\babel@toc {french}{}\relax 
\contentsline {chapter}{AVANT$-$PROPOS}{iii}{chapter*.1}%
\contentsline {chapter}{AUTRES OUVRAGES}{v}{chapter*.2}%
\contentsline {chapter}{SITES INTERNET}{vi}{chapter*.3}%
\contentsline {chapter}{\numberline {1}Le second degré}{1}{chapter.1}%
\contentsline {section}{\numberline {I}Introduction et motivation}{2}{section.1.1}%
\contentsline {subsection}{\numberline {1}Trajectoire d'un objet lancé avec un angle}{2}{subsection.1.1.1}%
\contentsline {subsection}{\numberline {2}Définition}{3}{subsection.1.1.2}%
\contentsline {section}{\numberline {II}Forme canonique}{3}{section.1.2}%
\contentsline {subsection}{\numberline {1}Définition}{3}{subsection.1.2.1}%
\contentsline {subsection}{\numberline {2}Sens de variation}{4}{subsection.1.2.2}%
\contentsline {section}{\numberline {III}Racines éventuelles}{4}{section.1.3}%
\contentsline {subsection}{\numberline {1}Définition}{4}{subsection.1.3.1}%
\contentsline {subsection}{\numberline {2}Existence de racines}{4}{subsection.1.3.2}%
\contentsline {subsubsection}{\numberline {a}Résultat préliminaire}{4}{subsubsection.1.3.2.1}%
\contentsline {subsubsection}{\numberline {b}Discriminant}{5}{subsubsection.1.3.2.2}%
\contentsline {subsubsection}{\numberline {c}Trouver les racines éventuelles}{5}{subsubsection.1.3.2.3}%
\contentsline {section}{\numberline {IV}Factorisation et signe d'un\ttl@linetosp polynôme de degré 2}{7}{section.1.4}%
\contentsline {subsection}{\numberline {1}Factorisation}{7}{subsection.1.4.1}%
\contentsline {subsection}{\numberline {2}Signe d'un polynôme de degré 2}{8}{subsection.1.4.2}%
\contentsline {section}{\numberline {V}Somme et produit des racines}{9}{section.1.5}%
\contentsline {subsection}{\numberline {1}Premiers résultats}{9}{subsection.1.5.1}%
\contentsline {subsection}{\numberline {2}Exploiter la somme et le produit des racines}{10}{subsection.1.5.2}%
\contentsline {section}{\numberline {VI}L'essentiel}{11}{section.1.6}%
\contentsline {section}{Enoncés}{12}{section*.5}%
\contentsline {section}{Corrigés des exercices}{25}{section*.7}%
\contentsline {chapter}{\numberline {2}Dérivation et ses applications}{57}{chapter.2}%
\contentsline {section}{\numberline {I}Première approche historique}{58}{section.2.1}%
\contentsline {section}{\numberline {II}Nombre dérivé}{59}{section.2.2}%
\contentsline {subsection}{\numberline {1}Approche géométrique}{59}{subsection.2.2.1}%
\contentsline {subsection}{\numberline {2}Définition et exemples fondamentaux}{61}{subsection.2.2.2}%
\contentsline {subsection}{\numberline {3}Interprétations du nombre dérivé}{63}{subsection.2.2.3}%
\contentsline {section}{\numberline {III}\'Equation de la tangente}{64}{section.2.3}%
\contentsline {subsection}{\numberline {1}Définition}{64}{subsection.2.3.1}%
\contentsline {subsection}{\numberline {2}\'Equation}{64}{subsection.2.3.2}%
\contentsline {section}{\numberline {IV}Fonction dérivée}{65}{section.2.4}%
\contentsline {subsection}{\numberline {1}Définition}{65}{subsection.2.4.1}%
\contentsline {subsection}{\numberline {2}Dérivées de référence}{65}{subsection.2.4.2}%
\contentsline {subsection}{\numberline {3}Dérivée d'une fonction composée}{66}{subsection.2.4.3}%
\contentsline {section}{\numberline {V}Fonction valeur absolue}{66}{section.2.5}%
\contentsline {subsection}{\numberline {1}Définition (rappel de Seconde)}{66}{subsection.2.5.1}%
\contentsline {subsection}{\numberline {2}Courbe représentative}{67}{subsection.2.5.2}%
\contentsline {subsection}{\numberline {3}Dérivée}{67}{subsection.2.5.3}%
\contentsline {section}{\numberline {VI}Opérations sur les dérivées}{68}{section.2.6}%
\contentsline {section}{\numberline {VII}Applications de la dérivation}{70}{section.2.7}%
\contentsline {subsection}{\numberline {1}Variation d'une fonction}{70}{subsection.2.7.1}%
