{"id":6767,"date":"2015-06-14T20:21:42","date_gmt":"2015-06-14T18:21:42","guid":{"rendered":"https:\/\/kamerpower.com\/?p=6767"},"modified":"2025-08-11T00:26:27","modified_gmt":"2025-08-10T23:26:27","slug":"epreuves-concours-iut-de-douala-mathematiques-2007-pftin-gi-filiere-1ere-annee","status":"publish","type":"post","link":"https:\/\/kamerpower.com\/fr\/epreuves-concours-iut-de-douala-mathematiques-2007-pftin-gi-filiere-1ere-annee\/","title":{"rendered":"Epreuves concours IUT de Douala Math\u00e9matiques 2007 PFTIN-GI Fili\u00e8re 1\u00e8re ANN\u00c9E IUT de l\u2019Universit\u00e9 de Douala Session juillet 2007"},"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 2007<\/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-69de7176529cf\" 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-69de7176529cf\"  aria-label=\"Toggle\" \/><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 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\/#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\/#exercice-1-4-points\" >Exercice 1 : 4 points<\/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\/#exercice-2-6-points\" >Exercice 2\u00a0: 6\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\/#exercice-3-4-points\" >Exercice 3\u00a0: 4\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\/#exercice-4-3-points\" >Exercice 4\u00a0: 3\u00a0points<\/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<p style=\"text-align: center;\"><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 2007 PFTIN-GI<\/a><\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"exercice-1-4-points\"><\/span><strong><span style=\"color: #ff0000;\">Exercice 1 : 4 points<\/span><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #3366ff;\"><strong>(I)<\/strong><\/span>. On consid\u00e8re le nombre complexe z de module p et d\u2019argument\u00e2 tels que \u00a0z = 24 \/ [(4 &#8211; <span style=\"color: #000000;\">\u03b1<\/span>)(2 &#8211;\u00a0<span style=\"color: #000000;\">\u03b1<\/span>i)<span style=\"color: #000000;\"><sup>2<\/sup><\/span>]<\/p>\n<p><span style=\"color: #000000;\">ou \u03b1 est un nombre r\u00e9el.<\/span><\/p>\n<ol>\n<li><span style=\"color: #000000;\">\u00a0Mettre z sous la forme alg\u00e9brique. (0.5 pt) kamerpower.com<\/span><\/li>\n<li><span style=\"color: #000000;\">Calculer en fonction de a le module \u03c1\u00a0et tan\u03b8. ( 1 pt)<\/span><\/li>\n<li><span style=\"color: #000000;\">Quelles sont les valeurs de a pour lesquelles z est un r\u00e9el ? ( 0.5 pt)<\/span><\/li>\n<li><span style=\"color: #000000;\">Quelles sont les valeurs de a pour lesquelles z est imaginaire pur? (0.5 pt)<\/span><\/li>\n<\/ol>\n<p><span style=\"color: #3366ff;\"><strong>(II)<\/strong><\/span>.\u00a0<span style=\"color: #000000;\">Soit E l\u2019ensemble des nombres complexes z v\u00e9rifiant: zz\u0304 &#8211; 2(z + z\u0304) = 0<\/span><\/p>\n<ol>\n<li><span style=\"color: #000000;\">Montrer que l\u2019ensemble des points M (x, y) image des nombres com-<\/span><br \/>\n<span style=\"color: #000000;\">plexes z appartenanta un cercle que l\u2019on pr\u00e9cisera. ( 1 pt<\/span><\/li>\n<li><span style=\"color: #000000;\">On suppose que z = [p, 6] D\u00e9terminer que pour \u03b8 donn\u00e9, la seule valeur de p telle que z \u03b5 E. (0.5 pt)<\/span><\/li>\n<\/ol>\n<p><span style=\"color: #000000;\"><span style=\"color: #3366ff;\">NB:<\/span> Les questions I\u00a0et\u00a0II\u00a0sont ind\u00e9pendantes<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"exercice-2-6-points\"><\/span><strong><span style=\"color: #ff0000;\">Exercice 2\u00a0: 6\u00a0points<\/span><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #000000;\">Soit la fonction \u00a0f(x) = 2Inx \/ (1+Inx)<\/span><\/p>\n<p><span style=\"color: #000000;\">une fonction r\u00e9elle d&#8217;une variable r\u00e9elle.<\/span><\/p>\n<ol>\n<li><span style=\"color: #000000;\">\u00a0D\u00e9terminer le domaine de d\u00e9finition de cette fonction et calculer les limites. ( 1.5 pt<\/span><\/li>\n<li><span style=\"color: #000000;\">Calculer la d\u00e9riv\u00e9e et dresser le tableau de variation. ( 1 pt)\u00a0kamerpower.com<\/span><\/li>\n<li><span style=\"color: #000000;\">Montrer que la courbe f admet un point d\u2019inflexion que l\u2019on pr\u00e9cisera .