\select@language {french}
\chapterbegin 
\contentsline {part}{I\hspace {1em}Num\'erique}{2}{part.1}
\contentsline {xpart}{Num\'erique}{3}{part.1}
\contentsline {chapter}{\numberline {1}Produit et quotient de 2 nombres relatifs}{3}{chapter.1}
\contentsline {section}{\numberline {1.1}Activit\'es}{4}{section.1.1}
\contentsline {subsection}{\numberline {1.1.1}Produit de deux nombres relatifs de signes diff\'erents}{4}{subsection.1.1.1}
\contentsline {subsection}{\numberline {1.1.2}Produit de deux nombres relatifs de m\^eme signe}{4}{subsection.1.1.2}
\contentsline {subsection}{\numberline {1.1.3}Distributivit\'e et nombres relatifs}{5}{subsection.1.1.3}
\contentsline {subsection}{\numberline {1.1.4}Signe d'un produit de plusieurs facteurs}{5}{subsection.1.1.4}
\contentsline {subsection}{\numberline {1.1.5}Quotient de 2 nombres relatifs}{6}{subsection.1.1.5}
\contentsline {section}{\numberline {1.2}Cours}{7}{section.1.2}
\contentsline {subsection}{\numberline {1.2.1}Multiplication de deux nombres relatifs}{7}{subsection.1.2.1}
\contentsline {paragraph}{Multiplication par 0}{7}{section*.2}
\contentsline {paragraph}{Multiplication par $-1$}{7}{section*.3}
\contentsline {paragraph}{Distributivit\'e}{7}{section*.4}
\contentsline {subsection}{\numberline {1.2.2}Signe d'un produit de plusieurs facteurs}{7}{subsection.1.2.2}
\contentsline {subsection}{\numberline {1.2.3}Quotient de deux nombres relatifs}{7}{subsection.1.2.3}
\contentsline {subsection}{\numberline {1.2.4}Inverse d'un nombre relatif diff\'erent de 0}{7}{subsection.1.2.4}
\contentsline {section}{\numberline {1.3}Exercices}{8}{section.1.3}
\contentsline {section}{\numberline {1.4}R\'ecapitulatif}{13}{section.1.4}
\contentsline {chapter}{\numberline {2}Nombres relatifs en \'ecriture fractionnaire}{14}{chapter.2}
\contentsline {section}{\numberline {2.1}Activit\'e}{15}{section.2.1}
\contentsline {subsection}{\numberline {2.1.1}Division et inverse}{15}{subsection.2.1.1}
\contentsline {subsection}{\numberline {2.1.2}Inverse d'une fraction}{15}{subsection.2.1.2}
\contentsline {section}{\numberline {2.2}Cours}{16}{section.2.2}
\contentsline {subsection}{\numberline {2.2.1}Quotients \'egaux de 2 nombres relatifs.}{16}{subsection.2.2.1}
\contentsline {subsection}{\numberline {2.2.2}Addition et soustraction de deux fractions}{16}{subsection.2.2.2}
\contentsline {paragraph}{Les d\'enominateurs sont identiques}{16}{section*.5}
\contentsline {paragraph}{Les d\'enominateurs sont diff\'erents}{16}{section*.6}
\contentsline {subsection}{\numberline {2.2.3}Multiplication de deux fractions}{16}{subsection.2.2.3}
\contentsline {subsection}{\numberline {2.2.4}Division de deux fractions}{17}{subsection.2.2.4}
\contentsline {section}{\numberline {2.3}Exercices}{18}{section.2.3}
\contentsline {section}{\numberline {2.4}R\'ecapitulatif}{22}{section.2.4}
\contentsline {chapter}{\numberline {3}Les Puissances}{23}{chapter.3}
\contentsline {section}{\numberline {3.1}Activit\'e}{24}{section.3.1}
\contentsline {subsection}{\numberline {3.1.1}Op\'erations sur les puissances de 10}{24}{subsection.3.1.1}
