Quiz — Série-Pratique-N-5 (1).pdf

Question 1 sur 5 10:00

[{"id":1899,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"f'(x) = 6x + 2","option_b":"f'(x) = 3x + 2","option_c":"f'(x) = 6x² + 2x","option_d":"f'(x) = 3x² + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d’une fonction polynôme se calcule terme par terme : la dérivée de 3x² est 6x, celle de 2x est 2, et celle de -5 est 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\": \"f'(x) = 6x + 2\", \"b\": \"f'(x) = 3x + 2\", \"c\": \"f'(x) = 6x² + 2x\",","_debug_options_count":4},{"id":1900,"question":"Soit une suite (Un) définie par U0 = 2 et Un+1 = 3Un - 1. Que vaut U2 ?","option_a":"U2 = 11","option_b":"U2 = 14","option_c":"U2 = 17","option_d":"U2 = 8","option_e":"","option_f":"","bonne_reponse":"b","explication":"Calculons U1 = 3*U0 - 1 = 5, puis U2 = 3*U1 - 1 = 14.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"U2 = 11\", \"b\": \"U2 = 14\", \"c\": \"U2 = 17\", \"d\": \"U2 = 8\"}}","_debug_options_count":4},{"id":1901,"question":"Quelle est la limite de la suite Un = (2n + 1)\/(n - 3) quand n tend vers l’infini ?","option_a":"0","option_b":"2","option_c":"1","option_d":"L’infini","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant numérateur et dénominateur par n, on obtient (2 + 1\/n)\/(1 - 3\/n) → 2\/1 = 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\": \"2\", \"c\": \"1\", \"d\": \"L’infini\"}}","_debug_options_count":4},{"id":1902,"question":"On lance un dé équilibré. Quelle est la probabilité d’obtenir un nombre pair ?","option_a":"1\/6","option_b":"1\/2","option_c":"1\/3","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"b","explication":"Un dé a 6 faces : 1, 2, 3, 4, 5, 6. Les nombres pairs sont 2, 4, 6 → 3 cas favorables sur 6 possibles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"1\/6\", \"b\": \"1\/2\", \"c\": \"1\/3\", \"d\": \"2\/3\"}}","_debug_options_count":4},{"id":1903,"question":"Quelle est l’équation du plan passant par le point A(1, 2, 3) et de vecteur normal n(2, -1, 4) ?","option_a":"2x - y + 4z = 0","option_b":"2x - y + 4z = 12","option_c":"2x + y - 4z = 12","option_d":"x - 2y + 3z = 12","option_e":"","option_f":"","bonne_reponse":"b","explication":"L’équation d’un plan est donnée par n·(X - A) = 0 → 2(x-1) -1(y-2) +4(z-3) = 0 → 2x - y + 4z = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"2x - y + 4z = 0\", \"b\": \"2x - y + 4z = 12\", \"c\": \"2x + y - 4z = 12","_debug_options_count":4}]