{"id":5997,"date":"2015-05-23T20:05:21","date_gmt":"2015-05-23T18:05:21","guid":{"rendered":"https:\/\/kamerpower.com\/?p=5997"},"modified":"2025-02-17T07:22:33","modified_gmt":"2025-02-17T06:22:33","slug":"epreuve-concours-enieg-cameroun-2013-mathematiques-niveau-bac","status":"publish","type":"post","link":"https:\/\/kamerpower.com\/fr\/epreuve-concours-enieg-cameroun-2013-mathematiques-niveau-bac\/","title":{"rendered":"Epreuve concours ENIEG Cameroun 2013 Mathematiques Niveau BAC"},"content":{"rendered":"<p style=\"text-align: center;\"><span style=\"color: #000000;\">Minist\u00e8re des Enseignements\u00a0Secondaires<\/span><br \/>\n<span style=\"color: #000000;\">Direction des Examens, des Concours<\/span><br \/>\n<span style=\"color: #000000;\">et de la Certification\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><\/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-69d94ea2bdaed\" 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-69d94ea2bdaed\"  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\/epreuve-concours-enieg-cameroun-2013-mathematiques-niveau-bac\/#epreuve-concours-enieg-cameroun-2013\" >Epreuve concours ENIEG Cameroun 2013<\/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-enieg-cameroun-2013-mathematiques-niveau-bac\/#partie-a-10-points-kamerpowercom\" >Partie A: (10 points)\u00a0KAMERPOWER.COM<\/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-enieg-cameroun-2013-mathematiques-niveau-bac\/#exercice-1-3-points\" >Exercice 1. (3 points)<\/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-enieg-cameroun-2013-mathematiques-niveau-bac\/#exercice-2-7-points\" >Exercice 2. (7 points)<\/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-enieg-cameroun-2013-mathematiques-niveau-bac\/#partie-b-10-points-kamerpowercom\" >Partie\u00a0B: (10 points)\u00a0KAMERPOWER.COM<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/kamerpower.com\/fr\/epreuve-concours-enieg-cameroun-2013-mathematiques-niveau-bac\/#epreuve-concours-enieg-cameroun-2013-mathematiques-niveau-bac\" >Epreuve concours ENIEG Cameroun 2013 Mathematiques Niveau BAC<\/a><\/li><\/ul><\/nav><\/div>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"epreuve-concours-enieg-cameroun-2013\"><\/span><span style=\"color: #3366ff;\"><a style=\"color: #3366ff;\" href=\"https:\/\/kamerpower.com\/fr\/concours-enieg-eniet-2015-2016-cameroun-ecoles-normales-privees-dinstituteurs-enieg-eniet\/\" target=\"_blank\" rel=\"noopener\">Epreuve concours ENIEG Cameroun 2013<\/a><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: center;\"><span style=\"color: #3366ff;\">CONCOURS ENIEG Session :<span style=\"color: #ff0000;\"> 2013<\/span><\/span><br \/>\n<span style=\"color: #3366ff;\">Niveau: <span style=\"color: #ff0000;\">BAC Cameroun<\/span><\/span><br \/>\n<span style=\"color: #3366ff;\">Epreuve: <span style=\"color: #ff0000;\">Mathematiques<\/span><\/span><br \/>\n<span style=\"color: #3366ff;\">Dur\u00e9e: <span style=\"color: #ff0000;\">3heures\u00a0Coefficient: 4<\/span><\/span><\/p>\n<hr \/>\n<p style=\"text-align: center;\"><span style=\"color: #000000;\">Cette \u00e9preuve comporte deux parties obligatoires.