Quiz — 6290a9eb472d0_Corrigé1-Maths-Prototype d’examen Bac N°5 (2).pdf

Question 1 sur 10 20:00

[{"id":29940,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) quand x tend vers l'infini ?","option_a":"A. 3","option_b":"B. 0","option_c":"C. +∞","option_d":"D. -1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La limite d'un quotient de polynômes de même degré est égale au rapport des coefficients dominants. Ici, 3x²\/x² = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. 3\", \"b\": \"B. 0\", \"c\": \"C. +∞\", \"d\": \"D. -1\"}}","_debug_options_count":4},{"id":29941,"question":"Soit une suite définie par u₀ = 2 et uₙ₊₁ = 0.5uₙ + 3. Cette suite est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La suite est convergente car elle est arithmético-géométrique avec |0.5| \u003C 1. Sa limite L vérifie L = 0.5L + 3, soit L = 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":29942,"question":"Quelle est la dérivée de la fonction f(x) = ln(3x² + 1) ?","option_a":"A. 6x\/(3x² + 1)","option_b":"B. 3\/(3x² + 1)","option_c":"C. 6x","option_d":"D. 1\/(3x² + 1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(u) est u'\/u. Ici, u = 3x² + 1, donc u' = 6x. D'où f'(x) = 6x\/(3x² + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. 6x\/(3x² + 1)\", \"b\": \"B. 3\/(3x² + 1)\", \"c\": \"C. 6x\", \"d\": \"D.","_debug_options_count":4},{"id":29943,"question":"Dans une classe de 30 élèves, 18 sont des filles. On choisit un élève au hasard. Quelle est la probabilité que ce soit un garçon ?","option_a":"A. 0.4","option_b":"B. 0.6","option_c":"C. 0.3","option_d":"D. 0.7","option_e":"","option_f":"","bonne_reponse":"b","explication":"Il y a 12 garçons (30 - 18). La probabilité est donc 12\/30 = 0.4. L'option B est incorrecte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. 0.4\", \"b\": \"B. 0.6\", \"c\": \"C. 0.3\", \"d\": \"D. 0.7\"}}","_debug_options_count":4},{"id":29944,"question":"L'équation différentielle y' + 2y = 0 a pour solution générale y = Ce^(-2x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La solution générale de y' + 2y = 0 est bien y = Ce^(-2x), où C est une constante réelle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":29945,"question":"Quelle est l'aire sous la courbe de f(x) = x² entre x = 0 et x = 2 ?","option_a":"A. 4\/3","option_b":"B. 8\/3","option_c":"C. 2","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'aire est donnée par l'intégrale ∫₀² x² dx = [x³\/3]₀² = 8\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. 4\/3\", \"b\": \"B. 8\/3\", \"c\": \"C. 2\", \"d\": \"D. 1\"}}","_debug_options_count":4},{"id":29946,"question":"Soit un vecteur u(2; -1; 3) dans l'espace. Quelle est sa norme ?","option_a":"A. √14","option_b":"B. 6","option_c":"C. √6","option_d":"D. 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"La norme de u est √(2² + (-1)² + 3²) = √(4 + 1 + 9) = √14.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. √14\", \"b\": \"B. 6\", \"c\": \"C. √6\", \"d\": \"D. 4\"}}","_debug_options_count":4},{"id":29947,"question":"La fonction f(x) = x³ - 3x est croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = 3x² - 3 s'annule en x = ±1. La fonction est décroissante sur ]-1; 1[.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":29948,"question":"Quelle est la probabilité d'obtenir un double 6 en lançant deux dés équilibrés ?","option_a":"A. 1\/36","option_b":"B. 1\/6","option_c":"C. 1\/12","option_d":"D. 1\/18","option_e":"","option_f":"","bonne_reponse":"a","explication":"Il y a 36 issues possibles, dont une seule correspond à (6;6). La probabilité est donc 1\/36.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. 1\/36\", \"b\": \"B. 1\/6\", \"c\": \"C. 1\/12\", \"d\": \"D. 1\/18\"}}","_debug_options_count":4},{"id":29949,"question":"Soit une variable aléatoire X suivant une loi normale N(μ; σ²). Que vaut P(μ - σ ≤ X ≤ μ + σ) ?","option_a":"A. 0.68","option_b":"B. 0.95","option_c":"C. 0.997","option_d":"D. 0.34","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi normale, environ 68% des valeurs sont dans l'intervalle [μ - σ; μ + σ].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. 0.68\", \"b\": \"B. 0.95\", \"c\": \"C. 0.997\", \"d\": \"D. 0.34\"}}","_debug_options_count":4}]