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

Question 1 sur 10 10:00

[{"id":10988,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"A. 6x + 2","option_b":"B. 3x + 2","option_c":"C. 6x² + 2","option_d":"D. 3x² + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme à terme : (3x²)' = 6x, (2x)' = 2 et (-5)' = 0. Donc f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":10989,"question":"L'équation x² - 5x + 6 = 0 admet 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 = b² - 4ac = 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":10990,"question":"Soit une suite géométrique de premier terme u₁ = 4 et de raison q = 2. Quel est le terme u₅ ?","option_a":"A. 64","option_b":"B. 128","option_c":"C. 256","option_d":"D. 512","option_e":"","option_f":"","bonne_reponse":"B","explication":"La formule d'une suite géométrique est uₙ = u₁ × q^(n-1). Donc u₅ = 4 × 2⁴ = 4 × 16 = 64. Attention, la question demande u₅, pas u₆ !","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":10991,"question":"Dans une classe de 30 élèves, 18 sont des filles. On choisit un élève au hasard. Quelle est la probabilité que ce soit un garçon ?","option_a":"A. 0,4","option_b":"B. 0,6","option_c":"C. 0,3","option_d":"D. 0,7","option_e":"","option_f":"","bonne_reponse":"A","explication":"Il y a 30 - 18 = 12 garçons. La probabilité est donc 12\/30 = 0,4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":10992,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle [-2 ; 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 3 s'annule en x = -1 et x = 1. La fonction est décroissante sur [-1 ; 1], donc pas croissante sur [-2 ; 2].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":10993,"question":"Quelle est la limite de la suite uₙ = (2n + 1)\/(n + 3) quand n tend vers l'infini ?","option_a":"A. 0","option_b":"B. 2","option_c":"C. 1","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"C","explication":"En divisant numérateur et dénominateur par n, on obtient uₙ = (2 + 1\/n)\/(1 + 3\/n). Quand n → ∞, 1\/n → 0, donc uₙ → 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":10994,"question":"Un sac contient 5 boules rouges et 3 boules bleues. On tire deux boules sans remise. Quelle est la probabilité d'obtenir deux boules rouges ?","option_a":"A. 5\/8","option_b":"B. 5\/14","option_c":"C. 25\/64","option_d":"D. 10\/28","option_e":"","option_f":"","bonne_reponse":"B","explication":"La probabilité est (5\/8) × (4\/7) = 20\/56 = 5\/14.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":10995,"question":"La fonction f(x) = 1\/x est dérivable en x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction f(x) = 1\/x n'est pas définie en x = 0, donc elle n'est pas dérivable en ce point.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":10996,"question":"Soit une suite arithmétique de premier terme u₁ = 7 et de raison r = -3. Quel est le terme u₁₀ ?","option_a":"A. -20","option_b":"B. -23","option_c":"C. -17","option_d":"D. -14","option_e":"","option_f":"","bonne_reponse":"A","explication":"La formule d'une suite arithmétique est uₙ = u₁ + (n-1)r. Donc u₁₀ = 7 + 9×(-3) = 7 - 27 = -20.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":10997,"question":"Quelle est la dérivée de la fonction f(x) = √(2x + 1) ?","option_a":"A. 1\/√(2x + 1)","option_b":"B. 1\/(2√(2x + 1))","option_c":"C. 2\/√(2x + 1)","option_d":"D. 1\/√(x + 1)","option_e":"","option_f":"","bonne_reponse":"B","explication":"En utilisant la formule de dérivation d'une fonction composée, f'(x) = (1\/2)(2x + 1)^(-1\/2) × 2 = 1\/√(2x + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]