\contentsline {subsection}{\numberline {2}Extremum local}{71}{subsection.2.7.2}%
\contentsline {subsection}{\numberline {3}Méthode de Newton}{71}{subsection.2.7.3}%
\contentsline {section}{Enoncés}{75}{section*.42}%
\contentsline {section}{Corrigés des exercices}{88}{section*.43}%
\contentsline {chapter}{\numberline {3}Suites numériques}{119}{chapter.3}%
\contentsline {section}{\numberline {I}Rappels sur la méthode de Newton}{120}{section.3.1}%
\contentsline {section}{\numberline {II}Introduction}{120}{section.3.2}%
\contentsline {subsection}{\numberline {1}Définition}{120}{subsection.3.2.1}%
\contentsline {subsection}{\numberline {2}Objectifs}{121}{subsection.3.2.2}%
\contentsline {subsection}{\numberline {3}Variations d'une suite}{121}{subsection.3.2.3}%
\contentsline {subsection}{\numberline {4}Majorants et minorants}{124}{subsection.3.2.4}%
\contentsline {section}{\numberline {III}Suites arithmétiques}{124}{section.3.3}%
\contentsline {subsection}{\numberline {1}Définition}{124}{subsection.3.3.1}%
\contentsline {subsection}{\numberline {2}Variations}{125}{subsection.3.3.2}%
\contentsline {subsection}{\numberline {3}Formule explicite}{125}{subsection.3.3.3}%
\contentsline {subsection}{\numberline {4}Représentation graphique}{126}{subsection.3.3.4}%
\contentsline {subsection}{\numberline {5}Somme des premiers termes}{127}{subsection.3.3.5}%
\contentsline {subsubsection}{\numberline {a}Somme des premiers entiers}{127}{subsubsection.3.3.5.1}%
\contentsline {subsubsection}{\numberline {b}Le symbole de sommation \@FB@og $\DOTSB \sum@ \slimits@ $ \@FB@fg \xspace }{128}{subsubsection.3.3.5.2}%
\contentsline {subsubsection}{\numberline {c}Somme des premiers termes d'une suite arithmétique}{128}{subsubsection.3.3.5.3}%
\contentsline {section}{\numberline {IV}Suites géométriques}{130}{section.3.4}%
\contentsline {subsection}{\numberline {1}Définition}{130}{subsection.3.4.1}%
\contentsline {subsection}{\numberline {2}Formule explicite}{130}{subsection.3.4.2}%
\contentsline {subsection}{\numberline {3}Représentation graphique}{131}{subsection.3.4.3}%
\contentsline {subsection}{\numberline {4}Somme des premiers termes}{132}{subsection.3.4.4}%
\contentsline {section}{\numberline {V}Algorithmes}{133}{section.3.5}%
\contentsline {subsection}{\numberline {1}Suites arithmétiques}{133}{subsection.3.5.1}%
\contentsline {subsection}{\numberline {2}Suites géométriques}{134}{subsection.3.5.2}%
\contentsline {section}{\numberline {VI}Pour aller plus loin : autres types de suites}{136}{section.3.6}%
\contentsline {section}{Enoncés}{141}{section*.71}%
\contentsline {section}{Corrigés des exercices}{159}{section*.72}%
\contentsline {chapter}{\numberline {4}La fonction exponentielle}{200}{chapter.4}%
\contentsline {section}{\numberline {I}Première approche}{201}{section.4.1}%
\contentsline {subsection}{\numberline {1}Notre objectif}{201}{subsection.4.1.1}%
\contentsline {subsection}{\numberline {2}La méthode d'Euler}{201}{subsection.4.1.2}%
\contentsline {section}{\numberline {II}Définition}{203}{section.4.2}%
\contentsline {subsection}{\numberline {1}Unicité de la fonction exponentielle}{203}{subsection.4.2.1}%
\contentsline {subsection}{\numberline {2}Définition}{204}{subsection.4.2.2}%
\contentsline {section}{\numberline {III}Relations fonctionnelles}{205}{section.4.3}%
\contentsline {subsection}{\numberline {1}Image d'un opposé}{205}{subsection.4.3.1}%
\contentsline {subsection}{\numberline {2}Image d'une somme}{205}{subsection.4.3.2}%
\contentsline {section}{\numberline {IV}Notation ${\rm e}^x$}{206}{section.4.4}%
\contentsline {subsection}{\numberline {1}Le nombre e}{206}{subsection.4.4.1}%
\contentsline {subsection}{\numberline {2}Vers la notation simplifiée}{207}{subsection.4.4.2}%
