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[{"id":45706,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 0.5 ou x = 2","option_c":"x = -1 ou x = 2","option_d":"x = 1 ou x = -2","option_e":"","option_f":"","bonne_reponse":"B","explication":"La résolution de l'équation du second degré donne x = 0.5 ou x = 2 (discriminant Δ = 9, racines x1 = (5-3)\/4 = 0.5 et x2 = (5+3)\/4 = 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45707,"question":"La fonction f(x) = x³ - 3x + 1 admet-elle un extremum local en x = 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 3 s'annule en x = 1, mais f''(1) = 6 \u003E 0, donc c'est un minimum local. L'affirmation est donc fausse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45708,"question":"Quelle est la dérivée de la fonction f(x) = ln(2x + 1) ?","option_a":"f'(x) = 1\/(2x + 1)","option_b":"f'(x) = 2\/(2x + 1)","option_c":"f'(x) = 2x\/(2x + 1)","option_d":"f'(x) = 1\/(x + 0.5)","option_e":"","option_f":"","bonne_reponse":"B","explication":"En utilisant la formule de dérivation des fonctions composées, f'(x) = (2)\/(2x + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45709,"question":"L'intégrale ∫(3x² + 2x) dx entre 0 et 1 vaut :","option_a":"2","option_b":"3","option_c":"1.5","option_d":"4","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale vaut [x³ + x²] entre 0 et 1 = (1 + 1) - (0 + 0) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45710,"question":"La suite définie par uₙ = 2n + 1 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La différence entre deux termes consécutifs est constante (uₙ₊₁ - uₙ = 2), donc la suite est arithmétique de raison 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45711,"question":"Quelle est l'équation de la tangente à la courbe y = x² - 4x + 3 au point d'abscisse x = 2 ?","option_a":"y = -4","option_b":"y = 2x - 5","option_c":"y = 4x - 7","option_d":"y = -2x + 3","option_e":"","option_f":"","bonne_reponse":"C","explication":"La tangente a pour équation y = f'(2)(x - 2) + f(2) = -4(x - 2) + (-1) = -4x + 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45712,"question":"La fonction f(x) = e^(2x) est-elle convexe sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée seconde f''(x) = 4e^(2x) \u003E 0 pour tout x, donc la fonction est convexe.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45713,"question":"Quelle est la limite de (3x² + 2x - 1)\/(x² + 1) quand x tend vers +∞ ?","option_a":"0","option_b":"3","option_c":"2","option_d":"+∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant numérateur et dénominateur par x², on obtient (3 + 2\/x - 1\/x²)\/(1 + 1\/x²) → 3 quand x → +∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45714,"question":"L'équation x³ - 6x² + 11x - 6 = 0 admet-elle 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 il admet trois solutions réelles distinctes : 1, 2 et 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45715,"question":"Quelle est l'aire sous la courbe y = x² entre x = 0 et x = 2 ?","option_a":"4\/3","option_b":"8\/3","option_c":"2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'aire est donnée par l'intégrale ∫₀² x² dx = [x³\/3]₀² = 8\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]