Quiz — 65df66376f985_Enoncé-Révision DS2.pdf

Question 1 sur 10 20:00

[{"id":27180,"question":"Quelle est la solution de l'équation du second degré 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 x² - 5x + 6 = 0 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":27181,"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 ≈ 0,42 et x ≈ 1,58. La fonction n'est donc pas croissante sur tout l'intervalle [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":27182,"question":"Quelle est la limite de la suite (uₙ) définie par uₙ = (2n + 1)\/(n + 3) quand n tend vers l'infini ?","option_a":"2","option_b":"1\/3","option_c":"0","option_d":"3","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant numérateur et dénominateur par n, on obtient uₙ = (2 + 1\/n)\/(1 + 3\/n), donc la limite est 2\/1 = 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\": \"2\", \"b\": \"1\/3\", \"c\": \"0\", \"d\": \"3\"}}","_debug_options_count":4},{"id":27183,"question":"L'équation de la droite passant par les points A(1, 2) et B(3, 4) est :","option_a":"y = x + 1","option_b":"y = 2x - 1","option_c":"y = x","option_d":"y = -x + 3","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le coefficient directeur est (4-2)\/(3-1) = 1, donc l'équation est y = x + b. En remplaçant par A(1,2), on trouve b = 1, soit y = x + 1. Cependant, avec B(3,4), on vérifie y = 2x - 2. L'équation correcte est y = x + 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\": \"y = x + 1\", \"b\": \"y = 2x - 1\", \"c\": \"y = x\", \"d\": \"y = -x + 3\"}}","_debug_options_count":4},{"id":27184,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est :","option_a":"1\/6","option_b":"1\/3","option_c":"1\/2","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"c","explication":"Un dé a 6 faces, dont 3 sont paires (2, 4, 6). La probabilité est donc 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":27185,"question":"La suite (uₙ) définie par uₙ = (-1)ⁿ est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La suite alterne entre -1 et 1 et n'a pas de limite finie, donc elle est divergente.","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":27186,"question":"Quelle est l'équation réduite de la droite d'équation cartésienne 2x - 3y + 6 = 0 ?","option_a":"y = (2\/3)x + 2","option_b":"y = (2\/3)x - 2","option_c":"y = (-2\/3)x + 2","option_d":"y = (3\/2)x + 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"En isolant y, on obtient 3y = 2x + 6, soit y = (2\/3)x + 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\": \"y = (2\/3)x + 2\", \"b\": \"y = (2\/3)x - 2\", \"c\": \"y = (-2\/3)x + 2\", \"","_debug_options_count":4},{"id":27187,"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":27188,"question":"Quelle est la valeur de la somme S = 1 + 2 + 3 + ... + 100 ?","option_a":"5050","option_b":"10100","option_c":"2525","option_d":"10000","option_e":"","option_f":"","bonne_reponse":"a","explication":"La somme des n premiers entiers est donnée par la formule S = n(n+1)\/2. Pour n=100, S = 100*101\/2 = 5050.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"5050\", \"b\": \"10100\", \"c\": \"2525\", \"d\": \"10000\"}}","_debug_options_count":4},{"id":27189,"question":"L'aire d'un triangle de base b et de hauteur h est donnée par la formule :","option_a":"A = b * h","option_b":"A = (b * h)\/2","option_c":"A = b + h","option_d":"A = sqrt(b² + h²)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La formule de l'aire d'un triangle est A = (base * hauteur)\/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\": \"A = b * h\", \"b\": \"A = (b * h)\/2\", \"c\": \"A = b + h\", \"d\": \"A = sqr","_debug_options_count":4}]