Quiz — ~$الدوال المرجعية -1-(تمارين).docx

Question 1 sur 10 20:00

[{"id":54277,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"f(x) = ax + b\", \"b\": \"f(x) = ax² + bx + c\", \"c\": \"f(x) = a^x\", \"","_debug_options_count":4},{"id":54278,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":54279,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"f'(x) = 6x + 2\", \"b\": \"f'(x) = 3x + 2\", \"c\": \"f'(x) = 6x - 5\", \"d","_debug_options_count":4},{"id":54280,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":54281,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"e^6\", \"b\": \"e^3\", \"c\": \"6e\", \"d\": \"3e\"}}","_debug_options_count":4},{"id":54282,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":54283,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x = e²\", \"b\": \"x = 2\", \"c\": \"x = 100\", \"d\": \"x = ln(2)\"}}","_debug_options_count":4},{"id":54284,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":54285,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"2\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":54286,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]