Quiz Maths Seconde : Algèbre, Fonctions et Géométrie

Question 1 sur 10 10:00

[{"id":16758,"question":"Quelle est la solution de l'équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = 12\/3","option_c":"x = 2","option_d":"x = -2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour résoudre 3x - 5 = 7, on ajoute 5 des deux côtés (3x = 12), puis on divise par 3 (x = 4).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16759,"question":"La fonction f(x) = x² - 4x + 3 est une fonction affine.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction affine s'écrit sous la forme f(x) = ax + b. Ici, f(x) = x² - 4x + 3 est une fonction du second degré (présence de x²).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16760,"question":"Quel est le discriminant de l'équation x² - 5x + 6 = 0 ?","option_a":"Δ = 1","option_b":"Δ = 16","option_c":"Δ = 25","option_d":"Δ = 12","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = b² - 4ac = (-5)² - 4(1)(6) = 25 - 24 = 1. Ici, la bonne réponse est Δ = 1, mais l'option correcte est Δ = 16 (erreur dans les options). Corrigé : Δ = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16761,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est l'énoncé du théorème de Pythagore, une propriété fondamentale en géométrie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16762,"question":"Quelle est la forme canonique de la fonction f(x) = 2x² - 8x + 5 ?","option_a":"f(x) = 2(x - 2)² - 3","option_b":"f(x) = 2(x - 4)² + 5","option_c":"f(x) = 2(x - 1)² + 3","option_d":"f(x) = 2(x - 2)² + 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La forme canonique s'obtient par f(x) = a(x - α)² + β. Ici, α = 2 et β = -3, donc f(x) = 2(x - 2)² - 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16763,"question":"L'inéquation 2x + 3 \u003E 7 a pour solution x \u003E 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvons 2x + 3 \u003E 7 : 2x \u003E 4 → x \u003E 2. La solution est donc x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16764,"question":"Quelle est l'image de 3 par la fonction f(x) = -x² + 4x - 1 ?","option_a":"f(3) = 2","option_b":"f(3) = -2","option_c":"f(3) = 0","option_d":"f(3) = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Calculons f(3) = -(3)² + 4(3) - 1 = -9 + 12 - 1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16765,"question":"Le théorème de Thalès s'applique uniquement dans les triangles rectangles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le théorème de Thalès s'applique à deux triangles emboîtés (ou sécants) et non uniquement aux triangles rectangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16766,"question":"Quelle est la solution de l'inéquation -3x + 5 ≤ 11 ?","option_a":"x ≥ -2","option_b":"x ≤ -2","option_c":"x ≥ 2","option_d":"x ≤ 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvons -3x + 5 ≤ 11 : -3x ≤ 6 → x ≥ -2 (attention au changement de sens de l'inégalité lors de la division par un nombre négatif).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16767,"question":"La fonction f(x) = 1\/x est 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 en x = 0 car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]