Quiz de révision : Mathématiques Bac — Exercices clés

Question 1 sur 10 10:00

[{"id":44686,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x + 2","option_c":"6x² + 2","option_d":"6x + 2x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de f(x) = 3x² + 2x - 5 est f'(x) = 6x + 2, car la dérivée de x² est 2x et celle de x est 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":44687,"question":"L'équation x² - 5x + 6 = 0 admet deux solutions réelles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = (-5)² - 4×1×6 = 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":44688,"question":"Quelle est la limite de la fonction f(x) = (2x + 1)\/(x - 3) lorsque x tend vers +∞ ?","option_a":"2","option_b":"1","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 → +∞, 1\/x → 0, donc la limite est 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":44689,"question":"La probabilité d'un événement impossible est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La probabilité d'un événement impossible est égale à 0, tandis que celle d'un événement certain est égale à 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":44690,"question":"Quelle est la somme des 5 premiers termes de la suite géométrique de premier terme 2 et de raison 3 ?","option_a":"242","option_b":"243","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 - q^n)\/(1 - q). 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":44691,"question":"La fonction f(x) = x³ - 3x² + 4 est croissante sur l'intervalle ]-∞, 0[.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 6x. Sur ]-∞, 0[, f'(x) \u003E 0 car 3x² - 6x = 3x(x - 2) \u003E 0 (x \u003C 0 et x - 2 \u003C 0). La fonction est donc croissante sur cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":44692,"question":"Quelle est la solution de l'inéquation 2x - 7 ≤ 3x + 1 ?","option_a":"x ≥ -8","option_b":"x ≤ -8","option_c":"x ≥ 8","option_d":"x ≤ 8","option_e":"","option_f":"","bonne_reponse":"B","explication":"En résolvant 2x - 7 ≤ 3x + 1, on obtient -x ≤ 8, soit x ≥ -8. L'inéquation est donc équivalente à x ≤ -8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":44693,"question":"La variance d'une série statistique mesure la dispersion des valeurs autour de la moyenne.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La variance est une mesure de la dispersion des valeurs d'une série statistique autour de sa moyenne. Plus la variance est grande, plus les valeurs sont dispersées.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":44694,"question":"Quelle est la primitive de la fonction f(x) = 4x³ - 2x + 1 ?","option_a":"x⁴ - x² + x + C","option_b":"x⁴ - x² + 1 + C","option_c":"4x⁴ - x² + x + C","option_d":"x⁴ - 2x² + x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de f(x) = 4x³ - 2x + 1 est F(x) = x⁴ - x² + x + C, car la primitive de x^n est x^(n+1)\/(n+1) et celle de 1 est x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":44695,"question":"La suite définie par u_n = 2n + 1 est une suite arithmétique de raison 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La suite u_n = 2n + 1 est arithmétique car u_{n+1} - u_n = 2(n+1) + 1 - (2n + 1) = 2, donc la raison est 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]