Quiz — cephalee fmm 2015.pdf

Question 1 sur 10 20:00

[{"id":36640,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"A) 2x + 3","option_b":"B) x² + 3","option_c":"C) 2x - 5","option_d":"D) 3x + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de x² est 2x, celle de 3x est 3, et celle de -5 est 0. Ainsi, f'(x) = 2x + 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) 2x + 3\", \"b\": \"B) x² + 3\", \"c\": \"C) 2x - 5\", \"d\": \"D) 3x + 2\"","_debug_options_count":4},{"id":36641,"question":"La limite de (sin x)\/x quand x tend vers 0 est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une limite fondamentale en analyse : lim (x→0) (sin x)\/x = 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":36642,"question":"Quel est le résultat de la somme des 5 premiers termes d'une suite géométrique de premier terme 2 et de raison 3 ?","option_a":"A) 242","option_b":"B) 122","option_c":"C) 62","option_d":"D) 32","option_e":"","option_f":"","bonne_reponse":"a","explication":"La somme des n premiers termes d'une suite géométrique est S_n = u_1 * (1 - q^n)\/(1 - q). Ici, S_5 = 2 * (1 - 3^5)\/(1 - 3) = 2 * (1 - 243)\/(-2) = 242.","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) 242\", \"b\": \"B) 122\", \"c\": \"C) 62\", \"d\": \"D) 32\"}}","_debug_options_count":4},{"id":36643,"question":"Dans une expérience aléatoire, la probabilité d'un événement A est P(A) = 0,6. Quelle est la probabilité de l'événement contraire ?","option_a":"A) 0,4","option_b":"B) 0,6","option_c":"C) 1,6","option_d":"D) -0,4","option_e":"","option_f":"","bonne_reponse":"a","explication":"La probabilité de l'événement contraire est P(A̅) = 1 - P(A) = 1 - 0,6 = 0,4.","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) 0,4\", \"b\": \"B) 0,6\", \"c\": \"C) 1,6\", \"d\": \"D) -0,4\"}}","_debug_options_count":4},{"id":36644,"question":"La fonction f(x) = x³ - 3x² + 2x est croissante sur l'intervalle [0, 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = 3x² - 6x + 2. En étudiant son signe, on trouve que f est décroissante sur [0, 2].","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":36645,"question":"Quel est le nombre de permutations possibles de 4 éléments distincts ?","option_a":"A) 4","option_b":"B) 12","option_c":"C) 24","option_d":"D) 48","option_e":"","option_f":"","bonne_reponse":"c","explication":"Le nombre de permutations de n éléments est n!. Ici, 4! = 4 × 3 × 2 × 1 = 24.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A) 4\", \"b\": \"B) 12\", \"c\": \"C) 24\", \"d\": \"D) 48\"}}","_debug_options_count":4},{"id":36646,"question":"Si une variable aléatoire X suit une loi binomiale B(n=10, p=0,3), quelle est son espérance ?","option_a":"A) 3","option_b":"B) 10","option_c":"C) 0,3","option_d":"D) 7","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'espérance d'une loi binomiale B(n,p) est E(X) = n × p = 10 × 0,3 = 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) 10\", \"c\": \"C) 0,3\", \"d\": \"D) 7\"}}","_debug_options_count":4},{"id":36647,"question":"La fonction f(x) = 1\/x est définie et continue sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = 1\/x n'est pas définie en x = 0 et présente une discontinuité en ce point.","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":36648,"question":"Quel est le résultat de l'intégrale ∫(2x + 1) dx entre 0 et 2 ?","option_a":"A) 4","option_b":"B) 6","option_c":"C) 8","option_d":"D) 10","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'intégrale de 2x + 1 est x² + x. Évaluée entre 0 et 2 : (2² + 2) - (0² + 0) = 6.","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\", \"b\": \"B) 6\", \"c\": \"C) 8\", \"d\": \"D) 10\"}}","_debug_options_count":4},{"id":36649,"question":"Dans un triangle ABC, si sin(A) = 0,5, alors A mesure 30°.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Si sin(A) = 0,5, alors A peut mesurer 30° ou 150° (car sin(150°) = 0,5). La réponse dépend du contexte du triangle.","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}]