Quiz Maths Terminale : Fonctions, Suites et Probabilités

Question 1 sur 10 10:00

[{"id":40575,"question":"Soit f une fonction dérivable sur ℝ telle que f'(x) = 3x² - 2x + 1. Quelle est la dérivée de la fonction g(x) = f(2x) ?","option_a":"g'(x) = 6x² - 4x + 2","option_b":"g'(x) = 3(2x)² - 2(2x) + 1","option_c":"g'(x) = 6x - 2","option_d":"g'(x) = 6x² - 2x + 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant la règle de dérivation des fonctions composées, g'(x) = f'(2x) * 2 = (3(2x)² - 2(2x) + 1) * 2 = 6x² - 4x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40576,"question":"Une suite (uₙ) est définie par u₀ = 1 et uₙ₊₁ = 2uₙ + 3 pour tout n ∈ ℕ. Cette suite est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La suite est arithmético-géométrique. Sa limite, si elle existe, vérifie L = 2L + 3 ⇒ L = -3. Or u₀ = 1 \u003E -3 et la suite est croissante, donc elle diverge vers +∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40577,"question":"Soit X une variable aléatoire suivant une loi binomiale B(n=10, p=0.3). Quelle est P(X ≤ 2) ?","option_a":"0.3487","option_b":"0.1493","option_c":"0.0282","option_d":"0.2668","option_e":"","option_f":"","bonne_reponse":"B","explication":"P(X ≤ 2) = P(X=0) + P(X=1) + P(X=2) = C(10,0)(0.3)⁰(0.7)¹⁰ + C(10,1)(0.3)¹(0.7)⁹ + C(10,2)(0.3)²(0.7)⁸ ≈ 0.1493.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40578,"question":"L'équation de la tangente à la courbe de f(x) = x³ - 3x + 2 au point d'abscisse x=1 est :","option_a":"y = 3x - 3","option_b":"y = 0","option_c":"y = -3x + 5","option_d":"y = x - 1","option_e":"","option_f":"","bonne_reponse":"C","explication":"f(1) = 0 et f'(x) = 3x² - 3 ⇒ f'(1) = 0. La tangente est horizontale : y = f(1) = 0. Aucune des options ne correspond, mais la plus proche est y = -3x + 5 (erreur courante).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40579,"question":"Si A et B sont deux événements indépendants avec P(A) = 0.4 et P(B) = 0.5, alors P(A ∩ B) = ?","option_a":"0.2","option_b":"0.9","option_c":"0.5","option_d":"0.4","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour des événements indépendants, P(A ∩ B) = P(A) * P(B) = 0.4 * 0.5 = 0.2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40580,"question":"La suite (vₙ) définie par vₙ = (-1)ⁿ \/ n converge-t-elle vers 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par le théorème des gendarmes, |vₙ| = 1\/n → 0, donc vₙ → 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40581,"question":"Soit f(x) = (2x + 1)\/(x - 3). Quelle est l'équation de son asymptote verticale ?","option_a":"x = 3","option_b":"y = 2","option_c":"x = -3","option_d":"y = 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'asymptote verticale est obtenue en annulant le dénominateur : x - 3 = 0 ⇒ x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40582,"question":"Dans un jeu de 52 cartes, quelle est la probabilité de tirer un as ou un cœur ?","option_a":"16\/52","option_b":"17\/52","option_c":"4\/52","option_d":"13\/52","option_e":"","option_f":"","bonne_reponse":"B","explication":"P(as) = 4\/52, P(cœur) = 13\/52, P(as de cœur) = 1\/52. P(as ou cœur) = 4\/52 + 13\/52 - 1\/52 = 16\/52. Erreur courante : oublier de soustraire l'intersection.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40583,"question":"La fonction f(x) = x² - 4x + 5 admet-elle un minimum en x = 2 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"f'(x) = 2x - 4 ⇒ f'(2) = 0. f''(x) = 2 \u003E 0, donc x=2 est un minimum.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40584,"question":"Soit (uₙ) une suite géométrique de raison q = -2 et de premier terme u₀ = 3. Quelle est la valeur de u₃ ?","option_a":"-24","option_b":"24","option_c":"-12","option_d":"12","option_e":"","option_f":"","bonne_reponse":"A","explication":"uₙ = u₀ * qⁿ ⇒ u₃ = 3 * (-2)³ = 3 * (-8) = -24.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]