Quiz — devoir de controle 3-3.pdf

Question 1 sur 10 20:00

[{"id":18899,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation se factorise en (x-2)(x-3)=0, donc les solutions sont x=2 et x=3.","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 = 2 ou x = 3\", \"b\": \"x = -2 ou x = -3\", \"c\": \"x = 1 ou x = 6\", ","_debug_options_count":4},{"id":18900,"question":"La fonction f(x) = x² - 4x + 3 est-elle croissante sur l'intervalle [2 ; +∞[ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 2x - 4 est positive pour x ≥ 2, donc la fonction est croissante sur cet intervalle.","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":18901,"question":"Quel est le coefficient directeur de la droite d'équation 3x - 2y + 5 = 0 ?","option_a":"3","option_b":"-2","option_c":"3\/2","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"c","explication":"En isolant y, on obtient y = (3\/2)x + 5\/2, donc le coefficient directeur est 3\/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\": \"3\", \"b\": \"-2\", \"c\": \"3\/2\", \"d\": \"2\/3\"}}","_debug_options_count":4},{"id":18902,"question":"Si A(1 ; 2) et B(4 ; 6), quelle est la distance AB ?","option_a":"5","option_b":"√7","option_c":"√13","option_d":"√25","option_e":"","option_f":"","bonne_reponse":"a","explication":"La distance AB = √[(4-1)² + (6-2)²] = √(9 + 16) = √25 = 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\": \"5\", \"b\": \"√7\", \"c\": \"√13\", \"d\": \"√25\"}}","_debug_options_count":4},{"id":18903,"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":18904,"question":"Quelle est la dérivée de la fonction f(x) = 3x³ - 2x² + x - 1 ?","option_a":"9x² - 4x + 1","option_b":"6x² - 4x + 1","option_c":"3x² - 2x + 1","option_d":"9x² - 4x - 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"En appliquant les règles de dérivation, f'(x) = 9x² - 4x + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"9x² - 4x + 1\", \"b\": \"6x² - 4x + 1\", \"c\": \"3x² - 2x + 1\", \"d\": ","_debug_options_count":4},{"id":18905,"question":"Dans un triangle ABC, si AB = 5, AC = 12 et BC = 13, le triangle est-il rectangle ?","option_a":"Oui, en A","option_b":"Non","option_c":"Oui, en B","option_d":"Oui, en C","option_e":"","option_f":"","bonne_reponse":"a","explication":"On vérifie que 5² + 12² = 13² (25 + 144 = 169), donc le triangle est rectangle en A.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Oui, en A\", \"b\": \"Non\", \"c\": \"Oui, en B\", \"d\": \"Oui, en C\"}}","_debug_options_count":4},{"id":18906,"question":"La probabilité d'un événement impossible est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité d'un événement impossible est égale à 0, tandis que celle d'un événement certain est 1.","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":18907,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 5 ?","option_a":"x \u003E 4","option_b":"x \u003C 4","option_c":"x \u003E 1","option_d":"x \u003C 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"En résolvant l'inéquation, on obtient 2x \u003E 8, donc 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 \u003C 4\", \"c\": \"x \u003E 1\", \"d\": \"x \u003C 1\"}}","_debug_options_count":4},{"id":18908,"question":"Quel est le centre de symétrie de la fonction f(x) = x³ - 3x ?","option_a":"(0 ; 0)","option_b":"(1 ; -2)","option_c":"(-1 ; 2)","option_d":"Le centre n'existe pas","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction f(x) = x³ - 3x est impaire, donc son centre de symétrie est l'origine (0 ; 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\": \"(0 ; 0)\", \"b\": \"(1 ; -2)\", \"c\": \"(-1 ; 2)\", \"d\": \"Le centre n'exi","_debug_options_count":4}]