Quiz : Maîtrisez les fonctions de référence en Terminale Maths

Question 1 sur 10 10:00

[{"id":55131,"question":"Quelle est la forme générale d'une fonction affine ?","option_a":"f(x) = ax + b","option_b":"f(x) = ax² + bx + c","option_c":"f(x) = a^x","option_d":"f(x) = ln(x)","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction affine s'écrit sous la forme f(x) = ax + b, où a et b sont des réels.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55132,"question":"La fonction exponentielle est-elle toujours croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction exponentielle est strictement croissante sur ℝ car sa dérivée est toujours positive (e^x \u003E 0).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55133,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"f'(x) = 6x + 2","option_b":"f'(x) = 3x + 2","option_c":"f'(x) = 6x - 5","option_d":"f'(x) = 3x² + 2x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55134,"question":"La fonction logarithme népérien est-elle définie pour x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction logarithme népérien n'est pas définie en x = 0 car ln(0) n'existe pas (limite tend vers -∞).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55135,"question":"Quelle est l'image de 2 par la fonction f(x) = e^(3x) ?","option_a":"e^6","option_b":"e^3","option_c":"6e","option_d":"3e","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour x = 2, f(2) = e^(3*2) = e^6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55136,"question":"La fonction carrée est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction est paire si f(-x) = f(x). Pour la fonction carrée, (-x)² = x², donc elle est paire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55137,"question":"Résolvez l'équation ln(x) = 2. Quelle est la solution ?","option_a":"x = e²","option_b":"x = 2","option_c":"x = 100","option_d":"x = ln(2)","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation ln(x) = 2 équivaut à x = e² par définition de la fonction logarithme.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55138,"question":"La fonction f(x) = 1\/x est-elle définie en 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":55139,"question":"Quelle est la limite de la fonction f(x) = (x² - 1)\/(x - 1) lorsque x tend vers 1 ?","option_a":"0","option_b":"1","option_c":"2","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"C","explication":"En factorisant le numérateur, f(x) = (x - 1)(x + 1)\/(x - 1) = x + 1 pour x ≠ 1. La limite lorsque x tend vers 1 est donc 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55140,"question":"La fonction exponentielle est-elle la réciproque de la fonction logarithme népérien ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Oui, les fonctions exponentielle et logarithme népérien sont réciproques l'une de l'autre : e^ln(x) = x et ln(e^x) = x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]