Quiz : Maîtrisez les dérivées et les primitives en Terminale Math

Question 1 sur 10 10:00

[{"id":12028,"question":"Quelle est la dérivée de la fonction f(x) = x³ + 2x² - 5x + 1 ?","option_a":"3x² + 4x - 5","option_b":"3x² + 4x + 1","option_c":"x³ + 4x - 5","option_d":"3x² + 4x - 5x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x³ est 3x², celle de 2x² est 4x, celle de -5x est -5, et celle de 1 est 0. On additionne ces résultats pour obtenir 3x² + 4x - 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12029,"question":"La primitive de f(x) = 4x³ est-elle F(x) = x⁴ + C ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En dérivant F(x) = x⁴ + C, on obtient f(x) = 4x³, ce qui correspond bien à la fonction initiale. La réponse est donc Vrai.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12030,"question":"Quelle est la primitive de f(x) = e^(2x) ?","option_a":"(1\/2)e^(2x) + C","option_b":"2e^(2x) + C","option_c":"e^(2x) + C","option_d":"(1\/2)e^x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de e^(kx) est (1\/k)e^(kx) + C. Ici, k = 2, donc la primitive est (1\/2)e^(2x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12031,"question":"Si f'(x) = 3x² + 2x, quelle est la fonction f(x) ?","option_a":"x³ + x² + C","option_b":"x³ + x²","option_c":"3x³ + x² + C","option_d":"x³ + 2x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"En intégrant terme à terme, on obtient x³ pour 3x² et x² pour 2x. La constante d'intégration C est ajoutée à la fin.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12032,"question":"La dérivée de ln(x) est-elle 1\/x ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de la fonction logarithme népérien ln(x) est bien 1\/x pour x \u003E 0. La réponse est donc Vrai.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12033,"question":"Quelle est la primitive de f(x) = 1\/(1+x²) ?","option_a":"arctan(x) + C","option_b":"ln(1+x²) + C","option_c":"x\/(1+x²) + C","option_d":"arcsin(x) + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de 1\/(1+x²) est arctan(x) + C, car la dérivée de arctan(x) est 1\/(1+x²).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12034,"question":"Si f(x) = sin(x), quelle est sa dérivée ?","option_a":"cos(x)","option_b":"-cos(x)","option_c":"sin(x)","option_d":"-sin(x)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de la fonction sinus sin(x) est cos(x). C'est une formule fondamentale à connaître.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12035,"question":"La primitive de f(x) = 1\/x est-elle ln|x| + C ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de 1\/x est ln|x| + C pour x ≠ 0. La réponse est donc Vrai.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12036,"question":"Quelle est la dérivée de f(x) = √x ?","option_a":"1\/(2√x)","option_b":"√x\/2","option_c":"1\/√x","option_d":"2√x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de √x = x^(1\/2) est (1\/2)x^(-1\/2) = 1\/(2√x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12037,"question":"Si f(x) = e^x, quelle est sa primitive ?","option_a":"e^x + C","option_b":"e^x","option_c":"x e^x + C","option_d":"ln(e^x) + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de e^x est e^x + C, car la dérivée de e^x est e^x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]