Quiz de révision : Mathématiques Terminale — Fonctions et Équations

Question 1 sur 10 10:00

[{"id":13283,"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":"x² + 2x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de 3x² est 6x, celle de 2x est 2, et la dérivée de -5 est 0. Ainsi, f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13284,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle [-2, 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction est décroissante sur [-1, 1] car sa dérivée f'(x) = 3x² - 3 est négative dans cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13285,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 et x = 2","option_b":"x = 0.5 et x = 2","option_c":"x = -1 et x = 2","option_d":"x = 1 et x = -2","option_e":"","option_f":"","bonne_reponse":"B","explication":"En résolvant l'équation, on trouve les racines x = 0.5 et x = 2 (utilisation du discriminant Δ = 9).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13286,"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. Évaluée entre 0 et 3, on obtient 3² - 0² = 9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13287,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est de 0.5.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un dé a 3 nombres pairs (2, 4, 6) sur 6 faces, donc la probabilité est 3\/6 = 0.5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13288,"question":"Quelle est la limite de la fonction f(x) = (x² - 1)\/(x - 1) quand x tend vers 1 ?","option_a":"0","option_b":"1","option_c":"2","option_d":"Indéterminée","option_e":"","option_f":"","bonne_reponse":"B","explication":"En factorisant, on obtient f(x) = (x - 1)(x + 1)\/(x - 1) = x + 1 pour x ≠ 1. Ainsi, la limite est 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13289,"question":"Un événement certain a une probabilité égale à :","option_a":"0","option_b":"0.5","option_c":"1","option_d":"100","option_e":"","option_f":"","bonne_reponse":"C","explication":"Un événement certain a une probabilité de 1 (ou 100%).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13290,"question":"La fonction f(x) = e^x est toujours positive sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction exponentielle e^x est toujours strictement positive pour tout x réel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13291,"question":"Quelle est la valeur de l'intégrale ∫(3x² + 2x) dx entre 0 et 1 ?","option_a":"1","option_b":"2","option_c":"3","option_d":"4","option_e":"","option_f":"","bonne_reponse":"C","explication":"L'intégrale de 3x² est x³ et celle de 2x est x². Évaluée entre 0 et 1, on obtient 1 + 1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":13292,"question":"La dérivée de la fonction f(x) = ln(x) est :","option_a":"1\/x","option_b":"x","option_c":"e^x","option_d":"1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de ln(x) est 1\/x pour x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]