Quiz Maths Terminale : Algèbre, Analyse et Probabilités

Question 1 sur 10 10:00

[{"id":73752,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 2 ou x = 0.5","option_c":"x = -1 ou x = -2","option_d":"x = 0.5 ou x = 2","option_e":"","option_f":"","bonne_reponse":"B","explication":"Résolvez l'équation quadratique en utilisant la formule des racines : x = [5 ± √(25 - 16)] \/ 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73753,"question":"La fonction f(x) = x³ - 3x + 2 est croissante sur l'intervalle [0, 1].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 3x² - 3 est négative sur [0, 1], donc la fonction est décroissante sur cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73754,"question":"Quelle est la limite de (sin x)\/x lorsque x tend vers 0 ?","option_a":"0","option_b":"1","option_c":"∞","option_d":"π\/2","option_e":"","option_f":"","bonne_reponse":"B","explication":"C'est une limite fondamentale en analyse : lim (x→0) sin x \/ x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73755,"question":"Une suite géométrique de raison q = -2 et de premier terme u₀ = 3 est-elle bornée ?","option_a":"Oui, car elle est géométrique","option_b":"Non, car elle diverge vers ±∞","option_c":"Oui, car q \u003E -1","option_d":"Non, car u₀ est positif","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite géométrique avec |q| \u003E 1 diverge et n'est pas bornée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73756,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est de 1\/2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 faces, donc la probabilité est 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73757,"question":"Quelle est la dérivée de la fonction f(x) = e^(2x) ?","option_a":"f'(x) = e^(2x)","option_b":"f'(x) = 2e^(2x)","option_c":"f'(x) = e^x","option_d":"f'(x) = 2e^x","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de e^(u(x)) est u'(x)e^(u(x)), ici u(x) = 2x donc u'(x) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73758,"question":"Un sac contient 4 boules rouges et 6 boules bleues. Quelle est la probabilité de tirer deux boules rouges sans remise ?","option_a":"1\/3","option_b":"2\/15","option_c":"4\/25","option_d":"1\/5","option_e":"","option_f":"","bonne_reponse":"B","explication":"Probabilité = (4\/10) * (3\/9) = 12\/90 = 2\/15.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73759,"question":"La fonction f(x) = ln(x) est définie pour tout x réel.","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.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73760,"question":"Quelle est l'intégrale de f(x) = 3x² entre 0 et 2 ?","option_a":"6","option_b":"8","option_c":"12","option_d":"4","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'intégrale de 3x² est x³, donc [x³] de 0 à 2 = 8 - 0 = 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73761,"question":"Une variable aléatoire X suit une loi normale N(μ=5, σ=2). Quelle est P(X ≤ 5) ?","option_a":"0.25","option_b":"0.5","option_c":"0.75","option_d":"1","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour une loi normale, P(X ≤ μ) = 0.5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]