From 92fa0f94cba051264c370b1fe28f2e7742ef33ce Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Thu, 4 Mar 2021 10:11:06 +0100 Subject: [PATCH] Feat: Documents pour 1E et cours sur les sommes --- TST/09_Somme_suites/1B_somme_suite.tex | 14 ---- TST/09_Somme_suites/1E_comparaison.pdf | Bin 37058 -> 37255 bytes TST/09_Somme_suites/1E_comparaison.tex | 2 +- TST/09_Somme_suites/2B_somme_suite.pdf | Bin 0 -> 82237 bytes TST/09_Somme_suites/2B_somme_suite.tex | 85 +++++++++++++++++++++++++ TST/09_Somme_suites/exercises.tex | 18 +++--- TST/09_Somme_suites/index.rst | 21 +++++- 7 files changed, 114 insertions(+), 26 deletions(-) delete mode 100644 TST/09_Somme_suites/1B_somme_suite.tex create mode 100644 TST/09_Somme_suites/2B_somme_suite.pdf create mode 100644 TST/09_Somme_suites/2B_somme_suite.tex diff --git a/TST/09_Somme_suites/1B_somme_suite.tex b/TST/09_Somme_suites/1B_somme_suite.tex deleted file mode 100644 index 08ffb68..0000000 --- a/TST/09_Somme_suites/1B_somme_suite.tex +++ /dev/null @@ -1,14 +0,0 @@ -\documentclass[a4paper,10pt]{article} -\usepackage{myXsim} - -\author{Benjamin Bertrand} -\title{Somme suites - Cours} -\date{février 2021} - -\pagestyle{empty} - -\begin{document} - -\maketitle - -\end{document} \ No newline at end of file diff --git a/TST/09_Somme_suites/1E_comparaison.pdf b/TST/09_Somme_suites/1E_comparaison.pdf index 1342e1507d4576eeb1f79d6ae75c51ac681f6a56..9a5ecf2413348647fc7967df526b1ce5aa749c7b 100644 GIT binary patch delta 5258 zcmV;56m{#up#q1a0G_aY3!8jiFBFf-rJYlAq-5}gKD?*f%Z+Qje?6KRnISDWB%c-b{gxmqhD!eOlTD=ETqp!S*` z<@=S=VYyq$BrK`{Mt{0`9cX2u1VpBy%Iur%nP*&q$g~pt{yr ziR!A!5GO~#5}-*ENEv0;DpY07fBUaBSine<;>Cfa#VQU_vqXk0M`V-OpnYR4!HE9p zHa5SrB5l((?dhUI^$U9}YTI~O$6? z;hUBbrEK@4N52E$U=xsv;5Y7YvJn9J-OHx0yZ?YVs0a6L%JIGbe?ryxnK)se*LUtm z7-Im^`BMDnFV#Fom5pQ)gGP{2u_leKg-jM}4&oZ$CfNH9C85nEJ-+6aaOQsg(qyx> zHjPv&{o;~l9DF^AlrernJ+m0tu$hpxf!yJt(ZALC%sBL#k2g)p!R>9x(0oETnZ;3@ zs0T|2nRzG8Su+C!e`hXa4npUthE@lL&Q97{K~U>IgPs3kpYinHwpOr)^Eizcai~sa 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a/TST/09_Somme_suites/1E_comparaison.tex b/TST/09_Somme_suites/1E_comparaison.tex index 2dae188..d3dcc3a 100644 --- a/TST/09_Somme_suites/1E_comparaison.tex +++ b/TST/09_Somme_suites/1E_comparaison.tex @@ -1,4 +1,4 @@ -\documentclass[a4paper,10pt]{article} +\documentclass[a5paper,10pt]{article} \usepackage{myXsim} \author{Benjamin Bertrand} diff --git a/TST/09_Somme_suites/2B_somme_suite.pdf b/TST/09_Somme_suites/2B_somme_suite.pdf new file mode 100644 index 0000000000000000000000000000000000000000..9aa822cc4993eb9771b12f7024e8fd16abf2df03 GIT binary patch literal 82237 zcmce+bC54h*CqOE+qP}nwrv}yZQG}9+qQk$w(aiIcF*&EGhfWyxHsa?Kkr)+Rgsms zGox0mT|0K=+GL8N;&e>(Y|vzLOCxL0tb~k&4#w8dyu8p1s-BK!gbbPr#@1#gF3=1r zuEs9^)g$iUWCzV4EbQPxsKfY=Jrm=9oqEs={~GzPSxnFjaz-vrR{vNq{bTXZ_`k0I zSSXu0JGeTTm^l-&{nMii%^+)LZ{cD|$iznYzm9)av9fhBb0TCAw>5Gx6E!n&Fg1hb z=ZAK7aWXTqgZ9{1M3_;eoY?~gKzsq+L7Ul|{;!dLTK{@{GZ>%{|evC9GoowGk*X7hwp108D|_0Ju7C4`qVf%v#`}%vj 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+\pagestyle{empty} + +\begin{document} + +\maketitle + +\section{Sommes}% +\label{sec:Sommes} + +\subsection*{Algorithmes} + +Pour calculer des sommes, nous avons utilisé des algorithmes avec une boucle \textbf{for} et un \textbf{accumulateur} comme le programme suivant: + +\begin{minipage}{0.4\linewidth} + \begin{lstlisting}[language=Python, basicstyle=\small, frame=] + # Initialisation + u = 100 + S = 0 + + # Boucle + for i in range(3): + u = u * 0.7 + S = S + u + + # Résultat final + print(S) + \end{lstlisting} +\end{minipage} +\begin{minipage}{0.6\linewidth} + Tableau des variables + + \begin{tabular}{|*{3}{p{2cm}|}} + \hline + u & S & i \\ + \hline + & & \\ + & & \\ + & & \\ + & & \\ + & & \\ + & & \\ + & & \\ + \hline + \end{tabular} +\end{minipage} + +\afaire{Exécuter la programme et compléter le tableau des variables} + +\subsection*{Symbole somme $\sum$} + +On rappelle que la somme de termes est l'addition