{"id":6762,"date":"2015-06-14T19:31:35","date_gmt":"2015-06-14T17:31:35","guid":{"rendered":"https:\/\/kamerpower.com\/?p=6762"},"modified":"2025-08-11T00:27:06","modified_gmt":"2025-08-10T23:27:06","slug":"epreuves-concours-iut-de-douala-mathematiques-2006-pfti-gi-filiere-1ere-annee","status":"publish","type":"post","link":"https:\/\/kamerpower.com\/fr\/epreuves-concours-iut-de-douala-mathematiques-2006-pfti-gi-filiere-1ere-annee\/","title":{"rendered":"Epreuves concours IUT de Douala Math\u00e9matiques 2006 PFTI-GI Fili\u00e8re 1\u00e8re ANN\u00c9E IUT de l\u2019Universit\u00e9 de Douala Session juillet 2006"},"content":{"rendered":"<p style=\"text-align: center;\"><span style=\"color: #000000;\">R\u00c9PUBLIQUE DU CAMEROUN<br \/>\nCONCOURS D\u2019ENTREE EN 1\u00e8re ANN\u00c9E<br \/>\n<span style=\"color: #ff0000;\">Session de juillet 2006<\/span> <strong>IUT<\/strong>\u00a0de l\u2019Universit\u00e9<br \/>\nde\u00a0Douala\u00a0Fili\u00e8re: <strong>PFTI-<\/strong><strong>GI<\/strong><br \/>\n<a href=\"https:\/\/kamerpower.com\/fr\/epreuves-concours-iut-douala-mathematiques-2011-pftin-gi-filiere-1ere-annee\/\" target=\"_blank\" rel=\"noopener\"><strong>\u00c9preuve de Math\u00e9matiques<\/strong><\/a><br \/>\nDUREE : 3\u00a0HEURES\u00a0<span style=\"color: #008000;\">KA<\/span><span style=\"color: #ff0000;\">M<\/span><span style=\"color: #ffcc00;\">ER<\/span><span style=\"color: #800080;\">POWER<\/span>.COM<br \/>\n<\/span><\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-custom ez-toc-container-direction\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Contents<\/p>\n<label for=\"ez-toc-cssicon-toggle-item-69de715c62333\" class=\"ez-toc-cssicon-toggle-label\"><span class=\"ez-toc-cssicon\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #000000;color:#000000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #000000;color:#000000\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/label><input type=\"checkbox\"  id=\"ez-toc-cssicon-toggle-item-69de715c62333\"  aria-label=\"Toggle\" \/><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/kamerpower.com\/fr\/epreuves-concours-iut-de-douala-mathematiques-2006-pfti-gi-filiere-1ere-annee\/#epreuves-concours-iut-de-douala\" >Epreuves concours IUT de Douala \n*******************************<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/kamerpower.com\/fr\/epreuves-concours-iut-de-douala-mathematiques-2006-pfti-gi-filiere-1ere-annee\/#epreuves-concours-iut-de-douala-mathematiques-2006-pfti-gi\" >Epreuves concours IUT de Douala Math\u00e9matiques 2006 PFTI-GI<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/kamerpower.com\/fr\/epreuves-concours-iut-de-douala-mathematiques-2006-pfti-gi-filiere-1ere-annee\/#i-6-points\" >I. ( 6 points)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/kamerpower.com\/fr\/epreuves-concours-iut-de-douala-mathematiques-2006-pfti-gi-filiere-1ere-annee\/#ii-4-points\" >II. ( 4 points)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/kamerpower.com\/fr\/epreuves-concours-iut-de-douala-mathematiques-2006-pfti-gi-filiere-1ere-annee\/#iii-10-points\" >III. ( 10\u00a0points)<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/kamerpower.com\/fr\/epreuves-concours-iut-de-douala-mathematiques-2006-pfti-gi-filiere-1ere-annee\/#epreuves-concours-iut-de-douala-mathematiques-2006-pfti-gi-filiere-1ere-annee-iut-de-luniversite-de-douala-session-juillet-2006\" >Epreuves concours IUT de Douala Math\u00e9matiques 2006 PFTI-GI Fili\u00e8re 1\u00e8re ANN\u00c9E IUT de l\u2019Universit\u00e9 de Douala Session juillet 2006<\/a><\/li><\/ul><\/nav><\/div>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"epreuves-concours-iut-de-douala\"><\/span><span style=\"color: #000000;\">Epreuves concours IUT de Douala<br \/>\n<span style=\"color: #ff0000;\"><span style=\"color: #00ff00;\">**********<\/span>***********<span style=\"color: #ffff00;\">**********<\/span><\/span><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"epreuves-concours-iut-de-douala-mathematiques-2006-pfti-gi\"><\/span><span style=\"color: #3366ff;\"><a style=\"color: #3366ff;\" href=\"https:\/\/kamerpower.com\/fr\/concours-iut-douala-2021-2022-cycle-bts-premiere-annee\/\" target=\"_blank\" rel=\"noopener\">Epreuves concours IUT de Douala Math\u00e9matiques 2006 PFTI-GI<\/a><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"i-6-points\"><\/span><strong><span style=\"color: #ff0000;\">I. ( 6 points)<\/span><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #000000;\">Soit l\u2019\u00e9quation (E) = x<sup>3<\/sup> &#8211; 