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Question 1 sur 10 10:00

[{"id":45566,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x - 5","option_d":"2x + 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45567,"question":"L'équation x² - 4x + 4 = 0 admet-elle deux solutions réelles distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = 0, donc l'équation admet une solution double : x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45568,"question":"Quelle est la limite de la fonction f(x) = (2x + 1)\/(x - 3) lorsque x tend vers +∞ ?","option_a":"2","option_b":"0","option_c":"1","option_d":"3","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par x, on obtient lim (2 + 1\/x)\/(1 - 3\/x) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45569,"question":"La fonction f(x) = x³ - 3x² + 2 est-elle croissante sur l'intervalle [0, 2] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 6x s'annule en x=0 et x=2. Sur [0,2], f'(x) ≤ 0, donc la fonction est décroissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45570,"question":"Quel est le résultat de l'intégrale ∫(3x² + 2x) dx ?","option_a":"x³ + x² + C","option_b":"x³ + x + C","option_c":"3x³ + x² + C","option_d":"x³ + 2x² + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale se calcule terme par terme : ∫3x² dx = x³ et ∫2x dx = x², d'où x³ + x² + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45571,"question":"La suite définie par uₙ = n²\/(n+1) est-elle bornée ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La suite tend vers +∞ lorsque n tend vers +∞, donc elle n'est pas bornée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45572,"question":"Quelle est la solution de l'inéquation 2x - 5 \u003E 3x + 1 ?","option_a":"x \u003C -6","option_b":"x \u003E -6","option_c":"x \u003C 6","option_d":"x \u003E 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant l'inéquation, on obtient 2x - 3x \u003E 1 + 5, soit -x \u003E 6, donc x \u003C -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45573,"question":"Le produit scalaire de deux vecteurs orthogonaux est-il toujours nul ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, deux vecteurs orthogonaux ont un produit scalaire égal à zéro.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45574,"question":"Quelle est la valeur de la limite lim (x→0) (sin x)\/x ?","option_a":"0","option_b":"1","option_c":"∞","option_d":"-1","option_e":"","option_f":"","bonne_reponse":"B","explication":"C'est une limite fondamentale en analyse : lim (x→0) (sin x)\/x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45575,"question":"La fonction f(x) = e^(2x) est-elle 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 f(x) = e^(2x) est f'(x) = 2e^(2x) = 2f(x), donc elle vérifie l'équation différentielle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]