<\/span><\/p>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"partie-a-10-points-kamerpowercom\"><\/span><span style=\"color: #ff0000;\">Partie A: (10 points)\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<p>Cette partie comporte au total dix questions. Pour chacune des questions, toute r\u00e9ponse juste Vaut 1\u00a0point, et toute r\u00e9ponse fausse au toute absence de r\u00e9ponse vaut 0 point.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"exercice-1-3-points\"><\/span><span style=\"color: #3366ff;\">Exercice 1. (3 points)<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #000000;\">Ecrire le num\u00e9ro de la question, suivi de la mention<span style=\"color: #ff0000;\"> vrai (V)<\/span> ou <span style=\"color: #ff0000;\">faux (F)<\/span> pour chacune des\u00a0affirmations suivantes.<\/span><\/p>\n<ol>\n<li><span style=\"color: #000000;\">On a <span style=\"color: #3366ff;\">e<sup>Inx<\/sup>\u00a0= x<\/span> \u00a0pour tout nombre r\u00e9el <span style=\"color: #ff0000;\">x<\/span>.<\/span><\/li>\n<li><span style=\"color: #000000;\">Le mode d&#8217;une s\u00e9rie statistique \u00e0 caract\u00e8re quantitatif ayant un nombre fini de\u00a0modalit\u00e9s est toujours la plus grande de ces modalit\u00e9s.<\/span><\/li>\n<li><span style=\"color: #000000;\">La fonction <span style=\"color: #3366ff;\">f: x -&gt; ln|x|<\/span> est d\u00e9finie pour tout r\u00e9el <span style=\"color: #ff0000;\">x<\/span> non nul.<\/span><\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"exercice-2-7-points\"><\/span><span style=\"color: #3366ff;\">Exercice 2. (7 points)<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #000000;\">Pour chacun des libell\u00e9s suivants, quatre affirmations<span style=\"color: #ff0000;\"> a) ; b) ; c) et d)<\/span> sont propos\u00e9es parmi\u00a0lesquelles une et une seule est correcte. Mentionner sur votre feuille de composition la\u00a0r\u00e9f\u00e9rence de la question suivie de la lettre de l&#8217;affirmation correcte.<\/span><\/p>\n<ol>\n<li><span style=\"color: #000000;\">\u00a0L&#8217;\u00e9quation <span style=\"color: #3366ff;\">x<sup>3<\/sup>-x-1=0<\/span> admet dans<span style=\"color: #ff0000;\"> IR<\/span> exactement : <\/span><br \/>\n<span style=\"color: #000000;\">a) trois solutions; b) deux solutions;\u00a0c) une solution ; d) quatre solutions.<\/span><\/li>\n<li><span style=\"color: #000000;\">L\u2019\u00e9quation <span style=\"color: #3366ff;\">ln(-3x + 4) = &#8211;\u00a05<\/span>\u00a0a pour ensemble solution :\u00a0<\/span><br \/>\n<span style=\"color: #000000;\">a) L\u2019ensemble vide ; b) l&#8217;ensemble <span style=\"color: #ff0000;\">IR<\/span> des nombres r\u00e9els : c) S = (4 &#8211;\u00a0e<sup>-5<\/sup>\u00a0) \/ 3\u00a0 ; d) S = (4 &#8211; e<sup>-5<\/sup>) \/ -3\u00a0<\/span><\/li>\n<li><span style=\"color: #000000;\">L&#8217;in\u00e9quation <span style=\"color: #3366ff;\">&#8211; e<sup>-4x-7\u00a0<\/sup>\u00a0 &lt; = 0<\/span> a pour ensemble solution<\/span><br \/>\n<span style=\"color: #000000;\">a) L&#8217;ensemble vide ; b) l\u2019ensemble <span style=\"color: #ff0000;\">IR<\/span> des nombres r\u00e9els ; c) L&#8217;intervalle ]- \u221e ; 0[;<\/span><br \/>\n<span style=\"color: #000000;\">d) l&#8217;intervalle ]0 ; +\u221e[.