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[{"id":15238,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 7 ?","option_a":"x = 12","option_b":"x = 2","option_c":"x = -5","option_d":"x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En soustrayant 2x des deux côtés et en ajoutant 5, on obtient x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15239,"question":"La fonction f(x) = x² - 4x + 3 est-elle croissante sur l'intervalle [2 ; +∞[ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 2x - 4 est positive pour x \u003E 2, donc la fonction est croissante sur cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15240,"question":"Quel est le coefficient directeur de la droite d'équation y = -3x + 5 ?","option_a":"-3","option_b":"5","option_c":"3","option_d":"-5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dans une équation de droite y = mx + p, m est le coefficient directeur. Ici, m = -3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15241,"question":"L'inéquation 2x + 1 \u003E 5 a pour solution :","option_a":"x \u003E 2","option_b":"x \u003C 2","option_c":"x \u003E 3","option_d":"x \u003C 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"En soustrayant 1 et en divisant par 2, on obtient x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15242,"question":"La fonction f(x) = -x² + 4x - 3 admet-elle un maximum en x = 2 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = -2x + 4 s'annule en x = 2, et comme le coefficient de x² est négatif, c'est un maximum.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15243,"question":"Quelle est l'image de 3 par la fonction f(x) = 2x² - x + 1 ?","option_a":"16","option_b":"14","option_c":"12","option_d":"10","option_e":"","option_f":"","bonne_reponse":"A","explication":"En remplaçant x par 3, on obtient f(3) = 2*(9) - 3 + 1 = 16.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15244,"question":"Les vecteurs u(2 ; -1) et v(-4 ; 2) sont-ils colinéaires ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les vecteurs sont colinéaires si leurs coordonnées sont proportionnelles. Ici, -4\/2 = -2 et 2\/-1 = -2, donc ils sont colinéaires.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15245,"question":"La suite définie par uₙ = 3n + 2 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 = 3, donc elle est arithmétique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15246,"question":"Quel est le résultat de l'expression (x + 2)² - (x - 2)² ?","option_a":"8x","option_b":"4x","option_c":"x²","option_d":"2x","option_e":"","option_f":"","bonne_reponse":"A","explication":"En développant, on obtient (x² + 4x + 4) - (x² - 4x + 4) = 8x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15247,"question":"La probabilité d'un événement impossible est-elle égale à 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La probabilité d'un événement impossible est égale à 0, tandis que celle d'un événement certain est égale à 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]