Quiz : Maîtrisez les primitives en Terminale Mathématiques

Question 1 sur 10 10:00

[{"id":65002,"question":"Quelle est la primitive de la fonction f(x) = 3x² + 2x + 1 ?","option_a":"x³ + x² + x + C","option_b":"x³ + x² + C","option_c":"3x³ + x² + x + C","option_d":"x³ + 2x² + x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de 3x² est x³, celle de 2x est x², et celle de 1 est x. On ajoute la constante C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65003,"question":"La primitive de e^x est-elle e^x + C ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de e^x est e^x, donc sa primitive est bien e^x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65004,"question":"Quelle est la primitive de f(x) = 1\/x (pour x \u003E 0) ?","option_a":"ln(x) + C","option_b":"x² + C","option_c":"1\/x² + C","option_d":"e^x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de ln(x) est 1\/x, donc sa primitive est ln(x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65005,"question":"La primitive de sin(x) est-elle -cos(x) + C ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de -cos(x) est sin(x), donc la primitive de sin(x) est bien -cos(x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65006,"question":"Quelle est la primitive de f(x) = 5e^(2x) ?","option_a":"5e^(2x)\/2 + C","option_b":"5e^(2x) + C","option_c":"e^(2x)\/2 + C","option_d":"10e^(2x) + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"On utilise la formule de primitive de e^(ax) : (1\/a)e^(ax) + C. Ici a=2, donc 5e^(2x)\/2 + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65007,"question":"La primitive de f(x) = cos(x) est-elle sin(x) + C ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de sin(x) est cos(x), donc la primitive de cos(x) est bien sin(x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65008,"question":"Quelle est la primitive de f(x) = 4x³ - 3x² + 2x - 1 ?","option_a":"x⁴ - x³ + x² - x + C","option_b":"x⁴ - x³ + x² - 1 + C","option_c":"4x⁴ - 3x³ + 2x² - x + C","option_d":"x⁴ - x³ + x² - x","option_e":"","option_f":"","bonne_reponse":"A","explication":"Primitive de 4x³ est x⁴, de -3x² est -x³, de 2x est x², et de -1 est -x. On ajoute C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65009,"question":"La primitive de f(x) = 1\/(1+x²) est-elle arctan(x) + C ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de arctan(x) est 1\/(1+x²), donc sa primitive est bien arctan(x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65010,"question":"Quelle est la primitive de f(x) = 2\/(x+3) (pour x \u003E -3) ?","option_a":"2ln(x+3) + C","option_b":"ln(2x+6) + C","option_c":"2\/(x+3)² + C","option_d":"2x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"On utilise la primitive de 1\/(x+a) qui est ln|x+a| + C. Ici a=3, donc 2ln(x+3) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65011,"question":"La primitive de f(x) = 3cos(3x) est-elle sin(3x) + C ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de sin(3x) est 3cos(3x), donc la primitive de 3cos(3x) est sin(3x) + C. La réponse proposée est donc fausse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]