Maths 1ère année : Équations, Fonctions et Géométrie

Question 1 sur 10 10:00

[{"id":43466,"question":"Quelle est la solution de l'équation 3x - 5 = 10 ?","option_a":"x = 5","option_b":"x = 15\/3","option_c":"x = 5\/3","option_d":"x = 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résoudre l'équation : 3x - 5 = 10 → 3x = 15 → x = 5. La solution est donc x = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43467,"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. Ici, a = 2 et b = 3, donc c'est bien une fonction affine.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43468,"question":"Quel est le coefficient directeur de la droite d'équation y = -4x + 7 ?","option_a":"7","option_b":"-4","option_c":"4","option_d":"1\/4","option_e":"","option_f":"","bonne_reponse":"B","explication":"Dans l'équation y = ax + b, a est le coefficient directeur. Ici, a = -4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43469,"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. Il ne peut pas être utilisé pour tous les triangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43470,"question":"Résoudre l'inéquation 2x + 1 \u003E 5.","option_a":"x \u003E 2","option_b":"x \u003C 2","option_c":"x \u003E 3","option_d":"x \u003C 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résoudre l'inéquation : 2x + 1 \u003E 5 → 2x \u003E 4 → x \u003E 2. La solution est x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43471,"question":"Quelle est l'image de 2 par la fonction f(x) = x² - 3x + 1 ?","option_a":"-1","option_b":"3","option_c":"1","option_d":"-3","option_e":"","option_f":"","bonne_reponse":"C","explication":"Calculer f(2) = (2)² - 3*(2) + 1 = 4 - 6 + 1 = -1. L'image de 2 est donc -1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43472,"question":"Les droites d'équations y = 2x + 1 et y = 2x - 3 sont-elles parallèles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Deux droites sont parallèles si elles ont le même coefficient directeur. Ici, les deux droites ont un coefficient directeur de 2, donc elles sont parallèles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43473,"question":"Quelle est la nature du triangle ABC avec AB = 5 cm, BC = 12 cm et AC = 13 cm ?","option_a":"Acute","option_b":"Rectangle","option_c":"Obtus","option_d":"Isocèle","option_e":"","option_f":"","bonne_reponse":"B","explication":"Vérifier si AB² + BC² = AC² : 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":43474,"question":"La fonction f(x) = 5 est-elle une fonction constante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction constante est de la forme f(x) = k (où k est une constante). Ici, f(x) = 5, donc c'est bien une fonction constante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43475,"question":"Quel est le résultat de l'expression (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":"Développer l'expression : (3x - 2)(x + 4) = 3x² + 12x - 2x - 8 = 3x² + 10x - 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]