Quiz : Fonctions dérivées, suites et équations différentielles — Terminale Math

Question 1 sur 10 10:00

[{"id":74432,"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":74433,"question":"Une suite géométrique de raison q = 2 et de premier terme u₀ = 3 est-elle 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 et de premier terme positif est croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74434,"question":"Quelle est la solution générale de l'équation différentielle y' = 2y ?","option_a":"y = Ce^(2x)","option_b":"y = 2x + C","option_c":"y = Cx²","option_d":"y = C\/2","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation différentielle y' = ky a pour solution y = Ce^(kx). Ici, k = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74435,"question":"Si une fonction f est dérivable en a, alors f est continue en a. Vrai ou faux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Toute fonction dérivable en un point est nécessairement continue en ce point.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74436,"question":"Quelle est la limite de la suite uₙ = (2n + 1)\/(n + 3) quand n tend vers l'infini ?","option_a":"0","option_b":"2","option_c":"1\/3","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant numérateur et dénominateur par n, on obtient lim(uₙ) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74437,"question":"La fonction f(x) = x³ - 3x² + 2 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":"f'(x) = 3x² - 6x. f'(1) = -3 ≠ 0, donc pas d'extremum en x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74438,"question":"Quelle est la solution particulière de l'équation différentielle y' + y = x avec y(0) = 1 ?","option_a":"y = x - 1 + 2e^(-x)","option_b":"y = x + 1","option_c":"y = 2e^(-x)","option_d":"y = x - e^(-x)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La solution générale est y = Ce^(-x) + x - 1. Avec y(0) = 1, on trouve C = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74439,"question":"Si une suite est bornée et monotone, alors elle est convergente. Vrai ou faux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est le théorème de convergence monotone : une suite bornée et monotone converge toujours.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74440,"question":"Quelle est la dérivée de la fonction f(x) = ln(2x + 1) ?","option_a":"1\/(2x + 1)","option_b":"2\/(2x + 1)","option_c":"2x\/(2x + 1)","option_d":"1\/(x + 1)","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de ln(u) est u'\/u. Ici, u = 2x + 1, donc u' = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74441,"question":"La suite uₙ = (-1)^n est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La suite alterne entre -1 et 1, elle n'a pas de limite finie : elle est divergente.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]