\contentsline {paragraph}{Multiplication de 2 puissances de 10}{24}{section*.7}
\contentsline {paragraph}{Division de 2 puissances de 10}{24}{section*.8}
\contentsline {paragraph}{Puisssance d'une puissance de 10}{24}{section*.9}
\contentsline {subsection}{\numberline {3.1.2}Effet de la multiplication par une puissance de 10}{24}{subsection.3.1.2}
\contentsline {subsection}{\numberline {3.1.3}Ecriture scientifique d'un nombre relatif}{24}{subsection.3.1.3}
\contentsline {subsection}{\numberline {3.1.4}Op\'erations sur les puissances d'un entier relatif}{25}{subsection.3.1.4}
\contentsline {paragraph}{Multiplication de deux puissances}{25}{section*.10}
\contentsline {paragraph}{Division de deux puissances}{25}{section*.11}
\contentsline {paragraph}{Puissance d'une puissance}{25}{section*.12}
\contentsline {paragraph}{Puissance d'un produit}{25}{section*.13}
\contentsline {section}{\numberline {3.2}Cours}{26}{section.3.2}
\contentsline {subsection}{\numberline {3.2.1}Puissances de 10}{26}{subsection.3.2.1}
\contentsline {paragraph}{D\'efinitions}{26}{section*.14}
\contentsline {paragraph}{Formules de calculs}{26}{section*.15}
\contentsline {paragraph}{Ecriture scientifique d'un nombre d\'ecimal}{27}{section*.16}
\contentsline {subsection}{\numberline {3.2.2}Puissance d'un entier relatif}{27}{subsection.3.2.2}
\contentsline {paragraph}{Utilisation de la calculatrice}{27}{section*.17}
\contentsline {paragraph}{Op\'erations sur les puissances}{27}{section*.18}
\contentsline {section}{\numberline {3.3}Exercices}{28}{section.3.3}
\contentsline {chapter}{\numberline {4}Calcul litt\'eral}{31}{chapter.4}
\contentsline {section}{\numberline {4.1}Activit\'es}{32}{section.4.1}
\contentsline {subsection}{\numberline {4.1.1}De l'int\'er\^et du calcul litt\'eral}{32}{subsection.4.1.1}
\contentsline {subsection}{\numberline {4.1.2}De l'int\'er\^et du d\'eveloppement}{32}{subsection.4.1.2}
\contentsline {subsection}{\numberline {4.1.3}Des sommes, des diff\'erences et des parenth\`eses}{34}{subsection.4.1.3}
\contentsline {paragraph}{Oppos\'e d'une somme}{34}{section*.19}
\contentsline {paragraph}{Oppos\'e d'une diff\'erence}{34}{section*.20}
\contentsline {paragraph}{Suppression de parenth\`eses dans une suite d'additions ou de soustraction}{34}{section*.21}
\contentsline {subsection}{\numberline {4.1.4}La double distributivit\'e}{35}{subsection.4.1.4}
\contentsline {paragraph}{Cas des nombres positifs}{35}{section*.22}
\contentsline {paragraph}{Cas des nombres relatifs}{35}{section*.23}
\contentsline {section}{\numberline {4.2}Cours}{36}{section.4.2}
\contentsline {subsection}{\numberline {4.2.1}Simple distributivit\'e}{36}{subsection.4.2.1}
\contentsline {paragraph}{Application : Regroupement de termes}{36}{section*.24}
\contentsline {subsection}{\numberline {4.2.2}Suppression des parenth\`eses}{36}{subsection.4.2.2}
\contentsline {subsection}{\numberline {4.2.3}R\'eduction d'une expression litt\'erale}{36}{subsection.4.2.3}
\contentsline {subsection}{\numberline {4.2.4}Double distributivit\'e}{37}{subsection.4.2.4}
