Quiz : Maîtrisez les concepts clés de Terminale Maths

Question 1 sur 10 10:00

[{"id":21218,"question":"Quelle est la dérivée de la fonction f(x) = e^(2x) ?","option_a":"2e^(2x)","option_b":"e^(2x)","option_c":"2xe^(2x)","option_d":"e^(x)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de e^(u(x)) est u'(x)*e^(u(x)). Ici, u(x)=2x donc u'(x)=2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21219,"question":"La suite définie par u_n = (-1)^n converge-t-elle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite alternée comme u_n = (-1)^n n'a pas de limite finie, elle diverge.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21220,"question":"Quel est le module du nombre complexe z = 3 + 4i ?","option_a":"5","option_b":"7","option_c":"12","option_d":"√7","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le module de z = a + bi est √(a² + b²) = √(9 + 16) = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21221,"question":"L'intégrale ∫(1\/x) dx est égale à :","option_a":"ln|x| + C","option_b":"e^x + C","option_c":"x²\/2 + C","option_d":"1\/x² + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de 1\/x est ln|x| + C, où C est une constante d'intégration.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21222,"question":"La fonction f(x) = x^3 est convexe sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée seconde f''(x) = 6x n'est pas toujours positive (nulle en x=0), donc la fonction n'est pas convexe sur tout ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21223,"question":"Quel est le résultat de la limite lim (n→∞) (n² + 3n) \/ (2n² - 5) ?","option_a":"1\/2","option_b":"0","option_c":"∞","option_d":"3\/5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par n², on obtient (1 + 3\/n) \/ (2 - 5\/n²) → 1\/2 quand n→∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21224,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est donné par :","option_a":"b² - 4ac","option_b":"4ac - b²","option_c":"b² + 4ac","option_d":"√(b² - 4ac)","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = b² - 4ac détermine la nature des racines de l'équation.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21225,"question":"La probabilité d'un événement impossible est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La probabilité d'un événement impossible est 0, celle d'un événement certain est 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21226,"question":"Quel est le développement limité de sin(x) à l'ordre 3 autour de 0 ?","option_a":"x - x³\/6","option_b":"x + x³\/6","option_c":"1 - x²\/2","option_d":"x²\/2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le développement limité de sin(x) à l'ordre 3 est sin(x) ≈ x - x³\/6 + o(x³).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21227,"question":"La fonction f(x) = ln(x) est définie pour tout x réel.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction ln(x) n'est définie que pour x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]