Quiz : Maîtrisez les fondamentaux des maths en Terminale !

Question 1 sur 10 10:00

[{"id":21848,"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":"3x² + 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle de dérivation terme par terme : f'(x) = 6x + 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21849,"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 de raison |q| \u003E 1 est divergente. Ici, q = 2 \u003E 1, donc la suite diverge.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21850,"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":"2\/3","option_d":"1\/6","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":21851,"question":"L'équation différentielle y' + 2y = 0 a pour solution générale :","option_a":"y = Ce^(-2x)","option_b":"y = Ce^(2x)","option_c":"y = Cx + C","option_d":"y = C\/x","option_e":"","option_f":"","bonne_reponse":"A","explication":"Cette équation est de la forme y' + ay = 0, dont la solution générale est y = Ce^(-ax). Ici, a = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21852,"question":"La fonction f(x) = x³ - 3x² + 4 admet-elle un extremum local en x = 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En calculant f'(x) = 3x² - 6x, on trouve f'(1) = -3 ≠ 0. Cependant, en étudiant les variations, on observe un extremum local en x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21853,"question":"Quelle est la limite de la suite uₙ = (2n + 1)\/(n + 3) quand n tend vers l'infini ?","option_a":"0","option_b":"1","option_c":"2","option_d":"3","option_e":"","option_f":"","bonne_reponse":"D","explication":"En divisant numérateur et dénominateur par n, on obtient uₙ = (2 + 1\/n)\/(1 + 3\/n). Quand n → ∞, uₙ → 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21854,"question":"La probabilité conditionnelle P(A|B) est toujours égale à P(A) × P(B).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"P(A|B) = P(A ∩ B)\/P(B). L'égalité P(A|B) = P(A) × P(B) n'est vraie que si A et B sont indépendants.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21855,"question":"Résoudre l'équation différentielle y'' + 4y = 0 :","option_a":"y = C₁cos(2x) + C₂sin(2x)","option_b":"y = C₁e^(2x) + C₂e^(-2x)","option_c":"y = Cx + C","option_d":"y = C\/x","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation caractéristique est r² + 4 = 0, dont les solutions sont r = ±2i. La solution générale est donc y = C₁cos(2x) + C₂sin(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21856,"question":"Quelle est la dérivée seconde de la fonction f(x) = e^(3x) ?","option_a":"9e^(3x)","option_b":"3e^(3x)","option_c":"e^(3x)","option_d":"0","option_e":"","option_f":"","bonne_reponse":"A","explication":"f'(x) = 3e^(3x) et f''(x) = 9e^(3x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21857,"question":"La suite uₙ = (-1)^n est-elle bornée ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour tout n, |uₙ| = 1, donc la suite est bornée par -1 et 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]