Maths Terminale : Testez vos connaissances en fonctions, suites et probabilités

Question 1 sur 10 10:00

[{"id":77062,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"6x - 5","option_b":"3x² - 5","option_c":"6x² - 5","option_d":"6x - 5x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : f'(x) = 6x - 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77063,"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, uₙ = 3 × 2ⁿ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77064,"question":"Soit A et B deux événements indépendants d'un univers Ω. Alors P(A ∩ B) = P(A) × P(B).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, deux événements sont indépendants si et seulement si P(A ∩ B) = P(A) × P(B).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77065,"question":"Quelle est la limite de la suite uₙ = (2n + 1)\/(n + 3) lorsque n tend vers l'infini ?","option_a":"0","option_b":"2","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant numérateur et dénominateur par n, on obtient uₙ = (2 + 1\/n)\/(1 + 3\/n), dont la limite est 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77066,"question":"Dans une classe de 30 élèves, 12 sont des filles. Quelle est la probabilité de choisir une fille au hasard ?","option_a":"0.4","option_b":"0.3","option_c":"0.6","option_d":"0.25","option_e":"","option_f":"","bonne_reponse":"A","explication":"La probabilité est le rapport du nombre de cas favorables sur le nombre total de cas : 12\/30 = 0.4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77067,"question":"La fonction exponentielle est toujours positive sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour tout réel x, eˣ \u003E 0. La fonction exponentielle est strictement positive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77068,"question":"Quelle est la solution de l'équation 2ˣ = 8 ?","option_a":"x = 2","option_b":"x = 3","option_c":"x = 4","option_d":"x = 1","option_e":"","option_f":"","bonne_reponse":"B","explication":"2ˣ = 8 équivaut à 2ˣ = 2³, donc x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77069,"question":"Soit f une fonction continue sur [a, b]. Alors f admet un maximum et un minimum sur cet intervalle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est le théorème des bornes atteintes : toute fonction continue sur un segment admet un maximum et un minimum.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77070,"question":"Quelle est la dérivée de la fonction g(x) = ln(x² + 1) ?","option_a":"g'(x) = 2x\/(x² + 1)","option_b":"g'(x) = 2x","option_c":"g'(x) = 1\/(x² + 1)","option_d":"g'(x) = x\/(x² + 1)","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant la dérivée d'une fonction composée : g'(x) = (2x)\/(x² + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77071,"question":"La probabilité de l'événement contraire de A est égale à 1 - P(A).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, P(A̅) = 1 - P(A), où A̅ est l'événement contraire de A.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]