Quiz Maths Terminale : Testez vos connaissances en analyse et algèbre

Question 1 sur 10 10:00

[{"id":15748,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"A. 6x + 2","option_b":"B. 3x + 2","option_c":"C. 6x - 5","option_d":"D. 6x² + 2x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de 3x² est 6x, celle de 2x est 2, et celle de -5 est 0. Donc f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15749,"question":"La suite définie par uₙ = 2n + 1 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une suite est arithmétique si la différence entre deux termes consécutifs est constante. Ici, uₙ₊₁ - uₙ = 2, donc elle est arithmétique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15750,"question":"Quelle est la limite de la fonction f(x) = (x² - 4)\/(x - 2) quand x tend vers 2 ?","option_a":"A. 0","option_b":"B. 4","option_c":"C. 2","option_d":"D. Indéterminée","option_e":"","option_f":"","bonne_reponse":"C","explication":"On peut simplifier f(x) = (x-2)(x+2)\/(x-2) = x+2 pour x ≠ 2. Donc la limite est 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15751,"question":"L'équation x² - 5x + 6 = 0 a pour solutions :","option_a":"A. 1 et 6","option_b":"B. 2 et 3","option_c":"C. -1 et -6","option_d":"D. 0 et 5","option_e":"","option_f":"","bonne_reponse":"B","explication":"En factorisant, on obtient (x-2)(x-3) = 0, donc les solutions sont 2 et 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15752,"question":"La fonction f(x) = x³ est-elle convexe sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction est convexe si sa dérivée seconde est positive. Ici, f''(x) = 6x, qui n'est pas toujours positive (ex. pour x \u003C 0).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15753,"question":"Quelle est l'espérance d'une variable aléatoire X suivant une loi binomiale B(n=5, p=0.4) ?","option_a":"A. 2","option_b":"B. 2.5","option_c":"C. 20","option_d":"D. 5","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'espérance d'une loi binomiale est E(X) = n*p = 5*0.4 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15754,"question":"La primitive de f(x) = 4x³ est :","option_a":"A. 12x² + C","option_b":"B. x⁴ + C","option_c":"C. 4x⁴ + C","option_d":"D. x³ + C","option_e":"","option_f":"","bonne_reponse":"B","explication":"La primitive de xⁿ est xⁿ⁺¹\/(n+1). Donc ∫4x³ dx = 4*(x⁴\/4) + C = x⁴ + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15755,"question":"La suite uₙ = (-1)ⁿ est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La suite alterne entre -1 et 1, donc elle n'a pas de limite. Elle est donc divergente.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15756,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 5 ?","option_a":"A. x \u003E 1","option_b":"B. x \u003E 4","option_c":"C. x \u003C 4","option_d":"D. x \u003C 1","option_e":"","option_f":"","bonne_reponse":"B","explication":"2x - 3 \u003E 5 ⇒ 2x \u003E 8 ⇒ x \u003E 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15757,"question":"La fonction f(x) = ln(x) est-elle définie pour x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction ln(x) est définie uniquement pour x \u003E 0. Elle n'est donc pas définie en x = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]