{"id":4548,"date":"2015-03-29T09:45:13","date_gmt":"2015-03-29T07:45:13","guid":{"rendered":"https:\/\/kamerpower.com\/?p=4548"},"modified":"2025-06-19T00:13:50","modified_gmt":"2025-06-18T23:13:50","slug":"concours-eamac-2011-epreuve-de-mathematiques-t-ts","status":"publish","type":"post","link":"https:\/\/kamerpower.com\/fr\/concours-eamac-2011-epreuve-de-mathematiques-t-ts\/","title":{"rendered":"Epreuve Concours EAMAC 2011 de Mathematiques T &#038; TS"},"content":{"rendered":"<p style=\"text-align: center;\"><span style=\"color: #000000;\">CONCOURS D\u2019ENTREE AUX CYCLES DE TECHNICIEN SUPERIEUR ET<\/span><br \/>\n<span style=\"color: #000000;\">TECHNICIEN DE L\u2019ECOLE AFRICAINE DE LA METEOROLOGIE ET DE<\/span><br \/>\n<span style=\"color: #000000;\">L\u2019AVIATION CIVILE ( EAMAC )<\/span><br \/>\n<span style=\"color: #000000;\">SESSION 2011\u00a0Concours EAMAC<\/span><br \/>\n<span style=\"color: #000000;\">EPREUVE DE : <span style=\"color: #3366ff;\">MATHEMATIQUES<\/span><\/span><br \/>\n<span style=\"color: #000000;\">DUREE : 3 HEURES\u00a0<\/span><br \/>\n<span style=\"color: #008000; text-shadow: 2px 0 2px #000;\">KA<\/span><span style=\"color: #ff0000; text-shadow: 2px 0 2px #000;\">M<\/span><span style=\"color: #ffcc00; text-shadow: 2px 0 2px #000;\">ER<\/span><span style=\"color: #800080; text-shadow: 2px 0 2px #000;\">POWER<\/span><span style=\"color: #3366ff; text-shadow: 2px 0 2px #000;\">.COM<\/span><\/p>\n<hr \/>\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-69e4dc1ee4f69\" 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-69e4dc1ee4f69\"  aria-label=\"Toggle\" \/><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/kamerpower.com\/fr\/concours-eamac-2011-epreuve-de-mathematiques-t-ts\/#telechargez-les-anciens-epreuves-dexamen-eamac-2006-a-2025-et-les-corrigees-depuis-notre-application-kamerpower-epreuves-sur-play-store\" >T\u00e9l\u00e9chargez les anciens \u00e9preuves d&#8217;examen EAMAC 2006 \u00e0 2025\u00a0et les Corrig\u00e9es depuis notre application Kamerpower Epreuves sur Play Store.<\/a><\/li><\/ul><\/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\/concours-eamac-2011-epreuve-de-mathematiques-t-ts\/#epreuve-concours-eamac-2011-de-mathematiques-t-ts\" >Epreuve Concours EAMAC 2011 de Mathematiques T &amp; TS<\/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\/concours-eamac-2011-epreuve-de-mathematiques-t-ts\/#exercice-1\" >Exercice 1<\/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\/concours-eamac-2011-epreuve-de-mathematiques-t-ts\/#exercice-2\" >Exercice\u00a02<\/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\/concours-eamac-2011-epreuve-de-mathematiques-t-ts\/#epreuve-concours-eamac-2011-de-mathematiques-t-ts-2\" >Epreuve Concours EAMAC 2011 de Mathematiques T &amp; TS<\/a><\/li><\/ul><\/nav><\/div>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"telechargez-les-anciens-epreuves-dexamen-eamac-2006-a-2025-et-les-corrigees-depuis-notre-application-kamerpower-epreuves-sur-play-store\"><\/span><span style=\"color: #000000;\"><strong><span style=\"color: #008000;\">T\u00e9l\u00e9chargez<\/span> les anciens <span style=\"color: #008000;\">\u00e9preuves d&#8217;examen EAMAC 2006 \u00e0 2025<\/span>\u00a0et les <span style=\"color: #008000;\">Corrig\u00e9es<\/span> depuis notre application Kamerpower Epreuves sur Play Store.<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><a href=\"https:\/\/play.google.com\/store\/apps\/details?id=com.kamerpower.cm\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-68899\" src=\"https:\/\/kamerpower.com\/wp-content\/uploads\/2025\/05\/google-play-badge-fr.png\" alt=\"Kamerpower Epreuves\" width=\"393\" height=\"152\" srcset=\"https:\/\/kamerpower.com\/wp-content\/uploads\/2025\/05\/google-play-badge-fr.png 646w, https:\/\/kamerpower.com\/wp-content\/uploads\/2025\/05\/google-play-badge-fr-600x232.png 600w, https:\/\/kamerpower.com\/wp-content\/uploads\/2025\/05\/google-play-badge-fr-300x116.png 300w, https:\/\/kamerpower.com\/wp-content\/uploads\/2025\/05\/google-play-badge-fr-520x201.png 520w, https:\/\/kamerpower.com\/wp-content\/uploads\/2025\/05\/google-play-badge-fr-320x124.png 320w, https:\/\/kamerpower.com\/wp-content\/uploads\/2025\/05\/google-play-badge-fr-150x58.png 150w\" sizes=\"auto, (max-width: 393px) 100vw, 393px\" \/><\/a><\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"epreuve-concours-eamac-2011-de-mathematiques-t-ts\"><\/span><span style=\"color: #3366ff;\"><strong><a href=\"https:\/\/kamerpower.com\/fr\/www-eamac-ne-inscription-2018-concours-eamac-2018-2019\/\">Epreuve Concours EAMAC<\/a> 2011 de Mathematiques T &amp; TS<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"exercice-1\"><\/span><span style=\"color: #ff0000;\">Exercice 