Quiz Maths Terminale : Algèbre, Analyse et Probabilités

Question 1 sur 10 10:00

[{"id":67312,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"2x + 3","option_b":"x² + 3","option_c":"2x - 5","option_d":"x + 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x² est 2x, celle de 3x est 3, et la dérivée d'une constante est 0. Ainsi, f'(x) = 2x + 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67313,"question":"La limite de 1\/x lorsque x tend vers 0+ est égale à +∞.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Lorsque x tend vers 0 par valeurs positives, 1\/x tend vers +∞. La proposition est donc vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67314,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"e²","option_b":"2","option_c":"ln(2)","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation ln(x) = 2 équivaut à x = e², car l'exponentielle est la fonction réciproque du logarithme.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67315,"question":"Soit une suite géométrique de premier terme u₀ = 3 et de raison q = 2. Quel est le terme u₃ ?","option_a":"6","option_b":"12","option_c":"24","option_d":"48","option_e":"","option_f":"","bonne_reponse":"C","explication":"Le terme général d'une suite géométrique est uₙ = u₀ × qⁿ. Ainsi, u₃ = 3 × 2³ = 3 × 8 = 24.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67316,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle [-1, 1].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 3 est négative sur [-1, 1], donc la fonction est décroissante sur cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67317,"question":"Quel est le coefficient binomial C(5, 2) ?","option_a":"10","option_b":"12","option_c":"15","option_d":"20","option_e":"","option_f":"","bonne_reponse":"A","explication":"C(5, 2) = 5! \/ (2! × 3!) = (5×4)\/(2×1) = 10.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67318,"question":"Soit une variable aléatoire X suivant une loi normale N(0, 1). Quelle est la probabilité P(X ≤ 1) ?","option_a":"0.6827","option_b":"0.8413","option_c":"0.9545","option_d":"0.9973","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour une loi normale centrée réduite, P(X ≤ 1) ≈ 0.8413 (valeur lue dans la table de la loi normale).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67319,"question":"La fonction f(x) = |x| est dérivable en x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction valeur absolue n'est pas dérivable en x = 0 car sa dérivée à gauche (-1) diffère de sa dérivée à droite (1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67320,"question":"Quelle est l'intégrale ∫(3x² + 2x) dx ?","option_a":"x³ + x² + C","option_b":"x³ + x + C","option_c":"3x³ + x² + C","option_d":"x³ + 2x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de 3x² est x³, celle de 2x est x², et on ajoute la constante d'intégration C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67321,"question":"Soit une suite arithmétique de premier terme u₀ = 5 et de raison r = -2. Quel est le terme u₅ ?","option_a":"-5","option_b":"-3","option_c":"3","option_d":"5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le terme général d'une suite arithmétique est uₙ = u₀ + n×r. Ainsi, u₅ = 5 + 5×(-2) = 5 - 10 = -5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]