de termes. + +\begin{definition} + Soit $(u_n)$ une suite alors on note + \[ + \sum_{i = m}^{n} u_n = u_m + u_{m+1} + ... + u_{n-1} + u_n + \] +\end{definition} + +\paragraph{Exemples}% +\label{par:Exemples} +\begin{itemize} + \item Somme des carrés + \[ + \sum_{i = 0}^{5} i^2 = + \] + \item Soit $(u_n)$ une suite géométrique de raison $q = 2$ et de premier terme $u_0 = 1$ + \[ + \sum_{i = 0}^{4} u_i = + \] +\end{itemize} +\afaire{Calculer les quantité précédentes} + + + + + +\end{document} diff --git a/TST/09_Somme_suites/exercises.tex b/TST/09_Somme_suites/exercises.tex index 9c4402c..bb72d58 100644 --- a/TST/09_Somme_suites/exercises.tex +++ b/TST/09_Somme_suites/exercises.tex @@ -1,7 +1,7 @@ \collectexercises{banque} \begin{exercise}[subtitle={Situations}, step={1}, origin={Créations}, topics={Somme suites}, tags={Suites, analyse, tableur, python}] Choisir une situation parmi celles proposées ci-dessous. Vous devrez interroger ces situations de façon pertinente et produire un dossier apportant les réponses à ces questions. - \begin{enumerate} + \begin{enumerate}[leftmargin=*] \item Une entreprise propose à ses employés deux primes étalées sur 3ans. \begin{itemize} \item Prime 1: 100\euro le premier mois puis la prime augmente de 2\euro par mois. @@ -30,14 +30,14 @@ \end{enumerate} \paragraph{Barème} \begin{itemize} - \item (raisonner) Pertinence des questions posées \dotfill 2pt - \item (communiquer) Clarté des explications \dotfill 2pt - \item (modélisation) Choix des outils mathématiques utilisés\dotfill 2pt - \item (représenter) Schémas pour illustrer \dotfill 2pt - \item (raisonner) Rigueur des explications apportés \dotfill 2pt - \item (calculs) Justesse des calculs \dotfill 2pt - \item (représenter) Graphiques des évolutions \dotfill 2pt - \item (communiquer) Description des évolutions \dotfill 2pt + \item (raisonner) Pertinence des questions posées \dotfill 1pt + \item (communiquer) Clarté des explications \dotfill 2pts + \item (modélisation) Choix des outils mathématiques utilisés\dotfill 1pt + \item (représenter) Schémas pour illustrer \dotfill 1pt + \item (raisonner) Rigueur des explications apportés \dotfill 1pt + \item (calculs) Justesse des calculs \dotfill 2pts + \item (représenter) Graphiques des évolutions \dotfill 1pt + \item (communiquer) Description des évolutions \dotfill 1pt \end{itemize} \end{exercise} diff --git a/TST/09_Somme_suites/index.rst b/TST/09_Somme_suites/index.rst index 625859d..b9527a8 100644 --- a/TST/09_Somme_suites/index.rst +++ b/TST/09_Somme_suites/index.rst @@ -2,7 +2,7 @@ Somme suites ############ :date: 2021-02-07 -:modified: 2021-02-07 +:modified: 2021-03-04 :authors: Benjamin Bertrand :tags: Suites, Analyse, Tableur, Python :category: TST @@ -13,11 +13,28 @@ Somme suites Comparaison de deux situations (arithmétique et géométrique) où il faudra non seulement calculer les termes consécutifs mais aussi faire la somme des termes. -Avant l'étape suivante, on donnera un bilan avec les formules pour calculer les sommes. +.. image:: ./1E_comparaison.pdf + :height: 200px + :alt: Scénarios à étudier en autonomie + +Étape 2: Boucles et accumulateur +================================ + +Séance de programmation où l'on va travailler sur les boucles et les accumulateurs pour calculer des sommes. On invitera les élèves à utiliser une feuille de papier pour vérifier les calculs faits par l'ordinateur. + +Les élèves retrouveront les scénarios de l'étape 1 pour faire les calculs avec l'outil de programmation. + +Bilan: algorithme d'accumulations et symbole somme + +.. image:: ./2B_somme_suite.pdf + :height: 200px + :alt: algorithme d'accumulations et symbole somme Étape 2: Formules de sommes =========================== +À la suite de la lecture du cours, on donnera les formules qui permettent de calculer les sommes de suites arithmétiques et géométriques. + Exercices techniques pour calculer des sommes de termes. Étape 3: Exercices bilan sur les suites