Quiz Mathématiques : Équations, Fonctions et Géométrie — 4ème Année Secondaire

Question 1 sur 10 10:00

[{"id":14658,"question":"Quelle est la solution de l'équation 3x - 5 = 10 ?","option_a":"x = 5","option_b":"x = 15","option_c":"x = 3","option_d":"x = 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour résoudre 3x - 5 = 10, on ajoute 5 des deux côtés (3x = 15), puis on divise par 3 (x = 5).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14659,"question":"La fonction f(x) = 2x + 3 est 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":14660,"question":"Quel est le coefficient directeur de la droite d'équation y = -4x + 7 ?","option_a":"-4","option_b":"7","option_c":"4","option_d":"-7","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dans l'équation y = ax + b, a représente le coefficient directeur. Ici, a = -4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14661,"question":"L'inéquation 2x + 1 ≤ 5 a pour solution :","option_a":"x ≤ 2","option_b":"x ≥ 2","option_c":"x ≤ 3","option_d":"x \u003C 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résoudre 2x + 1 ≤ 5 donne 2x ≤ 4, puis x ≤ 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14662,"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 = a² - 4bc","option_d":"Δ = 4b² - ac","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant est calculé par la formule Δ = b² - 4ac.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14663,"question":"La somme des angles d'un triangle est égale à 180°.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une propriété fondamentale de la géométrie plane : la somme des angles d'un triangle est toujours 180°.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14664,"question":"Résolvez le système d'équations : { 2x + y = 5 ; x - y = 1 }","option_a":"x = 2, y = 1","option_b":"x = 1, y = 3","option_c":"x = 3, y = -1","option_d":"x = 0, y = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En additionnant les deux équations, on obtient 3x = 6, donc x = 2. En remplaçant, y = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14665,"question":"La fonction f(x) = x² - 4x + 4 admet un minimum en x = 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction f(x) = x² - 4x + 4 est une parabole tournée vers le haut. Son sommet est en x = -b\/(2a) = 4\/2 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14666,"question":"Quel est le résultat de l'expression (3x² - 2x + 1) - (x² + 4x - 3) ?","option_a":"2x² - 6x + 4","option_b":"2x² - 6x - 2","option_c":"4x² - 6x + 4","option_d":"2x² + 2x + 4","option_e":"","option_f":"","bonne_reponse":"A","explication":"En développant, on obtient 3x² - 2x + 1 - x² - 4x + 3 = 2x² - 6x + 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14667,"question":"L'aire d'un cercle de rayon r est donnée par la formule :","option_a":"πr²","option_b":"2πr","option_c":"πr","option_d":"4πr²","option_e":"","option_f":"","bonne_reponse":"A","explication":"La formule de l'aire d'un cercle est A = πr².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]