Quiz Maths : Suites, Fonctions et Géométrie — 2ème Année Secondaire

Question 1 sur 10 10:00

[{"id":60787,"question":"Quelle est la raison d'une suite géométrique si le premier terme est 5 et le troisième terme est 45 ?","option_a":"3","option_b":"-3","option_c":"9","option_d":"1\/3","option_e":"","option_f":"","bonne_reponse":"A","explication":"La raison r se calcule par √(45\/5) = √9 = 3. Une suite géométrique a pour formule uₙ = u₀ × rⁿ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60788,"question":"La fonction f(x) = 2x² - 8x + 6 admet-elle un minimum ? Si oui, quelle est son ordonnée ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction est un polynôme du second degré avec a=2\u003E0, donc elle admet un minimum en x = -b\/(2a) = 2. f(2) = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60789,"question":"Soit la suite définie par uₙ = 3n + 2. Que vaut u₅ ?","option_a":"17","option_b":"15","option_c":"14","option_d":"20","option_e":"","option_f":"","bonne_reponse":"A","explication":"u₅ = 3×5 + 2 = 17. Il s'agit d'une suite arithmétique de raison 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60790,"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 deux solutions réelles distinctes : x = 2 et x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60791,"question":"Quelle est l'image de 3 par la fonction f(x) = (x² - 1)\/(x - 2) ?","option_a":"8","option_b":"4","option_c":"6","option_d":"10","option_e":"","option_f":"","bonne_reponse":"C","explication":"f(3) = (9 - 1)\/(3 - 2) = 8\/1 = 8. Attention à l'ensemble de définition (x ≠ 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60792,"question":"La suite (uₙ) définie par uₙ = 2ⁿ est-elle géométrique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"uₙ₊₁\/uₙ = 2ⁿ⁺¹\/2ⁿ = 2, donc la suite est géométrique de raison 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60793,"question":"Soit f(x) = x³ - 3x² + 2. Que vaut f'(2) ?","option_a":"0","option_b":"3","option_c":"6","option_d":"-3","option_e":"","option_f":"","bonne_reponse":"A","explication":"f'(x) = 3x² - 6x. f'(2) = 12 - 12 = 0. C'est un point critique (maximum ou minimum).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60794,"question":"L'inéquation x² - 4x + 3 ≤ 0 a-t-elle pour solution l'intervalle [1, 3] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les racines sont x=1 et x=3. Le polynôme est négatif entre les racines (a=1\u003E0), donc S = [1, 3].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60795,"question":"Quelle est la limite de la suite uₙ = (3n + 1)\/(2n - 5) quand n tend vers +∞ ?","option_a":"3\/2","option_b":"1","option_c":"+∞","option_d":"0","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par n, on obtient (3 + 1\/n)\/(2 - 5\/n) → 3\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60796,"question":"Le point A(2, -1) appartient-il à la droite d'équation y = 2x - 5 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour x=2, y = 2×2 - 5 = -1. Donc A appartient à la droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]