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[{"id":72012,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 2x + 1 ?","option_a":"6x - 2","option_b":"3x - 2","option_c":"6x² - 2x","option_d":"3x² - 2","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":72013,"question":"L'équation x² - 5x + 6 = 0 a pour solutions :","option_a":"x = 2 et x = 3","option_b":"x = -2 et x = -3","option_c":"x = 1 et x = 6","option_d":"x = 0 et x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En factorisant, on obtient (x-2)(x-3) = 0, donc les solutions sont x = 2 et x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72014,"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, notée exp(x), est toujours strictement positive pour tout x réel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72015,"question":"Quelle est la limite de (2x + 1)\/(x - 3) lorsque x tend vers l'infini ?","option_a":"2","option_b":"0","option_c":"1\/2","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par x, on obtient (2 + 1\/x)\/(1 - 3\/x), donc la limite est 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72016,"question":"Vrai ou Faux ? Une suite convergente est toujours croissante.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite convergente peut être décroissante, constante ou même non monotone, tant qu'elle tend vers une limite finie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72017,"question":"Quel est le discriminant de l'équation ax² + bx + c = 0 ?","option_a":"b² - 4ac","option_b":"a² - 4bc","option_c":"4ac - b²","option_d":"b² + 4ac","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = b² - 4ac détermine le nombre et la nature des solutions de l'équation du second degré.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72018,"question":"Vrai ou Faux ? La fonction logarithme népérien est définie pour tout x réel.","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.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72019,"question":"Quelle est la solution de l'inéquation 3x - 7 \u003E 2x + 1 ?","option_a":"x \u003E 8","option_b":"x \u003C 8","option_c":"x \u003E 6","option_d":"x \u003C 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"En simplifiant, on obtient x \u003E 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72020,"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), selon les règles de dérivation des fonctions trigonométriques.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72021,"question":"Quel est le résultat de ∫(2x + 1) dx ?","option_a":"x² + x + C","option_b":"2x² + x + C","option_c":"x² + 2x + C","option_d":"2x² + 2x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de 2x + 1 est x² + x + C, où C est la constante d'intégration.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]