Quiz — _Enoncé-Révision DC2.pdf

Question 1 sur 5 10:00

[{"id":668,"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":"L'équation x² - 5x + 6 = 0 se factorise en (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":669,"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 formule (ax^n)' = nax^(n-1). Ainsi, f'(x) = 6x - 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":670,"question":"Dans un triangle rectangle, si l'hypoténuse mesure 10 cm et un côté mesure 6 cm, quelle est la longueur du troisième côté ?","option_a":"8 cm","option_b":"4 cm","option_c":"12 cm","option_d":"5 cm","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après le théorème de Pythagore, si c est le côté inconnu, alors c² = 10² - 6² = 100 - 36 = 64. Donc c = 8 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":671,"question":"Quelle est la somme des 5 premiers termes d'une suite géométrique de premier terme 2 et de raison 3 ?","option_a":"242","option_b":"240","option_c":"244","option_d":"246","option_e":"","option_f":"","bonne_reponse":"A","explication":"La somme des n premiers termes d'une suite géométrique est S_n = u_1 * (1 - r^n) \/ (1 - r). Ici, S_5 = 2 * (1 - 3^5) \/ (1 - 3) = 2 * (1 - 243) \/ (-2) = 242.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":672,"question":"Quelle est l'image de -1 par la fonction f(x) = x³ + 2x² - x + 3 ?","option_a":"3","option_b":"5","option_c":"1","option_d":"-1","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour trouver l'image de -1, on remplace x par -1 dans la fonction : f(-1) = (-1)³ + 2*(-1)² - (-1) + 3 = -1 + 2 + 1 + 3 = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]