Quiz Mathématiques Terminale : Fonctions, Suites et Probabilités

Question 1 sur 10 10:00

[{"id":64832,"question":"Soit f une fonction dérivable sur ℝ telle que f'(x) \u003E 0 pour tout x ∈ ℝ. Que peut-on dire de f ?","option_a":"f est constante","option_b":"f est strictement croissante","option_c":"f est strictement décroissante","option_d":"f n'est pas monotone","option_e":"","option_f":"","bonne_reponse":"B","explication":"Si la dérivée est strictement positive sur un intervalle, la fonction est strictement croissante sur cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64833,"question":"La suite (u_n) définie par u_n = (-1)^n est convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Cette suite alterne entre -1 et 1, elle n'a donc pas de limite et n'est pas convergente.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64834,"question":"Quelle est la dérivée de la fonction f(x) = ln(3x + 2) ?","option_a":"f'(x) = 1\/(3x + 2)","option_b":"f'(x) = 3\/(3x + 2)","option_c":"f'(x) = 1\/(x + 2)","option_d":"f'(x) = 3\/(x + 2)","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de ln(u) est u'\/u. Ici, u = 3x + 2, donc u' = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64835,"question":"Soit X une variable aléatoire suivant une loi binomiale B(n, p). Quelle est son espérance ?","option_a":"E(X) = n + p","option_b":"E(X) = n * p","option_c":"E(X) = p\/n","option_d":"E(X) = n - p","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'espérance d'une loi binomiale B(n, p) est E(X) = n * p.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64836,"question":"La fonction f(x) = x^3 - 3x est convexe sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée seconde f''(x) = 6x est négative sur ]-∞, 0[ et positive sur ]0, +∞[, donc f n'est pas convexe sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64837,"question":"Quelle est la limite de la suite u_n = (2n + 1)\/(n + 3) quand n tend vers +∞ ?","option_a":"0","option_b":"2","option_c":"1\/3","option_d":"1","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant numérateur et dénominateur par n, on obtient u_n = (2 + 1\/n)\/(1 + 3\/n) → 2\/1 = 2 quand n → +∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64838,"question":"Soit A et B deux événements indépendants d'un même univers. Que vaut P(A ∩ B) ?","option_a":"P(A) + P(B)","option_b":"P(A) * P(B)","option_c":"P(A) - P(B)","option_d":"P(A) \/ P(B)","option_e":"","option_f":"","bonne_reponse":"B","explication":"Par définition de l'indépendance, P(A ∩ B) = P(A) * P(B).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64839,"question":"La fonction f(x) = e^(2x) est solution de l'équation différentielle y' = 2y.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de f(x) = e^(2x) est f'(x) = 2e^(2x) = 2f(x), donc f est bien solution de y' = 2y.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64840,"question":"Quelle est l'intégrale ∫(3x^2 + 2x + 1) dx ?","option_a":"x^3 + x^2 + x + C","option_b":"x^3 + x^2 + C","option_c":"3x^3 + 2x^2 + x + C","option_d":"x^3 + x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de 3x^2 est x^3, celle de 2x est x^2, et celle de 1 est x. Donc ∫(3x^2 + 2x + 1) dx = x^3 + x^2 + x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64841,"question":"Soit (u_n) une suite géométrique de raison q = -2 et de premier terme u_0 = 3. Que vaut u_3 ?","option_a":"-24","option_b":"24","option_c":"-12","option_d":"12","option_e":"","option_f":"","bonne_reponse":"A","explication":"u_n = u_0 * q^n, donc u_3 = 3 * (-2)^3 = 3 * (-8) = -24.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]