Quiz interactif : Mathématiques Seconde — Exercices types et corrections

Question 1 sur 10 10:00

[{"id":68822,"question":"Quelle est la solution de l'équation 2x - 5 = 3 ?","option_a":"x = 1","option_b":"x = 4","option_c":"x = -1","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour résoudre 2x - 5 = 3, on ajoute 5 des deux côtés : 2x = 8, puis on divise par 2 : x = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68823,"question":"La fonction f(x) = 3x + 2 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 = 3 et b = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68824,"question":"Quelle est l'image de 2 par la fonction f(x) = x² - 4x + 1 ?","option_a":"-3","option_b":"1","option_c":"-1","option_d":"3","option_e":"","option_f":"","bonne_reponse":"A","explication":"En remplaçant x par 2 : f(2) = 2² - 4*2 + 1 = 4 - 8 + 1 = -3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68825,"question":"L'inéquation 3x + 7 \u003E 10 a pour solution :","option_a":"x \u003E 1","option_b":"x \u003C 1","option_c":"x \u003E -1","option_d":"x \u003C -1","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvons 3x + 7 \u003E 10 : 3x \u003E 3, donc x \u003E 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68826,"question":"Le triangle ABC avec AB = 5 cm, BC = 12 cm et AC = 13 cm est-il rectangle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"On vérifie avec le théorème de Pythagore : 5² + 12² = 25 + 144 = 169 = 13². Le triangle est donc rectangle en B.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68827,"question":"Quelle est la solution de l'inéquation -2x + 6 ≤ 0 ?","option_a":"x ≥ 3","option_b":"x ≤ 3","option_c":"x \u003E 3","option_d":"x \u003C 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvons -2x + 6 ≤ 0 : -2x ≤ -6, puis x ≥ 3 (en divisant par un nombre négatif, le sens de l'inégalité change).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68828,"question":"La droite d'équation y = -2x + 5 a un coefficient directeur égal à :","option_a":"5","option_b":"-2","option_c":"-5","option_d":"2","option_e":"","option_f":"","bonne_reponse":"B","explication":"Dans l'équation y = ax + b, a est le coefficient directeur. Ici, a = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68829,"question":"Le point A(2 ; 5) appartient-il à la droite d'équation y = 3x - 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"En remplaçant x par 2 dans l'équation : y = 3*2 - 1 = 5. Le point A(2 ; 5) appartient donc à la droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68830,"question":"Quelle est la solution de l'équation x² - 9 = 0 ?","option_a":"x = 3","option_b":"x = -3","option_c":"x = 3 ou x = -3","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"C","explication":"x² - 9 = 0 ⇒ x² = 9 ⇒ x = 3 ou x = -3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68831,"question":"La fonction f(x) = 1\/x est-elle 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 pour x = 0 car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]