Quiz : Maîtrisez les notions clés du BAC Maths 2019 !

Question 1 sur 10 10:00

[{"id":45926,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"2x + 3","option_b":"x² + 3","option_c":"2x + 3x","option_d":"x + 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : la dérivée de x² est 2x, celle de 3x est 3, et celle de -5 est 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45927,"question":"Soit une suite géométrique de premier terme u₀ = 2 et de raison q = 3. Quelle est la valeur de u₃ ?","option_a":"18","option_b":"54","option_c":"162","option_d":"6","option_e":"","option_f":"","bonne_reponse":"B","explication":"La formule d'une suite géométrique est uₙ = u₀ × qⁿ. Ici, u₃ = 2 × 3³ = 2 × 27 = 54.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45928,"question":"Vrai ou Faux ? La fonction exponentielle est toujours positive sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction exponentielle, notée eˣ, est strictement positive pour tout x réel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45929,"question":"Quelle est l'intégrale de f(x) = 2x entre 0 et 3 ?","option_a":"9","option_b":"6","option_c":"3","option_d":"12","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de 2x est x². Évaluée entre 0 et 3, on obtient 3² - 0² = 9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45930,"question":"Vrai ou Faux ? Une probabilité conditionnelle P(A|B) peut être supérieure à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une probabilité est toujours comprise entre 0 et 1, y compris les probabilités conditionnelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45931,"question":"Soit une variable aléatoire X suivant une loi normale N(0,1). Quelle est la probabilité P(X ≤ 1) ?","option_a":"0.6826","option_b":"0.8413","option_c":"0.9772","option_d":"0.3413","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour une loi normale centrée réduite, P(X ≤ 1) ≈ 0.8413 (valeur lue dans la table de la loi normale).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45932,"question":"Quelle est la solution de l'équation différentielle y' + 2y = 0 ?","option_a":"y = Ce^{-2x}","option_b":"y = Ce^{2x}","option_c":"y = C + e^{-2x}","option_d":"y = Cx","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation différentielle linéaire du premier ordre y' + ay = 0 a pour solution générale y = Ce^{-ax}. Ici, a = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45933,"question":"Vrai ou Faux ? La fonction f(x) = x³ est impaire.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction est impaire si f(-x) = -f(x). Ici, f(-x) = (-x)³ = -x³ = -f(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45934,"question":"Quelle est la limite de (sin x)\/x lorsque x tend vers 0 ?","option_a":"0","option_b":"1","option_c":"∞","option_d":"n'existe pas","option_e":"","option_f":"","bonne_reponse":"B","explication":"C'est un résultat fondamental en analyse : lim(x→0) (sin x)\/x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45935,"question":"Soit A et B deux événements indépendants. Quelle est la probabilité de A ∩ B ?","option_a":"P(A) + P(B)","option_b":"P(A) × P(B)","option_c":"P(A) - P(B)","option_d":"P(A) \/ P(B)","option_e":"","option_f":"","bonne_reponse":"B","explication":"Par définition, deux événements sont indépendants si P(A ∩ B) = P(A) × P(B).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]