{"id":6781,"date":"2015-06-14T23:05:17","date_gmt":"2015-06-14T21:05:17","guid":{"rendered":"https:\/\/kamerpower.com\/?p=6781"},"modified":"2025-08-11T00:23:01","modified_gmt":"2025-08-10T23:23:01","slug":"epreuves-concours-iut-douala-mathematiques-2010-pftin-gi-filiere-1ere-annee","status":"publish","type":"post","link":"https:\/\/kamerpower.com\/fr\/epreuves-concours-iut-douala-mathematiques-2010-pftin-gi-filiere-1ere-annee\/","title":{"rendered":"Epreuves concours IUT Douala Math\u00e9matiques 2010 PFTIN-GI Fili\u00e8re 1\u00e8re ANN\u00c9E IUT de l\u2019Universit\u00e9 de Douala Session juillet 2010"},"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 2010<\/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-69de714b0393c\" 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-69de714b0393c\"  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-2010-pftin-gi-filiere-1ere-annee\/#epreuves-concours-iut-douala\" >Epreuves concours IUT 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-douala-mathematiques-2010-pftin-gi-filiere-1ere-annee\/#epreuves-concours-iut-douala-mathematiques-2010-pftin-gi\" >Epreuves concours IUT Douala Math\u00e9matiques 2010 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-2010-pftin-gi-filiere-1ere-annee\/#exercice-1\" >Exercice 1\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-2010-pftin-gi-filiere-1ere-annee\/#exercice-2\" >Exercice 2\u00a0<\/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-douala-mathematiques-2010-pftin-gi-filiere-1ere-annee\/#exercice-3\" >Exercice 3<\/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-douala-mathematiques-2010-pftin-gi-filiere-1ere-annee\/#exercice-4\" >Exercice\u00a04<\/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-douala-mathematiques-2010-pftin-gi-filiere-1ere-annee\/#epreuves-concours-iut-douala-mathematiques-2010-pftin-gi-filiere-1ere-annee-iut-de-luniversite-de-douala-session-juillet-2010\" >Epreuves concours IUT Douala Math\u00e9matiques 2010 PFTIN-GI Fili\u00e8re 1\u00e8re ANN\u00c9E IUT de l\u2019Universit\u00e9 de Douala Session juillet 2010<\/a><\/li><\/ul><\/nav><\/div>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"epreuves-concours-iut-douala\"><\/span><span style=\"color: #000000;\">Epreuves concours IUT 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><img decoding=\"async\" class=\"aligncenter size-full wp-image-38314\" src=\"https:\/\/kamerpower.com\/wp-content\/uploads\/2021\/06\/Concours-IUT-douala-2021-2022-filiere-universite-de-douala.png\" alt=\"Concours IUT douala 2025-2026 fili\u00e8re universit\u00e9 de douala\" width=\"1890\" height=\"945\" srcset=\"https:\/\/kamerpower.com\/wp-content\/uploads\/2021\/06\/Concours-IUT-douala-2021-2022-filiere-universite-de-douala.png 1890w, https:\/\/kamerpower.com\/wp-content\/uploads\/2021\/06\/Concours-IUT-douala-2021-2022-filiere-universite-de-douala-600x300.png 600w, https:\/\/kamerpower.com\/wp-content\/uploads\/2021\/06\/Concours-IUT-douala-2021-2022-filiere-universite-de-douala-300x150.png 300w, https:\/\/kamerpower.com\/wp-content\/uploads\/2021\/06\/Concours-IUT-douala-2021-2022-filiere-universite-de-douala-768x384.png 768w, https:\/\/kamerpower.com\/wp-content\/uploads\/2021\/06\/Concours-IUT-douala-2021-2022-filiere-universite-de-douala-1536x768.png 1536w, https:\/\/kamerpower.com\/wp-content\/uploads\/2021\/06\/Concours-IUT-douala-2021-2022-filiere-universite-de-douala-720x360.png 