Quiz Mathématiques Seconde : Algèbre, Fonctions et Géométrie

Question 1 sur 10 10:00

[{"id":41736,"question":"Quelle est la solution de l'équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = 2","option_c":"x = 12\/3","option_d":"x = -4","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvez l'équation en isolant x : 3x = 7 + 5 → 3x = 12 → x = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41737,"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":41738,"question":"Quel est l'ensemble des solutions de l'inéquation -2x + 1 \u003E 5 ?","option_a":"x \u003C -2","option_b":"x \u003E -2","option_c":"x \u003C 2","option_d":"x \u003E 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvez l'inéquation : -2x \u003E 4 → x \u003C -2 (en divisant par un nombre négatif, le sens de l'inégalité change).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41739,"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":"Deux vecteurs sont colinéaires s'il existe un réel k tel que u = k*v. Ici, -4 = -2*2 et 6 = -2*(-3), donc k = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41740,"question":"Quelle est l'image de 4 par la fonction f(x) = x² - 5x + 6 ?","option_a":"-2","option_b":"2","option_c":"10","option_d":"6","option_e":"","option_f":"","bonne_reponse":"C","explication":"Calculez f(4) = 4² - 5*4 + 6 = 16 - 20 + 6 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41741,"question":"La droite d'équation y = -3x + 1 a-t-elle un coefficient directeur égal à -3 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur d'une droite d'équation y = ax + b est a, ici a = -3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41742,"question":"Quel est le résultat de (3x - 2)(x + 4) ?","option_a":"3x² + 10x - 8","option_b":"3x² + 14x - 8","option_c":"3x² + 10x + 8","option_d":"3x² - 10x - 8","option_e":"","option_f":"","bonne_reponse":"A","explication":"Développez en utilisant la distributivité : 3x*x + 3x*4 - 2*x - 2*4 = 3x² + 12x - 2x - 8 = 3x² + 10x - 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41743,"question":"Les points A(1; 2), B(3; 4) et C(5; 6) sont-ils alignés ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Calculez les vecteurs AB(2; 2) et AC(4; 4). Comme AC = 2*AB, les points sont alignés.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41744,"question":"Quelle est la forme canonique de la fonction f(x) = x² - 6x + 5 ?","option_a":"(x - 3)² - 4","option_b":"(x + 3)² - 4","option_c":"(x - 3)² + 4","option_d":"(x + 3)² + 4","option_e":"","option_f":"","bonne_reponse":"A","explication":"Complétez le carré : f(x) = (x² - 6x + 9) - 9 + 5 = (x - 3)² - 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41745,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est donné par :","option_a":"Δ = b² - 4ac","option_b":"Δ = b² + 4ac","option_c":"Δ = 4ac - b²","option_d":"Δ = a² - 4bc","option_e":"","option_f":"","bonne_reponse":"A","explication":"La formule du discriminant est Δ = b² - 4ac.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]