\contentsline {section}{\numberline {V}La suite $({\rm e}^{na})$, $a$ réel}{207}{section.4.5}%
\contentsline {subsection}{\numberline {1}La suite est géométrique}{207}{subsection.4.5.1}%
\contentsline {subsection}{\numberline {2}Expression du terme général}{208}{subsection.4.5.2}%
\contentsline {section}{\numberline {VI}\'Etude de la fonction $x\DOTSB \mapstochar \rightarrow {\rm e}^x$}{208}{section.4.6}%
\contentsline {subsection}{\numberline {1}Positivité}{208}{subsection.4.6.1}%
\contentsline {subsection}{\numberline {2}Sens de variation}{209}{subsection.4.6.2}%
\contentsline {subsection}{\numberline {3}Courbe représentative}{209}{subsection.4.6.3}%
\contentsline {subsection}{\numberline {4}Propriétés de bijectivité}{210}{subsection.4.6.4}%
\contentsline {section}{\numberline {VII}\'Etude des fonctions $x\DOTSB \mapstochar \rightarrow {\rm e}^{kx}$}{210}{section.4.7}%
\contentsline {subsection}{\numberline {1}Variations}{210}{subsection.4.7.1}%
\contentsline {subsection}{\numberline {2}Représentations graphiques}{210}{subsection.4.7.2}%
\contentsline {subsection}{\numberline {3}Domaines où l'on rencontre l'exponentielle}{211}{subsection.4.7.3}%
\contentsline {section}{Enoncés}{213}{section*.111}%
\contentsline {section}{Corrigés des exercices}{223}{section*.113}%
\contentsline {chapter}{\numberline {5}Trigonométrie}{241}{chapter.5}%
\contentsline {section}{\numberline {I}Cercle trigonométrique}{242}{section.5.1}%
\contentsline {subsection}{\numberline {1}Définitions et représentation}{242}{subsection.5.1.1}%
\contentsline {subsection}{\numberline {2}Radians}{243}{subsection.5.1.2}%
\contentsline {subsection}{\numberline {3}Valeurs remarquables}{244}{subsection.5.1.3}%
\contentsline {section}{\numberline {II}Sinus et cosinus}{245}{section.5.2}%
\contentsline {subsection}{\numberline {1}Définitions}{245}{subsection.5.2.1}%
\contentsline {subsection}{\numberline {2}Propriété fondamentale}{245}{subsection.5.2.2}%
\contentsline {subsection}{\numberline {3}Sinus et cosinus des angles remarquables}{246}{subsection.5.2.3}%
\contentsline {subsection}{\numberline {4}Lien avec le sinus et le cosinus dans un triangle rectangle}{248}{subsection.5.2.4}%
\contentsline {section}{\numberline {III}Fonctions sinus et cosinus}{249}{section.5.3}%
\contentsline {subsection}{\numberline {1}Parité}{249}{subsection.5.3.1}%
\contentsline {subsection}{\numberline {2}Périodicité}{250}{subsection.5.3.2}%
\contentsline {subsection}{\numberline {3}Courbes représentatives}{250}{subsection.5.3.3}%
\contentsline {section}{Enoncés}{252}{section*.140}%
\contentsline {section}{Corrigés des exercices}{261}{section*.142}%
\contentsline {chapter}{\numberline {6}Produit scalaire}{277}{chapter.6}%
\contentsline {section}{\numberline {I}Géométrie non repérée}{278}{section.6.1}%
\contentsline {subsection}{\numberline {1}Définition du produit scalaire}{278}{subsection.6.1.1}%
\contentsline {subsection}{\numberline {2}Orthogonalité de deux vecteurs}{278}{subsection.6.1.2}%
\contentsline {subsection}{\numberline {3}Produit scalaire et projetés orthogonaux}{279}{subsection.6.1.3}%
\contentsline {subsection}{\numberline {4}Propriétés algébriques du produit scalaire}{281}{subsection.6.1.4}%
\contentsline {subsubsection}{\numberline {a}Distributivité}{281}{subsubsection.6.1.4.1}%
\contentsline {subsubsection}{\numberline {b}Symétrie (commutativité)}{282}{subsubsection.6.1.4.2}%
\contentsline {subsubsection}{\numberline {c}Bilinéarité}{282}{subsubsection.6.1.4.3}%
\contentsline {subsection}{\numberline {5}Identités avec les normes}{283}{subsection.6.1.5}%
\contentsline {section}{\numberline {II}Géométrie repérée}{285}{section.6.2}%
\contentsline {subsection}{\numberline {1}Calcul du produit scalaire}{285}{subsection.6.2.1}%
