{"id":1513,"date":"2026-09-08T08:06:57","date_gmt":"2026-09-08T08:06:57","guid":{"rendered":"https:\/\/maroczain.com\/scolaire.maroczain.com\/?page_id=1513"},"modified":"2026-09-08T08:06:57","modified_gmt":"2026-09-08T08:06:57","slug":"mathematiques-prepa-excellence","status":"publish","type":"page","link":"https:\/\/maroczain.com\/scolaire.maroczain.com\/mathematiques-prepa-excellence\/","title":{"rendered":"Math\u00e9matiques Pr\u00e9pa Excellence"},"content":{"rendered":"\n&#8220;`html\n<div id=\"mza-maths-cpge\">\n\n<style>\n#mza-maths-cpge,#mza-maths-cpge *{box-sizing:border-box}\n#mza-maths-cpge{\n --navy:#06172c;--navy2:#0d416d;--gold:#c89a3a;--gold2:#efd68c;\n --paper:#f5f6f8;--white:#fff;--text:#18283a;--muted:#687789;--line:#dfe5eb;\n font-family:Arial,Helvetica,sans-serif;background:var(--paper);color:var(--text);\n overflow:hidden\n}\n#mza-maths-cpge a{text-decoration:none;color:inherit}\n#mza-maths-cpge .wrap{max-width:1280px;margin:auto;padding:0 24px}\n#mza-maths-cpge section{padding:72px 0}\n\n\/* HERO *\/\n#mza-maths-cpge .hero{\n padding:75px 0;color:#fff;\n background:\n radial-gradient(circle at 85% 15%,rgba(211,166,65,.28),transparent 28%),\n linear-gradient(135deg,#041224,#082b4c 65%,#10517e)\n}\n#mza-maths-cpge .back{\n display:inline-flex;margin-bottom:25px;color:#dbe6ee;font-size:12px;font-weight:900\n}\n#mza-maths-cpge .badge{\n display:inline-block;padding:8px 13px;border-radius:999px;\n border:1px solid rgba(239,214,140,.4);color:var(--gold2);\n font-size:11px;font-weight:900;letter-spacing:1.2px\n}\n#mza-maths-cpge h1{\n color:#fff;font:500 clamp(43px,7vw,76px)\/1 Georgia,serif;margin:18px 0\n}\n#mza-maths-cpge .lead{\n max-width:870px;color:#d5e1ea;font-size:18px;line-height:1.75\n}\n#mza-maths-cpge .actions{display:flex;flex-wrap:wrap;gap:9px;margin-top:27px}\n#mza-maths-cpge .btn{\n min-height:48px;padding:0 19px;border:0;border-radius:10px;\n display:inline-flex;align-items:center;justify-content:center;\n cursor:pointer;font-size:12px;font-weight:900\n}\n#mza-maths-cpge .gold{background:linear-gradient(135deg,#bd892b,#efd483);color:#142238}\n#mza-maths-cpge .glass{background:rgba(255,255,255,.08);color:#fff;border:1px solid rgba(255,255,255,.18)}\n#mza-maths-cpge .stats{\n display:grid;grid-template-columns:repeat(4,1fr);gap:10px;margin-top:40px\n}\n#mza-maths-cpge .stat{\n padding:18px;border-radius:14px;background:rgba(255,255,255,.07);\n border:1px solid rgba(255,255,255,.11)\n}\n#mza-maths-cpge .stat strong{display:block;color:var(--gold2);font-size:24px}\n#mza-maths-cpge .stat small{color:#c7d6e1}\n\n\/* HEAD *\/\n#mza-maths-cpge .head{max-width:880px;margin-bottom:34px}\n#mza-maths-cpge .kicker{color:#987023;font-size:11px;font-weight:900;letter-spacing:1.3px}\n#mza-maths-cpge h2{\n color:var(--navy);font:500 clamp(31px,4vw,49px)\/1.1 Georgia,serif;\n margin:8px 0 11px\n}\n#mza-maths-cpge .head p{color:var(--muted);line-height:1.7}\n\n\/* CHAPTERS *\/\n#mza-maths-cpge .chapters{\n display:grid;grid-template-columns:repeat(3,1fr);gap:14px\n}\n#mza-maths-cpge .chapter{\n background:#fff;border:1px solid var(--line);border-radius:19px;padding:23px;\n transition:.2s\n}\n#mza-maths-cpge .chapter:hover{transform:translateY(-3px);box-shadow:0 15px 35px rgba(8,30,50,.08)}\n#mza-maths-cpge .chapter .num{\n display:inline-flex;width:38px;height:38px;align-items:center;justify-content:center;\n border-radius:10px;background:var(--navy);color:var(--gold2);font-weight:900\n}\n#mza-maths-cpge .chapter h3{color:var(--navy);margin:14px 0 7px;font-size:19px}\n#mza-maths-cpge .chapter p{color:var(--muted);font-size:13px;line-height:1.55}\n#mza-maths-cpge .tags{display:flex;flex-wrap:wrap;gap:5px;margin-top:13px}\n#mza-maths-cpge .tag{\n padding:6px 8px;border-radius:999px;background:#f1eee5;color:#785a1e;\n font-size:10px;font-weight:900\n}\n\n\/* METHOD *\/\n#mza-maths-cpge .dark{background:var(--navy);color:#fff}\n#mza-maths-cpge .dark h2{color:#fff}\n#mza-maths-cpge .dark .head p{color:#c5d3df}\n#mza-maths-cpge .method{\n display:grid;grid-template-columns:repeat(6,1fr);gap:9px\n}\n#mza-maths-cpge .method div{\n padding:18px 9px;text-align:center;border-radius:13px;\n background:rgba(255,255,255,.07);border:1px solid rgba(255,255,255,.1)\n}\n#mza-maths-cpge .method b{display:block;color:var(--gold2);font-size:22px;margin-bottom:7px}\n#mza-maths-cpge .method span{font-size:10px;font-weight:900}\n\n\/* LAB *\/\n#mza-maths-cpge .labs{display:grid;grid-template-columns:repeat(4,1fr);gap:13px}\n#mza-maths-cpge .lab{\n background:#fff;border:1px solid var(--line);border-radius:17px;padding:21px\n}\n#mza-maths-cpge .lab .ico{font-size:30px}\n#mza-maths-cpge .lab h3{color:var(--navy);margin:12px 0 7px}\n#mza-maths-cpge .lab p{color:var(--muted);font-size:13px;line-height:1.55}\n\n\/* PROBLEM *\/\n#mza-maths-cpge .problem{\n background:#fff;border:1px solid var(--line);border-radius:23px;padding:28px\n}\n#mza-maths-cpge .problem-head{\n display:flex;justify-content:space-between;gap:15px;align-items:center;\n margin-bottom:20px\n}\n#mza-maths-cpge .level{\n padding:7px 10px;border-radius:999px;background:#f1eee5;color:#795a1e;\n font-size:10px;font-weight:900\n}\n#mza-maths-cpge .problem-box{\n padding:22px;border-left:4px solid var(--gold);background:#f8f9fa;\n border-radius:0 14px 14px 0;line-height:1.75\n}\n#mza-maths-cpge .hidden-solution{display:none;margin-top:18px;padding:20px;border-radius:14px;background:#eef3f7}\n#mza-maths-cpge .hidden-solution strong{color:var(--navy)}\n\n\/* QCM *\/\n#mza-maths-cpge .qcm{\n background:#fff;border:1px solid var(--line);border-radius:23px;padding:28px\n}\n#mza-maths-cpge .question{\n padding:20px;margin:15px 0;background:#f7f8fa;border-radius:14px\n}\n#mza-maths-cpge .question strong{display:block;color:var(--navy);margin-bottom:12px}\n#mza-maths-cpge label{display:block;padding:8px 0;color:#526174;cursor:pointer}\n#mza-maths-cpge #mathResult{\n