{"id":6010,"date":"2015-05-23T23:22:15","date_gmt":"2015-05-23T21:22:15","guid":{"rendered":"https:\/\/kamerpower.com\/?p=6010"},"modified":"2025-02-17T07:44:24","modified_gmt":"2025-02-17T06:44:24","slug":"epreuve-concours-enset-de-bambili-2012-mathematiques-1er-annee","status":"publish","type":"post","link":"https:\/\/kamerpower.com\/fr\/epreuve-concours-enset-de-bambili-2012-mathematiques-1er-annee\/","title":{"rendered":"Epreuve concours ENSET de Bambili 2012 Mathematiques 1er annee du 1er cycle"},"content":{"rendered":"<p style=\"text-align: center;\"><span style=\"color: #3366ff;\"><a style=\"color: #3366ff;\" href=\"https:\/\/kamerpower.com\/enset-bambili-past-questions\/\" target=\"_blank\" rel=\"noopener\">Epreuve concours ENSET de\u00a0Bambili<\/a> 2012<\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #3366ff;\">CONCOURS ENSET DE BAMBILI\u00a0:<span style=\"color: #ff0000;\"> 1er\u00a0ANNEE DU 1er\u00a0CYCLE<\/span><\/span><br \/>\n<span style=\"color: #3366ff;\">Option :\u00a0<span style=\"color: #ff0000;\">Techniciens\u00a0<span style=\"color: #3366ff;\">Session<\/span> :<span style=\"color: #ff0000;\"> 2012<\/span><\/span><\/span><br \/>\n<span style=\"color: #3366ff;\">Epreuve: <span style=\"color: #ff0000;\">Mathematiques\u00a0<span style=\"color: #3366ff;\">Dur\u00e9e<\/span>: 3heures<br \/>\n<span style=\"color: #3366ff;\">Departement<\/span> : Science fondamentales<\/span><\/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-69e6042b2229b\" 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\" 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href=\"https:\/\/kamerpower.com\/fr\/epreuve-concours-enset-de-bambili-2012-mathematiques-1er-annee\/#-kamerpowercom\" >::::::\u00a0KAMERPOWER.COM :::::::<\/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\/epreuve-concours-enset-de-bambili-2012-mathematiques-1er-annee\/#question-1\" >Question 1<\/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\/epreuve-concours-enset-de-bambili-2012-mathematiques-1er-annee\/#question-2\" >Question\u00a02<\/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\/epreuve-concours-enset-de-bambili-2012-mathematiques-1er-annee\/#question-3\" >Question\u00a03<\/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\/epreuve-concours-enset-de-bambili-2012-mathematiques-1er-annee\/#question-4\" >Question\u00a04<\/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\/epreuve-concours-enset-de-bambili-2012-mathematiques-1er-annee\/#question-5\" >Question\u00a05<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/kamerpower.com\/fr\/epreuve-concours-enset-de-bambili-2012-mathematiques-1er-annee\/#question-1-2\" >Question 1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/kamerpower.com\/fr\/epreuve-concours-enset-de-bambili-2012-mathematiques-1er-annee\/#question-2-2\" >Question\u00a02<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/kamerpower.com\/fr\/epreuve-concours-enset-de-bambili-2012-mathematiques-1er-annee\/#question-3-2\" >Question\u00a03<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/kamerpower.com\/fr\/epreuve-concours-enset-de-bambili-2012-mathematiques-1er-annee\/#question-4-2\" >Question\u00a04<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/kamerpower.com\/fr\/epreuve-concours-enset-de-bambili-2012-mathematiques-1er-annee\/#question-5-2\" >Question\u00a05<\/a><\/li><\/ul><\/nav><\/div>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"-kamerpowercom\"><\/span><span