Quiz Maths Terminale : Fonctions, Probabilités & Suites

Question 1 sur 10 10:00

[{"id":61697,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x - 5","option_d":"3x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la formule (ax^n)' = n*ax^(n-1). Ici, f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61698,"question":"L'intégrale ∫(2x + 1) dx entre 0 et 1 vaut :","option_a":"2","option_b":"1","option_c":"3\/2","option_d":"0","option_e":"","option_f":"","bonne_reponse":"C","explication":"L'intégrale se calcule en trouvant la primitive F(x) = x² + x, puis en évaluant F(1) - F(0) = (1 + 1) - (0 + 0) = 2. Cependant, l'intégrale de 2x + 1 entre 0 et 1 est [x² + x]₀¹ = 1 + 1 - 0 = 2. Correction : la bonne réponse est 2 (option A).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61699,"question":"Une variable aléatoire X suit une loi binomiale B(10, 0.3). Quelle est P(X = 3) ?","option_a":"0.2668","option_b":"0.2334","option_c":"0.2001","option_d":"0.1502","option_e":"","option_f":"","bonne_reponse":"A","explication":"P(X = k) = C(n,k) * p^k * (1-p)^(n-k). Ici, P(X=3) = C(10,3) * (0.3)^3 * (0.7)^7 ≈ 0.2668.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61700,"question":"La suite définie par u₀ = 2 et uₙ₊₁ = 3uₙ - 1 est une suite géométrique.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite géométrique vérifie uₙ₊₁ = q*uₙ. Ici, uₙ₊₁ = 3uₙ - 1 ne correspond pas à cette forme. La suite est arithmético-géométrique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61701,"question":"Quelle est la limite de la suite uₙ = (2n² + 3n) \/ (n² + 1) quand n tend vers l'infini ?","option_a":"0","option_b":"2","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant numérateur et dénominateur par n², on obtient uₙ = (2 + 3\/n) \/ (1 + 1\/n²). Quand n → ∞, uₙ → 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61702,"question":"Si f est une fonction dérivable sur ℝ, alors f' est continue sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Un contre-exemple est la fonction f(x) = x² * sin(1\/x) pour x ≠ 0 et f(0) = 0. f est dérivable en 0 mais f' n'est pas continue en 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61703,"question":"Quelle est la primitive de f(x) = e^(2x) ?","option_a":"(1\/2)e^(2x) + C","option_b":"e^(2x) + C","option_c":"2e^(2x) + C","option_d":"(1\/2)e^x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de e^(ax) est (1\/a)e^(ax) + C. Ici, a = 2, donc la primitive est (1\/2)e^(2x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61704,"question":"Une loi normale N(μ, σ²) est symétrique par rapport à sa moyenne μ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une loi normale est toujours symétrique par rapport à sa moyenne μ, ce qui en fait une distribution unimodale et symétrique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61705,"question":"Soit la suite uₙ définie par u₀ = 1 et uₙ₊₁ = uₙ \/ 2. Quelle est sa limite ?","option_a":"0","option_b":"1","option_c":"2","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"Cette suite est géométrique de raison 1\/2. Comme |1\/2| \u003C 1, la suite converge vers 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61706,"question":"Quelle est la valeur de l'intégrale ∫(sin(x)) dx entre 0 et π\/2 ?","option_a":"0","option_b":"1","option_c":"-1","option_d":"π\/2","option_e":"","option_f":"","bonne_reponse":"B","explication":"La primitive de sin(x) est -cos(x). Ainsi, ∫(sin(x)) dx entre 0 et π\/2 = [-cos(π\/2)] - [-cos(0)] = 0 - (-1) = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]