Quiz interactif : Maîtrisez les équations et fonctions en Seconde !

Question 1 sur 10 10:00

[{"id":71882,"question":"Quelle est la solution de l'équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = 12","option_c":"x = 2","option_d":"x = 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"3x - 5 = 7 → 3x = 12 → x = 4. La solution est donc x = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71883,"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 = 16 - 12 = 4 \u003E 0, donc la fonction s'annule en deux points. Elle n'est pas toujours positive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71884,"question":"Quel est le développement de (2x + 3)(x - 1) ?","option_a":"2x² + x - 3","option_b":"2x² + 5x - 3","option_c":"2x² - x - 3","option_d":"2x² + x + 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"(2x + 3)(x - 1) = 2x² - 2x + 3x - 3 = 2x² + x - 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71885,"question":"L'inéquation 2x + 1 ≤ 5 a pour solution x ≤ 2. Vrai ou Faux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x + 1 ≤ 5 → 2x ≤ 4 → x ≤ 2. La solution est correcte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71886,"question":"Quelle est la forme factorisée de x² - 9 ?","option_a":"(x - 3)(x + 3)","option_b":"(x - 9)(x + 1)","option_c":"(x - 3)²","option_d":"(x + 3)²","option_e":"","option_f":"","bonne_reponse":"A","explication":"x² - 9 est une différence de carrés : (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71887,"question":"La fonction f(x) = -2x + 5 est-elle décroissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur est -2 \u003C 0, donc la fonction est décroissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71888,"question":"Résoudre l'inéquation (x - 1)(x + 2) \u003E 0.","option_a":"x ∈ ]-∞ ; -2[ ∪ ]1 ; +∞[","option_b":"x ∈ ]-2 ; 1[","option_c":"x ∈ ]-∞ ; 1[","option_d":"x ∈ ]-2 ; +∞[","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les racines sont x = -2 et x = 1. Le produit est positif à l'extérieur des racines.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71889,"question":"Quel est le résultat de √(16) + √(9) ?","option_a":"7","option_b":"5","option_c":"10","option_d":"13","option_e":"","option_f":"","bonne_reponse":"B","explication":"√(16) = 4 et √(9) = 3, donc 4 + 3 = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71890,"question":"La fonction f(x) = 3x² + 2x - 1 est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction paire vérifie f(-x) = f(x). Ici, f(-x) = 3x² - 2x - 1 ≠ f(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71891,"question":"Quelle est la solution de l'équation x² + 4x + 4 = 0 ?","option_a":"x = -2","option_b":"x = 2","option_c":"x = 0","option_d":"x = 4","option_e":"","option_f":"","bonne_reponse":"A","explication":"x² + 4x + 4 = (x + 2)² = 0 → x = -2 (solution double).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]