Quiz : Maîtrisez les fonctions dérivées et les intégrales en Terminale

Question 1 sur 10 10:00

[{"id":29208,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2x","option_c":"6x + 2x - 5","option_d":"3x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : (3x²)' = 6x, (2x)' = 2, et (-5)' = 0. Donc f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":29209,"question":"L'intégrale de f(x) = 2x entre 0 et 3 est égale à :","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":29210,"question":"Une suite géométrique de raison q = 2 et de premier terme u₀ = 1 est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite géométrique converge uniquement si |q| \u003C 1. Ici, q = 2 \u003E 1, donc la suite diverge.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":29211,"question":"Quelle est la primitive de f(x) = 4x³ ?","option_a":"x⁴ + C","option_b":"12x² + C","option_c":"4x⁴\/4 + C","option_d":"x³ + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de xⁿ est xⁿ⁺¹\/(n+1). Ici, n=3, donc la primitive est 4x⁴\/4 = x⁴ + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":29212,"question":"Si P(A) = 0.4 et P(B) = 0.3, et que A et B sont indépendants, alors P(A ∩ B) = :","option_a":"0.12","option_b":"0.7","option_c":"0.1","option_d":"0.07","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour deux événements indépendants, P(A ∩ B) = P(A) × P(B) = 0.4 × 0.3 = 0.12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":29213,"question":"La fonction f(x) = x³ - 3x + 2 admet-elle un extremum local en x = 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 3x² - 3 s'annule en x = 1. Le changement de signe de f' confirme un extremum local en ce point.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":29214,"question":"Quelle est la limite de la suite uₙ = (n² + 1)\/n² lorsque n tend vers l'infini ?","option_a":"0","option_b":"1","option_c":"∞","option_d":"n","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant numérateur et dénominateur par n², on obtient (1 + 1\/n²) → 1 lorsque n → ∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":29215,"question":"L'intégrale de f(x) = eˣ entre 0 et 1 est égale à :","option_a":"e - 1","option_b":"e","option_c":"1 - e","option_d":"e + 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de eˣ est eˣ. Évaluée entre 0 et 1, on obtient e¹ - e⁰ = e - 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":29216,"question":"Une variable aléatoire X suit une loi binomiale B(n=5, p=0.2). Quelle est P(X=2) ?","option_a":"0.2048","option_b":"0.3072","option_c":"0.1024","option_d":"0.5","option_e":"","option_f":"","bonne_reponse":"B","explication":"P(X=2) = C(5,2) × (0.2)² × (0.8)³ = 10 × 0.04 × 0.512 = 0.2048. La réponse correcte est 0.2048.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":29217,"question":"La fonction f(x) = ln(x) est-elle définie pour x = -1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction ln(x) est définie uniquement pour x \u003E 0. Elle n'est pas définie pour x = -1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]