Quiz — serie 8(corrigé).pdf

Question 1 sur 10 20:00

[{"id":21459,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x² + 2x","option_d":"6x + 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\": \"6x + 2\", \"b\": \"3x² + 2\", \"c\": \"6x² + 2x\", \"d\": \"6x + 2x\"}}","_debug_options_count":4},{"id":21460,"question":"L'équation x² - 4x + 4 = 0 admet-elle deux solutions réelles distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le discriminant Δ = b² - 4ac = 0, donc l'équation admet une solution double (x = 2).","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":21461,"question":"Quelle est l'intégrale de la fonction f(x) = 2x + 1 entre 0 et 2 ?","option_a":"6","option_b":"4","option_c":"5","option_d":"8","option_e":"","option_f":"","bonne_reponse":"c","explication":"∫(2x + 1)dx = x² + x, évaluée entre 0 et 2 donne (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\": \"c\", \"options\": {\"a\": \"6\", \"b\": \"4\", \"c\": \"5\", \"d\": \"8\"}}","_debug_options_count":4},{"id":21462,"question":"Le vecteur u(2, -3) et le vecteur v(-1, 4) sont-ils orthogonaux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Deux vecteurs sont orthogonaux si leur produit scalaire est nul : u·v = (2)(-1) + (-3)(4) = -2 -12 = -14 ≠ 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":21463,"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":"∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"En factorisant, f(x) = (x-1)(x+1)\/(x-1) = x+1 pour x ≠ 1, donc la limite est 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"2\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":21464,"question":"La fonction f(x) = x³ - 3x² + 2x est-elle croissante sur l'intervalle [0, 2] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = 3x² - 6x + 2 s'annule en x=1, et f'(0.5) \u003E 0, f'(1.5) \u003C 0 : la fonction n'est pas croissante sur [0, 2].","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":21465,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré ?","option_a":"1\/6","option_b":"1\/3","option_c":"1\/2","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"c","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 faces possibles, donc P = 3\/6 = 1\/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\": \"1\/6\", \"b\": \"1\/3\", \"c\": \"1\/2\", \"d\": \"2\/3\"}}","_debug_options_count":4},{"id":21466,"question":"L'équation 2^x = 8 admet-elle une solution réelle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"2^x = 8 ⇒ x = 3, donc l'équation admet une solution réelle.","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":21467,"question":"Quelle est la solution de l'inéquation 3x - 5 \u003E 7 ?","option_a":"x \u003E 4","option_b":"x \u003E 12","option_c":"x \u003C 4","option_d":"x \u003C 12","option_e":"","option_f":"","bonne_reponse":"a","explication":"3x - 5 \u003E 7 ⇒ 3x \u003E 12 ⇒ x \u003E 4.","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 \u003E 4\", \"b\": \"x \u003E 12\", \"c\": \"x \u003C 4\", \"d\": \"x \u003C 12\"}}","_debug_options_count":4},{"id":21468,"question":"La fonction f(x) = 1\/x est-elle continue sur ℝ* ?","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, donc elle n'est pas continue sur ℝ*.","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}]