display:none;padding:20px;margin-top:18px;border-radius:14px;background:var(--navy);color:#fff\n}\n\n\/* CTA *\/\n#mza-maths-cpge .cta{\n text-align:center;padding:50px 25px;border-radius:26px;\n color:#fff;background:linear-gradient(135deg,#06172c,#0d416d)\n}\n#mza-maths-cpge .cta h2{color:#fff}\n#mza-maths-cpge .cta p{max-width:720px;margin:0 auto 22px;color:#cfdae4;line-height:1.7}\n\n@media(max-width:950px){\n #mza-maths-cpge .chapters{grid-template-columns:repeat(2,1fr)}\n #mza-maths-cpge .labs{grid-template-columns:repeat(2,1fr)}\n #mza-maths-cpge .method{grid-template-columns:repeat(3,1fr)}\n}\n@media(max-width:620px){\n #mza-maths-cpge .chapters,#mza-maths-cpge .labs,\n #mza-maths-cpge .stats,#mza-maths-cpge .method{grid-template-columns:1fr}\n}\n<\/style>\n\n<!-- HERO -->\n<header class=\"hero\">\n<div class=\"wrap\">\n\n<a class=\"back\" href=\"https:\/\/maroczain.com\/scolaire.maroczain.com\/classes-preparatoires\/\">\n\u2190 MZA PR\u00c9PA EXCELLENCE\n<\/a>\n\n<br>\n<span class=\"badge\">MATH\u00c9MATIQUES \u2022 CPGE \u2022 MZA PR\u00c9PA<\/span>\n\n<h1>Math\u00e9matiques<br>Pr\u00e9pa Excellence<\/h1>\n\n<p class=\"lead\">\nComprendre profond\u00e9ment, d\u00e9montrer avec rigueur, d\u00e9velopper des strat\u00e9gies\nde r\u00e9solution et apprendre \u00e0 traiter des probl\u00e8mes complexes sous contrainte\nde temps.\n<\/p>\n\n<div class=\"actions\">\n<a href=\"#programme\" class=\"btn gold\">\ud83d\udcda PROGRAMME<\/a>\n<a href=\"#problem-lab\" class=\"btn glass\">\ud83e\udde9 PROBLEM LAB<\/a>\n<a href=\"#qcm\" class=\"btn glass\">\u2753 QCM DIAGNOSTIC<\/a>\n<\/div>\n\n<div class=\"stats\">\n<div class=\"stat\"><strong>18<\/strong><small>blocs de travail<\/small><\/div>\n<div class=\"stat\"><strong>4<\/strong><small>niveaux d&#8217;exercices<\/small><\/div>\n<div class=\"stat\"><strong>DS<\/strong><small>mode chronom\u00e9tr\u00e9<\/small><\/div>\n<div class=\"stat\"><strong>Concours<\/strong><small>objectif final<\/small><\/div>\n<\/div>\n\n<\/div>\n<\/header>\n\n<!-- PROGRAMME -->\n<section id=\"programme\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">PROGRAMME MATH\u00c9MATIQUES<\/span>\n<h2>Construire une puissance de raisonnement.<\/h2>\n<p>\nLa page organise les grands domaines math\u00e9matiques en blocs d&#8217;apprentissage,\npuis les relie \u00e0 des exercices, probl\u00e8mes et \u00e9valuations.\n<\/p>\n<\/div>\n\n<div class=\"chapters\">\n\n<div class=\"chapter\">\n<span class=\"num\">01<\/span>\n<h3>Logique &#038; Raisonnement<\/h3>\n<p>Implications, \u00e9quivalences, quantificateurs, raisonnement direct et contradiction.<\/p>\n<div class=\"tags\"><span class=\"tag\">COURS<\/span><span class=\"tag\">M\u00c9THODE<\/span><\/div>\n<\/div>\n\n<div class=\"chapter\">\n<span class=\"num\">02<\/span>\n<h3>Ensembles &#038; Applications<\/h3>\n<p>Applications, injections, surjections, bijections et structures fondamentales.