Quiz Maths Terminale : Algèbre et Analyse

Question 1 sur 10 10:00

[{"id":47681,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation x² - 5x + 6 = 0 se factorise en (x-2)(x-3) = 0, donc les solutions sont x = 2 et x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47682,"question":"La fonction f(x) = x³ - 3x 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":47683,"question":"Quelle est la limite de la suite uₙ = (2n + 1)\/(n - 3) quand n tend vers l'infini ?","option_a":"2","option_b":"1","option_c":"0","option_d":"+∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par n, on obtient uₙ = (2 + 1\/n)\/(1 - 3\/n), donc la limite est 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47684,"question":"Le théorème des valeurs intermédiaires garantit l'existence d'une solution pour f(x) = 0 si f est continue sur [a, b] et f(a) × f(b) \u003C 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le théorème des valeurs intermédiaires stipule que si f est continue sur [a, b] et f(a) × f(b) \u003C 0, alors il existe c ∈ [a, b] tel que f(c) = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47685,"question":"Quelle est la dérivée de la fonction f(x) = ln(3x² + 1) ?","option_a":"f'(x) = 6x\/(3x² + 1)","option_b":"f'(x) = 3x\/(3x² + 1)","option_c":"f'(x) = 6x²\/(3x² + 1)","option_d":"f'(x) = 3\/(3x² + 1)","option_e":"","option_f":"","bonne_reponse":"A","explication":"En appliquant la règle de dérivation des fonctions composées, f'(x) = (6x)\/(3x² + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47686,"question":"La suite uₙ = (-1)ⁿ est convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La suite uₙ = (-1)ⁿ alterne entre -1 et 1, donc elle ne converge pas.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47687,"question":"Quelle est la solution de l'inéquation x² - 4x + 3 ≤ 0 ?","option_a":"x ∈ [1, 3]","option_b":"x ∈ ]-∞, 1] ∪ [3, +∞[","option_c":"x ∈ [0, 4]","option_d":"x ∈ ]-∞, 0] ∪ [4, +∞[","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'inéquation x² - 4x + 3 ≤ 0 se résout en trouvant les racines (x=1 et x=3) et en étudiant le signe du polynôme.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47688,"question":"La fonction f(x) = e^(2x) est une fonction exponentielle de base e.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction f(x) = e^(2x) est bien une fonction exponentielle de base e, car elle peut s'écrire (e²)^x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47689,"question":"Quelle est la somme des solutions de l'équation 2x² - 8x + 6 = 0 ?","option_a":"4","option_b":"3","option_c":"2","option_d":"6","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour une équation du second degré ax² + bx + c = 0, la somme des solutions est -b\/a. Ici, -(-8)\/2 = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47690,"question":"La fonction f(x) = 1\/x est continue sur ℝ*.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction f(x) = 1\/x est continue sur son ensemble de définition, c'est-à-dire ℝ* (tous les réels sauf 0).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]