\contentsline {section}{\numberline {4.3}Exercices}{38}{section.4.3}
\contentsline {chapter}{\numberline {5}Equations du 1\up {\lowercase {er}}\xspace {} degr\'e \`a 1 inconnue}{44}{chapter.5}
\contentsline {section}{\numberline {5.1}Activit\'es}{45}{section.5.1}
\contentsline {subsection}{\numberline {5.1.1}Egalit\'e et op\'erations (addition, soustraction)}{45}{subsection.5.1.1}
\contentsline {subsection}{\numberline {5.1.2}Ecrire des \'egalit\'es}{45}{subsection.5.1.2}
\contentsline {subsection}{\numberline {5.1.3}Probl\`eme et \'equation}{45}{subsection.5.1.3}
\contentsline {section}{\numberline {5.2}Cours}{47}{section.5.2}
\contentsline {subsection}{\numberline {5.2.1}Egalit\'es et op\'erations}{47}{subsection.5.2.1}
\contentsline {subsection}{\numberline {5.2.2}Equation du 1\up {\lowercase {er}}\xspace {} degr\'e \`a 1 inconnue}{47}{subsection.5.2.2}
\contentsline {paragraph}{Equations de r\'ef\'erence}{48}{section*.25}
\contentsline {subsection}{\numberline {5.2.3}Mise en \'equation d'un probl\`eme}{48}{subsection.5.2.3}
\contentsline {section}{\numberline {5.3}Exercices}{50}{section.5.3}
\contentsline {chapter}{\numberline {6}Ordre}{52}{chapter.6}
\contentsline {section}{\numberline {6.1}Activit\'e}{53}{section.6.1}
\contentsline {subsection}{\numberline {6.1.1}Ordre et op\'erations}{53}{subsection.6.1.1}
\contentsline {section}{\numberline {6.2}Cours}{54}{section.6.2}
\contentsline {subsection}{\numberline {6.2.1}Vocabulaire}{54}{subsection.6.2.1}
\contentsline {subsection}{\numberline {6.2.2}Ordre et addition}{54}{subsection.6.2.2}
\contentsline {subsection}{\numberline {6.2.3}Ordre et multiplication}{54}{subsection.6.2.3}
\contentsline {section}{\numberline {6.3}Exercices}{55}{section.6.3}
\contentsline {part}{II\hspace {1em}G\'eom\'etrique}{57}{part.2}
\contentsline {xpart}{G\'eom\'etrique}{58}{part.2}
\contentsline {chapter}{\numberline {7}Triangle rectangle et cercle}{58}{chapter.7}
\contentsline {section}{\numberline {7.1}Activit\'es}{59}{section.7.1}
\contentsline {subsection}{\numberline {7.1.1}Cercle circonscrit \`a un triangle rectangle}{59}{subsection.7.1.1}
\contentsline {subsection}{\numberline {7.1.2}Comment obtenir un triangle rectangle \`a partir d'un cercle ?}{59}{subsection.7.1.2}
\contentsline {section}{\numberline {7.2}Cours}{61}{section.7.2}
\contentsline {subsection}{\numberline {7.2.1}Rappels}{61}{subsection.7.2.1}
\contentsline {subsection}{\numberline {7.2.2}Cercle circonscrit \`a un triangle rectangle}{61}{subsection.7.2.2}
\contentsline {subsection}{\numberline {7.2.3}Triangle rectangle inscrit dans un cercle}{61}{subsection.7.2.3}
\contentsline {section}{\numberline {7.3}Exercices}{62}{section.7.3}
\contentsline {chapter}{\numberline {8}Th\'eor\`eme des milieux}{64}{chapter.8}
\contentsline {section}{\numberline {8.1}Activit\'es}{65}{section.8.1}
\contentsline {subsection}{\numberline {8.1.1}Th\'eor\`eme des milieux}{65}{subsection.8.1.1}
\contentsline {subsection}{\numberline {8.1.2}Th\'eor\`eme des milieux -- Organigramme de d\'emonstration}{65}{subsection.8.1.2}
