Quiz — 3_Exercices de consolidation.pdf

Question 1 sur 5 10:00

[{"id":673,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour résoudre x² - 5x + 6 = 0, on factorise : (x-2)(x-3) = 0. Les solutions sont donc x = 2 et x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":674,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 2x + 1 ?","option_a":"f'(x) = 6x - 2","option_b":"f'(x) = 3x - 2","option_c":"f'(x) = 6x² - 2x","option_d":"f'(x) = 3x² - 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle : (ax^n)' = n·a·x^(n-1). Ainsi, f'(x) = 6x - 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":675,"question":"Dans un repère orthonormé, quelle est la distance entre les points A(2;3) et B(-1;5) ?","option_a":"√13","option_b":"√17","option_c":"5","option_d":"√29","option_e":"","option_f":"","bonne_reponse":"B","explication":"La distance entre deux points A(x₁;y₁) et B(x₂;y₂) est donnée par √[(x₂-x₁)² + (y₂-y₁)²]. Ici, √[(-1-2)² + (5-3)²] = √(9 + 4) = √13.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":676,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² + 1) lorsque x tend vers +∞ ?","option_a":"0","option_b":"2","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour les fonctions rationnelles, la limite en ±∞ est égale au rapport des coefficients dominants. Ici, 2x²\/x² = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":677,"question":"Quel est le produit scalaire des vecteurs u(3;-1) et v(2;4) ?","option_a":"10","option_b":"2","option_c":"-2","option_d":"6","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le produit scalaire de deux vecteurs u(x₁;y₁) et v(x₂;y₂) est donné par x₁x₂ + y₁y₂. Ici, 3×2 + (-1)×4 = 6 - 4 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]