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Question 1 sur 10 10:00

[{"id":23718,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"f'(x) = 2x + 3","option_b":"f'(x) = x² + 3","option_c":"f'(x) = 2x","option_d":"f'(x) = 3x - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle de dérivation terme à terme : (x²)' = 2x et (3x)' = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23719,"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":"Une suite est arithmétique si la différence entre deux termes consécutifs est constante. Ici, uₙ₊₁ - uₙ = 2, donc elle est arithmétique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23720,"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 d'un polynôme s'obtient en augmentant l'exposant de 1 et en divisant par le nouvel exposant : ∫3x² dx = x³ et ∫2x dx = x².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23721,"question":"L'équation x² - 4x + 4 = 0 admet-elle deux solutions distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = b² - 4ac = 16 - 16 = 0, donc l'équation admet une solution double : x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23722,"question":"Quel est le produit scalaire de deux vecteurs orthogonaux ?","option_a":"0","option_b":"1","option_c":"√2","option_d":"indéfini","option_e":"","option_f":"","bonne_reponse":"A","explication":"Deux vecteurs orthogonaux ont un produit scalaire nul, car cos(90°) = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23723,"question":"La fonction exponentielle est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour tout réel x, eˣ \u003E 0, donc la fonction exponentielle est toujours positive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23724,"question":"Quelle est la limite de (x² - 1)\/(x - 1) quand x tend vers 1 ?","option_a":"2","option_b":"0","option_c":"1","option_d":"indéterminée","option_e":"","option_f":"","bonne_reponse":"A","explication":"En factorisant le numérateur : (x² - 1) = (x - 1)(x + 1), donc (x² - 1)\/(x - 1) = x + 1. La limite est donc 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23725,"question":"Un événement impossible a une probabilité de :","option_a":"0","option_b":"1","option_c":"0.5","option_d":"100%","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, la probabilité d'un événement impossible est 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23726,"question":"La fonction f(x) = ln(x) est-elle définie pour x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction logarithme népérien est définie uniquement pour x \u003E 0, donc elle n'est pas définie en x = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23727,"question":"Quel est le centre de symétrie de la fonction f(x) = x³ - 3x ?","option_a":"0","option_b":"1","option_c":"-1","option_d":"3","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction f(x) = x³ - 3x est impaire, donc son centre de symétrie est l'origine O(0,0).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]