Quiz — serie4 (Ammar).pdf

Question 1 sur 5 10:00

[{"id":1784,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"A. 6x - 5","option_b":"B. 3x - 5","option_c":"C. 6x² - 5","option_d":"D. 3x² - 5x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle : (ax^n)' = n*ax^(n-1). Ici, f'(x) = 6x - 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. 6x - 5\", \"b\": \"B. 3x - 5\", \"c\": \"C. 6x² - 5\", \"d\": \"D. 3x² -","_debug_options_count":4},{"id":1785,"question":"Résolvez l'inéquation : 2x - 5 \u003E 3x + 1.","option_a":"A. x \u003C -6","option_b":"B. x \u003E -6","option_c":"C. x \u003C 6","option_d":"D. x \u003E 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"En simplifiant, on obtient : -x \u003E 6, soit x \u003C -6 (en divisant par un nombre négatif, le sens de l'inégalité change).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. x \u003C -6\", \"b\": \"B. x \u003E -6\", \"c\": \"C. x \u003C 6\", \"d\": \"D. x \u003E 6\"}}","_debug_options_count":4},{"id":1786,"question":"Quelle est la limite de la fonction f(x) = (x² - 4)\/(x - 2) lorsque x tend vers 2 ?","option_a":"A. 0","option_b":"B. 4","option_c":"C. Indéterminée","option_d":"D. 2","option_e":"","option_f":"","bonne_reponse":"c","explication":"La fonction est indéterminée en x=2 (forme 0\/0). En factorisant, on obtient f(x) = (x+2)(x-2)\/(x-2) = x+2 pour x≠2, donc la limite est 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A. 0\", \"b\": \"B. 4\", \"c\": \"C. Indéterminée\", \"d\": \"D. 2\"}}","_debug_options_count":4},{"id":1787,"question":"Calculez l'intégrale ∫(2x + 1) dx entre 0 et 2.","option_a":"A. 4","option_b":"B. 6","option_c":"C. 8","option_d":"D. 10","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'intégrale de 2x + 1 est x² + x. En évaluant entre 0 et 2, on obtient (4 + 2) - (0 + 0) = 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. 4\", \"b\": \"B. 6\", \"c\": \"C. 8\", \"d\": \"D. 10\"}}","_debug_options_count":4},{"id":1788,"question":"Dans un triangle ABC rectangle en A, si AB = 3 et AC = 4, quelle est la longueur de BC ?","option_a":"A. 5","option_b":"B. 7","option_c":"C. √7","option_d":"D. 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après le théorème de Pythagore, BC² = AB² + AC² = 9 + 16 = 25, donc BC = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. 5\", \"b\": \"B. 7\", \"c\": \"C. √7\", \"d\": \"D. 6\"}}","_debug_options_count":4}]