Quiz — 65ba74c1dea56_Enoncé-Fonction logarithme et matrices (2).pdf

Question 1 sur 5 10:00

[{"id":2444,"question":"Quelle est la dérivée de la fonction f(x) = ln(3x² + 2x + 1) ?","option_a":"f'(x) = (6x + 2) \/ (3x² + 2x + 1)","option_b":"f'(x) = (6x + 2) * ln(3x² + 2x + 1)","option_c":"f'(x) = 1 \/ (3x² + 2x + 1)","option_d":"f'(x) = (3x² + 2x + 1) \/ (6x + 2)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction composée ln(u(x)) est u'(x)\/u(x). Ici, u(x) = 3x² + 2x + 1, donc u'(x) = 6x + 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\": \"f'(x) = (6x + 2) \/ (3x² + 2x + 1)\", \"b\": \"f'(x) = (6x + 2) * ln(","_debug_options_count":4},{"id":2445,"question":"Si A = [[2, 1], [3, 4]] et B = [[1, 0], [2, -1]], que vaut A × B ?","option_a":"[[4, -1], [11, -4]]","option_b":"[[2, 1], [6, -4]]","option_c":"[[2, 0], [3, -4]]","option_d":"[[5, 1], [14, -3]]","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le produit matriciel se calcule en multipliant les lignes de A par les colonnes de B : (2×1 + 1×2, 2×0 + 1×(-1)) = (4, -1) pour la 1ère ligne, et (3×1 + 4×2, 3×0 + 4×(-1)) = (11, -4) pour la 2ème ligne.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"[[4, -1], [11, -4]]\", \"b\": \"[[2, 1], [6, -4]]\", \"c\": \"[[2, 0], [3","_debug_options_count":4},{"id":2446,"question":"Quelle est la solution du système linéaire suivant ? { x + 2y = 5 ; 3x - y = 1 }","option_a":"x = 1, y = 2","option_b":"x = 2, y = 1.5","option_c":"x = 0, y = 2.5","option_d":"x = 3, y = 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"En résolvant par substitution ou combinaison linéaire : de la 2ème équation, y = 3x - 1. En remplaçant dans la 1ère : x + 2(3x - 1) = 5 → 7x = 7 → x = 1, donc y = 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\": \"x = 1, y = 2\", \"b\": \"x = 2, y = 1.5\", \"c\": \"x = 0, y = 2.5\", \"d\":","_debug_options_count":4},{"id":2447,"question":"Soit la matrice A = [[0, 1], [1, 0]]. Que vaut A² ?","option_a":"[[1, 0], [0, 1]]","option_b":"[[0, 1], [1, 0]]","option_c":"[[0, 0], [0, 0]]","option_d":"[[1, 1], [1, 1]]","option_e":"","option_f":"","bonne_reponse":"a","explication":"A² = A × A = [[0×0 + 1×1, 0×1 + 1×0], [1×0 + 0×1, 1×1 + 0×0]] = [[1, 0], [0, 1]], qui est la matrice identité I₂.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"[[1, 0], [0, 1]]\", \"b\": \"[[0, 1], [1, 0]]\", \"c\": \"[[0, 0], [0, 0]","_debug_options_count":4},{"id":2448,"question":"Quelle est la valeur de log₅(125) ?","option_a":"3","option_b":"5","option_c":"25","option_d":"1\/3","option_e":"","option_f":"","bonne_reponse":"a","explication":"log₅(125) = log₅(5³) = 3, car 5³ = 125. La fonction logarithme base b de b^k est égale à k.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"3\", \"b\": \"5\", \"c\": \"25\", \"d\": \"1\/3\"}}","_debug_options_count":4}]