Quiz — correc serie n2 femme srandard.pdf

Question 1 sur 10 20:00

[{"id":26554,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 5x - 2 ?","option_a":"A. 6x + 5","option_b":"B. 3x + 5","option_c":"C. 6x² + 5","option_d":"D. 6x + 5x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle : (ax^n)' = n*ax^(n-1). Ici, f'(x) = 6x + 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\": \"A. 6x + 5\", \"b\": \"B. 3x + 5\", \"c\": \"C. 6x² + 5\", \"d\": \"D. 6x + 5","_debug_options_count":4},{"id":26555,"question":"L'intégrale ∫(2x + 1) dx entre 0 et 1 vaut :","option_a":"A. 1","option_b":"B. 2","option_c":"C. 1,5","option_d":"D. 0,5","option_e":"","option_f":"","bonne_reponse":"c","explication":"Calculons l'intégrale : ∫(2x + 1) dx = x² + x + C. Entre 0 et 1, cela donne (1 + 1) - (0 + 0) = 2. L'intégrale définie vaut 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\": \"A. 1\", \"b\": \"B. 2\", \"c\": \"C. 1,5\", \"d\": \"D. 0,5\"}}","_debug_options_count":4},{"id":26556,"question":"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":"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\": \"A. 3\", \"b\": \"B. 10\", \"c\": \"C. 0,3\", \"d\": \"D. 7\"}}","_debug_options_count":4},{"id":26557,"question":"Vrai ou Faux ? La dérivée de ln(x) est 1\/x.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de la fonction logarithme népérien ln(x) est bien 1\/x, pour x \u003E 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":26558,"question":"Quelle est la limite de la suite u_n = (n² + 3n)\/(2n² - 1) quand n tend vers l'infini ?","option_a":"A. 0","option_b":"B. 1\/2","option_c":"C. 1","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant le numérateur et le dénominateur par n², on obtient u_n = (1 + 3\/n)\/(2 - 1\/n²). La limite est donc 1\/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\": \"A. 0\", \"b\": \"B. 1\/2\", \"c\": \"C. 1\", \"d\": \"D. +∞\"}}","_debug_options_count":4},{"id":26559,"question":"Vrai ou Faux ? L'intégrale ∫(1\/x) dx entre 1 et e est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de 1\/x est ln(x). Entre 1 et e, cela donne ln(e) - ln(1) = 1 - 0 = 1. 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":26560,"question":"Quelle est la probabilité d'obtenir exactement 2 fois le chiffre 6 en lançant un dé 5 fois ?","option_a":"A. 0,1608","option_b":"B. 0,3216","option_c":"C. 0,0804","option_d":"D. 0,2001","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une loi binomiale B(5, 1\/6). P(X=2) = C(5,2)*(1\/6)²*(5\/6)³ ≈ 0,1608.","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. 0,1608\", \"b\": \"B. 0,3216\", \"c\": \"C. 0,0804\", \"d\": \"D. 0,2001\"}","_debug_options_count":4},{"id":26561,"question":"Vrai ou Faux ? Si une suite est croissante et majorée, alors elle converge.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est le théorème de convergence monotone : toute suite croissante et majorée converge vers sa borne supérieure.","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":26562,"question":"Quelle est la primitive de f(x) = e^(2x) ?","option_a":"A. (1\/2)e^(2x) + C","option_b":"B. e^(2x) + C","option_c":"C. 2e^(2x) + C","option_d":"D. e^x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La primitive de e^(kx) est (1\/k)e^(kx) + C. Ici, k=2, donc la primitive est (1\/2)e^(2x) + C.","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\/2)e^(2x) + C\", \"b\": \"B. e^(2x) + C\", \"c\": \"C. 2e^(2x) + C\",","_debug_options_count":4},{"id":26563,"question":"Vrai ou Faux ? La dérivée de e^x est e^x.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction exponentielle e^x a pour dérivée elle-même, donc la réponse est 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}]