<\/p>\n<div class=\"tags\"><span class=\"tag\">EXERCICES<\/span><\/div>\n<\/div>\n\n<div class=\"chapter\">\n<span class=\"num\">03<\/span>\n<h3>Nombres complexes<\/h3>\n<p>Calcul complexe, g\u00e9om\u00e9trie, formes alg\u00e9brique et exponentielle.<\/p>\n<div class=\"tags\"><span class=\"tag\">PROBL\u00c8MES<\/span><\/div>\n<\/div>\n\n<div class=\"chapter\">\n<span class=\"num\">04<\/span>\n<h3>Suites num\u00e9riques<\/h3>\n<p>Convergence, monotonie, suites r\u00e9currentes et comparaisons.<\/p>\n<div class=\"tags\"><span class=\"tag\">ANALYSE<\/span><\/div>\n<\/div>\n\n<div class=\"chapter\">\n<span class=\"num\">05<\/span>\n<h3>Fonctions<\/h3>\n<p>Limites, continuit\u00e9, d\u00e9rivation et \u00e9tude qualitative.<\/p>\n<div class=\"tags\"><span class=\"tag\">ANALYSE<\/span><\/div>\n<\/div>\n\n<div class=\"chapter\">\n<span class=\"num\">06<\/span>\n<h3>D\u00e9veloppements limit\u00e9s<\/h3>\n<p>Approximation locale et m\u00e9thodes asymptotiques.<\/p>\n<div class=\"tags\"><span class=\"tag\">M\u00c9THODE<\/span><\/div>\n<\/div>\n\n<div class=\"chapter\">\n<span class=\"num\">07<\/span>\n<h3>Int\u00e9gration<\/h3>\n<p>Calcul int\u00e9gral, techniques d&#8217;int\u00e9gration et applications.<\/p>\n<div class=\"tags\"><span class=\"tag\">ANALYSE<\/span><\/div>\n<\/div>\n\n<div class=\"chapter\">\n<span class=\"num\">08<\/span>\n<h3>S\u00e9ries num\u00e9riques<\/h3>\n<p>Convergence, comparaison et comportement asymptotique.<\/p>\n<div class=\"tags\"><span class=\"tag\">AVANC\u00c9<\/span><\/div>\n<\/div>\n\n<div class=\"chapter\">\n<span class=\"num\">09<\/span>\n<h3>\u00c9quations diff\u00e9rentielles<\/h3>\n<p>\u00c9quations lin\u00e9aires et mod\u00e9lisation de ph\u00e9nom\u00e8nes.<\/p>\n<div class=\"tags\"><span class=\"tag\">APPLICATIONS<\/span><\/div>\n<\/div>\n\n<div class=\"chapter\">\n<span class=\"num\">10<\/span>\n<h3>Alg\u00e8bre lin\u00e9aire<\/h3>\n<p>Espaces vectoriels, sous-espaces, familles et bases.<\/p>\n<div class=\"tags\"><span class=\"tag\">ALG\u00c8BRE<\/span><\/div>\n<\/div>\n\n<div class=\"chapter\">\n<span class=\"num\">11<\/span>\n<h3>Applications lin\u00e9aires<\/h3>\n<p>Noyau, image, rang et repr\u00e9sentation matricielle.<\/p>\n<div class=\"tags\"><span class=\"tag\">ALG\u00c8BRE<\/span><\/div>\n<\/div>\n\n<div class=\"chapter\">\n<span class=\"num\">12<\/span>\n<h3>Matrices<\/h3>\n<p>Calcul matriciel, inversion, syst\u00e8mes et changements de base.<\/p>\n<div class=\"tags\"><span class=\"tag\">CALCUL<\/span><\/div>\n<\/div>\n\n<div class=\"chapter\">\n<span class=\"num\">13<\/span>\n<h3>D\u00e9terminants<\/h3>\n<p>Propri\u00e9t\u00e9s, calculs et applications aux syst\u00e8mes lin\u00e9aires.<\/p>\n<div class=\"tags\"><span class=\"tag\">ALG\u00c8BRE<\/span><\/div>\n<\/div>\n\n<div class=\"chapter\">\n<span class=\"num\">14<\/span>\n<h3>R\u00e9duction<\/h3>\n<p>Valeurs propres, vecteurs propres et diagonalisation.<\/p>\n<div class=\"tags\"><span class=\"tag\">AVANC\u00c9<\/span><\/div>\n<\/div>\n\n<div class=\"chapter\">\n<span class=\"num\">15<\/span>\n<h3>Espaces euclidiens<\/h3>\n<p>Produit scalaire, orthogonalit\u00e9 et projections.