Maths 4ème année : Testez vos connaissances avec ce quiz interactif !

Question 1 sur 10 10:00

[{"id":32888,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation se factorise en (x-2)(x-3)=0, donc les solutions sont x=2 et x=3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32889,"question":"La fonction f(x) = x³ - 3x est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x)=3x²-3 s'annule en x=±1. La fonction n'est pas croissante sur tout ℝ (elle décroît entre -1 et 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32890,"question":"Quelle est la dérivée de la fonction f(x) = e^(2x) ?","option_a":"f'(x) = 2e^(2x)","option_b":"f'(x) = e^(2x)","option_c":"f'(x) = 2xe^(2x)","option_d":"f'(x) = e^x","option_e":"","option_f":"","bonne_reponse":"A","explication":"En appliquant la règle de dérivation des fonctions composées, f'(x) = 2e^(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32891,"question":"L'intégrale de 0 à 1 de x² dx vaut :","option_a":"1\/3","option_b":"1","option_c":"0","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de x² est [x³\/3] de 0 à 1, soit 1\/3 - 0 = 1\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32892,"question":"La limite de (sin x)\/x quand x tend vers 0 est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est un résultat fondamental en analyse : lim(x→0) (sin x)\/x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32893,"question":"Quelle est la solution de l'inéquation 2x - 5 \u003E 3x + 1 ?","option_a":"x \u003C -6","option_b":"x \u003E -6","option_c":"x \u003E 6","option_d":"x \u003C 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"En simplifiant, on obtient -x \u003E 6, soit x \u003C -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32894,"question":"La fonction f(x) = ln(x) est définie pour :","option_a":"x \u003E 0","option_b":"x ≥ 0","option_c":"x \u003C 0","option_d":"x ∈ ℝ","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le logarithme naturel est défini uniquement pour les nombres strictement positifs.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32895,"question":"L'aire sous la courbe de f(x)=x² entre 0 et 2 est :","option_a":"8\/3","option_b":"4","option_c":"2","option_d":"16\/3","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de x² de 0 à 2 vaut [x³\/3] de 0 à 2 = 8\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32896,"question":"La dérivée de sin(2x) est :","option_a":"2cos(2x)","option_b":"cos(2x)","option_c":"2sin(2x)","option_d":"-2cos(2x)","option_e":"","option_f":"","bonne_reponse":"A","explication":"En appliquant la règle de dérivation des fonctions composées, f'(x) = 2cos(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32897,"question":"L'équation cos(x) = 0 admet pour solutions dans [0, π] :","option_a":"x = π\/2","option_b":"x = 0","option_c":"x = π","option_d":"x = π\/4","option_e":"","option_f":"","bonne_reponse":"A","explication":"cos(π\/2) = 0, et c'est la seule solution dans l'intervalle [0, π].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]