720w, https:\/\/kamerpower.com\/wp-content\/uploads\/2021\/06\/Concours-IUT-douala-2021-2022-filiere-universite-de-douala-520x260.png 520w, https:\/\/kamerpower.com\/wp-content\/uploads\/2021\/06\/Concours-IUT-douala-2021-2022-filiere-universite-de-douala-320x160.png 320w, https:\/\/kamerpower.com\/wp-content\/uploads\/2021\/06\/Concours-IUT-douala-2021-2022-filiere-universite-de-douala-150x75.png 150w, https:\/\/kamerpower.com\/wp-content\/uploads\/2021\/06\/Concours-IUT-douala-2021-2022-filiere-universite-de-douala-1200x600.png 1200w\" sizes=\"(max-width: 1890px) 100vw, 1890px\" \/><\/p>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"epreuves-concours-iut-douala-mathematiques-2010-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 Math\u00e9matiques<\/a> 2010 PFTIN-GI<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"exercice-1\"><\/span><strong><span style=\"color: #ff0000;\">Exercice 1\u00a0<\/span><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #000000;\">Soit<\/span><\/p>\n<p>A = cos2<span style=\"color: #000000;\">\u03b1<\/span> + cos4<span style=\"color: #000000;\">\u03b1<\/span> + cos6<span style=\"color: #000000;\">\u03b1<\/span> + cos8<span style=\"color: #000000;\">\u03b1<\/span><br \/>\nB = sin2<span style=\"color: #000000;\">\u03b1<\/span> + sin4<span style=\"color: #000000;\">\u03b1<\/span> + sin6<span style=\"color: #000000;\">\u03b1<\/span> + sin8<span style=\"color: #000000;\">\u03b1<\/span><\/p>\n<p>avec <span style=\"color: #000000;\">\u03b1 = \u03c0\/5<\/span><\/p>\n<ol>\n<li><span style=\"color: #000000;\">1. Montrer que 1 + A = 4 cos<sup>2<\/sup>\u03b1 \u2212 2cos \u03b1 \u2212 1<\/span><br \/>\n<span style=\"color: #000000;\">2. Calculer la valeur du nombre complexe Z = A + i B<\/span><br \/>\n<span style=\"color: #000000;\">3. En d\u00e9duire que 1 + A = 0 \u00a0kamerpower.com<\/span><br \/>\n<span style=\"color: #000000;\">4. Calculer les valeurs r\u00e9elles de cos\u03b1 et sin\u03b1<\/span><\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"exercice-2\"><\/span><span style=\"color: #ff0000;\"><strong>Exercice 2\u00a0<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #000000;\">Soit\u00a0<\/span><\/p>\n<p><em>f(x) = In<\/em>(<em>| cosx\/sinx |<\/em>)<\/p>\n<p><span style=\"color: #000000;\">\u00a0une fonction r\u00e9elle d\u2019une variable r\u00e9elle x<\/span><\/p>\n<ol>\n<li><span style=\"color: #000000;\">Determiner le domaine de d\u00e9finition de cette fonction.<\/span><\/li>\n<li><span style=\"color: #000000;\">Dresser le tableau de variation de cette fonction dans l\u2019intervalle ]0,\u03c0\/2[<\/span><\/li>\n<li><span style=\"color: #000000;\">Montrer que dans l\u2019intervalle ]0,\u03c0\/2[\u00a0\u00a0la courbe de f admet un point d\u2019inflexion<\/span><\/li>\n<li><span style=\"color: #000000;\">Montrer que cette fonction est paire et tracer sa courbe representative dans<\/span><br \/>\n<span style=\"color: #000000;\">l\u2019intervalle\u00a0]-\u03c0\/2,\u03c0\/2[ \u00a0\u00a0kamerpower.com<\/span><\/li>\n<li><span style=\"color: #000000;\">Montrer que cette fonction est p\u00e9riodique et tracer sa courbe dans l\u2019intervalle ] \u2212 \u03c0, \u03c0[<\/span><\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"exercice-3\"><\/span><span style=\"color: #ff0000;\"><strong>Exercice 3<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #000000;\">Soit I<i><sub>n<\/sub><\/i>\u00a0 = \u222b 1 e \u00a0Inxdx\u00a0<\/span><span style=\"color: #000000;\">ou n est un entier naturel.