{"id":6772,"date":"2015-06-14T21:04:52","date_gmt":"2015-06-14T19:04:52","guid":{"rendered":"https:\/\/kamerpower.com\/?p=6772"},"modified":"2025-08-11T00:25:48","modified_gmt":"2025-08-10T23:25:48","slug":"epreuves-concours-iut-de-douala-mathematiques-2007-pftin-gi-filiere-1ere-annee-iut","status":"publish","type":"post","link":"https:\/\/kamerpower.com\/fr\/epreuves-concours-iut-de-douala-mathematiques-2007-pftin-gi-filiere-1ere-annee-iut\/","title":{"rendered":"Epreuves concours IUT de Douala Math\u00e9matiques 2008 PFTIN-GI Fili\u00e8re 1\u00e8re ANN\u00c9E IUT de l\u2019Universit\u00e9 de Douala Session juillet 2008"},"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 2008<\/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-69e7e8a12453b\" 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-69e7e8a12453b\"  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-2007-pftin-gi-filiere-1ere-annee-iut\/#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-2007-pftin-gi-filiere-1ere-annee-iut\/#epreuves-concours-iut-de-douala-mathematiques-2008-pftin-gi\" >Epreuves concours IUT de Douala Math\u00e9matiques 2008 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-de-douala-mathematiques-2007-pftin-gi-filiere-1ere-annee-iut\/#exercice-1-2-points\" >Exercice 1 : 2\u00a0points<\/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-2007-pftin-gi-filiere-1ere-annee-iut\/#exercice-2-5-points\" >Exercice 2\u00a0: 5\u00a0points<\/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-2007-pftin-gi-filiere-1ere-annee-iut\/#exercice-3-5-points\" >Exercice 3\u00a0: 5\u00a0points<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/kamerpower.com\/fr\/epreuves-concours-iut-de-douala-mathematiques-2007-pftin-gi-filiere-1ere-annee-iut\/#probleme-08-points\" >Probl\u00e8me: (08 points)<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/kamerpower.com\/fr\/epreuves-concours-iut-de-douala-mathematiques-2007-pftin-gi-filiere-1ere-annee-iut\/#epreuves-concours-iut-de-douala-mathematiques-2008-pftin-gi-filiere-1ere-annee-iut-de-luniversite-de-douala-session-juillet-2008\" >Epreuves concours IUT de Douala Math\u00e9matiques 2008 PFTIN-GI Fili\u00e8re 1\u00e8re ANN\u00c9E IUT de l\u2019Universit\u00e9 de Douala Session juillet 2008<\/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-2008-pftin-gi\"><\/span><span style=\"color: #3366ff;\">Epreuves concours IUT de Douala Math\u00e9matiques 2008 PFTIN-GI<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"exercice-1-2-points\"><\/span><strong><span style=\"color: #ff0000;\">Exercice 1 : 2\u00a0points<\/span><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #000000;\">Soit P = x<sup>4<\/sup> &#8211; x<sup>3<\/sup> + ax<sup>2<\/sup> + 6x &#8211;\u00a04, (a un r\u00e9el).<\/span><\/p>\n<ol>\n<li><span style=\"color: #000000;\">D\u00e9terminer a pour que P ait deux dont le produit est 2.<\/span><\/li>\n<li><span style=\"color: #000000;\">Calculer alors les racines de P dans C. kamerpower.com<\/span><\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"exercice-2-5-points\"><\/span><strong><span style=\"color: #ff0000;\">Exercice 2\u00a0: 5\u00a0points<\/span><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #000000;\">Soita un r\u00e9el.<\/span><\/p>\n<ol>\n<li><span style=\"color: #000000;\">Developer (cos \u03b1 + isin \u03b1)<sup>2<\/sup><\/span><\/li>\n<li><span style=\"color: #000000;\">En d\u00e9duire cos(6\u03b1) et sin(6\u03b1) en fonction de cos a et sin \u03b1<\/span><\/li>\n<li><span style=\"color: #000000;\">En d\u00e9duire tan\u00a0\u03b1 en fonction de tan \u03b1.\u00a0kamerpower.com<\/span><\/li>\n<li><span style=\"color: #000000;\">Montrer que tan \u03c0\/4\u00a0est une solution d\u2019une \u00e9quation du 6ieme degr\u00e9s que\u00a0l\u2019on pr\u00e9cisera.<\/span><\/li>\n<li><span style=\"color: #000000;\">Lin\u00e9arit\u00e9 cos<sup>5<\/sup>\u03b1.