Quiz : Maîtrisez les fonctions et dérivées en Terminale Sciences

Question 1 sur 10 10:00

[{"id":28708,"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 d'une fonction polynôme se calcule terme par terme : dérivée de x² = 2x, dérivée de 3x = 3, et la constante -5 disparaît.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28709,"question":"L'intégrale de f(x) = 2x entre 0 et 1 est égale à :","option_a":"0","option_b":"1","option_c":"2","option_d":"x²","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'intégrale de 2x est x². Évaluée entre 0 et 1 : 1² - 0² = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28710,"question":"La fonction f(x) = e^x est toujours positive sur ℝ.","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":28711,"question":"Quelle est la limite de (sin x)\/x quand x tend vers 0 ?","option_a":"0","option_b":"1","option_c":"∞","option_d":"n'existe pas","option_e":"","option_f":"","bonne_reponse":"B","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":28712,"question":"L'équation différentielle y' = 2y a pour solution générale :","option_a":"y = Ce^(2x)","option_b":"y = Cx²","option_c":"y = 2x + C","option_d":"y = e^(2x) + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La solution d'une équation différentielle y' = ky est y = Ce^(kx). Ici, k = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28713,"question":"La dérivée de la fonction f(x) = ln(x) est 1\/x.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de ln(x) est bien 1\/x pour x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28714,"question":"Quelle est l'aire sous la courbe de f(x) = x entre 0 et 2 ?","option_a":"1","option_b":"2","option_c":"4","option_d":"8","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'aire est donnée par l'intégrale de 0 à 2 de x, soit [x²\/2] de 0 à 2 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28715,"question":"La suite u_n = n² est convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La suite n² tend vers +∞ quand n tend vers +∞, donc elle est divergente.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28716,"question":"Quelle est la dérivée seconde de f(x) = x³ ?","option_a":"6x","option_b":"3x²","option_c":"x³","option_d":"6","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée première est 3x², et sa dérivée (dérivée seconde) est 6x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28717,"question":"La probabilité d'obtenir un 6 en lançant un dé équilibré est :","option_a":"1\/2","option_b":"1\/3","option_c":"1\/6","option_d":"1\/12","option_e":"","option_f":"","bonne_reponse":"C","explication":"Un dé équilibré a 6 faces, donc la probabilité d'obtenir un 6 est 1\/6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]