style=\"color: #ff0000;\">::::::\u00a0<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><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"question-1\"><\/span><span style=\"color: #3366ff;\">Question 1<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #000000;\">Soient les nombres complexes:\u00a0<\/span><\/p>\n<p><span style=\"color: #000000;\">z<sub>1<\/sub>\u00a0= \u00a03(-[1\/2] \u00a0+ i[\u221a3\/2]) et z<sub>2<\/sub>\u00a0= \u00a03(-[\u221a2\/2] \u00a0+ i[\u221a2\/2])<\/span><\/p>\n<ol>\n<li><span style=\"color: #000000;\">Mettre sous forrne trigonom\u00e9trique les trois complexes z<sub>1<\/sub>\u00a0; z<sub>2<\/sub>\u00a0et z = z<sub>1<\/sub>\/z<sub>2<\/sub> \u00a0<\/span><\/li>\n<li><span style=\"color: #000000;\"> D\u00e9montrer que , pour tout entier naturel n, z<sup>12n<\/sup>\u00a0\u00a0est un r\u00e9el.<\/span><\/li>\n<li><span style=\"color: #000000;\">Donner les valeurs exactes de <strong>cos 5\u03c0\/12<\/strong> \u00a0et \u00a0<strong> sin 5\u03c0\/12<\/strong> <\/span><\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"question-2\"><\/span><span style=\"color: #3366ff;\">Question\u00a02<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #000000;\">Trouver la solution de l\u2019\u00e9quation diff\u00e9rentielle <span style=\"color: #3366ff;\">4f &#8220;(x) &#8211; 4f &#8216;(x) + f(x)\u00a0=\u00a00<\/span>\u00a0telle que <span style=\"color: #3366ff;\">f(0) = 4<\/span> et la tangente \u00e0 la courbe de f au point d&#8217;abscisse <span style=\"color: #3366ff;\">x = 2<\/span> est horizontale.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"question-3\"><\/span><span style=\"color: #3366ff;\">Question\u00a03<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>D\u00e9termine la solution (x; y) du syst\u00e8me suivant \u00e0 inconnues r\u00e9elles :<\/p>\n<p>{ <em><span style=\"color: #000000;\">x<sup>2<\/sup>+\u00a0y<sup>2\u00a0<\/sup><\/span>= 145<\/em><br \/>\n<em>Inx + Iny = In72<\/em><\/p>\n<h3><span class=\"ez-toc-section\" id=\"question-4\"><\/span><span style=\"color: #3366ff;\">Question\u00a04<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #000000;\">Soient la droite d\u2019\u00e9quation <span style=\"color: #3366ff;\">L: y = 2x + 4<\/span> et le cercle d\u2019\u00e9quation\u00a0<span style=\"color: #3366ff;\">x<sup>2<\/sup>+\u00a0y<sup>2\u00a0<\/sup>&#8211; 4x &#8211; 6y &#8211; 12 = 0<\/span>.\u00a0<\/span><\/p>\n<ol>\n<li><span style=\"color: #000000;\">Les points d\u2019intersection de la droite avec le cercle sont :\u00a0<\/span><br \/>\n<span style=\"color: #000000;\">a) A(-2,0);B(2,8) \u00a0 \u00a0b) A(2,0);B(-2,8) \u00a0 \u00a0 c) A(-2,8);B(0,8) \u00a0 \u00a0 \u00a0d) A(0,-2);B(8,2)<\/span><\/li>\n<li><span style=\"color: #000000;\">La longueur de la corde d\u00e9finie par ces deux points d\u2019intersection est<\/span><br \/>\n<span style=\"color: #000000;\">a) 4\u221a5 \u00a0b) 5\u221a4 c) \u221a68\u00a0 d)\u00a08<\/span><\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"question-5\"><\/span><span style=\"color: #3366ff;\">Question\u00a05<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #000000;\">On consid\u00e8re la fonction f(x) = (2x<sup>2\u00a0<\/sup>&#8211; 7x + 7)e<sup>x<\/sup>. Choisir et recopi\u00e9r les\u00a0affirmations correctes.