{"id":2057,"date":"2016-09-24T22:54:50","date_gmt":"2016-09-24T21:54:50","guid":{"rendered":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/?p=2057"},"modified":"2018-02-17T02:05:33","modified_gmt":"2018-02-17T01:05:33","slug":"fonction-inverse-1","status":"publish","type":"post","link":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/fonction-inverse-1\/","title":{"rendered":"Fonction inverse"},"content":{"rendered":"<h2>Objectifs<\/h2>\n<ul>\n<li class=\"P1\">Tracer une courbe \u00e0 partir de donn\u00e9es g\u00e9om\u00e9triques en utilisant Geoplan.<\/li>\n<li class=\"P1\">Utiliser le logiciel pour conjecturer un r\u00e9sultat.<\/li>\n<li class=\"P1\">D\u00e9montrer la conjecture<\/li>\n<\/ul>\n<h2>Pr\u00e9requis<\/h2>\n<p class=\"P1\">Notion de fonction et th\u00e9or\u00e8me de Thal\u00e8s.<\/p>\n<p class=\"P1\">Utilisation de base d\u2019un logiciel de g\u00e9om\u00e9trie dynamique\u00a0:<\/p>\n<ul>\n<li>points rep\u00e9r\u00e9s<\/li>\n<li>points libres<\/li>\n<li>droites parall\u00e8les<\/li>\n<li>intersection de deux droites<\/li>\n<li>trace d\u2019un point<\/li>\n<\/ul>\n<h2>Organisation pratique<\/h2>\n<p class=\"P1\">Les \u00e9l\u00e8ves r\u00e9alisent la construction avec un logiciel de g\u00e9om\u00e9trie dynamique, la font valider par le professeur\u00a0; ils \u00e9mettent ensuite une conjecture.<\/p>\n<p class=\"P1\">La d\u00e9monstration est envisag\u00e9e apr\u00e8s validation de la conjecture par le professeur.<\/p>\n<h2>Probl\u00e8me<\/h2>\n<p class=\"P1\">Dans un rep\u00e8re orthonorm\u00e9 \u00a0on consid\u00e8re les points A(1\u00a0;\u00a00) et B(0\u00a0; 1).<\/p>\n<p class=\"P1\">M est un point mobile sur le droite (OA).<\/p>\n<p class=\"P1\">La parall\u00e8le \u00e0 la droite (MB) passant par A coupe l\u2019axe des ordonn\u00e9es au point N.<\/p>\n<p class=\"P1\">Le point H est tel que le quadrilat\u00e8re OMHN soit un rectangle.<\/p>\n<p class=\"P1\">Sur quelle courbe le point H se d\u00e9place-t-il lorsque M se d\u00e9place sur la droite (OA)\u00a0?<\/p>\n<h2>Fichiers disponibles<\/h2>\n<ul class=\"niv1\">\n<li><a href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2016\/09\/inv1_elv.pdf\">Fiche \u00e9l\u00e8ve Fonction inverse<\/a> <span class=\"PetitInLine\">(pdf)<\/span><\/li>\n<li><a href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2016\/09\/inv1.zip\">Fichier professeur Fonction inverse<\/a> (G\u00e9oplan<a href=\"http:\/\/mathematiques.ac-bordeaux.fr\/lycee2010\/mathsettice\/seconde\/fonctions\/inverse_1\/inv1.zip\" target=\"_blank\">)<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Objectifs Tracer une courbe \u00e0 partir de donn\u00e9es g\u00e9om\u00e9triques en utilisant Geoplan. Utiliser le logiciel pour conjecturer un r\u00e9sultat. D\u00e9montrer la conjecture Pr\u00e9requis Notion de fonction et th\u00e9or\u00e8me de Thal\u00e8s. Utilisation de base d\u2019un logiciel de g\u00e9om\u00e9trie dynamique\u00a0: points rep\u00e9r\u00e9s points libres droites parall\u00e8les intersection de deux droites trace d\u2019un point Organisation pratique Les \u00e9l\u00e8ves &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/fonction-inverse-1\/\">Lire la suite<\/a><\/p>\n","protected":false},"author":351,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"footnotes":""},"categories":[23,22,14],"tags":[],"class_list":["post-2057","post","type-post","status-publish","format-standard","hentry","category-seconde","category-lycee","category-numerique","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/2057","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/users\/351"}],"replies":[{"embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/comments?post=2057"}],"version-history":[{"count":3,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/2057\/revisions"}],"predecessor-version":[{"id":2064,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/2057\/revisions\/2064"}],"wp:attachment":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/media?parent=2057"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/categories?post=2057"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/tags?post=2057"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}