\contentsline {subsection}{\numberline {2}Application pour trouver la mesure d'un angle}{286}{subsection.6.2.2}%
\contentsline {section}{Enoncés}{287}{section*.165}%
\contentsline {section}{Corrigés des exercices}{296}{section*.167}%
\contentsline {chapter}{\numberline {7}Applications du produit scalaire}{318}{chapter.7}%
\contentsline {section}{\numberline {I}Géométrie non repérée}{319}{section.7.1}%
\contentsline {subsection}{\numberline {1}Formule d'Al-Kashi}{319}{subsection.7.1.1}%
\contentsline {subsection}{\numberline {2}Théorèmes de la médiane}{319}{subsection.7.1.2}%
\contentsline {subsection}{\numberline {3}Propriétés sur le cercle}{321}{subsection.7.1.3}%
\contentsline {subsection}{\numberline {4}Centre de gravité d'un triangle}{321}{subsection.7.1.4}%
\contentsline {section}{\numberline {II}Géométrie repérée}{323}{section.7.2}%
\contentsline {subsection}{\numberline {1}Vecteur normal d'une droite}{323}{subsection.7.2.1}%
\contentsline {subsection}{\numberline {2}\'Equations cartésiennes de cercles}{324}{subsection.7.2.2}%
\contentsline {section}{Enoncés}{326}{section*.191}%
\contentsline {section}{Corrigés des exercices}{335}{section*.193}%
\contentsline {chapter}{\numberline {8}Probabilités conditionnelles}{372}{chapter.8}%
\contentsline {section}{\numberline {I}Probabilités conditionnelles}{373}{section.8.1}%
\contentsline {subsection}{\numberline {1}Définition}{373}{subsection.8.1.1}%
\contentsline {subsection}{\numberline {2}\'Evénement contraire}{374}{subsection.8.1.2}%
\contentsline {subsection}{\numberline {3}Partition de l'univers}{374}{subsection.8.1.3}%
\contentsline {section}{\numberline {II}Probabilités totales}{375}{section.8.2}%
\contentsline {subsection}{\numberline {1}Version \@FB@og light \@FB@fg \xspace de la formule des probabilités totales}{375}{subsection.8.2.1}%
\contentsline {subsection}{\numberline {2}Formule des probabilités totales}{375}{subsection.8.2.2}%
\contentsline {section}{\numberline {III}Indépendance}{376}{section.8.3}%
\contentsline {section}{\numberline {IV}Succession de deux épreuves\ttl@linetosp indépendantes}{378}{section.8.4}%
\contentsline {section}{Enoncés}{379}{section*.222}%
\contentsline {section}{Corrigés des exercices}{392}{section*.223}%
\contentsline {chapter}{\numberline {9}Variables aléatoires}{412}{chapter.9}%
\contentsline {section}{\numberline {I}Introduction}{413}{section.9.1}%
\contentsline {subsection}{\numberline {1}Une expérience aléatoire}{413}{subsection.9.1.1}%
\contentsline {subsection}{\numberline {2}Définition}{413}{subsection.9.1.2}%
\contentsline {subsection}{\numberline {3}Définition plus théorique}{414}{subsection.9.1.3}%
\contentsline {section}{\numberline {II}Loi de probabilité}{414}{section.9.2}%
\contentsline {subsection}{\numberline {1}Définition}{414}{subsection.9.2.1}%
\contentsline {subsection}{\numberline {2}Espérance d'une variable aléatoire}{415}{subsection.9.2.2}%
\contentsline {subsection}{\numberline {3}Variance et écart-type d'une variable aléatoire}{416}{subsection.9.2.3}%
\contentsline {subsubsection}{\numberline {a}Définitions}{416}{subsubsection.9.2.3.1}%
\contentsline {subsubsection}{\numberline {b}Interprétation}{416}{subsubsection.9.2.3.2}%
\contentsline {subsubsection}{\numberline {c}Théorème de König-Huygens}{417}{subsubsection.9.2.3.3}%
\contentsline {section}{Enoncés}{418}{section*.251}%
\contentsline {section}{Corrigés des exercices}{429}{section*.252}%
\contentsline {chapter}{\numberline {10}Entraînement aux épreuves finales}{445}{chapter.10}%
\contentsline {section}{Enoncés}{446}{section*.274}%
\contentsline {section}{Corrigés des exercices}{457}{section*.275}%
\vspace *{1cm}
\hspace *{8mm}\textit {{\fontencoding {U}\fontfamily {futs}\selectfont M}~~250 exercices entièrement corrigés}
\contentsfinish