Quiz : Mathématiques — Équations, fonctions et géométrie pour la 1ère année

Question 1 sur 10 10:00

[{"id":22948,"question":"Quelle est la solution de l'équation 3x - 5 = 10 ?","option_a":"x = 5","option_b":"x = 3","option_c":"x = 15\/3","option_d":"x = 2","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":22949,"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":22950,"question":"Quelle est l'image de x = 4 par la fonction f(x) = -x + 7 ?","option_a":"f(4) = 3","option_b":"f(4) = -3","option_c":"f(4) = 11","option_d":"f(4) = -11","option_e":"","option_f":"","bonne_reponse":"A","explication":"En remplaçant x par 4 dans f(x) = -x + 7, on obtient f(4) = -4 + 7 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22951,"question":"Le théorème de Pythagore s'applique-t-il à tous les triangles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le théorème de Pythagore ne s'applique qu'aux triangles rectangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22952,"question":"Quelle est la solution de l'équation 2(x + 1) = 4x - 6 ?","option_a":"x = 4","option_b":"x = -4","option_c":"x = 2","option_d":"x = -2","option_e":"","option_f":"","bonne_reponse":"B","explication":"En développant : 2x + 2 = 4x - 6. On soustrait 2x : 2 = 2x - 6, puis on ajoute 6 : 8 = 2x, donc x = -4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22953,"question":"La droite d'équation y = -3x + 2 est-elle décroissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur de la droite est -3, qui est négatif. Une droite avec un coefficient directeur négatif est décroissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22954,"question":"Quelle est la valeur de x dans l'équation 5x\/2 = 10 ?","option_a":"x = 4","option_b":"x = 5","option_c":"x = 20","option_d":"x = 10","option_e":"","option_f":"","bonne_reponse":"A","explication":"On multiplie les deux côtés par 2 : 5x = 20, puis on divise par 5 : x = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22955,"question":"Un triangle avec des côtés de 3 cm, 4 cm et 5 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 : 3² + 4² = 9 + 16 = 25 = 5². Le triangle est donc rectangle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22956,"question":"Quelle est la pente de la droite passant par les points A(1, 2) et B(3, 6) ?","option_a":"2","option_b":"4","option_c":"1\/2","option_d":"-2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La pente m = (yB - yA)\/(xB - xA) = (6 - 2)\/(3 - 1) = 4\/2 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22957,"question":"L'équation x² - 5x + 6 = 0 a-t-elle deux solutions réelles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = 25 - 24 = 1 \u003E 0, donc l'équation a deux solutions réelles distinctes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]