Quiz — correction magazaine n24.pdf

Question 1 sur 5 10:00

[{"id":1982,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 2 ou x = 0,5","option_c":"x = -1 ou x = -2","option_d":"x = 1 ou x = -2","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour résoudre 2x² - 5x + 2 = 0, utilisez la formule du discriminant Δ = b² - 4ac = 25 - 16 = 9. Les solutions sont x = (5 ± 3)\/4, soit x = 2 ou x = 0,5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"x = 1 ou x = 2\", \"b\": \"x = 2 ou x = 0,5\", \"c\": \"x = -1 ou x = -2\"","_debug_options_count":4},{"id":1983,"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) = 9x² - 2x + 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : f'(x) = 9x² - 4x + 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\": \"f'(x) = 9x² - 4x + 5\", \"b\": \"f'(x) = 6x² - 4x + 5\", \"c\": \"f'(x)","_debug_options_count":4},{"id":1984,"question":"Dans un repère orthonormé, quelle est l'équation d'une droite passant par les points A(1, 2) et B(3, 4) ?","option_a":"y = x + 1","option_b":"y = 2x - 1","option_c":"y = x - 1","option_d":"y = 2x + 1","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le coefficient directeur est (4-2)\/(3-1) = 1. L'équation est y = x + b. En remplaçant A(1,2), on trouve b = 0. D'où y = x. Cependant, en vérifiant avec B(3,4), l'équation correcte est y = 2x - 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 - 1\", \"d\": \"y = 2x + 1","_debug_options_count":4},{"id":1985,"question":"Quelle est la probabilité d'obtenir exactement 2 fois 'pile' en 4 lancers d'une pièce équilibrée ?","option_a":"1\/4","option_b":"3\/8","option_c":"1\/2","option_d":"5\/16","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est une loi binomiale B(n=4, p=0,5). P(X=2) = C(4,2) * (0,5)^4 = 6\/16 = 3\/8.","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\/4\", \"b\": \"3\/8\", \"c\": \"1\/2\", \"d\": \"5\/16\"}}","_debug_options_count":4},{"id":1986,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"3","option_b":"0","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour x → ∞, on divise numérateur et dénominateur par x². La limite est donc 3\/1 = 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\": \"3\", \"b\": \"0\", \"c\": \"1\", \"d\": \"∞\"}}","_debug_options_count":4}]