\contentsline {subsection}{\numberline {8.1.3}Th\'eor\`eme des milieux -- Suite}{66}{subsection.8.1.3}
\contentsline {subsection}{\numberline {8.1.4}Un triangle, un milieu d'un c\^ot\'e et une parall\`ele \`a un des c\^ot\'es}{67}{subsection.8.1.4}
\contentsline {subsection}{\numberline {8.1.5}Un triangle, un milieu d'un c\^ot\'e et une parall\`ele \`a un des c\^ot\'es -- Organigramme de d\'emonstration}{67}{subsection.8.1.5}
\contentsline {section}{\numberline {8.2}Cours}{69}{section.8.2}
\contentsline {subsection}{\numberline {8.2.1}Le th\'eor\`eme des milieux}{69}{subsection.8.2.1}
\contentsline {subsection}{\numberline {8.2.2}Milieu et parall\`ele}{69}{subsection.8.2.2}
\contentsline {section}{\numberline {8.3}Exercices}{70}{section.8.3}
\contentsline {chapter}{\numberline {9}L'\'egalit\'e des 3 rapports}{73}{chapter.9}
\contentsline {section}{\numberline {9.1}Activit\'es}{74}{section.9.1}
\contentsline {subsection}{\numberline {9.1.1}Approche du th\'eor\`eme}{74}{subsection.9.1.1}
\contentsline {paragraph}{Exp\'erience connue}{74}{section*.26}
\contentsline {paragraph}{Etude d'un cas particulier}{74}{section*.27}
\contentsline {section}{\numberline {9.2}Cours}{75}{section.9.2}
\contentsline {subsection}{\numberline {9.2.1}L'\'egalit\'e des 3 rapports}{75}{subsection.9.2.1}
\contentsline {paragraph}{Formulation}{75}{section*.28}
\contentsline {paragraph}{Remarques}{75}{section*.29}
\contentsline {subsection}{\numberline {9.2.2}Application : calcul de longueur}{75}{subsection.9.2.2}
\contentsline {section}{\numberline {9.3}Exercices}{77}{section.9.3}
\contentsline {chapter}{\numberline {10}Le Th\'eor\`eme de Pythagore}{81}{chapter.10}
\contentsline {section}{\numberline {10.1}Activit\'es}{82}{section.10.1}
\contentsline {subsection}{\numberline {10.1.1}Carr\'e d'un nombre positif}{82}{subsection.10.1.1}
\contentsline {subsection}{\numberline {10.1.2}Deux carr\'es pour un grand carr\'e}{82}{subsection.10.1.2}
\contentsline {subsection}{\numberline {10.1.3}D\'emontrer qu'un triangle est rectangle}{83}{subsection.10.1.3}
\contentsline {section}{\numberline {10.2}Cours}{85}{section.10.2}
\contentsline {subsection}{\numberline {10.2.1}Enonc\'e du th\'eor\`eme}{85}{subsection.10.2.1}
\contentsline {subsection}{\numberline {10.2.2}Application : calcul de longueur}{85}{subsection.10.2.2}
\contentsline {subsection}{\numberline {10.2.3}La r\'eciproque du th\'eor\`eme de Pythagore}{85}{subsection.10.2.3}
\contentsline {section}{\numberline {10.3}Exercices}{87}{section.10.3}
\contentsline {chapter}{\numberline {11}Cosinus d'un angle aigu}{91}{chapter.11}
\contentsline {section}{\numberline {11.1}Activit\'es}{92}{section.11.1}
\contentsline {section}{\numberline {11.2}Cours}{93}{section.11.2}
\contentsline {subsection}{\numberline {11.2.1}Vocabulaire}{93}{subsection.11.2.1}
\contentsline {subsection}{\numberline {11.2.2}Cosinus d'un angle aigu}{93}{subsection.11.2.2}
\contentsline {subsection}{\numberline {11.2.3}Applications}{93}{subsection.11.2.3}
\contentsline {paragraph}{Calculer une longueur}{94}{section*.30}
\contentsline {paragraph}{Calculer un angle}{94}{section*.31}
