Quiz Maths Terminale : Dérivées, Suites et Probabilités

Question 1 sur 10 10:00

[{"id":61187,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 2x² + 5 ?","option_a":"3x² - 4x","option_b":"3x² - 4x + 5","option_c":"x² - 2x","option_d":"x³ - 4x + 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x³ est 3x², celle de -2x² est -4x, et la constante 5 a une dérivée nulle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61188,"question":"Une suite croissante et majorée converge toujours.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est le théorème de convergence monotone : une suite croissante et majorée converge vers sa borne supérieure.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61189,"question":"Soit X une variable aléatoire suivant une loi binomiale B(n=5, p=0.3). Quelle est E(X) ?","option_a":"1.5","option_b":"0.3","option_c":"5","option_d":"15","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'espérance d'une loi binomiale B(n,p) est E(X) = n × p = 5 × 0.3 = 1.5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61190,"question":"La fonction f(x) = ln(x) est-elle dérivable sur ]0, +∞[ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction ln(x) est dérivable sur son domaine de définition ]0, +∞[ avec f'(x) = 1\/x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61191,"question":"Quelle est la limite de la suite uₙ = (2n + 1)\/(n + 3) quand n tend vers +∞ ?","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) → 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61192,"question":"Soit A et B deux événements indépendants avec P(A) = 0.4 et P(B) = 0.5. Quelle est P(A ∩ B) ?","option_a":"0.2","option_b":"0.9","option_c":"0.45","option_d":"0.1","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour des événements indépendants, P(A ∩ B) = P(A) × P(B) = 0.4 × 0.5 = 0.2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61193,"question":"La dérivée de f(x) = e^(2x) est-elle f'(x) = 2e^(2x) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de e^(u(x)) est u'(x)e^(u(x)). Ici, u(x) = 2x, donc u'(x) = 2. D'où f'(x) = 2e^(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61194,"question":"Quelle est la nature de la suite définie par uₙ₊₁ = 0.5uₙ + 3 avec u₀ = 4 ?","option_a":"Arithmétique","option_b":"Géométrique","option_c":"Constante","option_d":"Ni l'une ni l'autre","option_e":"","option_f":"","bonne_reponse":"D","explication":"Cette suite n'est ni arithmétique (car uₙ₊₁ - uₙ n'est pas constant) ni géométrique (car uₙ₊₁\/uₙ n'est pas constant).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61195,"question":"Soit X une variable aléatoire discrète avec P(X=1)=0.2, P(X=2)=0.3 et P(X=3)=0.5. Quelle est E(X) ?","option_a":"2.3","option_b":"2","option_c":"2.5","option_d":"1.5","option_e":"","option_f":"","bonne_reponse":"A","explication":"E(X) = 1×0.2 + 2×0.3 + 3×0.5 = 0.2 + 0.6 + 1.5 = 2.3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61196,"question":"La fonction f(x) = x² - 4x + 3 admet-elle 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. Comme f''(x)=2\u003E0, c'est un minimum.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]