( 1pt)<\/span><\/li>\n<li><span style=\"color: #000000;\">Montrer que f est prolongeable en continuit\u00e9 en x = 0 et \u00e9tudier la d\u00e9rivabilit\u00e9.. (0.5 pt<\/span><\/li>\n<li><span style=\"color: #000000;\">R\u00e9soudre graphiquement les inequations suivantes;<\/span><br \/>\n<span style=\"color: #000000;\">f(x) &lt; 0, \u00a0f(x) &gt;\u00a00<\/span><\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"exercice-3-4-points\"><\/span><strong><span style=\"color: #ff0000;\">Exercice 3\u00a0: 4\u00a0points<\/span><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ol>\n<li><span style=\"color: #000000;\">Calculer l\u2019integrale I = \u222b cos<strong>ax<\/strong> sin<strong>bx<\/strong> dx. (1 pt)<\/span><\/li>\n<li><span style=\"color: #000000;\">Soit \u00a0I<sub>n<\/sub>\u00a0= \u222b cos<strong>x<\/strong> sinn<strong>x<\/strong> dxn<br \/>\n<\/span>0 \u2192\u00a0<span style=\"color: #000000;\">\u03c0<\/span><br \/>\n<span style=\"color: #000000;\"><span style=\"color: #000000;\">etant un entier naturel. Montrer que \u00a0\u2200<sub>n<\/sub> \u2260\u00a01<\/span><\/span><\/p>\n<p>((-1)<span style=\"color: #000000;\"><sup>n<\/sup><\/span>\u00a0+ 1) \/ n<span style=\"color: #000000;\"><sup>2<\/sup><\/span> &#8211; 1<span style=\"color: #000000;\">On rappele que cosn\u03c0 = (-1)<sup>n<\/sup>. (2pts)<\/span><\/li>\n<li><span style=\"color: #000000;\">pour n = 2p, p e\u2019tant un entier naturel, calculer I<sub>2p<\/sub>\u00a0<\/span><br \/>\n<span style=\"color: #000000;\">pour n = 2p + 1, p \u2260 0 e\u2019tant un entier naturel, calculer I<sub>2p+1<\/sub>\u00a0 \u00a0<\/span><\/li>\n<li><span style=\"color: #000000;\">la suite(In) est elle convergente ? ( 1 pt)<\/span><\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"exercice-4-3-points\"><\/span><strong><span style=\"color: #ff0000;\">Exercice 4\u00a0: 3\u00a0points<\/span><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ol>\n<li><span style=\"color: #000000;\">Soient a,b et c trois r\u00e9els qui v\u00e9rifient le syst\u00e8me d \u2019\u00e9quution suivant:<\/span><br \/>\n{ a + b + c = 312<br \/>\nc + a + c = 192<br \/>\n<span style=\"color: #000000;\">D\u00e9terminer ces r\u00e9els pour qu\u2019ils soient trois termes cons\u00e9cutifs d\u2019une suite\u00a0g\u00e9om\u00e9trique. (2 pts)<\/span><\/li>\n<li><span style=\"color: #000000;\">Soitx un r\u00e9el. On consid\u00e8re les nombres r\u00e9els suivants:<br \/>\n<span style=\"font-size: revert;\">U<\/span><sub>1<\/sub><span style=\"font-size: revert;\"> = (x<\/span><sup>2<\/sup><span style=\"font-size: revert;\"> &#8211; 2x &#8211; 1) , \u00a0 \u00a0 U<\/span><sub>2<\/sub><span style=\"font-size: revert;\"> = <\/span><span style=\"font-size: revert;\"> (x<\/span><sup>2<\/sup><span style=\"font-size: revert;\"> + 1)<\/span><sup>2<\/sup><span style=\"font-size: revert;\"> , \u00a0 U<\/span><sub>3<\/sub><span style=\"font-size: revert;\"> = <\/span><span style=\"font-size: revert;\">(x<\/span><sup>2<\/sup><span style=\"font-size: revert;\">\u00a0+ 2x &#8211; 1)<\/span><sup>2<\/sup><\/span><\/li>\n<\/ol>\n<p><span style=\"color: #000000;\">Montrer que U1, U2 et U3 sont trois termes cons\u00e9cutifs d\u2019une suite g\u00e9om\u00e9trie. (1 pt)<\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #3366ff;\">Epreuves concours IUT de Douala Math\u00e9matiques 2007 PFTIN-GI Fili\u00e8re 1\u00e8re ANN\u00c9E IUT de l\u2019Universit\u00e9 de Douala Session juillet 2007<\/span><\/p>\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-6767","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\/6767","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=6767"}],"version-history":[{"count":3,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/posts\/6767\/revisions"}],"predecessor-version":[{"id":70252,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/posts\/6767\/revisions\/70252"}],"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=6767"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/categories?post=6767"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/tags?post=6767"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}