Quiz : Maîtrisez les fonctions et dérivées en Terminale Math

Question 1 sur 10 10:00

[{"id":62772,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"2x + 3","option_b":"x² + 3","option_c":"2x + 5","option_d":"x + 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x² est 2x, celle de 3x est 3, et la dérivée d'une constante est 0. Donc f'(x) = 2x + 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62773,"question":"La fonction f(x) = 1\/x est définie pour x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction f(x) = 1\/x n'est pas définie en x = 0 car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62774,"question":"Quelle est la limite de la fonction f(x) = (x² - 4)\/(x - 2) lorsque x tend vers 2 ?","option_a":"0","option_b":"4","option_c":"2","option_d":"indéterminée","option_e":"","option_f":"","bonne_reponse":"C","explication":"En factorisant, on obtient f(x) = (x-2)(x+2)\/(x-2) = x+2 pour x ≠ 2. Donc la limite est 2+2 = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62775,"question":"Une fonction dérivable est toujours continue.","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 continue en ce point, c'est un théorème fondamental du calcul différentiel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62776,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 0.5 ou x = 2","option_c":"x = -1 ou x = -2","option_d":"x = 1 ou x = -2","option_e":"","option_f":"","bonne_reponse":"B","explication":"En utilisant le discriminant Δ = 25 - 16 = 9, les solutions sont x = (5 ± 3)\/4, soit x = 2 ou x = 0.5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62777,"question":"La fonction f(x) = e^x est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction exponentielle e^x est strictement positive pour tout x réel, car e^x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62778,"question":"Quelle est la dérivée de la fonction f(x) = ln(x) ?","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 la fonction logarithme népérien ln(x) est 1\/x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62779,"question":"Une suite croissante est toujours convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite croissante peut diverger vers l'infini (exemple : u_n = n). Elle n'est convergente que si elle est majorée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62780,"question":"Quelle est la primitive de la fonction f(x) = 3x² ?","option_a":"x³ + C","option_b":"6x + C","option_c":"x² + C","option_d":"3x³ + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de 3x² est x³ + C, car la dérivée de x³ est 3x².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62781,"question":"La fonction f(x) = sin(x) est périodique de période 2π.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction sinus est périodique de période 2π, car sin(x + 2π) = sin(x) pour tout x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]