<\/span><\/p>\n<ol>\n<li><span style=\"color: #000000;\">lim<sub>x\u2192\u221e<\/sub> f(x) = 0 ; lim<sub>x\u2192\u221e<\/sub> f(x) = +\u221e ; f(-[1\/2]) = 9\/\u221ae\u00a0;\u00a0\u00a0<\/span><\/li>\n<li><span style=\"color: #000000;\">lim<sub>x\u2192\u221e<\/sub> f(x) = -\u221e ; lim<sub>x\u2192\u221e<\/sub> f(x) = 0 ; f(-[1\/2]) = 9\/\u221ae\u00a0;\u00a0<\/span><\/li>\n<li><\/li>\n<li><\/li>\n<li><span style=\"color: #000000;\">\u00a0La fonction f est positive et croissante dans ]-\u221e;- 1\/2]<\/span><\/li>\n<li><span style=\"color: #000000;\"> La fonction f est n\u00e9gative et croissante dans [2:+\u221e[<\/span><\/li>\n<li><span style=\"color: #000000;\">Le minimum de la fonction f est\u00a00<\/span><\/li>\n<li><span style=\"color: #000000;\">\u00a0f(x) \u2265\u00a0-e<sup>2<\/sup> pour tout nombre r\u00e9el x<\/span><\/li>\n<\/ol>\n<p style=\"text-align: center;\"><strong><span style=\"color: #3366ff;\">ENTRANCE EXAM INTO YEAR I, 1st CYCLE HTTTC BAMBILI<\/span><\/strong><br \/>\n<span style=\"color: #3366ff;\">Option :\u00a0<span style=\"color: #ff0000;\">All technical\/Industiral series\u00a02012<\/span><\/span><br \/>\n<span style=\"color: #3366ff;\">Department: <span style=\"color: #ff0000;\">Fundamental series<\/span><\/span><br \/>\n<span style=\"color: #3366ff;\">Subject: <span style=\"color: #ff0000;\">Mathematics\u00a0<span style=\"color: #3366ff;\">Time<\/span>: 3 Hours\u00a0<\/span><\/span><\/p>\n<hr \/>\n<h3><span class=\"ez-toc-section\" id=\"question-1-2\"><\/span><span style=\"color: #3366ff;\">Question 1<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #000000;\">Given the complex numbers:<\/span><\/p>\n<p><span style=\"color: #000000;\">z<sub>1<\/sub>\u00a0= \u00a03(-[1\/2] \u00a0+ i[\u221a3\/2]) et z<sub>2<\/sub>\u00a0= \u00a03(-[\u221a2\/2] \u00a0+ i[\u221a2\/2])<\/span><\/p>\n<ol>\n<li><span style=\"color: #000000;\">Give the trigonometric form of the following complex numbers z1 ; z2 et z= z1\/z2\u00a0<\/span><\/li>\n<li><span style=\"color: #000000;\">Prove\u00a0that for all integer n, z<sup>12n<\/sup>\u00a0 is a real number.<\/span><\/li>\n<li><span style=\"color: #000000;\">What are the\u00a0exact values of \u00a0<strong>cos 5\u03c0\/12<\/strong> \u00a0et \u00a0 <strong>sin 5\u03c0\/12<\/strong>\u00a0\u00a0?<\/span><\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"question-2-2\"><\/span><span style=\"color: #3366ff;\">Question\u00a02<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #000000;\">Find the particuiar solution of the differential equation <span style=\"color: #3366ff;\">4f &#8220;(x) &#8211; 4f &#8216;(x) + f(x)\u00a0=\u00a00<\/span>\u00a0such that\u00a0<span style=\"color: #3366ff;\">f(0) = 4<\/span> and the tangent to the curve of f at the point\u00a0with <span style=\"color: #3366ff;\">x = 2<\/span>\u00a0is horizontal.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"question-3-2\"><\/span><span style=\"color: #3366ff;\">Question\u00a03<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Solve for\u00a0 (x; y) the following system in the set of real numbers :<\/p>\n<p>{ <em><span style=\"color: #000000;\">x<sup>2<\/sup>+\u00a0y<sup>2\u00a0<\/sup><\/span>= 145<\/em><br \/>\n<em>Inx + Iny = In72<\/em><\/p>\n<h3><span class=\"ez-toc-section\" id=\"question-4-2\"><\/span><span style=\"color: #3366ff;\">Question\u00a04<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #000000;\">Given the line\u00a0<span style=\"color: #3366ff;\">L: y = 2x + 4<\/span> and the circle\u00a0<span style=\"color: #3366ff;\">x<sup>2<\/sup>+\u00a0y<sup>2\u00a0<\/sup>&#8211; 4x &#8211; 6y &#8211; 12 = 0<\/span>.