Quiz : Maîtrisez les fondamentaux des maths en 4ème année secondaire

Question 1 sur 10 10:00

[{"id":29888,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"Factorisez l'équation : (x-2)(x-3) = 0. Les solutions sont donc x = 2 et x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":29889,"question":"La fonction f(x) = x² - 4x + 3 est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction s'annule en x=1 et x=3 et est négative entre ces deux valeurs.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":29890,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"f'(x) = 6x + 2","option_b":"f'(x) = 3x + 2","option_c":"f'(x) = 6x² + 2","option_d":"f'(x) = 6x - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'un polynôme est obtenue en multipliant chaque terme par son exposant et en réduisant l'exposant de 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":29891,"question":"L'inéquation 2x - 3 \u003E 5 a pour solution :","option_a":"x \u003E 4","option_b":"x \u003C 4","option_c":"x \u003E 1","option_d":"x \u003C 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvez l'inéquation : 2x \u003E 8 → x \u003E 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":29892,"question":"La fonction f(x) = 1\/x est définie pour x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction f(x) = 1\/x n'est pas définie en x = 0 car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":29893,"question":"Quelle est la limite de la fonction f(x) = (x² - 1)\/(x - 1) quand x tend vers 1 ?","option_a":"0","option_b":"1","option_c":"2","option_d":"Indéterminée","option_e":"","option_f":"","bonne_reponse":"C","explication":"Factorisez le numérateur : (x-1)(x+1)\/(x-1) = x+1 pour x ≠ 1. La limite est donc 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":29894,"question":"L'équation |x - 2| = 3 a pour solutions :","option_a":"x = 5 ou x = -1","option_b":"x = 2 ou x = -2","option_c":"x = 3 ou x = -3","option_d":"x = 1 ou x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvez |x - 2| = 3 → x - 2 = 3 ou x - 2 = -3 → x = 5 ou x = -1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":29895,"question":"La fonction f(x) = x³ est strictement croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 3x² est toujours positive (sauf en x=0 où elle est nulle), donc la fonction est strictement croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":29896,"question":"Quelle est la solution de l'inéquation x² - 4x + 3 ≤ 0 ?","option_a":"x ∈ [1, 3]","option_b":"x ∈ ]-∞, 1] ∪ [3, +∞[","option_c":"x ∈ [0, 4]","option_d":"x ∈ ℝ","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvez l'inéquation en trouvant les racines (x=1 et x=3) et en étudiant le signe du polynôme.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":29897,"question":"La fonction f(x) = √(x² + 1) est paire.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction est paire si f(-x) = f(x). Ici, f(-x) = √((-x)² + 1) = √(x² + 1) = f(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]