<\/span><\/li>\n<li><span style=\"color: #000000;\">Une primitive de la fonction<span style=\"color: #3366ff;\"> : x -&gt; e<sup>2x<\/sup><\/span> est la fonction f d\u00e9finie dans <span style=\"color: #ff0000;\">IR<\/span> par:<\/span><br \/>\n<span style=\"color: #000000;\">a) f(x)=2e<sup>2x<\/sup> ; b) f(x) = <span style=\"color: #3366ff;\">e<sup>x^e<\/sup><\/span>\u00a0 \u00a0\u00a0; c) f(x) = (1\/2)e<sup>2x <\/sup>+ In5 \u00a0\u00a0 ; d) f(x) = (1\/2)e<sup>2x<\/sup>\u00a0+ x &#8211; 1.<\/span><\/li>\n<li><span style=\"color: #000000;\">L&#8217;ensemble de d\u00e9finition de la fonction<span style=\"color: #3366ff;\"> h: x -&gt;\u00a0ln\u00a0|-2x + 4|<\/span> est:<\/span><br \/>\n<span style=\"color: #000000;\">a) L\u2019intervalle ]- \u221e ; 2[ ; b) l\u2019intervalle ]2 ; + \u221e[ ; c) l\u2019intervalle ]0 ; + \u221e[ ; \u00a0d) la r\u00e9union\u00a0d&#8217;intervalles ]- \u221e ; 2[ U ]2 ; + \u221e[.<\/span><\/li>\n<li><span style=\"color: #000000;\">Soient f et g les fonctions d\u00e9finies par <span style=\"color: #3366ff;\">f(x) = ln(x &#8211; 2)<\/span> et <span style=\"color: #3366ff;\">g(x) =In(1 + x<sup>2<\/sup>)<\/span>. Pour tout r\u00e9el\u00a0x &gt; 2 on a:\n<p>a)\u00a0<em><strong>f(x) + g(x) = In<\/strong><\/em><strong>([x-2]\/1+x<sup>2<\/sup>)<\/strong><\/span><span style=\"color: #000000;\">\u00a0 ; b) <em><strong>f(x) &#8211; g(x) = In<\/strong><\/em><strong>([x-2]\/1+x<sup>2<\/sup>)<\/strong>\u00a0\u00a0\u00a0: c) <em><strong>f(x) \/ g(x) = In<\/strong><\/em><strong>([x-2]\/1+x<sup>2<\/sup>)<\/strong>\u00a0 ;<br \/>\nd ) <em><strong>g(x) \/ f(x) = In<\/strong><\/em><strong>([x-2]\/1+x<sup>2<\/sup>)<\/strong>\u00a0<\/span><\/li>\n<li><span style=\"color: #000000;\">On a la limite en + \u221e de la fonction <span style=\"color: #3366ff;\">h : x -&gt;\u00a0In(3x &#8211; 4) &#8211; x<sup>2<\/sup><\/span> \u00e9gale \u00e0:<\/span><br \/>\n<span style=\"color: #000000;\">a) +\u221e; b)-\u221e; c) 0; \u00a0d)4\u00a0<\/span><\/li>\n<\/ol>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"partie-b-10-points-kamerpowercom\"><\/span><span style=\"color: #ff0000;\">Partie\u00a0B: (10 points)\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<p><span style=\"color: #000000;\"><span style=\"color: #ff0000;\">f<\/span> est une fonction definie en un reel x par : \u00a0f(x) = 1+Inx \/ (x-2)<span style=\"color: #3366ff;\"><sup>2<\/sup><\/span> \u00a0 \u00a0 \u00a0 \u00a0; <span style=\"color: #3366ff;\">(C)<\/span> est la courbe representative de f\u00a0dans un plan rapport\u00e9 \u00e0 un rep\u00e8re orthonorm\u00e9 (0 ; i ; j\u00a0) : l\u2019unit\u00e9 sur chacun des axes est de 2\u00a0cm.<\/span><\/p>\n<ol>\n<li><span style=\"color: #000000;\"><span style=\"color: #ff0000;\">a.<\/span> D\u00e9terminer sous forme de r\u00e9union d\u2019intervalles l\u2019onsemble de d\u00e9finition de f. <span style=\"color: #ff0000;\">(0,25 pt)<\/span><\/span><br \/>\n<span style=\"color: #000000;\"><span style=\"color: #ff0000;\">b.<\/span> Calculerles limites de f en 0+ ; en 1 et en +\u221e .<span style=\"color: #ff0000;\"> (0,75 pt)<\/span><\/span><\/li>\n<li><span style=\"color: #000000;\">Calculer f\u00a0&#8216;(x) o\u00f9 f &#8216; est la fonction d\u00e9riv\u00e9e de f et x un \u00e9l\u00e9ment quelconque\u00a0de l&#8217;ensemble de d\u00e9finition de f. \u00a0<span style=\"color: #ff0000;\">(1 pt)<\/span><\/span><\/li>\n<li><span style=\"color: #000000;\">Soit g la fonction num\u00e9rique d\u00e9finie par: g(x) = -x &#8211; 1 -2xlnx.