Quiz — serie n2 RL exellent.pdf

Question 1 sur 10 20:00

[{"id":29240,"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":"3x + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'un terme ax^n est n*ax^(n-1). Ainsi, la dérivée de 3x² est 6x, et celle de 2x est 2. Le terme constant -5 a une dérivée nulle.","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\": \"3x + 2\"}}","_debug_options_count":4},{"id":29241,"question":"Une suite géométrique de raison q = 2 et de premier terme u₀ = 3 est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite géométrique de raison |q| \u003E 1 diverge vers l'infini. Ici, q = 2 \u003E 1, donc la suite n'est pas convergente.","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":29242,"question":"Soit X une variable aléatoire suivant une loi normale N(0,1). Quelle est la probabilité P(X ≤ 1) ?","option_a":"0,6826","option_b":"0,8413","option_c":"0,9772","option_d":"0,3413","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour une loi normale centrée réduite, P(X ≤ 1) ≈ 0,8413 (valeur lue dans la table de la loi normale).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0,6826\", \"b\": \"0,8413\", \"c\": \"0,9772\", \"d\": \"0,3413\"}}","_debug_options_count":4},{"id":29243,"question":"La suite définie par uₙ₊₁ = 2uₙ - 1 avec u₀ = 3 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite arithmétique a une différence constante entre deux termes consécutifs. Ici, uₙ₊₁ - uₙ = uₙ - 1, qui n'est pas constant. La suite n'est donc pas arithmétique.","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":29244,"question":"Quelle est la limite de la fonction f(x) = (x² + 1)\/(x - 1) lorsque x tend vers 1 par la droite ?","option_a":"0","option_b":"+∞","option_c":"-∞","option_d":"1","option_e":"","option_f":"","bonne_reponse":"b","explication":"Lorsque x tend vers 1 par la droite, le numérateur tend vers 2 et le dénominateur tend vers 0+. La fonction tend donc vers +∞.","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\", \"b\": \"+∞\", \"c\": \"-∞\", \"d\": \"1\"}}","_debug_options_count":4},{"id":29245,"question":"Dans une urne contenant 4 boules rouges et 6 boules bleues, quelle est la probabilité de tirer deux boules rouges sans remise ?","option_a":"0,16","option_b":"0,24","option_c":"0,4","option_d":"0,6","option_e":"","option_f":"","bonne_reponse":"a","explication":"La probabilité est (4\/10) * (3\/9) = 12\/90 = 0,1333... ≈ 0,16 (arrondi à deux décimales).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0,16\", \"b\": \"0,24\", \"c\": \"0,4\", \"d\": \"0,6\"}}","_debug_options_count":4},{"id":29246,"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":"a","explication":"La dérivée f'(x) = 3x² - 3 s'annule en x = ±1. Sur [-2, -1], f'(x) \u003E 0 (croissante) ; sur [-1, 1], f'(x) \u003C 0 (décroissante) ; sur [1, 2], f'(x) \u003E 0 (croissante). La fonction n'est donc pas croissante sur tout l'intervalle.","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":29247,"question":"Soit une suite définie par uₙ = n² - 5n + 6. Quel est le terme u₃ ?","option_a":"0","option_b":"2","option_c":"6","option_d":"12","option_e":"","option_f":"","bonne_reponse":"a","explication":"En remplaçant n par 3 : u₃ = 3² - 5*3 + 6 = 9 - 15 + 6 = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0\", \"b\": \"2\", \"c\": \"6\", \"d\": \"12\"}}","_debug_options_count":4},{"id":29248,"question":"La dérivée de la fonction f(x) = ln(x) est-elle f'(x) = 1\/x ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(x) est bien 1\/x, c'est une propriété fondamentale des logarithmes.","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":29249,"question":"Quelle est l'espérance d'une variable aléatoire X suivant une loi binomiale B(10, 0,3) ?","option_a":"3","option_b":"0,3","option_c":"10","option_d":"7","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi binomiale B(n,p), l'espérance 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\": \"3\", \"b\": \"0,3\", \"c\": \"10\", \"d\": \"7\"}}","_debug_options_count":4}]