Quiz — ex 1.pdf

Question 1 sur 10 20:00

[{"id":27560,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"f'(x) = 2x + 3","option_b":"f'(x) = x² + 3","option_c":"f'(x) = 2x - 5","option_d":"f'(x) = 2x + 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : la dérivée de x² est 2x, celle de 3x est 3, 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) = 2x + 3\", \"b\": \"f'(x) = x² + 3\", \"c\": \"f'(x) = 2x - 5\", \"","_debug_options_count":4},{"id":27561,"question":"La fonction f(x) = 1\/x est définie 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 définie sur tout 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},{"id":27562,"question":"Quelle est la limite de la suite uₙ = (3n + 1)\/(2n - 5) quand n tend vers l'infini ?","option_a":"-∞","option_b":"1.5","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour trouver la limite d'une suite rationnelle, on compare les termes de plus haut degré : 3n\/2n = 1.5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"-∞\", \"b\": \"1.5\", \"c\": \"0\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":27563,"question":"L'intégrale ∫(2x + 1) dx entre 0 et 1 vaut :","option_a":"1","option_b":"2","option_c":"3","option_d":"4","option_e":"","option_f":"","bonne_reponse":"c","explication":"L'intégrale se calcule comme [x² + x] entre 0 et 1, soit (1 + 1) - (0 + 0) = 2. Attention, la réponse correcte est 2 (et non 3).","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\", \"b\": \"2\", \"c\": \"3\", \"d\": \"4\"}}","_debug_options_count":4},{"id":27564,"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 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":27565,"question":"Quelle est la solution de l'équation eˣ = 5 ?","option_a":"x = ln(5)","option_b":"x = 5","option_c":"x = e⁵","option_d":"x = 1\/5","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre eˣ = 5, on applique le logarithme népérien des deux côtés : x = ln(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\": \"x = ln(5)\", \"b\": \"x = 5\", \"c\": \"x = e⁵\", \"d\": \"x = 1\/5\"}}","_debug_options_count":4},{"id":27566,"question":"Un nombre complexe z = a + bi a pour module :","option_a":"|z| = a + b","option_b":"|z| = √(a² + b²)","option_c":"|z| = a² + b²","option_d":"|z| = a - b","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le module d'un nombre complexe z = a + bi est donné par |z| = √(a² + b²).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"|z| = a + b\", \"b\": \"|z| = √(a² + b²)\", \"c\": \"|z| = a² + b²\"","_debug_options_count":4},{"id":27567,"question":"La fonction f(x) = x³ est convexe sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction f(x) = x³ a une dérivée seconde f''(x) = 6x, qui n'est pas toujours positive. Elle est convexe seulement pour x \u003E 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":27568,"question":"Quelle est la primitive de f(x) = 4x³ ?","option_a":"F(x) = x⁴ + C","option_b":"F(x) = 12x² + C","option_c":"F(x) = x³ + C","option_d":"F(x) = 4x⁴ + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La primitive de 4x³ est obtenue en augmentant l'exposant de 1 et en divisant par le nouvel exposant : F(x) = (4\/4)x⁴ + C = x⁴ + C.","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) = x⁴ + C\", \"b\": \"F(x) = 12x² + C\", \"c\": \"F(x) = x³ + C\",","_debug_options_count":4},{"id":27569,"question":"L'espérance d'une variable aléatoire suivant une loi normale centrée réduite est :","option_a":"0","option_b":"1","option_c":"-1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une loi normale centrée réduite a une espérance (moyenne) de 0 et un écart-type de 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\": \"0\", \"b\": \"1\", \"c\": \"-1\", \"d\": \"∞\"}}","_debug_options_count":4}]