Maths Terminale : Testez vos connaissances en analyse, algèbre et géométrie !

Question 1 sur 10 10:00

[{"id":69222,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(2x² - x + 4) quand x tend vers +∞ ?","option_a":"A. 3\/2","option_b":"B. 0","option_c":"C. +∞","option_d":"D. -1\/4","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\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":69223,"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":"B","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":69224,"question":"Quel est le résultat de l'intégrale ∫(2x + 1)dx entre 0 et 2 ?","option_a":"A. 4","option_b":"B. 6","option_c":"C. 8","option_d":"D. 10","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'intégrale vaut [x² + x] entre 0 et 2 = (4 + 2) - (0 + 0) = 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":69225,"question":"Soit la suite définie par u₀ = 1 et uₙ₊₁ = 2uₙ + 1. Quelle est la limite de uₙ quand n tend vers +∞ ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. +∞","option_d":"D. -1","option_e":"","option_f":"","bonne_reponse":"B","explication":"La suite est croissante et majorée (par exemple par 2), donc elle converge vers 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":69226,"question":"Le produit scalaire de deux vecteurs orthogonaux est toujours égal à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, le produit scalaire de deux vecteurs orthogonaux est égal à 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":69227,"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 = Cx² + C","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'équation 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":69228,"question":"Soit z = 3 + 4i. Quel est le module de z ?","option_a":"A. 5","option_b":"B. 7","option_c":"C. √7","option_d":"D. 25","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le module de z = a + bi est √(a² + b²) = √(9 + 16) = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":69229,"question":"La dérivée de la fonction f(x) = ln(x² + 1) est f'(x) = 2x\/(x² + 1).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En appliquant la règle de dérivation des fonctions composées, f'(x) = (2x)\/(x² + 1) est correcte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":69230,"question":"Quel est le déterminant de la matrice A = [[1, 2], [3, 4]] ?","option_a":"A. -2","option_b":"B. 2","option_c":"C. 0","option_d":"D. -1","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le déterminant de A est (1×4) - (2×3) = 4 - 6 = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":69231,"question":"Soit X une variable aléatoire suivant une loi normale N(0, 1). Quelle est la probabilité P(X ≤ 1,96) ?","option_a":"A. 0,85","option_b":"B. 0,95","option_c":"C. 0,975","option_d":"D. 0,99","option_e":"","option_f":"","bonne_reponse":"C","explication":"La table de la loi normale centrée réduite donne P(X ≤ 1,96) ≈ 0,975.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]