<\/p>\n<div class=\"tags\"><span class=\"tag\">G\u00c9OM\u00c9TRIE<\/span><\/div>\n<\/div>\n\n<div class=\"chapter\">\n<span class=\"num\">16<\/span>\n<h3>D\u00e9nombrement<\/h3>\n<p>Principes combinatoires et strat\u00e9gies de comptage.<\/p>\n<div class=\"tags\"><span class=\"tag\">PROBABILIT\u00c9S<\/span><\/div>\n<\/div>\n\n<div class=\"chapter\">\n<span class=\"num\">17<\/span>\n<h3>Probabilit\u00e9s<\/h3>\n<p>\u00c9v\u00e9nements, conditionnement, ind\u00e9pendance et variables al\u00e9atoires.<\/p>\n<div class=\"tags\"><span class=\"tag\">PROBABILIT\u00c9S<\/span><\/div>\n<\/div>\n\n<div class=\"chapter\">\n<span class=\"num\">18<\/span>\n<h3>Strat\u00e9gies Concours<\/h3>\n<p>Lecture d&#8217;\u00e9nonc\u00e9, choix des questions, gestion du temps et r\u00e9daction.<\/p>\n<div class=\"tags\"><span class=\"tag\">CONCOURS<\/span><span class=\"tag\">DS<\/span><\/div>\n<\/div>\n\n<\/div>\n<\/div>\n<\/section>\n\n<!-- METHOD -->\n<section class=\"dark\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\" style=\"color:#efd68c\">MZA MATH ENGINE<\/span>\n<h2>Ne pas apprendre les math\u00e9matiques. Apprendre \u00e0 les faire.<\/h2>\n<p>Chaque notion passe par six niveaux de ma\u00eetrise.<\/p>\n<\/div>\n\n<div class=\"method\">\n<div><b>01<\/b><span>COMPRENDRE<\/span><\/div>\n<div><b>02<\/b><span>D\u00c9MONTRER<\/span><\/div>\n<div><b>03<\/b><span>APPLIQUER<\/span><\/div>\n<div><b>04<\/b><span>COMBINER<\/span><\/div>\n<div><b>05<\/b><span>R\u00c9SOUDRE<\/span><\/div>\n<div><b>06<\/b><span>ACC\u00c9L\u00c9RER<\/span><\/div>\n<\/div>\n\n<\/div>\n<\/section>\n\n<!-- LABS -->\n<section>\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">ENTRA\u00ceNEMENT INTENSIF<\/span>\n<h2>Les laboratoires MZA.<\/h2>\n<\/div>\n\n<div class=\"labs\">\n\n<div class=\"lab\">\n<div class=\"ico\">\ud83d\udfe2<\/div>\n<h3>Niveau 1 \u2014 Fondations<\/h3>\n<p>Applications imm\u00e9diates du cours et automatismes essentiels.<\/p>\n<\/div>\n\n<div class=\"lab\">\n<div class=\"ico\">\ud83d\udfe1<\/div>\n<h3>Niveau 2 \u2014 Ma\u00eetrise<\/h3>\n<p>Exercices combinant plusieurs m\u00e9thodes classiques.<\/p>\n<\/div>\n\n<div class=\"lab\">\n<div class=\"ico\">\ud83d\udfe0<\/div>\n<h3>Niveau 3 \u2014 Pr\u00e9pa<\/h3>\n<p>Probl\u00e8mes demandant analyse, strat\u00e9gie et r\u00e9daction.<\/p>\n<\/div>\n\n<div class=\"lab\">\n<div class=\"ico\">\ud83d\udd34<\/div>\n<h3>Niveau 4 \u2014 Concours<\/h3>\n<p>Sujets longs, questions imbriqu\u00e9es et gestion du temps.<\/p>\n<\/div>\n\n<div class=\"lab\">\n<div class=\"ico\">\u23f1\ufe0f<\/div>\n<h3>Speed Lab<\/h3>\n<p>Exercices courts chronom\u00e9tr\u00e9s pour am\u00e9liorer la rapidit\u00e9.<\/p>\n<\/div>\n\n<div class=\"lab\">\n<div class=\"ico\">\ud83e\udde0<\/div>\n<h3>Proof Lab<\/h3>\n<p>Apprendre \u00e0 construire et r\u00e9diger une d\u00e9monstration rigoureuse.