Quiz — corr syn 2 4M 09010.pdf

Question 1 sur 10 20:00

[{"id":37950,"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 x² - 5x + 6 = 0 se factorise en (x-2)(x-3) = 0. Les solutions sont donc 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":37951,"question":"La suite (un) définie par un = n² est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La suite un = n² tend vers l'infini lorsque n tend vers l'infini, donc elle n'est pas convergente.","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":37952,"question":"Quelle est la dérivée de la fonction f(x) = 3x³ - 2x² + 5x - 1 ?","option_a":"f'(x) = 9x² - 4x + 5","option_b":"f'(x) = 6x² - 4x + 5","option_c":"f'(x) = 9x² - 4x - 1","option_d":"f'(x) = 3x² - 2x + 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de f(x) = 3x³ - 2x² + 5x - 1 est f'(x) = 9x² - 4x + 5 (en appliquant la règle de dérivation des polynômes).","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) = 9x² - 4x + 5\", \"b\": \"f'(x) = 6x² - 4x + 5\", \"c\": \"f'(x)","_debug_options_count":4},{"id":37953,"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","option_c":"y = x","option_d":"y = -x + 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le coefficient directeur est (4-2)\/(3-1) = 1. L'équation est donc y = x + 1 (en utilisant le point A pour déterminer l'ordonnée à l'origine).","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 = x + 1\", \"b\": \"y = 2x\", \"c\": \"y = x\", \"d\": \"y = -x + 3\"}}","_debug_options_count":4},{"id":37954,"question":"La fonction f(x) = 1\/x est-elle dérivable 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, donc elle n'est pas dérivable en ce point.","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":37955,"question":"Quelle est la limite de la suite (un) définie par un = (2n + 1)\/(n + 3) lorsque n tend vers l'infini ?","option_a":"2","option_b":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant le numérateur et le dénominateur par n, on obtient un = (2 + 1\/n)\/(1 + 3\/n). Lorsque n tend vers l'infini, 1\/n tend vers 0, 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\", \"c\": \"0\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":37956,"question":"L'aire sous la courbe de f(x) = x² entre x = 0 et x = 2 est :","option_a":"8\/3","option_b":"4","option_c":"2","option_d":"16\/3","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'aire est donnée par l'intégrale ∫₀² x² dx = [x³\/3]₀² = 8\/3 - 0 = 8\/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\": \"8\/3\", \"b\": \"4\", \"c\": \"2\", \"d\": \"16\/3\"}}","_debug_options_count":4},{"id":37957,"question":"La fonction f(x) = x³ - 3x est-elle croissante sur l'intervalle [-2, 2] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = 3x² - 3 s'annule en x = ±1. La fonction est décroissante sur [-1, 1], donc elle n'est pas croissante sur [-2, 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":37958,"question":"Quelle est la solution de l'inéquation x² - 4x + 3 \u003E 0 ?","option_a":"x ∈ ]-∞, 1[ ∪ ]3, +∞[","option_b":"x ∈ ]1, 3[","option_c":"x ∈ ]-∞, 3[","option_d":"x ∈ ]0, 4[","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'inéquation x² - 4x + 3 \u003E 0 se résout en étudiant le signe du polynôme. Les racines sont x = 1 et x = 3. Le polynôme est positif à l'extérieur des racines.","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 ∈ ]-∞, 1[ ∪ ]3, +∞[\", \"b\": \"x ∈ ]1, 3[\", \"c\": \"x ∈ ","_debug_options_count":4},{"id":37959,"question":"L'équation du cercle de centre O(0, 0) et de rayon 5 est :","option_a":"x² + y² = 25","option_b":"x² + y² = 5","option_c":"x² + y² = 10","option_d":"x² + y² = 50","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation d'un cercle de centre (a, b) et de rayon r est (x-a)² + (y-b)² = r². Ici, a = 0, b = 0 et r = 5, donc x² + y² = 25.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x² + y² = 25\", \"b\": \"x² + y² = 5\", \"c\": \"x² + y² = 10\", \"d\"","_debug_options_count":4}]