Quiz de révision : Mathématiques Bac — Équations, Fonctions et Probabilités

Question 1 sur 10 10:00

[{"id":43106,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation x² - 5x + 6 = 0 se factorise en (x-2)(x-3) = 0, donc les solutions sont x = 2 et x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43107,"question":"La dérivée de f(x) = x³ - 3x² + 2x est f'(x) = 3x² - 6x + 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x³ est 3x², celle de -3x² est -6x, et celle de 2x est 2. Donc f'(x) = 3x² - 6x + 2 est correcte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43108,"question":"Quelle est la limite de la suite uₙ = (2n + 1)\/(n + 3) lorsque n tend vers l'infini ?","option_a":"2","option_b":"1\/3","option_c":"0","option_d":"1","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant le numérateur et le dénominateur par n, on obtient (2 + 1\/n)\/(1 + 3\/n), donc la limite est 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43109,"question":"Si A et B sont deux événements indépendants, alors P(A ∩ B) = P(A) × P(B).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, deux événements sont indépendants si et seulement si P(A ∩ B) = P(A) × P(B).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43110,"question":"Quelle est la solution de l'inéquation 2x - 5 \u003E 3x + 1 ?","option_a":"x \u003C -6","option_b":"x \u003E -6","option_c":"x \u003C 6","option_d":"x \u003E 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"En simplifiant, on obtient -x \u003E 6, donc x \u003C -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43111,"question":"La fonction f(x) = x² - 4x + 5 admet un minimum en x = 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 2x - 4 s'annule en x = 2, et comme f''(x) = 2 \u003E 0, il s'agit bien d'un minimum.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43112,"question":"Quelle est l'espérance d'une variable aléatoire X suivant une loi binomiale B(n=10, p=0,3) ?","option_a":"3","option_b":"0,3","option_c":"10","option_d":"7","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'espérance d'une loi binomiale B(n,p) est E(X) = n × p = 10 × 0,3 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43113,"question":"La suite uₙ = 3 × 2ⁿ est une suite géométrique de raison 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une suite géométrique a la forme uₙ = u₀ × rⁿ. Ici, uₙ = 3 × 2ⁿ, donc la raison est bien 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43114,"question":"Quelle est la dérivée de f(x) = ln(x² + 1) ?","option_a":"f'(x) = 2x\/(x² + 1)","option_b":"f'(x) = 1\/(x² + 1)","option_c":"f'(x) = 2x","option_d":"f'(x) = x\/(x² + 1)","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant la dérivée de ln(u), on obtient f'(x) = (2x)\/(x² + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43115,"question":"Si P(A) = 0,4 et P(B) = 0,5, alors P(A ∪ B) = 0,9 si A et B sont incompatibles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Si A et B sont incompatibles, alors P(A ∪ B) = P(A) + P(B) = 0,4 + 0,5 = 0,9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]