Quiz Maths Seconde : Équations, Fonctions et Géométrie

Question 1 sur 10 10:00

[{"id":8383,"question":"Quelle est la solution de l'équation 3x - 7 = 2x + 5 ?","option_a":"x = 12","option_b":"x = 2","option_c":"x = -12","option_d":"x = -2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En isolant x, on obtient 3x - 2x = 5 + 7, soit x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":8384,"question":"La fonction f(x) = x² - 4x + 3 est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = (-4)² - 4×1×3 = 4 \u003E 0, donc la fonction s'annule en deux points et n'est pas toujours positive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":8385,"question":"Quel est le coefficient directeur de la droite d'équation y = -2x + 5 ?","option_a":"5","option_b":"-2","option_c":"2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"B","explication":"Dans l'équation réduite y = mx + p, m est le coefficient directeur. Ici, m = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":8386,"question":"L'inéquation 2x + 3 ≥ 7 a pour solution :","option_a":"x ≥ 2","option_b":"x ≤ 2","option_c":"x ≥ -2","option_d":"x ≤ -2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant 2x ≥ 4, on obtient x ≥ 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":8387,"question":"Le théorème de Pythagore s'applique-t-il dans un triangle rectangle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le théorème de Pythagore énonce que dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":8388,"question":"Quelle est la forme canonique de la fonction f(x) = x² - 6x + 8 ?","option_a":"(x - 3)² - 1","option_b":"(x - 2)² - 1","option_c":"(x - 3)² + 1","option_d":"(x - 2)² + 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La forme canonique est f(x) = (x - α)² + β, où α = 3 et β = -1 après complétion du carré.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":8389,"question":"Si f(x) = 3x + 1, alors f(2) = ?","option_a":"5","option_b":"7","option_c":"6","option_d":"4","option_e":"","option_f":"","bonne_reponse":"B","explication":"En remplaçant x par 2 dans f(x), on obtient f(2) = 3×2 + 1 = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":8390,"question":"L'équation x² + 4 = 0 a-t-elle des solutions réelles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = 0² - 4×1×4 = -16 \u003C 0, donc aucune solution réelle n'existe.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":8391,"question":"Quelle est l'image de -1 par la fonction g(x) = 2x² - 3x + 1 ?","option_a":"6","option_b":"-6","option_c":"0","option_d":"2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En remplaçant x par -1, on obtient g(-1) = 2×(-1)² - 3×(-1) + 1 = 2 + 3 + 1 = 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":8392,"question":"La droite d'équation y = 4x - 1 est-elle parallèle à la droite d'équation y = 4x + 5 ?","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, m = 4 pour les deux droites.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]