Maths Terminale : Dérivées, Suites et Probabilités — Quiz d'Entraînement

Question 1 sur 10 10:00

[{"id":44666,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"6x - 5","option_b":"3x - 5","option_c":"6x² - 5","option_d":"3x² - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de 3x² est 6x, celle de -5x est -5, et celle de 2 est 0. Donc f'(x) = 6x - 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":44667,"question":"Une suite géométrique de raison q = 2 et de premier terme u₁ = 3 a pour terme général :","option_a":"uₙ = 3 × 2ⁿ","option_b":"uₙ = 3 × 2ⁿ⁻¹","option_c":"uₙ = 2 × 3ⁿ","option_d":"uₙ = 3 × n²","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour une suite géométrique, uₙ = u₁ × qⁿ⁻¹. Ici, uₙ = 3 × 2ⁿ⁻¹.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":44668,"question":"Si P(A) = 0.4 et P(B|A) = 0.5, alors P(A ∩ B) = ?","option_a":"0.2","option_b":"0.9","option_c":"0.5","option_d":"0.8","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, P(A ∩ B) = P(A) × P(B|A) = 0.4 × 0.5 = 0.2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":44669,"question":"Vrai ou Faux : Toute suite croissante est convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite croissante peut diverger vers +∞ (exemple : uₙ = n). Elle n'est convergente que si elle est majorée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":44670,"question":"Quelle est l'équation de la tangente à la courbe de f(x) = x³ au point d'abscisse x = 1 ?","option_a":"y = 3x - 2","option_b":"y = 3x - 1","option_c":"y = 3x + 2","option_d":"y = x³ - 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La tangente en x = 1 a pour équation y = f'(1)(x - 1) + f(1). f'(x) = 3x² ⇒ f'(1) = 3 et f(1) = 1. Donc y = 3(x - 1) + 1 = 3x - 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":44671,"question":"Si deux événements A et B sont indépendants, alors P(A ∩ B) = P(A) × P(B).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est la définition de l'indépendance de deux événements. Si P(A ∩ B) = P(A) × P(B), alors A et B sont indépendants.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":44672,"question":"Quelle est la limite de la suite uₙ = (2n + 1)\/(n + 3) quand n tend vers +∞ ?","option_a":"0","option_b":"1","option_c":"2","option_d":"+∞","option_e":"","option_f":"","bonne_reponse":"C","explication":"En divisant numérateur et dénominateur par n, on obtient uₙ = (2 + 1\/n)\/(1 + 3\/n). Quand n → +∞, 1\/n → 0, donc uₙ → 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":44673,"question":"Vrai ou Faux : La dérivée de eˣ est eˣ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une propriété fondamentale : la dérivée de la fonction exponentielle eˣ est elle-même, eˣ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":44674,"question":"Soit une suite arithmétique de premier terme u₁ = 5 et de raison r = -2. Quel est le terme u₅ ?","option_a":"-3","option_b":"3","option_c":"-5","option_d":"5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour une suite arithmétique, uₙ = u₁ + (n - 1)r. Donc u₅ = 5 + 4 × (-2) = 5 - 8 = -3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":44675,"question":"Quelle est la probabilité de tirer un as dans un jeu de 32 cartes ?","option_a":"1\/8","option_b":"1\/4","option_c":"1\/32","option_d":"4\/32","option_e":"","option_f":"","bonne_reponse":"B","explication":"Un jeu de 32 cartes contient 4 as. La probabilité est donc 4\/32 = 1\/8. Cependant, la réponse correcte est 1\/8 (4\/32 simplifié). La bonne option est donc 1\/8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]