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Question 1 sur 10 10:00

[{"id":41726,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"A) x = 2 ou x = 3","option_b":"B) x = -2 ou x = -3","option_c":"C) x = 1 ou x = 6","option_d":"D) x = 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation x² - 5x + 6 = 0 se factorise en (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":41727,"question":"La fonction f(x) = x³ - 3x² + 2x est-elle croissante sur l'intervalle [0, 1] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 6x + 2 est négative sur [0, 1] (car f'(0) = 2 et f'(1) = -1), donc la fonction est décroissante sur cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41728,"question":"Quel est le domaine de définition de la fonction f(x) = (x² - 1)\/(x - 2) ?","option_a":"A) ℝ","option_b":"B) ℝ \\ {2}","option_c":"C) ℝ \\ {-1, 1}","option_d":"D) ℝ \\ {1}","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction est définie pour tout x réel sauf x = 2 (car le dénominateur s'annule en x = 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41729,"question":"L'équation cos(x) = 0,5 admet-elle des solutions dans l'intervalle [0, π] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Oui, car cos(π\/3) = 0,5 et π\/3 ∈ [0, π].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41730,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 5)\/(x² - 4) lorsque x tend vers +∞ ?","option_a":"A) 0","option_b":"B) 2","option_c":"C) +∞","option_d":"D) -∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant le numérateur et le dénominateur par x², on obtient (2 + 3\/x - 5\/x²)\/(1 - 4\/x²), dont la limite est 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41731,"question":"La dérivée de la fonction f(x) = ln(x² + 1) est-elle f'(x) = 2x\/(x² + 1) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée est bien f'(x) = 2x\/(x² + 1), car la dérivée de ln(u) est u'\/u avec u = x² + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41732,"question":"Quel est le résultat de l'intégrale ∫(3x² - 2x + 1)dx ?","option_a":"A) x³ - x² + x + C","option_b":"B) x³ - x + C","option_c":"C) 3x³ - x² + x + C","option_d":"D) x³ - x² + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de 3x² est x³, de -2x est -x², et de 1 est x. Donc le résultat est x³ - x² + x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41733,"question":"La fonction f(x) = e^(2x) est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Oui, car l'exponentielle e^(2x) est toujours strictement positive pour tout x réel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41734,"question":"Quelle est la valeur de sin(π\/6) ?","option_a":"A) 0","option_b":"B) 1\/2","option_c":"C) √2\/2","option_d":"D) 1","option_e":"","option_f":"","bonne_reponse":"B","explication":"La valeur de sin(π\/6) est 1\/2, car π\/6 correspond à 30° et sin(30°) = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41735,"question":"L'équation x² + y² - 4x + 6y + 9 = 0 représente-t-elle un cercle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Oui, car on peut écrire l'équation sous la forme (x-2)² + (y+3)² = 4, qui est l'équation d'un cercle de centre (2, -3) et de rayon 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]