Quiz — serie8-3-20.pdf

Question 1 sur 5 10:00

[{"id":128,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation x² - 5x + 6 = 0 se factorise en (x-2)(x-3) = 0. Les solutions sont donc x = 2 et x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":129,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"f'(x) = 6x + 2","option_b":"f'(x) = 3x + 2","option_c":"f'(x) = 6x² + 2","option_d":"f'(x) = 3x² + 2x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme à terme. La dérivée de 3x² est 6x, celle de 2x est 2, et celle de -5 est 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":130,"question":"Dans un repère orthonormé, quelle est l'équation de la droite passant par les points A(1;2) et B(3;4) ?","option_a":"y = x + 1","option_b":"y = 2x - 1","option_c":"y = x - 1","option_d":"y = 2x + 1","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le coefficient directeur est (4-2)\/(3-1) = 1. En utilisant le point A, on obtient 2 = 1*1 + b ⇒ b = 1. L'équation est donc y = x + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":131,"question":"Soit une variable aléatoire X suivant une loi binomiale B(10; 0,3). Quelle est son espérance mathématique E(X) ?","option_a":"E(X) = 3","option_b":"E(X) = 0,3","option_c":"E(X) = 10","option_d":"E(X) = 7","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour une loi binomiale B(n,p), l'espérance est E(X) = n*p. Ici, n=10 et p=0,3, donc E(X) = 10*0,3 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":132,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"Limite = 2","option_b":"Limite = 0","option_c":"Limite = 1","option_d":"Limite = -∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour les fonctions rationnelles, la limite à l'infini est le rapport des coefficients dominants. Ici, 2x²\/x² = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]