Quiz Maths Bac Sciences : Testez vos connaissances en fonctions et probabilités !

Question 1 sur 5 10:00

[{"id":1138,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"f'(x) = 6x - 5","option_b":"f'(x) = 3x - 5","option_c":"f'(x) = 6x² - 5","option_d":"f'(x) = 3x² - 5x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d’une fonction polynôme se calcule terme à terme : la dérivée de 3x² est 6x, celle de -5x est -5, et celle de 2 est 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":1139,"question":"Quelle est la solution de l’équation x² - 4x + 3 = 0 ?","option_a":"x = 1 ou x = 3","option_b":"x = -1 ou x = -3","option_c":"x = 2 ou x = 2","option_d":"x = 0 ou x = 4","option_e":"","option_f":"","bonne_reponse":"A","explication":"On factorise l’équation : (x-1)(x-3) = 0, donc les solutions sont x = 1 et x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":1140,"question":"Quelle est la probabilité d’obtenir un nombre pair en lançant un dé équilibré ?","option_a":"1\/2","option_b":"1\/3","option_c":"2\/3","option_d":"1\/6","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un dé a 6 faces, dont 3 sont paires (2, 4, 6). La probabilité est donc 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":1141,"question":"Quelle est l’équation de la tangente à la courbe de f(x) = x² au point d’abscisse x = 1 ?","option_a":"y = 2x - 1","option_b":"y = x + 1","option_c":"y = 2x + 1","option_d":"y = x - 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La tangente a pour équation y = f'(a)(x-a) + f(a). Ici, f'(1) = 2 et f(1) = 1, donc y = 2(x-1) + 1 = 2x - 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":1142,"question":"Quelle est la limite de la fonction 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":"En divisant numérateur et dénominateur par x, on obtient f(x) = (2 + 1\/x)\/(1 - 3\/x). Lorsque x tend vers l’infini, 1\/x et 3\/x tendent vers 0, donc la limite est 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]