Quiz — 657898ef97146_corrigé_Série 21.pdf

Question 1 sur 10 20:00

[{"id":2837,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"6x + 5","option_c":"3x + 2","option_d":"5x + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme est obtenue en appliquant la règle de dérivation : f'(x) = 6x + 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\": \"6x + 5\", \"c\": \"3x + 2\", \"d\": \"5x + 2\"}}","_debug_options_count":4},{"id":2838,"question":"Une suite géométrique de raison q = 2 et de premier terme u₀ = 3 a pour terme général :","option_a":"uₙ = 3 * 2ⁿ","option_b":"uₙ = 3 + 2ⁿ","option_c":"uₙ = 2 * 3ⁿ","option_d":"uₙ = 3 * n²","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le terme général d'une suite géométrique est donné par uₙ = u₀ * qⁿ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"uₙ = 3 * 2ⁿ\", \"b\": \"uₙ = 3 + 2ⁿ\", \"c\": \"uₙ = 2 * 3ⁿ\",","_debug_options_count":4},{"id":2839,"question":"La limite de la fonction f(x) = (2x² + 3x - 1)\/(x² + 1) lorsque x tend vers +∞ est :","option_a":"0","option_b":"1","option_c":"2","option_d":"+∞","option_e":"","option_f":"","bonne_reponse":"c","explication":"En divisant numérateur et dénominateur par x², on obtient f(x) = (2 + 3\/x - 1\/x²)\/(1 + 1\/x²), donc la limite est 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\": \"1\", \"c\": \"2\", \"d\": \"+∞\"}}","_debug_options_count":4},{"id":2840,"question":"Vrai ou Faux : Une suite croissante est toujours convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite croissante peut diverger vers +∞ (exemple : uₙ = n).","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":2841,"question":"L'espérance d'une variable aléatoire suivant une loi binomiale B(n=5, p=0.3) est :","option_a":"1.5","option_b":"2.5","option_c":"3.5","option_d":"5","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'espérance d'une loi binomiale est E(X) = n * p = 5 * 0.3 = 1.5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"1.5\", \"b\": \"2.5\", \"c\": \"3.5\", \"d\": \"5\"}}","_debug_options_count":4},{"id":2842,"question":"Vrai ou Faux : La fonction f(x) = e^(3x) a pour dérivée f'(x) = 3e^(3x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de e^(u(x)) est u'(x) * e^(u(x)), ici u(x) = 3x donc u'(x) = 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":2843,"question":"Le produit scalaire de deux vecteurs orthogonaux est toujours égal à :","option_a":"0","option_b":"1","option_c":"la norme d'un vecteur","option_d":"impossible à déterminer","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, deux vecteurs orthogonaux ont un produit scalaire nul.","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\": \"1\", \"c\": \"la norme d'un vecteur\", \"d\": \"impossible à d","_debug_options_count":4},{"id":2844,"question":"Vrai ou Faux : Une suite arithmétique de raison r = -2 est décroissante.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite arithmétique est décroissante si sa raison est négative (ici r = -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":2845,"question":"L'équation de la tangente à la courbe de f(x) = x³ - 2x² + 1 au point d'abscisse x = 1 est :","option_a":"y = x - 1","option_b":"y = -x + 1","option_c":"y = 2x - 1","option_d":"y = x + 1","option_e":"","option_f":"","bonne_reponse":"c","explication":"La tangente a pour équation y = f'(1)(x - 1) + f(1). f'(x) = 3x² - 4x, donc f'(1) = -1 et f(1) = 0. Ainsi, y = -1(x - 1) + 0 = -x + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"y = x - 1\", \"b\": \"y = -x + 1\", \"c\": \"y = 2x - 1\", \"d\": \"y = x + 1","_debug_options_count":4},{"id":2846,"question":"La probabilité d'obtenir exactement 2 fois le chiffre 6 en lançant un dé équilibré 5 fois est :","option_a":"0.1608","option_b":"0.3216","option_c":"0.4096","option_d":"0.5","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\": \"0.1608\", \"b\": \"0.3216\", \"c\": \"0.4096\", \"d\": \"0.5\"}}","_debug_options_count":4}]