\u00a0<\/span><\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"exercice-3-5-points\"><\/span><strong><span style=\"color: #ff0000;\">Exercice 3\u00a0: 5\u00a0points<\/span><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #000000;\">Dans un rep\u00e8re vectoriel R<sup>3<\/sup>\u00a0on appelle f l\u2019application lin\u00e9aire d\u00e9finie par:<\/span><br \/>\n<span style=\"color: #000000;\">u =\u00a0f(i) =\u00a0i+2j-k; \u00a0v\u00a0=\u00a0f(j) =\u00a02i+7j+3k; k\u00a0=\u00a0f(k) = 3j+5k<\/span><\/p>\n<ol>\n<li><span style=\"color: #000000;\"><strong>a)<\/strong> \u00c9crire la matrice de f dans la base {i, j,k}.<\/span><br \/>\n<span style=\"color: #000000;\"><strong>b)<\/strong> Montrer que u et v sont ind\u00e9pendants.\u00a0kamerpower.com<\/span><br \/>\n<span style=\"color: #000000;\"><strong>c)<\/strong> D\u00e9terminer les r\u00e9els a et b tels que w = au + bv<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>a)<\/strong> Soit U(x, y, z) un vecteur de R<sup>3<\/sup>. Montrer que<br \/>\nf(U) = (x &#8211; 2z) u + (y + z)v<\/span><br \/>\n<span style=\"color: #000000;\"><strong>b)<\/strong> D\u00e9montrer que f(U) = 0 &lt;=&gt; U colin\u00e9aire au vecteur n = 2i-j+ k.<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>a)<\/strong> Montrer que {i, j, n} est une base de R<sup>3<\/sup>.<\/span><br \/>\n<span style=\"color: #000000;\"><strong>b)<\/strong> D\u00e9terminer la matrice de f dans la base {i, j, n}.<\/span><\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"probleme-08-points\"><\/span><span style=\"color: #ff0000;\"><strong>Probl\u00e8me: (08 points)<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #000000;\">Soit la fonction r\u00e9elle \u00a0f(x) = arcsin<em>x<\/em> \/ \u221a(1-x<sup>3<\/sup><\/span><span style=\"color: #000000;\">)<\/span><\/p>\n<ol>\n<li><span style=\"color: #000000;\">Quelle est le domaine de d\u00e9finition de f(x)?<\/span><\/li>\n<li><span style=\"color: #000000;\">\u00a0f(x) est elle une fonction continue dans son domaine de d\u00e9finition?<\/span><\/li>\n<li><span style=\"color: #000000;\">\u00a0f(x) est elle une fonction impaire ? si oui d\u00e9terminer votre intervalle d\u2019\u00e9tude.<\/span><\/li>\n<li><span style=\"color: #000000;\">D\u00e9terminer les limites de f(x) aux bornes du domaine de d\u00e9finition. Admet\u00a0elle des directions asymptotiques?<\/span><\/li>\n<li><span style=\"color: #000000;\">Calculer sa d\u00e9riv\u00e9e et \u00e9tudier son signe.\u00a0kamerpower.com<\/span><\/li>\n<li><span style=\"color: #000000;\">Tracer le tableau de variation de f(x).<\/span><\/li>\n<li><span style=\"color: #000000;\">Tracer le graphe y = f(x)<\/span><\/li>\n<\/ol>\n<h2 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"epreuves-concours-iut-de-douala-mathematiques-2008-pftin-gi-filiere-1ere-annee-iut-de-luniversite-de-douala-session-juillet-2008\"><\/span><span style=\"color: #3366ff;\">Epreuves concours IUT de Douala Math\u00e9matiques 2008 PFTIN-GI Fili\u00e8re <a style=\"color: #3366ff;\" href=\"https:\/\/kamerpower.com\/fr\/concours-iut-douala-2021-2022-cycle-bts-premiere-annee\/\" target=\"_blank\" rel=\"noopener\">1\u00e8re ANN\u00c9E IUT de l\u2019Universit\u00e9 de Douala<\/a> Session juillet 2008<\/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-6772","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\/6772","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=6772"}],"version-history":[{"count":2,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/posts\/6772\/revisions"}],"predecessor-version":[{"id":70251,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/posts\/6772\/revisions\/70251"}],"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=6772"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/categories?post=6772"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/tags?post=6772"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}