk`O0RibH z1Vp4a0U`9z5$S;t0wj6+IQPE0)?M$d_5QfOci&^NW`-o^YK#?8Xj%F5Br*2#T-ONA;5C5qCzq;|_Qer8}Q!kFPlUDwU-$m3m! zMDaQAKM^K(rvBDxqr$8Nh4EV>Tqg`tPICJELeZ{~HzTzj2Yf89MD6P_cy~JNm6pqv z^9~oeA6CwEte5a=zSIiZw`s>`CsY{@n|$HT`lpJ`Jf*FqR{f0hbYuzr7WDQl@b3lZ zKVTK8eQjlt$0g64v9h;6#UgMVo8i6Be(9ZdDIHT|bzy(X(>IKIFP0V*L=HQ98U<{E z1I+}2)u-?zc^2}Hw?(UMa+_vqM@d0FoX*qi0cqf+dh*NK(Ky^h)Z^u+I;jyBwIKs7 zZ{c0^LkV2j>*nTWBg2}@!SI6kh0x6?)b+nax1msf?@)v5JHO}gJ{0QVk*z1-?aMo0 zvr*4?|GLn_n(*cSB?mOOZ@Gnq^}No^%ye*cBn&V0&f*UoIM8k@tC!I^H~bfTY5(ul 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