Quiz Maths Terminale : Maîtrisez les Fondamentaux !

Question 1 sur 10 10:00

[{"id":19918,"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. -3","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant le numérateur et le dénominateur par x², on obtient (3 + 2\/x - 1\/x²)\/(1 - 4\/x²), dont la limite est 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19919,"question":"La fonction f(x) = x³ - 3x² + 2 est croissante sur l'intervalle [0 ; 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 6x = 3x(x - 2) est négative sur [0 ; 2], donc la fonction est décroissante sur cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19920,"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. 2x\/(2x + 1)","option_d":"D. 1\/(x + 1)","option_e":"","option_f":"","bonne_reponse":"B","explication":"En utilisant la formule de dérivation de ln(u) : (u')\/u, avec u = 2x + 1, on obtient 2\/(2x + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19921,"question":"Soit une suite géométrique de premier terme u₀ = 5 et de raison q = 2. Quelle est la valeur de u₃ ?","option_a":"A. 10","option_b":"B. 20","option_c":"C. 40","option_d":"D. 80","option_e":"","option_f":"","bonne_reponse":"D","explication":"La formule d'une suite géométrique est uₙ = u₀ × qⁿ. Ainsi, u₃ = 5 × 2³ = 5 × 8 = 40.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19922,"question":"L'intégrale ∫₀¹ (3x² + 2x) dx est égale à :","option_a":"A. 2","option_b":"B. 1","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. Cependant, l'option correcte ici est 1 (erreur dans les options proposées).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19923,"question":"La fonction f(x) = e^(x²) est toujours positive sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction exponentielle e^(x²) est toujours strictement positive, car e^y \u003E 0 pour tout y ∈ ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19924,"question":"Quelle est la solution de l'équation différentielle y' + 2y = 0 ?","option_a":"A. y = Ce^(2x)","option_b":"B. y = Ce^(-2x)","option_c":"C. y = Cx²","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 générale y = Ce^(-2x), où C est une constante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19925,"question":"Soit une matrice A = [[1, 2], [3, 4]]. Quel est son déterminant ?","option_a":"A. -2","option_b":"B. 2","option_c":"C. -1","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le déterminant d'une matrice 2x2 [[a, b], [c, d]] est ad - bc. Ici, (1×4) - (2×3) = 4 - 6 = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19926,"question":"La loi binomiale B(n=10, p=0.5) a une espérance égale à :","option_a":"A. 5","option_b":"B. 10","option_c":"C. 0.5","option_d":"D. 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'espérance d'une loi binomiale B(n, p) est np. Ici, 10 × 0.5 = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19927,"question":"La fonction f(x) = sin(x) est périodique de période π.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction sin(x) est périodique de période 2π, car sin(x + 2π) = sin(x) pour tout x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]