1<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #000000;\">Soient les int\u00e9grales suivantes: I = \u222b 0-\u03c0 \u00a0e<i><sup>t<\/sup><\/i><strong>cost<\/strong>tdt \u00a0 et \u00a0 J = \u222b 0-\u03c0 \u00a0e<i><sup>t<\/sup><\/i><strong>sin<i><sup>2<\/sup><\/i><\/strong>tdt<\/span><\/p>\n<ol>\n<li><span style=\"color: #000000;\">Calculer I\u00a0+\u00a0J et I &#8211; J<\/span><\/li>\n<li><span style=\"color: #000000;\">En d\u00e9duire les valeurs de I et J<\/span><\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"exercice-2\"><\/span><span style=\"color: #ff0000;\">Exercice\u00a02<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #000000;\">Soitf _{{a}}\u00a0la fonction d\u00e9finie par: fa(x) = log(x^2 &#8211; 2ax + 1)<\/span><\/p>\n<p><span style=\"color: #000000;\">o\u00f9\u00a0-1 \\leq a\\leq 1\u00a0et log d\u00e9signe la fonction logarithme n\u00e9p\u00e9rien. On notera\u00a0C_{{a}}\u00a0la courbe\u00a0<\/span><span style=\"color: #000000;\">repr\u00e9sentative de\u00a0f_{{a}}\u00a0dans un rep\u00e8re orthonorm\u00e9.<\/span><\/p>\n<p><span style=\"color: #000000;\"><span style=\"color: #3366ff;\">A)<\/span> Dans cette partie du probl\u00e8me on suppose <em>a = -1.<\/em><\/span><\/p>\n<p><span style=\"color: #000000;\">1.\u00a0Etudier les variations de\u00a0f_{{-1}}\u00a0et tracer la courbe repr\u00e9sentative\u00a0C_{{-1}}<\/span><\/p>\n<p><span style=\"color: #000000;\">2. a)\u00a0D\u00e9terminer une primitive de la fonction g d\u00e9finie par: <em>g(x) = log (x + 1)<\/em><\/span><br \/>\n<span style=\"color: #000000;\">b) Calculer l\u2019aire de ensemble des points de coordonn\u00e9es <em>(x, y)<\/em> satisfaisant aux conditions:<\/span><br \/>\n<span style=\"color: #000000;\">\u00a00\\leq x\\leq e-1 et\u00a00\\leq y\\leq f_{{-1}}(x).<\/span><\/p>\n<p><span style=\"color: #000000;\"><span style=\"color: #3366ff;\">B)<\/span> Dans cette partie, on suppose <em>0\u00a0&lt; a &lt; 1<\/em>.<\/span><\/p>\n<ol>\n<li><span style=\"color: #000000;\">\u00a0D\u00e9terminer le domaine de d\u00e9finition de\u00a0f_{{a}}\u00a0<\/span><\/li>\n<li><span style=\"color: #000000;\">\u00a0Etudier les variations de la fonction\u00a0f_{{a}}\u00a0<\/span><\/li>\n<li><span style=\"color: #000000;\">Montrer que la courbe\u00a0C_{{a}}\u00a0admet la droite d\u2019\u00e9quation x\u00a0= a pour axe de sym\u00e9trie.<\/span><\/li>\n<li><span style=\"color: #000000;\">Soit <em>h<\/em> la fonction d\u00e9finie par: <em>h\u00a0= 2log x, \u00a0x\u00a0&gt; 0<\/em>.<\/span><br \/>\n<span style=\"color: #000000;\">Donner, selon la valeur\u00a0de\u00a0<em>x<\/em>, le signe de l\u2019expression\u00a0f_{{a}}(x)-h(x)<\/span><br \/>\n<span style=\"color: #000000;\">Cette expression admet-elle une limite quand <em>x<\/em>\u00a0tend vers +\u221e ? p<\/span><\/li>\n<li><span style=\"color: #000000;\">Tracer la courbe repr\u00e9sentative de<em> h<\/em> et utiliser ce qui pr\u00e9c\u00e8de pour tracer C2\/3\u00a0\u00a0\u00a0dans le m\u00eame\u00a0<\/span><span style=\"color: #000000;\">rep\u00e8re.\u00a0<\/span><\/li>\n<\/ol>\n<p><span style=\"color: #000000;\"><span style=\"color: #3366ff;\">C)<\/span> Montrer que les co\u00f9rbes\u00a0C_{{a}}\u00a0\u00a0et\u00a0C_{{-a}}\u00a0sont sym\u00e9triques par rapport \u00e0 la droite d\u2019\u00e9quation\u00a0<\/span><span style=\"color: #000000;\"><em>x\u00a0= 0<\/em>.<\/span><\/p>\n<h2 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"epreuve-concours-eamac-2011-de-mathematiques-t-ts-2\"><\/span><span style=\"color: #3366ff;\">Epreuve Concours EAMAC 2011 de Mathematiques T &amp; TS<\/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":4530,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_themeisle_gutenberg_block_has_review":false,"footnotes":""},"categories":[1701],"tags":[1738,1735,1712,1706],"class_list":["post-4548","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-epreuves","tag-annales-epreuves-concours-eamac","tag-concours-eamac-ecole-africaine-de-la-meteorologie-et-de-laviation-civile","tag-epreuve-de-concours-dentree-aux-grandes-ecoles-cameroun","tag-mathematiques"],"_links":{"self":[{"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/posts\/4548","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=4548"}],"version-history":[{"count":2,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/posts\/4548\/revisions"}],"predecessor-version":[{"id":69936,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/posts\/4548\/revisions\/69936"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/media\/4530"}],"wp:attachment":[{"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/media?parent=4548"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/categories?post=4548"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/tags?post=4548"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}