{"id":6785,"date":"2015-06-14T23:48:21","date_gmt":"2015-06-14T21:48:21","guid":{"rendered":"https:\/\/kamerpower.com\/?p=6785"},"modified":"2025-08-11T00:21:59","modified_gmt":"2025-08-10T23:21:59","slug":"epreuves-concours-iut-douala-mathematiques-2011-pftin-gi-filiere-1ere-annee","status":"publish","type":"post","link":"https:\/\/kamerpower.com\/fr\/epreuves-concours-iut-douala-mathematiques-2011-pftin-gi-filiere-1ere-annee\/","title":{"rendered":"Epreuves concours IUT Douala Mathematiques 2011 PFTIN-GI Fili\u00e8re 1\u00e8re ANN\u00c9E IUT de l\u2019Universit\u00e9 de Douala Session juillet 2011"},"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 2011<\/span>\u00a0<strong>IUT<\/strong>\u00a0de l\u2019Universit\u00e9<br \/>\nde\u00a0Douala\u00a0Fili\u00e8re: <strong>PFTIN-<\/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-69e5ed6b3bc65\" 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-69e5ed6b3bc65\"  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-douala-mathematiques-2011-pftin-gi-filiere-1ere-annee\/#epreuves-concours-iut-douala-mathematiques\" >Epreuves concours IUT Douala\u00a0Mathematiques \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-douala-mathematiques-2011-pftin-gi-filiere-1ere-annee\/#epreuves-concours-iut-douala-mathematiques-2011-pftin-gi\" >Epreuves concours IUT Douala Mathematiques 2011 PFTIN-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-douala-mathematiques-2011-pftin-gi-filiere-1ere-annee\/#exercice-i\" >Exercice I\u00a0<\/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-douala-mathematiques-2011-pftin-gi-filiere-1ere-annee\/#exercice-ii\" >Exercice II<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/kamerpower.com\/fr\/epreuves-concours-iut-douala-mathematiques-2011-pftin-gi-filiere-1ere-annee\/#epreuves-concours-iut-douala-mathematiques-2011-pftin-gi-filiere-1ere-annee-iut-de-luniversite-de-douala-session-juillet-2011\" >Epreuves concours IUT Douala Mathematiques 2011 PFTIN-GI Fili\u00e8re 1\u00e8re ANN\u00c9E IUT de l\u2019Universit\u00e9 de Douala Session juillet 2011<\/a><\/li><\/ul><\/nav><\/div>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"epreuves-concours-iut-douala-mathematiques\"><\/span><span style=\"color: #000000;\">Epreuves concours IUT Douala\u00a0Mathematiques<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-douala-mathematiques-2011-pftin-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 Douala Mathematiques<\/a> 2011 PFTIN-GI<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"exercice-i\"><\/span><strong><span style=\"color: #ff0000;\">Exercice I\u00a0<\/span><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>1)<\/strong> Soit f une fonction r\u00e9elle d\u2019une variable r\u00e9elle d\u00e9finie par:<br \/>\nf (x ) = e<sup>2x<\/sup>\u00a0\u2212 4e<sup>x<\/sup>\u00a0+ 3<\/p>\n<ol>\n<li>Determiner le domaine de definition de f et calculer ses limites.<\/li>\n<li>Dresser le tableau de variation de f .<\/li>\n<li>R\u00e9soudre l\u2019equation f(x ) = 0.<\/li>\n<li>En d\u00e9duire le signe de f.<\/li>\n<\/ol>\n<p><strong>2)\u00a0<\/strong>Soit g une fonction r\u00e9elle d\u2019une variable r\u00e9elle d\u00e9finie par:<\/p>\n<p>g(x ) = ln(e<sup>2x<\/sup>\u00a0\u2212 4e<sup>x<\/sup>\u00a0+ 3)<\/p>\n<ol>\n<li>Determiner le domaine de d ?finition de g et calculer ses limites.<\/li>\n<li>Dresser le tableau de variation de g .<\/li>\n<li>Montrer que g(x ) se met sous la forme g(x ) = 2x + h(x ) ou h est une<br \/>\nfonction qui tend vers 0\u00a0quand x tend vers +\u221e<\/li>\n<li>Que peut on en deduire ?<\/li>\n<li>Calculer g(\u22121)et g(2) puis tracer soigneusement la courbe de g.<\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"exercice-ii\"><\/span><strong><span style=\"color: #ff0000;\">Exercice II<\/span><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #000000;\">Soit P(z ) = 4z<sup>4<\/sup>\u00a0+ 4(cos \u03b1)\u03bbz<sup>2<\/sup>\u00a0+ \u03bb<sup>2<\/sup>\u00a0ou \u03bb = 1 + cos \u03b1 ,\u03b1 \u2208 [0; \u03c0]<\/span><\/p>\n<ol>\n<li><span style=\"color: #000000;\">Exprimer P(x) avec x = (2\/\u03bb)z<sup>2<\/sup><\/span><\/li>\n<li><span style=\"color: #000000;\">Determiner en fonction \u03b1,le module et argument de chacun des nombres\u00a0complexes x1\u00a0et x2\u00a0qui sont les racines de l\u2019equation P(x) = 0.