Quiz : Testez vos connaissances en Terminale Mathématiques !

Question 1 sur 10 10:00

[{"id":42466,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 5)\/(2x² - x + 1) lorsque x tend vers l'infini ?","option_a":"A. 3\/2","option_b":"B. 0","option_c":"C. +∞","option_d":"D. -∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"La limite d'un polynôme de degré n est équivalente à son terme de plus haut degré. Ici, on divise les coefficients dominants : 3\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42467,"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 tout ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42468,"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 = C + e^(-2x)","option_d":"D. y = Cx + e^(-2x)","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'équation différentielle linéaire du premier ordre y' + ay = 0 a pour solution y = Ce^(-ax). Ici, a = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42469,"question":"Le nombre complexe z = 3 + 4i a pour module :","option_a":"A. 5","option_b":"B. 7","option_c":"C. 1","option_d":"D. 25","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le module d'un nombre complexe z = a + bi est √(a² + b²). Ici, √(3² + 4²) = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42470,"question":"La suite définie par uₙ = (-1)ⁿ \/ n est convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La suite alterne entre valeurs positives et négatives et tend vers 0, donc elle converge vers 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42471,"question":"Quelle est la dérivée de la fonction f(x) = ln(x² + 1) ?","option_a":"A. 2x\/(x² + 1)","option_b":"B. 1\/(x² + 1)","option_c":"C. 2x","option_d":"D. x\/(x² + 1)","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant la formule de dérivation des fonctions composées, f'(x) = (2x)\/(x² + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42472,"question":"Un dé équilibré est lancé deux fois. Quelle est la probabilité d'obtenir deux fois le chiffre 6 ?","option_a":"A. 1\/6","option_b":"B. 1\/12","option_c":"C. 1\/36","option_d":"D. 1\/3","option_e":"","option_f":"","bonne_reponse":"C","explication":"La probabilité d'obtenir un 6 est 1\/6. Pour deux lancers indépendants, on multiplie les probabilités : (1\/6) × (1\/6) = 1\/36.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42473,"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":42474,"question":"Quelle est l'intégrale de f(x) = 2x + 1 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 de 2x + 1 est x² + x. Entre 0 et 2, on obtient (4 + 2) - (0 + 0) = 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":42475,"question":"Le produit scalaire de deux vecteurs orthogonaux est toujours égal à :","option_a":"A. 1","option_b":"B. 0","option_c":"C. -1","option_d":"D. Leur norme","option_e":"","option_f":"","bonne_reponse":"B","explication":"Par définition, deux vecteurs orthogonaux ont un produit scalaire nul.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]