Quiz : Maîtrisez les bases de Terminale Maths

Question 1 sur 10 10:00

[{"id":54141,"question":"Quelle est la limite de la suite définie par uₙ = (2n² + 3n - 1)\/(n² + 5) lorsque n tend vers +∞ ?","option_a":"A. 0","option_b":"B. 2","option_c":"C. +∞","option_d":"D. -∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"La limite est égale au rapport des coefficients dominants, soit 2n²\/n² = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54142,"question":"La fonction f(x) = x³ - 3x² + 2x est dérivable sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Toute fonction polynôme est dérivable sur ℝ, donc la réponse est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54143,"question":"Quelle est la dérivée de la fonction f(x) = ln(3x + 1) ?","option_a":"A. 3\/(3x + 1)","option_b":"B. 1\/(3x + 1)","option_c":"C. 3x\/(3x + 1)","option_d":"D. 3\/(x + 1)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de ln(u) est u'\/u, ici u = 3x + 1, donc u' = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54144,"question":"Soit une variable aléatoire X suivant une loi binomiale B(10 ; 0,3). Quelle est l'espérance de X ?","option_a":"A. 3","option_b":"B. 0,3","option_c":"C. 10","option_d":"D. 7","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'espérance d'une loi binomiale B(n,p) est np, soit 10 × 0,3 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54145,"question":"La fonction f(x) = e^(2x) est solution de l'équation différentielle y' = 2y.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de e^(2x) est 2e^(2x), qui est bien égale à 2y.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54146,"question":"Quelle est la valeur de C(5,2) ?","option_a":"A. 10","option_b":"B. 20","option_c":"C. 5","option_d":"D. 15","option_e":"","option_f":"","bonne_reponse":"A","explication":"C(5,2) = 5!\/(2!×3!) = 10.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54147,"question":"Soit f une fonction dérivable sur ℝ. Si f'(x) \u003E 0 pour tout x ∈ ℝ, alors f est strictement croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est un théorème fondamental du cours : si la dérivée est strictement positive, la fonction est strictement croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54148,"question":"Quelle est la solution générale de l'équation différentielle y' + y = 0 ?","option_a":"A. y = Ce^x","option_b":"B. y = Cx","option_c":"C. y = Ce^(-x)","option_d":"D. y = C","option_e":"","option_f":"","bonne_reponse":"C","explication":"La solution générale est y = Ce^(-x), où C est une constante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54149,"question":"Soit X une variable aléatoire continue de densité f(x) = 2x sur [0,1]. Quelle est P(X ≤ 0,5) ?","option_a":"A. 0,25","option_b":"B. 0,5","option_c":"C. 0,125","option_d":"D. 0,75","option_e":"","option_f":"","bonne_reponse":"A","explication":"P(X ≤ 0,5) = ∫₀^0.5 2x dx = [x²]₀^0.5 = 0,25.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54150,"question":"La fonction f(x) = x² - 4x + 3 admet un minimum en x = 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 2x - 4 s'annule en x = 2, et f''(x) = 2 \u003E 0, donc c'est un minimum.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]