<\/span><br \/>\n<span style=\"color: #000000;\">3. En d\u00e9duire en fonction \u03b1,le module et argument de chacun des nombres\u00a0complexes z1, z2, z3\u00a0et z4\u00a0qui sont les racines de l\u2019equation P(z) = 0.<\/span><\/li>\n<\/ol>\n<p><strong><span style=\"color: #ff0000;\">Exercice III<\/span><\/strong><\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-67831\" src=\"https:\/\/kamerpower.com\/wp-content\/uploads\/2015\/06\/Exercice-III-et-IV-Epreuves-concours-IUT-Douala-Mathematiques.png\" alt=\"Exercice III et IV Epreuves concours IUT Douala Mathematiques\" width=\"1232\" height=\"1538\" srcset=\"https:\/\/kamerpower.com\/wp-content\/uploads\/2015\/06\/Exercice-III-et-IV-Epreuves-concours-IUT-Douala-Mathematiques.png 1232w, https:\/\/kamerpower.com\/wp-content\/uploads\/2015\/06\/Exercice-III-et-IV-Epreuves-concours-IUT-Douala-Mathematiques-600x749.png 600w, https:\/\/kamerpower.com\/wp-content\/uploads\/2015\/06\/Exercice-III-et-IV-Epreuves-concours-IUT-Douala-Mathematiques-240x300.png 240w, https:\/\/kamerpower.com\/wp-content\/uploads\/2015\/06\/Exercice-III-et-IV-Epreuves-concours-IUT-Douala-Mathematiques-865x1080.png 865w, https:\/\/kamerpower.com\/wp-content\/uploads\/2015\/06\/Exercice-III-et-IV-Epreuves-concours-IUT-Douala-Mathematiques-768x959.png 768w, https:\/\/kamerpower.com\/wp-content\/uploads\/2015\/06\/Exercice-III-et-IV-Epreuves-concours-IUT-Douala-Mathematiques-1230x1536.png 1230w, https:\/\/kamerpower.com\/wp-content\/uploads\/2015\/06\/Exercice-III-et-IV-Epreuves-concours-IUT-Douala-Mathematiques-720x899.png 720w, https:\/\/kamerpower.com\/wp-content\/uploads\/2015\/06\/Exercice-III-et-IV-Epreuves-concours-IUT-Douala-Mathematiques-520x649.png 520w, https:\/\/kamerpower.com\/wp-content\/uploads\/2015\/06\/Exercice-III-et-IV-Epreuves-concours-IUT-Douala-Mathematiques-320x399.png 320w\" sizes=\"(max-width: 1232px) 100vw, 1232px\" \/><\/p>\n<p><span style=\"color: #000000;\">Soient (Un) et (Vn) deux suites d\u00e9finies par:<\/span><\/p>\n<ol>\n<li><span style=\"color: #000000;\">Montrer que la suite(Vn) est g\u00e9om\u00e9trique et preciser sa raison.<\/span><\/li>\n<li><span style=\"color: #000000;\">Exprimer ()\u00a0et ()\u00a0en fonction de n<\/span><\/li>\n<li><span style=\"color: #000000;\">La suite()\u00a0est elle convergente ?<\/span><\/li>\n<li><span style=\"color: #000000;\">Calculer la limite de ln() \u00a0quand n tend vers +\u221e.<\/span><\/li>\n<li><span style=\"color: #000000;\">En deduire que la suite ()\u00a0est-elle convergente.<\/span><\/li>\n<\/ol>\n<p><strong><span style=\"color: #ff0000;\">Exercice IV<\/span><\/strong><\/p>\n<ol>\n<li><span style=\"color: #000000;\">Sans se servir de la r\u00e8gle de l\u2019hospital<\/span><br \/>\n<span style=\"color: #000000;\"><strong>a<\/strong>. Calculer la limite quand x tend vers<\/span><span style=\"color: #000000;\"><strong>b<\/strong>. Calculer la limite quand x tend vers<\/span><\/li>\n<li><span style=\"color: #000000;\"><span style=\"color: #000000;\">Calculer les int\u00e9grales<\/span><\/span><\/li>\n<li><span style=\"color: #000000;\">D\u00e9montrer que \u2200x \u2208 [0; 1]<\/span><\/li>\n<\/ol>\n<h2 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"epreuves-concours-iut-douala-mathematiques-2011-pftin-gi-filiere-1ere-annee-iut-de-luniversite-de-douala-session-juillet-2011\"><\/span><span style=\"color: #3366ff;\">Epreuves concours IUT Douala Mathematiques 2011 PFTIN-GI Fili\u00e8re 1\u00e8re ANN\u00c9E IUT de l\u2019Universit\u00e9 de Douala Session juillet 2011<\/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-6785","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\/6785","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=6785"}],"version-history":[{"count":2,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/posts\/6785\/revisions"}],"predecessor-version":[{"id":70247,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/posts\/6785\/revisions\/70247"}],"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=6785"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/categories?post=6785"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/tags?post=6785"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}