<\/p>\n<\/div>\n\n<div class=\"lab\">\n<div class=\"ico\">\ud83d\udd0d<\/div>\n<h3>Error DNA<\/h3>\n<p>Classifier les erreurs : cours, calcul, m\u00e9thode, logique ou temps.<\/p>\n<\/div>\n\n<div class=\"lab\">\n<div class=\"ico\">\ud83c\udfc6<\/div>\n<h3>Concours Lab<\/h3>\n<p>DS, probl\u00e8mes longs et simulations en conditions d&#8217;\u00e9preuve.<\/p>\n<\/div>\n\n<\/div>\n<\/div>\n<\/section>\n\n<!-- PROBLEM LAB -->\n<section id=\"problem-lab\" style=\"background:#efede7\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">PROBLEM LAB<\/span>\n<h2>Mission math\u00e9matique.<\/h2>\n<p>Un exemple de probl\u00e8me interactif int\u00e9gr\u00e9 directement dans la page.<\/p>\n<\/div>\n\n<div class=\"problem\">\n\n<div class=\"problem-head\">\n<div>\n<strong style=\"font-size:21px;color:#06172c\">Suite d\u00e9finie par r\u00e9currence<\/strong>\n<\/div>\n<span class=\"level\">NIVEAU PR\u00c9PA<\/span>\n<\/div>\n\n<div class=\"problem-box\">\nOn consid\u00e8re la suite d\u00e9finie par :\n<br><br>\n<strong>u\u2080 = 1<\/strong>\n<br>\net\n<br>\n<strong>u\u2099\u208a\u2081 = \u221a(2 + u\u2099)<\/strong>.\n<br><br>\nVotre mission :\n<br>\n1. Montrer que la suite est bien d\u00e9finie.\n<br>\n2. \u00c9tudier sa monotonie.\n<br>\n3. Montrer qu&#8217;elle converge.\n<br>\n4. D\u00e9terminer sa limite.\n<br>\n5. Identifier pr\u00e9cis\u00e9ment les th\u00e9or\u00e8mes utilis\u00e9s.\n<\/div>\n\n<div class=\"actions\">\n<button type=\"button\" class=\"btn gold\" onclick=\"mzaMathHint()\">\ud83d\udca1 INDICE<\/button>\n<button type=\"button\" class=\"btn\" style=\"background:#06172c;color:#fff\" onclick=\"mzaMathMethod()\">\ud83e\udde0 VOIR LA M\u00c9THODE<\/button>\n<\/div>\n\n<div id=\"mathHint\" class=\"hidden-solution\">\n<strong>Indice :<\/strong>\n<p>\nCommencez par rechercher un intervalle stable, puis comparez\nu\u2099\u208a\u2081 et u\u2099. Si une limite existe, elle doit satisfaire une \u00e9quation\nobtenue \u00e0 partir de la relation de r\u00e9currence.\n<\/p>\n<\/div>\n\n<div id=\"mathMethod\" class=\"hidden-solution\">\n<strong>M\u00e9thode \u2014 sans donner la solution finale :<\/strong>\n<p>\n1. Trouver des bornes compatibles avec la r\u00e9currence.<br>\n2. Prouver la propri\u00e9t\u00e9 par r\u00e9currence.<br>\n3. \u00c9tudier le signe de u\u2099\u208a\u2081 \u2212 u\u2099 ou utiliser une fonction auxiliaire.<br>\n4. Appliquer le th\u00e9or\u00e8me de convergence des suites monotones born\u00e9es.<br>\n5. Passer \u00e0 la limite dans la relation seulement apr\u00e8s avoir justifi\u00e9 la convergence.\n<\/p>\n<\/div>\n\n<\/div>\n<\/div>\n<\/section>\n\n<!-- QCM -->\n<section id=\"qcm\">\n<div class=\"wrap\">\n\n<div class=\"head\">\n<span class=\"kicker\">QCM DIAGNOSTIC<\/span>\n<h2>Test express Math\u00e9matiques Pr\u00e9pa.<\/h2>\n<p>Aucune correction d\u00e9taill\u00e9e n&#8217;est affich\u00e9e apr\u00e8s validation.