Quiz Maths Bac : Testez vos connaissances en séries et analyse

Question 1 sur 10 10:00

[{"id":58366,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x² + 2x","option_d":"6x + 2x - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : (3x²)' = 6x, (2x)' = 2, et la dérivée de -5 est 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58367,"question":"L'intégrale ∫(2x + 1)dx entre 0 et 1 est égale à :","option_a":"2","option_b":"1.5","option_c":"3","option_d":"2.5","option_e":"","option_f":"","bonne_reponse":"B","explication":"Calcul : [x² + x] entre 0 et 1 = (1 + 1) - (0 + 0) = 2. Erreur fréquente : oublier de remplacer x par les bornes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58368,"question":"Vrai ou Faux ? La fonction f(x) = x³ - 3x est croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Faux. La dérivée f'(x) = 3x² - 3 s'annule en x = ±1. La fonction est décroissante sur ]-1, 1[.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58369,"question":"Résoudre l'équation x² - 4x + 3 = 0 :","option_a":"x = 1 ou x = 3","option_b":"x = -1 ou x = -3","option_c":"x = 2 ou x = 2","option_d":"x = 0 ou x = 4","option_e":"","option_f":"","bonne_reponse":"A","explication":"Factorisation : (x-1)(x-3) = 0. Les solutions sont x = 1 et x = 3. Méthode alternative : utiliser le discriminant Δ = b² - 4ac.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58370,"question":"Vrai ou Faux ? L'intégrale ∫(1\/x)dx = ln|x| + C.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai. C'est une primitive fondamentale en calcul intégral, valable pour x ≠ 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58371,"question":"La limite lim(x→+∞) (3x² + 2x - 1)\/(2x² + 5) est égale à :","option_a":"0","option_b":"1.5","option_c":"+∞","option_d":"3\/2","option_e":"","option_f":"","bonne_reponse":"D","explication":"On divise numérateur et dénominateur par x² : lim (3 + 2\/x - 1\/x²)\/(2 + 5\/x²) = 3\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58372,"question":"Quelle est la forme algébrique du nombre complexe z = 3(cos(π\/3) + i sin(π\/3)) ?","option_a":"3 + 3i√3","option_b":"1.5 + i(3√3\/2)","option_c":"3\/2 + i(3√3\/2)","option_d":"(3√3)\/2 + i(3\/2)","option_e":"","option_f":"","bonne_reponse":"C","explication":"Forme trigonométrique → forme algébrique : z = 3cos(π\/3) + i 3sin(π\/3) = 3*(1\/2) + i 3*(√3\/2) = 3\/2 + i(3√3\/2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58373,"question":"Vrai ou Faux ? La fonction f(x) = e^x est sa propre dérivée.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai. C'est une propriété fondamentale des fonctions exponentielles : (e^x)' = e^x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58374,"question":"Résoudre l'inéquation 2x - 5 \u003E 3x + 1 :","option_a":"x \u003C -6","option_b":"x \u003E -6","option_c":"x \u003C 6","option_d":"x \u003E 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x - 3x \u003E 1 + 5 → -x \u003E 6 → x \u003C -6 (en multipliant par -1, on inverse le sens de l'inégalité).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58375,"question":"Quelle est l'aire sous la courbe de f(x) = x² entre x = 0 et x = 2 ?","option_a":"4\/3","option_b":"8\/3","option_c":"2","option_d":"16\/3","option_e":"","option_f":"","bonne_reponse":"B","explication":"Calcul de l'intégrale : ∫x²dx entre 0 et 2 = [x³\/3] entre 0 et 2 = 8\/3 - 0 = 8\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]