Quiz : Dérivées, Intégrales et Probabilités — Terminale Maths

Question 1 sur 10 10:00

[{"id":65762,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x + 5","option_d":"3x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de 3x² est 6x, celle de 2x est 2, et celle de -5 est 0. Donc f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65763,"question":"L'intégrale de 0 à 1 de x² dx est égale à 1\/3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de x² est x³\/3. Évaluée entre 0 et 1, on obtient (1³\/3) - (0³\/3) = 1\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65764,"question":"Quelle est la dérivée de 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. Ainsi, la dérivée est 2e^(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65765,"question":"Si P(A) = 0.4 et P(B) = 0.5, avec A et B indépendants, alors P(A ∩ B) = ?","option_a":"0.2","option_b":"0.9","option_c":"0.1","option_d":"0.45","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour des événements indépendants, P(A ∩ B) = P(A) × P(B) = 0.4 × 0.5 = 0.2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65766,"question":"La fonction f(x) = x³ est croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de f(x) = x³ est f'(x) = 3x², qui est toujours positive (sauf en x=0 où elle est nulle). Donc f est croissante sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65767,"question":"Quelle est la primitive de 1\/(1+x²) ?","option_a":"arctan(x) + C","option_b":"ln(1+x²) + C","option_c":"x + 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":65768,"question":"Si X suit une loi binomiale B(n=10, p=0.3), alors E(X) = ?","option_a":"3","option_b":"7","option_c":"0.3","option_d":"10","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'espérance d'une loi binomiale B(n,p) est n×p = 10×0.3 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65769,"question":"La dérivée de 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, une propriété fondamentale des logarithmes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65770,"question":"Quelle est l'intégrale de 0 à π de sin(x) dx ?","option_a":"0","option_b":"2","option_c":"-2","option_d":"π","option_e":"","option_f":"","bonne_reponse":"B","explication":"La primitive de sin(x) est -cos(x). Évaluée entre 0 et π, on obtient -cos(π) - (-cos(0)) = -(-1) - (-1) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65771,"question":"Si P(A) = 0.6 et P(B|A) = 0.5, alors P(A ∩ B) = ?","option_a":"0.3","option_b":"0.8","option_c":"0.1","option_d":"0.12","option_e":"","option_f":"","bonne_reponse":"A","explication":"P(A ∩ B) = P(A) × P(B|A) = 0.6 × 0.5 = 0.3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]