<\/p>\n<\/div>\n\n<div class=\"qcm\">\n\n<form id=\"mathQuiz\">\n\n<div class=\"question\">\n<strong>1. Pour d\u00e9montrer qu&#8217;une suite converge, une strat\u00e9gie classique consiste \u00e0 montrer qu&#8217;elle est :<\/strong>\n<label><input type=\"radio\" name=\"m1\" value=\"1\"> monotone et born\u00e9e<\/label>\n<label><input type=\"radio\" name=\"m1\" value=\"0\"> uniquement positive<\/label>\n<label><input type=\"radio\" name=\"m1\" value=\"0\"> uniquement croissante<\/label>\n<label><input type=\"radio\" name=\"m1\" value=\"0\"> toujours enti\u00e8re<\/label>\n<\/div>\n\n<div class=\"question\">\n<strong>2. Une application lin\u00e9aire est injective lorsque :<\/strong>\n<label><input type=\"radio\" name=\"m2\" value=\"0\"> son image est toujours nulle<\/label>\n<label><input type=\"radio\" name=\"m2\" value=\"1\"> son noyau est r\u00e9duit au vecteur nul<\/label>\n<label><input type=\"radio\" name=\"m2\" value=\"0\"> sa matrice est toujours diagonale<\/label>\n<label><input type=\"radio\" name=\"m2\" value=\"0\"> elle poss\u00e8de toujours deux valeurs propres<\/label>\n<\/div>\n\n<div class=\"question\">\n<strong>3. En situation de concours, face \u00e0 une question bloquante, il est g\u00e9n\u00e9ralement pr\u00e9f\u00e9rable de :<\/strong>\n<label><input type=\"radio\" name=\"m3\" value=\"0\"> y consacrer tout le temps restant<\/label>\n<label><input type=\"radio\" name=\"m3\" value=\"1\"> avancer puis revenir si le temps le permet<\/label>\n<label><input type=\"radio\" name=\"m3\" value=\"0\"> arr\u00eater l&#8217;\u00e9preuve<\/label>\n<label><input type=\"radio\" name=\"m3\" value=\"0\"> supprimer les r\u00e9ponses pr\u00e9c\u00e9dentes<\/label>\n<\/div>\n\n<div class=\"question\">\n<strong>4. Une bonne d\u00e9monstration commence notamment par :<\/strong>\n<label><input type=\"radio\" name=\"m4\" value=\"1\"> identifier clairement hypoth\u00e8ses et objectif<\/label>\n<label><input type=\"radio\" name=\"m4\" value=\"0\"> \u00e9crire imm\u00e9diatement la conclusion<\/label>\n<label><input type=\"radio\" name=\"m4\" value=\"0\"> tester des formules au hasard<\/label>\n<label><input type=\"radio\" name=\"m4\" value=\"0\"> \u00e9viter les notations<\/label>\n<\/div>\n\n<button type=\"button\" class=\"btn gold\" onclick=\"mzaMathScore()\">\nVALIDER MON DIAGNOSTIC\n<\/button>\n\n<\/form>\n\n<div id=\"mathResult\"><\/div>\n\n<\/div>\n<\/div>\n<\/section>\n\n<!-- CTA -->\n<section>\n<div class=\"wrap\">\n\n<div class=\"cta\">\n<div style=\"font-size:43px\">\u2797<\/div>\n<h2>De la compr\u00e9hension au niveau concours.<\/h2>\n<p>\nLa performance en Pr\u00e9pa ne vient pas d&#8217;une accumulation de formules.\nElle vient de la ma\u00eetrise du cours, de la qualit\u00e9 du raisonnement,\nde l&#8217;entra\u00eenement et de la capacit\u00e9 \u00e0 d\u00e9cider rapidement quelle m\u00e9thode utiliser.