15x &#8211; 4 = 0 \u00a0<\/span><\/p>\n<p><span style=\"color: #000000;\">a) V\u00e9rifier graphiquement que (E) admet trois racines r\u00e9elles. ( 1 pt)<\/span><br \/>\n<span style=\"color: #000000;\">b) Montrer que u et v sont deux nombre r\u00e9els tels que<br \/>\nu<sup>4<\/sup>+ v<sup>3<\/sup> = 4 et u v =\u00a05 alors u + v estsolution de (E) . (2 pts)<\/span><br \/>\n<span style=\"color: #000000;\">c) Montrer u<sup>3<\/sup>+\u00a0v<sup>3<\/sup>\u00a0sont solutions de x<sup>2<\/sup> &#8211; 4x + 125 = 0. Cette \u00e9quation\u00a0admet-elle des solutions dans R ? R\u00e9soudre l\u2019\u00e9quation dans C. ( 1 pt) kamerpower.com<\/span><br \/>\n<span style=\"color: #000000;\">d)\u00a0Calculer (2 + i)<sup>2<\/sup>\u00a0et (2 &#8211;\u00a0i)<sup>2<\/sup> . En d\u00e9duire les solutions de (E). (2 pts)<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"ii-4-points\"><\/span><span style=\"color: #ff0000;\"><strong>II. ( 4 points)<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Le quart d\u2019un population a \u00e9t\u00e9 vaccin\u00e9e contre une maladie contagieuse. Au\u00a0cours d\u2019une \u00e9pid\u00e9mie ,on a constat\u00e9 qu\u2019il y a parmi les malades un vaccin\u00e9\u00a0pour quatre non vaccin\u00e9s . [kamerpower.com] On sait que de plus qu\u2019au cours de cette \u00e9pid\u00e9mie, il y avait un malade parmi les douze vaccin\u00e9s. Quelle est la probabilit\u00e9\u00a0de tomber malade pour un individu non vaccin\u00e9 ? le vaccin est-il efficace?<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"iii-10-points\"><\/span><span style=\"color: #ff0000;\"><strong>III. ( 10\u00a0points)<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #000000;\">Soit la fonction f d\u00e9finie sur R \u00a0par:\u00a0<\/span><\/p>\n<p>f(x) = { x-1+ 1\/x \u00a0 si \u00a0x \u2264 1<br \/>\n1 &#8211; (In(x))<span style=\"color: #000000;\"><sup>2<\/sup><\/span> , si \u00a0x \u2264 1<\/p>\n<ol>\n<li><span style=\"color: #000000;\">Montrer que f est continue et derivable en 1. (2 pts)<\/span><\/li>\n<li><span style=\"color: #000000;\">\u00a0Calculer les limites aux bornes de son ensemble de d\u00e9finition et pr\u00e9ciser les branches infinies de la courbe repr\u00e9sentative de f. (3 pts) \u00a0kamerpower.com<\/span><\/li>\n<li><span style=\"color: #000000;\">\u00c9tudier les variations de f .D\u00e9montrer que le point d\u2019abscisse e est un\u00a0point d\u2019inflection de la courbe repr\u00e9sentative de f. (4 pts)\u00a0kamerpower.com<\/span><\/li>\n<li><span style=\"color: #000000;\">Tracer cette courbe dans un plan muni d\u2019un rep\u00e8re ortonorm\u00e9 (<em>O, i, j<\/em>) \u00a0<\/span><br \/>\n<span style=\"color: #000000;\">(1 pt)<\/span><\/li>\n<\/ol>\n<h2 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"epreuves-concours-iut-de-douala-mathematiques-2006-pfti-gi-filiere-1ere-annee-iut-de-luniversite-de-douala-session-juillet-2006\"><\/span><span style=\"color: #3366ff;\"><a style=\"color: #3366ff;\" href=\"https:\/\/kamerpower.com\/fr\/concours-iut-douala-2021-2022-cycle-bts-premiere-annee\/\" target=\"_blank\" rel=\"noopener\">Epreuves concours IUT de Douala Math\u00e9matiques 2006<\/a> PFTI-GI Fili\u00e8re 1\u00e8re ANN\u00c9E IUT de l\u2019Universit\u00e9 de Douala Session juillet 2006 <\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n","protected":false},"excerpt":{"rendered":"<p>&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":38314,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_themeisle_gutenberg_block_has_review":false,"footnotes":""},"categories":[1701],"tags":[1712,1856,1706],"class_list":["post-6762","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-epreuves","tag-epreuve-de-concours-dentree-aux-grandes-ecoles-cameroun","tag-epreuves-de-concours-de-liut-de-douala","tag-mathematiques"],"_links":{"self":[{"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/posts\/6762","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/comments?post=6762"}],"version-history":[{"count":3,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/posts\/6762\/revisions"}],"predecessor-version":[{"id":70253,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/posts\/6762\/revisions\/70253"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/media\/38314"}],"wp:attachment":[{"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/media?parent=6762"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/categories?post=6762"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/tags?post=6762"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}