Quiz : Maîtrisez les fonctions dérivées et les intégrales en Terminale

Question 1 sur 10 10:00

[{"id":59217,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x + 2","option_c":"6x² + 2","option_d":"3x² + 2x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : (3x²)' = 6x, (2x)' = 2, et (-5)' = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59218,"question":"L'intégrale de f(x) = 2x entre 0 et 3 est égale à :","option_a":"3","option_b":"6","option_c":"9","option_d":"12","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'intégrale de 2x est x². On calcule F(3) - F(0) = 9 - 0 = 9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59219,"question":"La probabilité d'obtenir exactement 2 succès en 5 essais pour une loi binomiale de paramètre p = 0.4 est :","option_a":"C(5,2) * (0.4)² * (0.6)³","option_b":"C(5,2) * (0.4)³ * (0.6)²","option_c":"(0.4)²","option_d":"(0.6)³","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour une loi binomiale B(n,p), P(k succès) = C(n,k) * p^k * (1-p)^(n-k).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59220,"question":"Vrai ou Faux ? La suite définie par uₙ = 3n + 2 est une suite géométrique.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite géométrique a un rapport constant entre deux termes consécutifs. Ici, uₙ₊₁\/uₙ = (3(n+1)+2)\/(3n+2) n'est pas constant.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59221,"question":"Quelle est la limite de la suite uₙ = (2n² + 3n) \/ (n² - 1) quand n tend vers l'infini ?","option_a":"0","option_b":"2","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"C","explication":"En divisant numérateur et dénominateur par n², on obtient (2 + 3\/n) \/ (1 - 1\/n²), dont la limite est 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59222,"question":"L'aire sous la courbe de f(x) = x² entre 0 et 2 est égale à :","option_a":"4\/3","option_b":"8\/3","option_c":"2","option_d":"4","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'intégrale de x² entre 0 et 2 est [x³\/3]₀² = 8\/3 - 0 = 8\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59223,"question":"Vrai ou Faux ? Si deux événements A et B sont indépendants, 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":"C'est la définition de l'indépendance de deux événements.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59224,"question":"Quelle est la dérivée de la fonction f(x) = e^(3x) ?","option_a":"e^(3x)","option_b":"3e^(3x)","option_c":"e^(x)","option_d":"3e^(x)","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de e^(u(x)) est u'(x) * e^(u(x)). Ici, u(x) = 3x, donc u'(x) = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59225,"question":"La suite uₙ = 5 - 2\/n est :","option_a":"Décroissante","option_b":"Croissante","option_c":"Constante","option_d":"Non monotone","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour n ≥ 1, uₙ₊₁ - uₙ = (5 - 2\/(n+1)) - (5 - 2\/n) = 2\/n - 2\/(n+1) \u003E 0. La suite est donc croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59226,"question":"Vrai ou Faux ? L'intégrale de f(x) = 1\/x entre 1 et e est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de 1\/x est ln(x). On calcule ln(e) - ln(1) = 1 - 0 = 1. L'affirmation est donc vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]