\n<\/p>\n\n<div class=\"actions\" style=\"justify-content:center\">\n<a href=\"#programme\" class=\"btn gold\">\ud83d\udcda REPRENDRE LE PROGRAMME<\/a>\n<a href=\"#problem-lab\" class=\"btn glass\">\ud83e\udde9 PROBLEM LAB<\/a>\n<\/div>\n<\/div>\n\n<\/div>\n<\/section>\n\n<script>\nfunction mzaMathHint(){\n document.getElementById(\"mathHint\").style.display=\"block\";\n}\n\nfunction mzaMathMethod(){\n document.getElementById(\"mathMethod\").style.display=\"block\";\n}\n\nfunction mzaMathScore(){\n\n const form=document.getElementById(\"mathQuiz\");\n const result=document.getElementById(\"mathResult\");\n\n let score=0;\n let complete=true;\n\n [\"m1\",\"m2\",\"m3\",\"m4\"].forEach(function(name){\n   const a=form.querySelector('input[name=\"'+name+'\"]:checked');\n   if(!a){complete=false}\n   else score+=Number(a.value);\n });\n\n result.style.display=\"block\";\n\n if(!complete){\n   result.innerHTML=\"<strong>R\u00e9pondez aux 4 questions avant validation.<\/strong>\";\n   return;\n }\n\n const pct=Math.round(score\/4*100);\n\n let level=\"Fondations \u00e0 consolider\";\n if(pct>=50)level=\"Bases prometteuses\";\n if(pct>=75)level=\"Bon niveau de d\u00e9part\";\n if(pct===100)level=\"Excellent diagnostic\";\n\n result.innerHTML=\n \"<strong style='font-size:30px;color:#efd68c'>\"+pct+\"%<\/strong>\"+\n \"<p><b>\"+level+\"<\/b><\/p>\"+\n \"<p>\"+score+\" \/ 4 r\u00e9ponses valid\u00e9es.<\/p>\"+\n \"<p>Les bonnes r\u00e9ponses et le corrig\u00e9 restent masqu\u00e9s dans l'espace apprenant.<\/p>\";\n}\n<\/script>\n\n<\/div>\n&#8220;`\n","protected":false},"excerpt":{"rendered":"<p>&#8220;`html \u2190 MZA PR\u00c9PA EXCELLENCE MATH\u00c9MATIQUES \u2022 CPGE \u2022 MZA PR\u00c9PA Math\u00e9matiquesPr\u00e9pa Excellence Comprendre profond\u00e9ment, d\u00e9montrer avec rigueur, d\u00e9velopper des strat\u00e9gies de r\u00e9solution et apprendre \u00e0 traiter des probl\u00e8mes complexes sous contrainte de temps. \ud83d\udcda PROGRAMME \ud83e\udde9 PROBLEM LAB \u2753 QCM DIAGNOSTIC 18blocs de travail 4niveaux d&#8217;exercices DSmode chronom\u00e9tr\u00e9 Concoursobjectif final PROGRAMME MATH\u00c9MATIQUES Construire une [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1513","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/maroczain.com\/scolaire.maroczain.com\/wp-json\/wp\/v2\/pages\/1513","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/maroczain.com\/scolaire.maroczain.com\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/maroczain.com\/scolaire.maroczain.com\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/maroczain.com\/scolaire.maroczain.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/maroczain.com\/scolaire.maroczain.com\/wp-json\/wp\/v2\/comments?post=1513"}],"version-history":[{"count":1,"href":"https:\/\/maroczain.com\/scolaire.maroczain.com\/wp-json\/wp\/v2\/pages\/1513\/revisions"}],"predecessor-version":[{"id":1515,"href":"https:\/\/maroczain.com\/scolaire.maroczain.com\/wp-json\/wp\/v2\/pages\/1513\/revisions\/1515"}],"wp:attachment":[{"href":"https:\/\/maroczain.com\/scolaire.maroczain.com\/wp-json\/wp\/v2\/media?parent=1513"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}