\contentsline {section}{\numberline {11.3}Exercices}{95}{section.11.3}
\contentsline {chapter}{\numberline {12}Droites remarquables du triangle}{99}{chapter.12}
\contentsline {section}{\numberline {12.1}Activit\'es}{100}{section.12.1}
\contentsline {subsection}{\numberline {12.1.1}M\'ediatrices}{100}{subsection.12.1.1}
\contentsline {subsection}{\numberline {12.1.2}Hauteurs}{100}{subsection.12.1.2}
\contentsline {subsection}{\numberline {12.1.3}M\'edianes}{101}{subsection.12.1.3}
\contentsline {subsection}{\numberline {12.1.4}Bissectrices}{101}{subsection.12.1.4}
\contentsline {section}{\numberline {12.2}Cours}{102}{section.12.2}
\contentsline {subsection}{\numberline {12.2.1}Les hauteurs}{102}{subsection.12.2.1}
\contentsline {subsection}{\numberline {12.2.2}Les m\'ediatrices}{102}{subsection.12.2.2}
\contentsline {subsection}{\numberline {12.2.3}Les m\'edianes}{103}{subsection.12.2.3}
\contentsline {subsection}{\numberline {12.2.4}Les bissectrices.}{103}{subsection.12.2.4}
\contentsline {section}{\numberline {12.3}Exercices}{104}{section.12.3}
\contentsline {section}{\numberline {12.4}Approfondissement}{107}{section.12.4}
\contentsline {subsection}{\numberline {12.4.1}Droite d'Euler}{107}{subsection.12.4.1}
\contentsline {subsection}{\numberline {12.4.2}Cercle d'Euler ou cercle des neuf points}{108}{subsection.12.4.2}
\contentsline {chapter}{\numberline {13}Translations}{110}{chapter.13}
\contentsline {section}{\numberline {13.1}Activit\'es}{111}{section.13.1}
\contentsline {subsection}{\numberline {13.1.1}Notion de translation}{111}{subsection.13.1.1}
\contentsline {subsection}{\numberline {13.1.2}Image d'une droite par une translation}{112}{subsection.13.1.2}
\contentsline {section}{\numberline {13.2}Cours}{113}{section.13.2}
\contentsline {subsection}{\numberline {13.2.1}D\'efinitions}{113}{subsection.13.2.1}
\contentsline {subsection}{\numberline {13.2.2}Propri\'et\'es}{113}{subsection.13.2.2}
\contentsline {section}{\numberline {13.3}Exercices}{115}{section.13.3}
\contentsline {chapter}{\numberline {14}Distance, droite et cercle}{118}{chapter.14}
\contentsline {section}{\numberline {14.1}Activit\'es}{119}{section.14.1}
\contentsline {subsection}{\numberline {14.1.1}Distance d'un point \`a une droite}{119}{subsection.14.1.1}
\contentsline {subsection}{\numberline {14.1.2}Intersection d'une droite avec un cercle}{119}{subsection.14.1.2}
\contentsline {section}{\numberline {14.2}Cours}{120}{section.14.2}
\contentsline {subsection}{\numberline {14.2.1}Distance d'un point \`a une droite}{120}{subsection.14.2.1}
\contentsline {subsection}{\numberline {14.2.2}Tangente \`a un cercle}{120}{subsection.14.2.2}
\contentsline {section}{\numberline {14.3}Exercices}{121}{section.14.3}
\contentsline {chapter}{\numberline {15}G\'eom\'etrie dans l'espace}{122}{chapter.15}
\contentsline {section}{\numberline {15.1}Activit\'es}{123}{section.15.1}
\contentsline {section}{\numberline {15.2}Cours}{124}{section.15.2}
\contentsline {subsection}{\numberline {15.2.1}Pyramide}{124}{subsection.15.2.1}
\contentsline {paragraph}{Pyramide de sommet $S$}{124}{section*.32}
