Quiz Maths Terminale : Testez vos connaissances en analyse et algèbre

Question 1 sur 10 10:00

[{"id":49231,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) quand x tend vers l'infini ?","option_a":"A. 3","option_b":"B. 0","option_c":"C. -3","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"La limite d'un quotient de polynômes quand x tend vers l'infini est égale au rapport des coefficients dominants. Ici, 3x²\/x² = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49232,"question":"La fonction f(x) = x³ - 3x² + 2x est croissante sur l'intervalle [-1, 1].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 3x² - 6x + 2 est positive sur [-1, 1] (car son discriminant est négatif), donc la fonction est bien croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49233,"question":"Quelle est la solution générale de l'équation différentielle y' + 2y = 0 ?","option_a":"A. y = Ce^(2x)","option_b":"B. y = Ce^(-2x)","option_c":"C. y = Cx + C","option_d":"D. y = C\/x","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'équation différentielle linéaire du premier ordre y' + 2y = 0 a pour solution y = Ce^(-2x), où C est une constante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49234,"question":"Si une variable aléatoire X suit une loi normale N(μ, σ²), que vaut P(μ - σ ≤ X ≤ μ + σ) ?","option_a":"A. 0,68","option_b":"B. 0,95","option_c":"C. 0,997","option_d":"D. 0,5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour une loi normale, environ 68% des valeurs se situent dans l'intervalle [μ - σ, μ + σ].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49235,"question":"Le déterminant d'une matrice triangulaire est égal au produit des éléments de sa diagonale.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une propriété fondamentale des matrices triangulaires : leur déterminant est bien le produit des éléments diagonaux.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49236,"question":"Quelle est la dérivée de la fonction f(x) = ln(2x + 1) ?","option_a":"A. 1\/(2x + 1)","option_b":"B. 2\/(2x + 1)","option_c":"C. 1\/(x + 1)","option_d":"D. 2x\/(2x + 1)","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de ln(u) est u'\/u. Ici, u = 2x + 1, donc u' = 2, d'où f'(x) = 2\/(2x + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49237,"question":"Dans une suite géométrique de raison q = -2, le terme u₅ est égal à u₀ × (-2)^5.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La formule générale d'une suite géométrique est uₙ = u₀ × qⁿ. Ici, u₅ = u₀ × (-2)^5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49238,"question":"Quelle est la valeur de l'intégrale ∫₀¹ (3x² + 2x) dx ?","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 [x³ + x²]₀¹ = (1 + 1) - (0 + 0) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49239,"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":49240,"question":"Quelle est la solution de l'équation complexe z² = -4 ?","option_a":"A. z = 2i ou z = -2i","option_b":"B. z = 4i ou z = -4i","option_c":"C. z = 2 ou z = -2","option_d":"D. z = i ou z = -i","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les solutions de z² = -4 sont z = 2i et z = -2i, car (2i)² = -4 et (-2i)² = -4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]