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[{"id":46801,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"2x + 3","option_b":"2x² + 3","option_c":"x² + 3","option_d":"2x + 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x² est 2x, celle de 3x est 3, et celle de -5 est 0. Donc f'(x) = 2x + 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46802,"question":"Une suite géométrique de raison q = 2 et de premier terme u₀ = 3 a pour terme général :","option_a":"uₙ = 3 * 2ⁿ","option_b":"uₙ = 3 * n²","option_c":"uₙ = 2 * 3ⁿ","option_d":"uₙ = 3 + 2n","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le terme général d'une suite géométrique est uₙ = u₀ * qⁿ. Ici, uₙ = 3 * 2ⁿ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46803,"question":"Vrai ou Faux ? La fonction exponentielle est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction exponentielle eˣ est strictement positive pour tout x réel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46804,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² + 1) quand x tend vers +∞ ?","option_a":"3","option_b":"1","option_c":"2","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par x², on obtient f(x) = (3 + 2\/x - 1\/x²)\/(1 + 1\/x²). La limite est donc 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46805,"question":"Vrai ou Faux ? Une suite croissante est toujours convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite croissante peut diverger vers +∞ (exemple : uₙ = n). Elle n'est pas forcément convergente.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46806,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré à 6 faces ?","option_a":"1\/2","option_b":"1\/3","option_c":"1\/6","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les nombres pairs sont 2, 4 et 6. Il y a 3 cas favorables sur 6 possibles, donc P = 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46807,"question":"Vrai ou Faux ? La fonction f(x) = ln(x) est 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 ln(x) est définie uniquement pour x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46808,"question":"Quelle est la solution de l'équation différentielle y' = 2y avec y(0) = 5 ?","option_a":"y = 5e²ˣ","option_b":"y = 5eˣ","option_c":"y = 2e⁵ˣ","option_d":"y = 5 + 2x","option_e":"","option_f":"","bonne_reponse":"B","explication":"La solution générale est y = Ce²ˣ. Avec y(0) = 5, on trouve C = 5. Donc y = 5e²ˣ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46809,"question":"Vrai ou Faux ? La dérivée de sin(x) est cos(x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de sin(x) est bien cos(x), une propriété fondamentale en analyse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46810,"question":"Quelle est l'intégrale de f(x) = 3x² entre 0 et 2 ?","option_a":"4","option_b":"8","option_c":"12","option_d":"16","option_e":"","option_f":"","bonne_reponse":"C","explication":"L'intégrale de 3x² est x³. Entre 0 et 2, on obtient 2³ - 0³ = 8 - 0 = 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]