\u00a0kamerpower.com<\/span><\/p>\n<ol>\n<li><span style=\"color: #000000;\">Calculer I<i><sub>0\u00a0<\/sub><\/i>et\u00a0I<i><sub>1<\/sub><\/i><\/span><\/li>\n<li><span style=\"color: #000000;\">Calculer I<i><sub>n<\/sub><\/i>\u00a0<\/span><\/li>\n<li><span style=\"color: #000000;\">Calculer la limite de I<i><sub>n<\/sub><\/i>\u00a0 quand n tend vers +\u221e.<\/span><\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"exercice-4\"><\/span><span style=\"color: #ff0000;\"><strong>Exercice\u00a04<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #000000;\">Soient a \u2208 [\u03bb, \u03b1] un nombre complexe donn\u00e9e,\u03bb et \u03b1 \u00e9tant des r\u00e9els.<\/span><br \/>\n<span style=\"color: #000000;\">On consid\u00e8re l\u2019application S du plan complexe d\u00e9finie ci-apres : S : M(Z) =&gt; M'(Z&#8217; = aZ)<\/span><\/p>\n<p><span style=\"color: #000000;\">Ou Z est un nombre complexe,M est un point du plan d\u2019affixe Z et ayant pour\u00a0image le point M<strong>&#8216;<\/strong><\/span><br \/>\n<span style=\"color: #000000;\">du plan d\u2019affixe Z<strong>&#8216;<\/strong>.<\/span><\/p>\n<ol>\n<li style=\"text-align: justify;\"><span style=\"color: #000000;\">Soient M1(1, 0),M2(0, 1) et M3(0, \u22121) trois points du plan<\/span><br \/>\n<span style=\"color: #000000;\">a. D\u00e9terminer la nature du triangle form\u00e9 par M1,M2 et M3.<\/span><br \/>\n<span style=\"color: #000000;\">b. D\u00e9terminer ,en fonction de \u03bb et les affixes Z&#8217;1, Z&#8217;2\u00a0et Z&#8217;3\u00a0des images pas\u00a0S de M1, M2, et M3\u00a0respectivement.<\/span><\/li>\n<li><span style=\"color: #000000;\">On consid\u00e8re \u03bb =1 et \u03b1=\u03c0\/6<\/span><br \/>\n<span style=\"color: #000000;\">a. Exprimer Z&#8217;1, Z&#8217;2et Z&#8217;3<\/span><br \/>\n<span style=\"color: #000000;\">b.\u00a0D\u00e9terminer la nature du triangle form\u00e9 par les points M&#8217;1, M&#8217;2\u00a0et M&#8217;3<\/span><\/li>\n<li style=\"text-align: justify;\"><span style=\"color: #000000;\">On consid\u00e8re la suite des points du plan M0, M1,\u00b7\u00b7\u00b7 , Mn d\u00e9finie par Mn =S (Mn\u22121) ou Mn\u00a0est le point d\u2019affixe Zn = [\u03c1n\u00a0, \u03b8n] et n un entier naturel.\u00a0kamerpower.com<\/span><br \/>\n<span style=\"color: #000000;\">Montrer que la suite (\u03c1n) est g\u00e9om\u00e9trique et que la suite (\u03b8n) est arithm\u00e9tique.<\/span><\/li>\n<\/ol>\n<h2 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"epreuves-concours-iut-douala-mathematiques-2010-pftin-gi-filiere-1ere-annee-iut-de-luniversite-de-douala-session-juillet-2010\"><\/span><span style=\"color: #3366ff;\">Epreuves concours IUT Douala Math\u00e9matiques 2010 PFTIN-GI Fili\u00e8re 1\u00e8re ANN\u00c9E IUT de l\u2019Universit\u00e9 de Douala Session juillet 2010<\/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-6781","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\/6781","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=6781"}],"version-history":[{"count":2,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/posts\/6781\/revisions"}],"predecessor-version":[{"id":70248,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/posts\/6781\/revisions\/70248"}],"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=6781"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/categories?post=6781"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/tags?post=6781"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}