Quiz : Maîtrisez les fonctions dérivées et les intégrales en Terminale

Question 1 sur 10 10:00

[{"id":64862,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x - 5","option_d":"2x + 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme à terme : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64863,"question":"L'intégrale de f(x) = 2x entre 0 et 3 est égale à :","option_a":"9","option_b":"6","option_c":"3","option_d":"12","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de 2x est x², donc F(3) - F(0) = 9 - 0 = 9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64864,"question":"Si X suit une loi normale N(0,1), alors P(-1 ≤ X ≤ 1) est environ égal à :","option_a":"0,68","option_b":"0,95","option_c":"0,34","option_d":"0,99","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour une loi normale centrée réduite, environ 68% des valeurs sont dans l'intervalle [-1,1].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64865,"question":"Une suite géométrique de raison q = 2 et de premier terme u₀ = 3 est croissante.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une suite géométrique de raison q \u003E 1 est croissante si u₀ \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64866,"question":"Quelle est la primitive de f(x) = eˣ + 2x ?","option_a":"eˣ + x² + C","option_b":"eˣ + x + C","option_c":"eˣ + 2x² + C","option_d":"eˣ + x²","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de eˣ est eˣ, et celle de 2x est x² + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64867,"question":"Si une variable aléatoire X suit une loi uniforme sur [0,10], alors E(X) = 5.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour une loi uniforme sur [a,b], l'espérance est (a+b)\/2, donc (0+10)\/2 = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64868,"question":"La dérivée de f(x) = ln(x) est :","option_a":"1\/x","option_b":"x","option_c":"1","option_d":"eˣ","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de ln(x) est 1\/x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64869,"question":"Une suite arithmétique de raison r = -2 et de premier terme u₀ = 5 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 r \u003C 0 est décroissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64870,"question":"Quelle est l'intégrale de f(x) = sin(x) entre 0 et π ?","option_a":"0","option_b":"1","option_c":"2","option_d":"-1","option_e":"","option_f":"","bonne_reponse":"C","explication":"L'intégrale de sin(x) est -cos(x), donc F(π) - F(0) = -(-1) - (-1) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64871,"question":"Si P(A) = 0,3 et P(B) = 0,4 avec A et B indépendants, alors P(A ∩ B) = 0,12.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour des événements indépendants, P(A ∩ B) = P(A) × P(B) = 0,3 × 0,4 = 0,12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]