<\/span><br \/>\n<span style=\"color: #000000;\"><span style=\"color: #ff0000;\">a.<\/span> D\u00e9terminer le sens de variations de g, puis le signe de g sur ]0; +\u221e[. <span style=\"color: #ff0000;\">(2,5 pts)<\/span><\/span><br \/>\n<span style=\"color: #000000;\"><span style=\"color: #ff0000;\">b.<\/span> En d\u00e9duire le tableau de variation de f sur son ensemble de d\u00e9finition.<span style=\"color: #ff0000;\"> (1 pt)<\/span><\/span><\/li>\n<li><span style=\"color: #000000;\">Construire <span style=\"color: #3366ff;\">(C)<\/span> . \u00a0(2 pts)<\/span><\/li>\n<li><span style=\"color: #000000;\">Soit <span style=\"color: #3366ff;\">H<\/span> la fonction num\u00e9rique d\u00e9finie dans ]1 ; +\u221e[ par:\n<p>H(x) = In([x-1]\/x) &#8211; Inx\/x-1 \u00a0&#8211; \u00a01\/x-1<\/span><\/p>\n<p><span style=\"color: #000000;\"><span style=\"color: #ff0000;\">a.<\/span> Montrer que H est une primitive de f sur ]1 ; +\u221e[ <span style=\"color: #ff0000;\">(1pt)<\/span><\/span><br \/>\n<span style=\"color: #000000;\"><span style=\"color: #ff0000;\">b.<\/span> Soit a un r\u00e9el sup\u00e9rieur ou \u00e9gal \u00e0 2. On pose :<span style=\"color: #3366ff;\">A(a) = H(a) &#8211; H(2)<\/span>.<\/span><br \/>\n<span style=\"color: #000000;\">Exprimer <span style=\"color: #3366ff;\">A(a)<\/span> en fonction de <span style=\"color: #3366ff;\">a<\/span> et calculer la limite de <span style=\"color: #3366ff;\">A(a)<\/span> quand <span style=\"color: #3366ff;\">a<\/span><em> tend vers<\/em> <span style=\"color: #3366ff;\">+ \u221e<\/span>.<span style=\"color: #ff0000;\">(1,5 pt)<\/span><\/span><\/li>\n<\/ol>\n<h2 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"epreuve-concours-enieg-cameroun-2013-mathematiques-niveau-bac\"><\/span><span style=\"color: #3366ff;\">Epreuve concours ENIEG Cameroun 2013 Mathematiques Niveau BAC <\/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":3283,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_themeisle_gutenberg_block_has_review":false,"footnotes":""},"categories":[1701],"tags":[1827,1712,1706],"class_list":["post-5997","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-epreuves","tag-epreuve-concours-dentree-aux-enieg-cameroun","tag-epreuve-de-concours-dentree-aux-grandes-ecoles-cameroun","tag-mathematiques"],"_links":{"self":[{"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/posts\/5997","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=5997"}],"version-history":[{"count":1,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/posts\/5997\/revisions"}],"predecessor-version":[{"id":67993,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/posts\/5997\/revisions\/67993"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/media\/3283"}],"wp:attachment":[{"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/media?parent=5997"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/categories?post=5997"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kamerpower.com\/fr\/wp-json\/wp\/v2\/tags?post=5997"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}