Quiz Maths 4ème Année Secondaire : Algèbre, Fonctions et Suites

Question 1 sur 10 10:00

[{"id":40886,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 1 ?","option_a":"x = 4","option_b":"x = 6","option_c":"x = -4","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"C","explication":"Pour résoudre 3x - 5 = 2x + 1, on soustrait 2x des deux côtés : x - 5 = 1, puis on ajoute 5 : x = 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40887,"question":"La fonction f(x) = 2x + 3 est-elle une fonction affine ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction affine s'écrit sous la forme f(x) = ax + b, ce qui est le cas ici avec a=2 et b=3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40888,"question":"Quelle est la raison d'une suite géométrique si u3 = 8 et u5 = 32 ?","option_a":"r = 2","option_b":"r = 4","option_c":"r = 1\/2","option_d":"r = -2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Avec u5 = u3 * r^(5-3), on a 32 = 8 * r^2, donc r^2 = 4 et r = 2 (car r \u003E 0).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40889,"question":"L'inéquation 2x + 7 \u003E 3x - 1 a pour solution :","option_a":"x \u003C 8","option_b":"x \u003E 8","option_c":"x \u003C -8","option_d":"x \u003E -8","option_e":"","option_f":"","bonne_reponse":"A","explication":"En simplifiant, on obtient -x \u003E -8, soit x \u003C 8 (en multipliant par -1, on inverse le sens de l'inégalité).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40890,"question":"Une suite arithmétique de premier terme u0 = 5 et de raison r = 3 a pour terme général :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le terme général d'une suite arithmétique est un = u0 + n*r, soit un = 5 + 3n.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40891,"question":"Quelle est la solution de l'inéquation x² - 5x + 6 ≤ 0 ?","option_a":"x ∈ [2 ; 3]","option_b":"x ∈ ]-∞ ; 2] ∪ [3 ; +∞[","option_c":"x ∈ [0 ; 5]","option_d":"x ∈ ℝ","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les racines de x² - 5x + 6 sont 2 et 3. Le polynôme est négatif entre ses racines, donc x ∈ [2 ; 3].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40892,"question":"La fonction f(x) = -4x + 1 est-elle décroissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur est -4 (négatif), donc la fonction est décroissante sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40893,"question":"Quelle est la somme des 5 premiers termes d'une suite arithmétique de premier terme 2 et de raison 3 ?","option_a":"S = 40","option_b":"S = 45","option_c":"S = 50","option_d":"S = 55","option_e":"","option_f":"","bonne_reponse":"B","explication":"La somme des n premiers termes est S = n\/2 * (2u0 + (n-1)r). Ici, S = 5\/2 * (4 + 12) = 5\/2 * 16 = 40.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40894,"question":"L'équation x² + 4x + 4 = 0 admet :","option_a":"Deux solutions distinctes","option_b":"Une solution double","option_c":"Aucune solution réelle","option_d":"Trois solutions","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = 16 - 16 = 0, donc l'équation admet une solution double x = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40895,"question":"La suite définie par un = 2n + 1 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La différence entre deux termes consécutifs est constante : un+1 - un = 2, donc la suite est arithmétique de raison 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]