Quiz Maths Terminale : Dérivées, Suites et Probabilités

Question 1 sur 10 10:00

[{"id":61897,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"6x - 5","option_b":"3x - 5","option_c":"6x² - 5","option_d":"3x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de 3x² est 6x, celle de -5x est -5, et celle de 2 est 0. Donc f'(x) = 6x - 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61898,"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":"Pour une suite géométrique, uₙ = u₀ × qⁿ. Ici, u₀ = 3 et q = 2, donc uₙ = 3 × 2ⁿ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61899,"question":"Vrai ou Faux ? La limite d'une suite croissante non majorée est toujours +∞.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une suite croissante non majorée diverge vers +∞, donc la limite est bien +∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61900,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré à 6 faces ?","option_a":"1\/2","option_b":"1\/3","option_c":"1\/6","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 faces possibles, donc la probabilité est 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61901,"question":"Vrai ou Faux ? Si f est dérivable en a, alors f est continue en a.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction dérivable en un point est nécessairement continue en ce point.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61902,"question":"Soit une variable aléatoire X suivant une loi binomiale B(n=5, p=0.4). Quelle est l'espérance de X ?","option_a":"2","option_b":"1.2","option_c":"2.5","option_d":"0.4","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour une loi binomiale B(n,p), l'espérance est E(X) = n × p = 5 × 0.4 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61903,"question":"Quelle est la limite de la fonction f(x) = (2x² - 3x + 1)\/(x - 1) quand x tend vers 1 ?","option_a":"0","option_b":"1","option_c":"2","option_d":"+∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"En factorisant le numérateur, on obtient f(x) = (2x - 1)(x - 1)\/(x - 1) = 2x - 1 pour x ≠ 1. Donc la limite est 2 × 1 - 1 = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61904,"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 de raison négative est décroissante, donc c'est vrai.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61905,"question":"Soit X une variable aléatoire suivant une loi uniforme sur [0, 1]. Quelle est P(X ≤ 0.5) ?","option_a":"0.25","option_b":"0.5","option_c":"0.75","option_d":"1","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour une loi uniforme sur [0, 1], P(X ≤ a) = a. Donc P(X ≤ 0.5) = 0.5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61906,"question":"Quelle est la dérivée de la fonction f(x) = ln(x² + 1) ?","option_a":"2x\/(x² + 1)","option_b":"1\/(x² + 1)","option_c":"2x","option_d":"x\/(x² + 1)","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant la dérivée de ln(u), on obtient f'(x) = (2x)\/(x² + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]