Quiz d’Analyse : Fonctions, Dérivées et Intégrales — Terminale

Question 1 sur 10 10:00

[{"id":72352,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"2x + 3","option_b":"x² + 3","option_c":"2x + 3x","option_d":"x + 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d’une somme est la somme des dérivées. La dérivée de x² est 2x, celle de 3x est 3, et celle de -5 est 0. Donc f’(x) = 2x + 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72353,"question":"La fonction f(x) = 1\/x est définie sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction f(x) = 1\/x n’est pas définie en x = 0, donc son domaine de définition est ℝ*.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72354,"question":"Quelle est l’intégrale de f(x) = 2x entre 0 et 2 ?","option_a":"2","option_b":"4","option_c":"8","option_d":"16","option_e":"","option_f":"","bonne_reponse":"B","explication":"L’intégrale de 2x est x². Entre 0 et 2, cela donne 2² - 0² = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72355,"question":"La limite de f(x) = (x² - 1)\/(x - 1) quand x tend vers 1 est égale à :","option_a":"0","option_b":"1","option_c":"2","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"On factorise : (x² - 1) = (x - 1)(x + 1). Donc f(x) = x + 1 pour x ≠ 1. La limite quand x→1 est donc 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72356,"question":"La fonction exponentielle est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction exponentielle e^x est strictement positive pour tout x réel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72357,"question":"Quelle est la primitive de f(x) = 3x² qui s’annule en x = 1 ?","option_a":"x³ + C","option_b":"x³ - 1","option_c":"x³ - 2","option_d":"x³","option_e":"","option_f":"","bonne_reponse":"B","explication":"La primitive de 3x² est x³ + C. Pour qu’elle s’annule en x = 1, on a 1³ + C = 0 ⇒ C = -1. Donc la primitive est x³ - 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72358,"question":"La dérivée de f(x) = ln(x) est :","option_a":"1\/x","option_b":"x","option_c":"e^x","option_d":"1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de la fonction logarithme népérien ln(x) est 1\/x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72359,"question":"L’intégrale de f(x) = sin(x) entre 0 et π est égale à :","option_a":"0","option_b":"1","option_c":"2","option_d":"π","option_e":"","option_f":"","bonne_reponse":"B","explication":"L’intégrale de sin(x) est -cos(x). Entre 0 et π, cela donne -cos(π) - (-cos(0)) = -(-1) - (-1) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72360,"question":"La fonction f(x) = x³ - 3x est croissante sur l’intervalle [-2 ; 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f’(x) = 3x² - 3. Sur [-2 ; 2], f’(x) est négative entre -1 et 1, donc la fonction n’est pas croissante sur tout l’intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72361,"question":"Quelle est la valeur de l’intégrale de f(x) = e^x entre 0 et 1 ?","option_a":"e - 1","option_b":"1","option_c":"e","option_d":"2","option_e":"","option_f":"","bonne_reponse":"A","explication":"L’intégrale de e^x est e^x. Entre 0 et 1, cela donne e^1 - e^0 = e - 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]