Quiz : Maîtrisez le calcul des primitives en 9ème année secondaire

Question 1 sur 10 10:00

[{"id":50581,"question":"Quelle est la primitive de la fonction f(x) = 3x^2 ?","option_a":"x^3 + C","option_b":"x^3","option_c":"3x^3 + C","option_d":"x^2 + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de 3x^2 est obtenue en appliquant la formule (x^(n+1))\/(n+1) avec n=2, soit (x^3)\/1 = x^3. On ajoute la constante C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50582,"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 la primitive de e^x est bien e^x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50583,"question":"Quelle est la primitive de la fonction f(x) = 1\/x ?","option_a":"ln(x) + C","option_b":"ln(x)","option_c":"1\/x^2 + C","option_d":"x^(-1) + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de 1\/x est ln|x| + C, car la dérivée de ln|x| est 1\/x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50584,"question":"La primitive de 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 sin(x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50585,"question":"Quelle est la primitive de la fonction f(x) = 5x^4 ?","option_a":"x^5 + C","option_b":"5x^5 + C","option_c":"x^4 + C","option_d":"5x^5","option_e":"","option_f":"","bonne_reponse":"B","explication":"La primitive de 5x^4 est obtenue en appliquant la formule (x^(n+1))\/(n+1) avec n=4, soit (x^5)\/1 = x^5. On multiplie par 5, donc 5x^5. On ajoute la constante C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50586,"question":"La primitive de 1\/(1+x^2) 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+x^2), donc la primitive de 1\/(1+x^2) est arctan(x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50587,"question":"Quelle est la primitive de la fonction f(x) = 2x + 3 ?","option_a":"x^2 + 3x + C","option_b":"x^2 + 3","option_c":"2x^2 + 3x + C","option_d":"x^2 + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de 2x est x^2 et celle de 3 est 3x. En additionnant, on obtient x^2 + 3x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50588,"question":"La primitive de sin(2x) est-elle -cos(2x)\/2 + C ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de -cos(2x)\/2 est sin(2x), donc la primitive de sin(2x) est bien -cos(2x)\/2 + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50589,"question":"Quelle est la primitive de la fonction f(x) = x^(-2) ?","option_a":"-1\/x + C","option_b":"-x^(-1) + C","option_c":"x^(-1) + C","option_d":"1\/x + C","option_e":"","option_f":"","bonne_reponse":"B","explication":"La primitive de x^(-2) est obtenue en appliquant la formule (x^(n+1))\/(n+1) avec n=-2, soit (x^(-1))\/(-1) = -1\/x. On ajoute la constante C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50590,"question":"La primitive de 1\/sqrt(1-x^2) est-elle arcsin(x) + C ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de arcsin(x) est 1\/sqrt(1-x^2), donc la primitive de 1\/sqrt(1-x^2) est arcsin(x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]