Quiz Maths Terminale : Testez vos connaissances en analyse et algèbre

Question 1 sur 10 10:00

[{"id":73692,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) lorsque x tend vers +∞ ?","option_a":"A. 3","option_b":"B. 0","option_c":"C. +∞","option_d":"D. -∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"La limite d'un quotient de polynômes de même degré est égale au rapport des coefficients dominants, ici 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73693,"question":"La fonction f(x) = x³ - 3x + 2 est strictement croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 3x² - 3 s'annule en x = ±1, donc la fonction n'est pas strictement croissante sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73694,"question":"Quelle est la solution de l'équation différentielle y' + 2y = 0 avec y(0) = 1 ?","option_a":"A. y = e^(-2x)","option_b":"B. y = e^(2x)","option_c":"C. y = 1 - 2x","option_d":"D. y = 2e^(-x)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La solution générale est y = Ce^(-2x). Avec y(0) = 1, on trouve C = 1, donc y = e^(-2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73695,"question":"Soit une suite définie par u₀ = 2 et uₙ₊₁ = (uₙ + 4)\/2. Cette suite est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La suite est arithmético-géométrique et converge vers la solution de L = (L + 4)\/2, soit L = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73696,"question":"Quelle est la dérivée de la fonction f(x) = ln(3x² + 1) ?","option_a":"A. 6x\/(3x² + 1)","option_b":"B. 3x\/(3x² + 1)","option_c":"C. 6x","option_d":"D. 1\/(3x² + 1)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de ln(u) est u'\/u, ici u = 3x² + 1, donc u' = 6x. La dérivée est 6x\/(3x² + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73697,"question":"L'intégrale ∫₀¹ (2x + 1) dx vaut :","option_a":"A. 1","option_b":"B. 2","option_c":"C. 3","option_d":"D. 4","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'intégrale se calcule comme [x² + x]₀¹ = (1 + 1) - (0 + 0) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73698,"question":"Soit une variable aléatoire X suivant une loi normale N(0,1). P(X ≤ 1) est environ égal à :","option_a":"A. 0.68","option_b":"B. 0.84","option_c":"C. 0.95","option_d":"D. 0.99","option_e":"","option_f":"","bonne_reponse":"B","explication":"D'après la table de la loi normale centrée réduite, P(X ≤ 1) ≈ 0.8413.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73699,"question":"La fonction f(x) = e^(-x²) est paire.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction est paire si f(-x) = f(x). Ici, f(-x) = e^(-(-x)²) = e^(-x²) = f(x), donc elle est paire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73700,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"A. x = 2 ou x = 3","option_b":"B. x = -2 ou x = -3","option_c":"C. x = 1 ou x = 6","option_d":"D. x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les solutions sont obtenues en factorisant : (x-2)(x-3) = 0, donc x = 2 ou x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73701,"question":"Soit une suite géométrique de raison q = 2 et de premier terme u₀ = 3. La somme S₅ = u₀ + u₁ + ... + u₅ vaut :","option_a":"A. 93","option_b":"B. 189","option_c":"C. 315","option_d":"D. 63","option_e":"","option_f":"","bonne_reponse":"A","explication":"La somme d'une suite géométrique est Sₙ = u₀ * (1 - q^(n+1))\/(1 - q). Ici, S₅ = 3 * (1 - 2⁶)\/(1 - 2) = 3 * (1 - 64)\/(-1) = 189.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]