Quiz — serie 21 p2.pdf

Question 1 sur 10 20:00

[{"id":43935,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x - 5","option_d":"6x + 2x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle de dérivation terme à terme : (3x²)' = 6x et (2x)' = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"6x + 2\", \"b\": \"3x² + 2\", \"c\": \"6x - 5\", \"d\": \"6x + 2x - 5\"}}","_debug_options_count":4},{"id":43936,"question":"La suite définie par uₙ = 2n + 1 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite est arithmétique si la différence entre deux termes consécutifs est constante. Ici, uₙ₊₁ - uₙ = 2, donc elle est arithmétique de raison 2.","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":43937,"question":"Quelle est la limite de la fonction f(x) = (x² - 1)\/(x - 1) lorsque x tend vers 1 ?","option_a":"0","option_b":"2","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"c","explication":"En factorisant le numérateur : (x² - 1) = (x - 1)(x + 1), on obtient f(x) = x + 1 pour x ≠ 1. La limite est donc 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0\", \"b\": \"2\", \"c\": \"1\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":43938,"question":"Dans une classe de 30 élèves, 18 sont des filles. Quelle est la probabilité qu'un élève choisi au hasard soit une fille ?","option_a":"0.4","option_b":"0.6","option_c":"0.5","option_d":"0.3","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité est le rapport du nombre de cas favorables sur le nombre total de cas : 18\/30 = 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\": \"0.4\", \"b\": \"0.6\", \"c\": \"0.5\", \"d\": \"0.3\"}}","_debug_options_count":4},{"id":43939,"question":"L'équation différentielle y' = 2y admet-elle pour solution y = Ce^(2x) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En dérivant y = Ce^(2x), on obtient y' = 2Ce^(2x) = 2y. Cette solution vérifie donc l'équation différentielle.","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":43940,"question":"Quel est le module du nombre complexe z = 3 + 4i ?","option_a":"5","option_b":"7","option_c":"1","option_d":"25","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le module d'un nombre complexe z = a + bi est donné par √(a² + b²). Ici, √(3² + 4²) = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"5\", \"b\": \"7\", \"c\": \"1\", \"d\": \"25\"}}","_debug_options_count":4},{"id":43941,"question":"La fonction f(x) = x³ - 3x est-elle croissante sur l'intervalle [-2, 2] ?","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. Sur [-2, -1] et [1, 2], f est croissante, mais 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":43942,"question":"Quelle est la somme des 10 premiers termes de la suite géométrique de premier terme 2 et de raison 3 ?","option_a":"59048","option_b":"177146","option_c":"39366","option_d":"118096","option_e":"","option_f":"","bonne_reponse":"b","explication":"La somme des n premiers termes d'une suite géométrique est Sₙ = u₁(1 - rⁿ)\/(1 - r). Ici, S₁₀ = 2(1 - 3¹⁰)\/(1 - 3) = 177146.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"59048\", \"b\": \"177146\", \"c\": \"39366\", \"d\": \"118096\"}}","_debug_options_count":4},{"id":43943,"question":"L'intégrale ∫(0 à 1) x² dx vaut-elle 1\/3 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de x² entre 0 et 1 est [x³\/3]₀¹ = 1\/3 - 0 = 1\/3. L'affirmation est donc vraie.","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":43944,"question":"Quel est le discriminant de l'équation x² - 5x + 6 = 0 ?","option_a":"1","option_b":"25","option_c":"1","option_d":"-1","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le discriminant Δ = b² - 4ac = (-5)² - 4(1)(6) = 25 - 24 = 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\": \"1\", \"b\": \"25\", \"c\": \"1\", \"d\": \"-1\"}}","_debug_options_count":4}]