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[{"id":47181,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"A. 2x + 3","option_b":"B. x² + 3","option_c":"C. 2x + 3x - 5","option_d":"D. 2x² + 3","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":47182,"question":"La suite définie par uₙ = n² est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite arithmétique a une différence constante entre deux termes consécutifs. Ici, uₙ₊₁ - uₙ = (n+1)² - n² = 2n + 1, qui n'est pas constante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47183,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"A. 0","option_b":"B. 3","option_c":"C. +∞","option_d":"D. -∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant numérateur et dénominateur par x², on obtient f(x) = (3 + 2\/x - 1\/x²)\/(1 - 4\/x²). La limite est donc 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47184,"question":"L'équation différentielle y' + 2y = 0 a pour solution générale y = Ce^(-2x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La solution générale de y' + 2y = 0 est bien y = Ce^(-2x), car la dérivée de Ce^(-2x) est -2Ce^(-2x), ce qui vérifie l'équation.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47185,"question":"Quel est le coefficient binomial C(5,2) ?","option_a":"A. 10","option_b":"B. 20","option_c":"C. 5","option_d":"D. 15","option_e":"","option_f":"","bonne_reponse":"A","explication":"C(5,2) = 5! \/ (2! * 3!) = (5×4)\/(2×1) = 10.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47186,"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 ln(x) n'est définie que pour x \u003E 0. Elle n'est pas définie en x = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47187,"question":"Quelle est la primitive de la fonction f(x) = 4x³ - 2x + 1 ?","option_a":"A. x⁴ - x² + x + C","option_b":"B. 12x² - 2 + C","option_c":"C. x⁴ - x² + C","option_d":"D. 4x⁴ - 2x² + x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de 4x³ est x⁴, celle de -2x est -x², et celle de 1 est x. Donc F(x) = x⁴ - x² + x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47188,"question":"Une probabilité peut-elle être supérieure à 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une probabilité est toujours comprise entre 0 et 1. Elle ne peut pas être supérieure à 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47189,"question":"Quelle est la valeur de la somme des angles d'un triangle ?","option_a":"A. 90°","option_b":"B. 180°","option_c":"C. 270°","option_d":"D. 360°","option_e":"","option_f":"","bonne_reponse":"B","explication":"La somme des angles d'un triangle est toujours égale à 180°.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47190,"question":"La fonction f(x) = e^(2x) a pour dérivée f'(x) = 2e^(2x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de e^(2x) est 2e^(2x), car la dérivée de e^u est u'e^u avec u = 2x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]