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Question 1 sur 10 10:00

[{"id":33123,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) quand x tend vers l'infini ?","option_a":"A) 0","option_b":"B) 3","option_c":"C) -∞","option_d":"D) 1","option_e":"","option_f":"","bonne_reponse":"B","explication":"La limite d'un quotient de polynômes de même degré est égale au rapport des coefficients dominants. Ici, 3x²\/x² = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":33124,"question":"La fonction f(x) = x³ - 3x² + 2x est strictement croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 3x² - 6x + 2 s'annule en x = 1 ± √(1\/3), donc la fonction n'est pas strictement croissante sur tout ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":33125,"question":"Quelle est la solution de l'équation ln(x) + ln(x-1) = ln(6) ?","option_a":"A) x = 2","option_b":"B) x = 3","option_c":"C) x = -2","option_d":"D) x = 4","option_e":"","option_f":"","bonne_reponse":"B","explication":"ln(x(x-1)) = ln(6) ⇒ x(x-1) = 6 ⇒ x² - x - 6 = 0 ⇒ x = 3 (solution positive).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":33126,"question":"La suite définie par uₙ = (2n + 1)\/(n + 3) est convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La limite de uₙ quand n tend vers l'infini est 2, donc la suite est convergente.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":33127,"question":"Quel est le déterminant de la matrice A = [[1, 2], [3, 4]] ?","option_a":"A) -2","option_b":"B) 2","option_c":"C) 5","option_d":"D) -5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le déterminant est calculé par ad - bc = (1×4) - (2×3) = 4 - 6 = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":33128,"question":"La fonction f(x) = e^(2x) est solution de l'équation différentielle y' = 2y.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de e^(2x) est 2e^(2x) = 2f(x), donc c'est bien une solution.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":33129,"question":"Quelle est la probabilité d'obtenir un double 6 en lançant deux dés équilibrés ?","option_a":"A) 1\/6","option_b":"B) 1\/12","option_c":"C) 1\/36","option_d":"D) 1\/18","option_e":"","option_f":"","bonne_reponse":"C","explication":"Il y a 36 issues possibles, et une seule favorable (6-6), donc P = 1\/36.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":33130,"question":"La suite uₙ = n² - 5n + 6 est minorée.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La suite tend vers +∞ quand n tend vers l'infini, donc elle n'est pas minorée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":33131,"question":"Quel est le coefficient directeur de la tangente à la courbe de f(x) = x² - 3x + 2 au point d'abscisse x = 1 ?","option_a":"A) -1","option_b":"B) 1","option_c":"C) -2","option_d":"D) 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 2x - 3, donc f'(1) = -1 (coefficient directeur de la tangente).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":33132,"question":"L'équation x³ - 6x² + 11x - 6 = 0 admet trois solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le polynôme se factorise en (x-1)(x-2)(x-3), donc trois solutions réelles distinctes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]