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[{"id":74022,"question":"Quelle est la solution de l'équation 3x - 7 = 2x + 5 ?","option_a":"x = 12","option_b":"x = 2","option_c":"x = -2","option_d":"x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour résoudre 3x - 7 = 2x + 5, soustrayez 2x des deux côtés : x - 7 = 5, puis ajoutez 7 : x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74023,"question":"L'équation x² - 4x + 4 = 0 admet-elle une solution double ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = (-4)² - 4*1*4 = 16 - 16 = 0. Un discriminant nul signifie une solution double : x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74024,"question":"Quelle est la forme factorisée de l'expression 4x² - 9 ?","option_a":"(2x - 3)(2x + 3)","option_b":"(4x - 9)(x + 1)","option_c":"(2x + 3)²","option_d":"(2x - 3)²","option_e":"","option_f":"","bonne_reponse":"A","explication":"4x² - 9 est une différence de carrés : (2x)² - 3² = (2x - 3)(2x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74025,"question":"La fonction f(x) = 2x + 1 est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur de f(x) = 2x + 1 est positif (2 \u003E 0), donc la fonction est croissante sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74026,"question":"Quelle est la solution de l'inéquation 5 - 2x \u003E 1 ?","option_a":"x \u003C 2","option_b":"x \u003E 2","option_c":"x ≤ 2","option_d":"x ≥ 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"5 - 2x \u003E 1 ⇒ -2x \u003E -4 ⇒ x \u003C 2 (en divisant par -2, le sens de l'inégalité change).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74027,"question":"Le polynôme P(x) = x³ - 3x² + 3x - 1 est-il factorisable par (x - 1)³ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En développant (x - 1)³, on obtient x³ - 3x² + 3x - 1, donc P(x) = (x - 1)³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74028,"question":"Quelle est la valeur de x pour laquelle la fonction f(x) = x² - 6x + 10 atteint son minimum ?","option_a":"x = 3","option_b":"x = -3","option_c":"x = 0","option_d":"x = 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction f(x) = x² - 6x + 10 est une parabole ouverte vers le haut. Son sommet est en x = -b\/(2a) = 6\/2 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74029,"question":"L'équation 2^x = 8 admet-elle pour solution x = 3 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"2^3 = 8, donc x = 3 est bien la solution de l'équation 2^x = 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74030,"question":"Quelle est la solution de l'équation (x + 2)(x - 3) = 0 ?","option_a":"x = -2 ou x = 3","option_b":"x = 2 ou x = -3","option_c":"x = 0","option_d":"x = 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un produit de facteurs est nul si l'un des facteurs est nul : x + 2 = 0 ⇒ x = -2, ou x - 3 = 0 ⇒ x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74031,"question":"La fonction f(x) = -x² + 4x - 5 est-elle toujours négative ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = 4² - 4*(-1)*(-5) = 16 - 20 = -4 \u003C 0. Comme a = -1 \u003C 0, la parabole est toujours en dessous de l'axe des abscisses.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]