Quiz : Maîtrisez les fondamentaux des mathématiques en Terminale

Question 1 sur 10 10:00

[{"id":4114,"question":"Quelle est la limite de la suite définie par u_n = (3n + 2)\/(2n - 1) quand n tend vers l'infini ?","option_a":"A. 1","option_b":"B. 3\/2","option_c":"C. 2","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"La limite d'une suite rationnelle est égale au rapport des coefficients dominants. Ici, 3\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4115,"question":"La fonction f(x) = e^(2x) est-elle strictement croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de f(x) = 2e^(2x) est toujours positive, donc la fonction est strictement croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4116,"question":"Quelle est la solution générale de l'équation différentielle y' + 2y = 0 ?","option_a":"A. y = Ce^(-2x)","option_b":"B. y = Ce^(2x)","option_c":"C. y = Cx^2","option_d":"D. y = Cx","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation est linéaire du premier ordre. La solution générale est y = Ce^(-2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4117,"question":"L'intégrale ∫(de 0 à 1) x^2 dx est-elle égale à 1\/3 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de x^2 entre 0 et 1 est [x^3\/3] de 0 à 1 = 1\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4118,"question":"Quelle est la dérivée de la fonction f(x) = ln(3x + 1) ?","option_a":"A. 3\/(3x + 1)","option_b":"B. 1\/(3x + 1)","option_c":"C. 3x\/(3x + 1)","option_d":"D. 1\/x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de ln(u) est u'\/u. Ici, u = 3x + 1, donc u' = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4119,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est-elle de 1\/2 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les nombres pairs sont 2, 4, 6, soit 3 cas favorables sur 6 possibles. La probabilité est donc 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4120,"question":"Quelle est la valeur de l'intégrale ∫(de 0 à π) sin(x) dx ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. 2","option_d":"D. π","option_e":"","option_f":"","bonne_reponse":"C","explication":"L'intégrale de sin(x) entre 0 et π est [-cos(x)] de 0 à π = -(-1) - (-1) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4121,"question":"La fonction f(x) = x^3 - 3x 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) = -x^3 + 3x ≠ f(x). La fonction est impaire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4122,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"A. x = e^2","option_b":"B. x = 2","option_c":"C. x = 1\/e^2","option_d":"D. x = ln(2)","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation ln(x) = 2 équivaut à x = e^2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":4123,"question":"La suite définie par u_n = (-1)^n est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La suite alterne entre -1 et 1, donc elle n'a pas de limite. Elle est divergente.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]