Quiz : Maîtrisez l'algèbre de Terminale en 10 questions

Question 1 sur 10 10:00

[{"id":20698,"question":"Quelle est la limite de la suite définie par u_n = (3n² + 2n - 1)\/(n² + 5) lorsque n tend vers l'infini ?","option_a":"A. 0","option_b":"B. 3","option_c":"C. 1","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"La limite d'une suite rationnelle est égale au rapport des termes de plus haut degré. Ici, u_n tend vers 3n²\/n² = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20699,"question":"L'équation x² - 5x + 6 = 0 admet-elle deux solutions réelles distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = 25 - 24 = 1 \u003E 0, donc l'équation admet deux solutions réelles distinctes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20700,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 4x² + 5x - 2 ?","option_a":"A. 3x² - 8x + 5","option_b":"B. x² - 4x + 5","option_c":"C. 3x² - 4x + 5","option_d":"D. x³ - 8x + 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x³ est 3x², celle de -4x² est -8x, celle de 5x est 5, et celle de -2 est 0. Donc f'(x) = 3x² - 8x + 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20701,"question":"La suite définie par u_0 = 1 et u_{n+1} = 2u_n + 3 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite arithmétique a une différence constante entre deux termes consécutifs. Ici, u_{n+1} - u_n = u_n + 3, qui n'est pas constant.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20702,"question":"Quelle est la solution de l'inéquation (x - 2)(x + 3) \u003E 0 ?","option_a":"A. x ∈ ]-∞, -3[ ∪ ]2, +∞[","option_b":"B. x ∈ ]-3, 2[","option_c":"C. x ∈ ]-∞, 2[","option_d":"D. x ∈ ]-3, +∞[","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le produit (x - 2)(x + 3) est positif lorsque les deux facteurs sont de même signe, c'est-à-dire x \u003C -3 ou x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20703,"question":"La fonction f(x) = 1\/x est-elle continue sur son ensemble de définition ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction f(x) = 1\/x est continue sur son ensemble de définition, qui est ℝ*, car elle est dérivable sur cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20704,"question":"Quelle est la limite de la fonction f(x) = (x² - 1)\/(x - 1) lorsque x tend vers 1 ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. 2","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"C","explication":"En factorisant, f(x) = (x - 1)(x + 1)\/(x - 1) = x + 1 pour x ≠ 1. Donc la limite lorsque x tend vers 1 est 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20705,"question":"L'équation x³ - 6x² + 11x - 6 = 0 admet-elle trois solutions réelles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En factorisant, on obtient (x - 1)(x - 2)(x - 3) = 0, donc les solutions sont x = 1, x = 2 et x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20706,"question":"Quelle est la dérivée de la fonction f(x) = √(x² + 1) ?","option_a":"A. x\/√(x² + 1)","option_b":"B. (x² + 1)\/√(x² + 1)","option_c":"C. 2x\/√(x² + 1)","option_d":"D. x\/√(x + 1)","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant la dérivée d'une fonction composée, f'(x) = (1\/2)(x² + 1)^{-1\/2} * 2x = x\/√(x² + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20707,"question":"La suite définie par u_n = (-1)^n est-elle bornée ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La suite u_n = (-1)^n prend alternativement les valeurs -1 et 1, donc elle est bornée par -1 et 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]