Maths Terminale : Fonctions, Suites et Probabilités — Quiz d'entraînement

Question 1 sur 10 10:00

[{"id":60847,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 2x² + 5x - 1 ?","option_a":"3x² - 4x + 5","option_b":"x² - 2x + 5","option_c":"3x² - 4x + 1","option_d":"x³ - 4x + 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 : (x^n)' = n*x^(n-1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60848,"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 converge si et seulement si |q| \u003C 1. Ici, q = 2 \u003E 1, donc la suite diverge vers +∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60849,"question":"Soit X une variable aléatoire suivant une loi binomiale B(n=10, p=0.3). Quelle est la probabilité P(X=3) ?","option_a":"C(10,3) * 0.3³ * 0.7⁷","option_b":"C(10,3) * 0.3⁷ * 0.7³","option_c":"0.3³","option_d":"0.7⁷","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour une loi binomiale, P(X=k) = C(n,k) * p^k * (1-p)^(n-k). Ici, n=10, k=3, p=0.3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60850,"question":"La fonction f(x) = e^(2x) a pour dérivée f'(x) = 2e^(2x).","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)=2x, donc u'(x)=2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60851,"question":"Quelle est la limite de la suite uₙ = (3n + 1)\/(2n - 5) quand n tend vers +∞ ?","option_a":"0","option_b":"3\/2","option_c":"1","option_d":"+∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour une suite rationnelle, la limite est le rapport des coefficients dominants : 3\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60852,"question":"Si A et B sont deux événements indépendants avec P(A)=0.4 et P(B)=0.5, alors P(A∩B) = ?","option_a":"0.2","option_b":"0.9","option_c":"0.1","option_d":"0.5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour des événements indépendants, P(A∩B) = P(A) * P(B) = 0.4 * 0.5 = 0.2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60853,"question":"La fonction f(x) = ln(x) est définie pour tout x réel.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction ln(x) est définie uniquement pour x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60854,"question":"Quelle est la dérivée de la fonction f(x) = sin(3x) ?","option_a":"cos(3x)","option_b":"3cos(3x)","option_c":"sin(3x)","option_d":"-3sin(3x)","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de sin(u(x)) est u'(x)*cos(u(x)). Ici, u(x)=3x, donc u'(x)=3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60855,"question":"Une suite arithmétique de raison r = -2 et de premier terme u₀ = 5 est-elle 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 r est négative. Ici, r = -2 \u003C 0, donc la suite est décroissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60856,"question":"Soit X une variable aléatoire suivant une loi normale N(μ=5, σ=2). Quelle est la probabilité P(3 ≤ X ≤ 7) ?","option_a":"P(X ≤ 7) - P(X ≤ 3)","option_b":"P(X ≤ 5)","option_c":"P(X ≤ 3) + P(X ≤ 7)","option_d":"P(X ≤ 7) + P(X ≤ 3)","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour une loi normale, P(a ≤ X ≤ b) = P(X ≤ b) - P(X ≤ a).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]