Maths 4ème année secondaire : Évaluez vos connaissances en équations et fonctions

Question 1 sur 10 10:00

[{"id":23908,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 7 ?","option_a":"x = 2","option_b":"x = 12","option_c":"x = -2","option_d":"x = 5","option_e":"","option_f":"","bonne_reponse":"B","explication":"En isolant x, on obtient 3x - 2x = 7 + 5 → x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23909,"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 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":23910,"question":"Quelle est la forme factorisée de x² - 9 ?","option_a":"(x - 3)(x + 3)","option_b":"(x - 9)(x + 1)","option_c":"(x - 3)²","option_d":"(x + 3)²","option_e":"","option_f":"","bonne_reponse":"A","explication":"x² - 9 est une différence de carrés : (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23911,"question":"Le système {2x + y = 5; x - y = 1} admet-il une solution unique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Ce système de deux équations à deux inconnues admet une solution unique (x=2, y=1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23912,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 1 ?","option_a":"f'(x) = 6x + 2","option_b":"f'(x) = 3x + 2","option_c":"f'(x) = 6x² + 2x","option_d":"f'(x) = 6x - 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme à terme : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23913,"question":"L'inéquation 4x - 7 \u003E 5x + 1 a-t-elle pour solution x \u003C -8 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"En résolvant l'inéquation, on obtient x \u003C -8, donc la réponse est Vrai.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23914,"question":"Quelle est l'image de 2 par la fonction f(x) = x² - 4x + 5 ?","option_a":"f(2) = 1","option_b":"f(2) = 5","option_c":"f(2) = 3","option_d":"f(2) = -3","option_e":"","option_f":"","bonne_reponse":"A","explication":"En remplaçant x par 2 : f(2) = 4 - 8 + 5 = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23915,"question":"Les vecteurs u(2; -3) et v(-4; 6) 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 car v = -2u (coordonnées proportionnelles).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23916,"question":"Quelle est la solution de l'inéquation (x - 1)(x + 3) ≥ 0 ?","option_a":"x ∈ [-3; 1]","option_b":"x ∈ ]-∞; -3] ∪ [1; +∞[","option_c":"x ∈ ]-3; 1[","option_d":"x ∈ ℝ","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le produit est positif lorsque les deux facteurs sont de même signe, donc x ≤ -3 ou x ≥ 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23917,"question":"La fonction f(x) = 1\/x est-elle définie en 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}]