Quiz : Révisons les fonctions et dérivées en Terminale Math

Question 1 sur 10 10:00

[{"id":57521,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2x","option_c":"6x - 5","option_d":"6x + 2x - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : (3x²)' = 6x, (2x)' = 2, et (-5)' = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57522,"question":"L'équation f'(x) = 0 permet de trouver les extrema d'une fonction f.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai. Les points où la dérivée s'annule correspondent aux extrema (minimum ou maximum) de la fonction.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57523,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 5 ?","option_a":"x \u003E 4","option_b":"x \u003E 1","option_c":"x \u003C 4","option_d":"x \u003C 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvez l'inéquation : 2x \u003E 8 → x \u003E 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57524,"question":"La fonction f(x) = x³ est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai. Sa dérivée f'(x) = 3x² est toujours positive ou nulle, donc la fonction est croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57525,"question":"Quelle est la limite de f(x) = (2x + 1)\/(x - 3) lorsque x tend vers l'infini ?","option_a":"2","option_b":"1\/3","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"Divisez numérateur et dénominateur par x : (2 + 1\/x)\/(1 - 3\/x) → 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57526,"question":"La dérivée de f(x) = sin(x) est f'(x) = cos(x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai. C'est une propriété fondamentale des fonctions trigonométriques.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57527,"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":"Factorisez : (x - 2)(x - 3) = 0 → x = 2 ou x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57528,"question":"La fonction f(x) = 1\/x est-elle définie en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Faux. La fonction 1\/x n'est pas définie en x = 0 (division par zéro).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57529,"question":"Quelle est la dérivée de f(x) = ln(x) ?","option_a":"1\/x","option_b":"x","option_c":"e^x","option_d":"1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de ln(x) est 1\/x, une propriété essentielle des logarithmes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57530,"question":"La fonction f(x) = e^x est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai. La fonction exponentielle e^x est strictement positive pour tout x réel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]