\contentsline {paragraph}{Pyramides r\'eguli\`eres}{124}{section*.33}
\contentsline {paragraph}{Un patron de la pyramide.}{125}{section*.34}
\contentsline {paragraph}{Volume d'une pyramide}{125}{section*.35}
\contentsline {subsection}{\numberline {15.2.2}C\^one de r\'evolution}{125}{subsection.15.2.2}
\contentsline {paragraph}{Patron d'un c\^one}{126}{section*.36}
\contentsline {paragraph}{Volume d'un c\^one}{126}{section*.37}
\contentsline {section}{\numberline {15.3}Exercices}{127}{section.15.3}
\contentsline {paragraph}{Partie 1}{127}{section*.38}
\contentsline {paragraph}{Partie 2}{127}{section*.39}
\contentsline {part}{III\hspace {1em}Gestion de donn\'ees}{129}{part.3}
\contentsline {xpart}{Gestion de donn\'ees}{130}{part.3}
\contentsline {chapter}{\numberline {16}Applications de la proportionnalit\'e}{130}{chapter.16}
\contentsline {section}{\numberline {16.1}Activit\'es}{131}{section.16.1}
\contentsline {subsection}{\numberline {16.1.1}Repr\'esentations graphiques}{131}{subsection.16.1.1}
\contentsline {subsection}{\numberline {16.1.2}Vitesse moyenne}{131}{subsection.16.1.2}
\contentsline {section}{\numberline {16.2}Cours}{132}{section.16.2}
\contentsline {subsection}{\numberline {16.2.1}Proportionnalit\'e et repr\'esentation graphique}{132}{subsection.16.2.1}
\contentsline {subsection}{\numberline {16.2.2}Vitesse moyenne}{132}{subsection.16.2.2}
\contentsline {section}{\numberline {16.3}Exercices}{133}{section.16.3}
\contentsline {chapter}{\numberline {17}Statistiques}{137}{chapter.17}
\contentsline {section}{\numberline {17.1}Activit\'es}{138}{section.17.1}
\contentsline {section}{\numberline {17.2}Cours}{140}{section.17.2}
\contentsline {subsection}{\numberline {17.2.1}Effectifs et fr\'equences}{140}{subsection.17.2.1}
\contentsline {subsection}{\numberline {17.2.2}Effectifs et fr\'equences cumul\'es}{140}{subsection.17.2.2}
\contentsline {subsection}{\numberline {17.2.3}Moyenne}{140}{subsection.17.2.3}
\contentsline {subsection}{\numberline {17.2.4}Moyenne pond\'er\'ee}{141}{subsection.17.2.4}
\contentsline {subsection}{\numberline {17.2.5}R\'epartition en classes et moyenne}{141}{subsection.17.2.5}
\contentsline {section}{\numberline {17.3}Exercices}{143}{section.17.3}
\contentsline {part}{IV\hspace {1em}Annexes}{145}{part.4}
\contentsline {xpart}{Annexes}{146}{part.4}
\contentsline {chapter}{\numberline {A}Compl\'ements}{146}{appendix.A}
\contentsline {section}{\numberline {A.1}P\'erim\`etre et aire d'une surface}{146}{section.A.1}
\contentsline {section}{\numberline {A.2}Se m\'efier\ldots }{147}{section.A.2}
\contentsline {section}{\numberline {A.3}Les quadrilat\`eres particuliers}{148}{section.A.3}
\contentsline {subsection}{\numberline {A.3.1}D\'emontrer un parall\'elogramme?}{148}{subsection.A.3.1}
\contentsline {subsection}{\numberline {A.3.2}D\'emontrer un losange?}{148}{subsection.A.3.2}
\contentsline {subsection}{\numberline {A.3.3}D\'emontrer un rectangle?}{148}{subsection.A.3.3}
\contentsline {subsection}{\numberline {A.3.4}D\'emontrer un carr\'e ?}{149}{subsection.A.3.4}