\u00a0<\/span><\/p>\n<ol>\n<li><span style=\"color: #000000;\">The points of intersection of the line and the circle are :\u00a0<\/span><br \/>\n<span style=\"color: #000000;\">a) A(-2,0);B(2,8) \u00a0 \u00a0b) A(2,0);B(-2,8) \u00a0 \u00a0 c) A(-2,8);B(0,8) \u00a0 \u00a0 \u00a0d) A(0,-2);B(8,2)<\/span><\/li>\n<li><span style=\"color: #000000;\">The length of the cord cut off is<\/span><br \/>\n<span style=\"color: #000000;\">a) 4\u221a5 \u00a0b) 5\u221a4 c) \u221a68\u00a0 d)\u00a08<\/span><\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"question-5-2\"><\/span><span style=\"color: #3366ff;\">Question\u00a05<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #000000;\">Given the\u00a0function f(x) = (2x<sup>2\u00a0<\/sup>&#8211; 7x + 7)e<sup>x<\/sup>. Choose the correct answers.<\/span><\/p>\n<ol>\n<li><span style=\"color: #000000;\">lim<sub>x\u2192\u221e<\/sub> f(x) = 0 ; lim<sub>x\u2192\u221e<\/sub> f(x) = +\u221e ; f(-[1\/2]) = 9\/\u221ae\u00a0;\u00a0\u00a0<\/span><\/li>\n<li><span style=\"color: #000000;\">lim<sub>x\u2192\u221e<\/sub> f(x) = -\u221e ; lim<sub>x\u2192\u221e<\/sub> f(x) = 0 ; f(-[1\/2]) = 9\/\u221ae\u00a0;\u00a0<\/span><\/li>\n<li><span style=\"color: #000000;\">The function f is\u00a0positive and\u00a0increasing in ]-\u221e;- 1\/2]<\/span><\/li>\n<li><span style=\"color: #000000;\">The function f is\u00a0negative and increasing in \u00a0[2:+\u221e[<\/span><\/li>\n<li><span style=\"color: #000000;\">The minimum of the\u00a0function f est\u00a00<\/span><\/li>\n<li><span style=\"color: #000000;\">\u00a0f(x) \u2265\u00a0-e<sup>2<\/sup>\u00a0for all real number x.<\/span><\/li>\n<\/ol>\n<p style=\"text-align: center;\"><span style=\"color: #3366ff;\">Epreuve concours ENSET de Bambili 2012 Mathematiques 1er annee du 1er cycle Cameroun<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":218,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_themeisle_gutenberg_block_has_review":false,"footnotes":""},"categories":[1701],"tags":[1828,1712,1706],"class_list":["post-6010","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-epreuves","tag-epreuve-concours-enset-de-bambili","tag-epreuve-de-concours-dentree-aux-grandes-ecoles-cameroun","tag-mathematiques"],"_links":{"self":[{"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/posts\/6010","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=6010"}],"version-history":[{"count":1,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/posts\/6010\/revisions"}],"predecessor-version":[{"id":67994,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/posts\/6010\/revisions\/67994"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/media\/218"}],"wp:attachment":[{"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/media?parent=6010"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/categories?post=6010"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/tags?post=6010"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}