Quiz Mathématiques Terminale : Dérivées, Intégrales & Probabilités

Question 1 sur 10 10:00

[{"id":29838,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"A. 6x + 2","option_b":"B. 3x + 2","option_c":"C. 6x² + 2","option_d":"D. 3x² + 2x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme à terme : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":29839,"question":"L'intégrale ∫(2x + 1)dx est égale à :","option_a":"A. x² + x + C","option_b":"B. 2x² + x + C","option_c":"C. x² + C","option_d":"D. 2x + 1 + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale d'une somme est la somme des intégrales : ∫2x dx + ∫1 dx = x² + x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":29840,"question":"Une suite géométrique de premier terme u₀ = 2 et de raison q = 3 a pour terme général :","option_a":"A. uₙ = 2 × 3ⁿ","option_b":"B. uₙ = 2 + 3n","option_c":"C. uₙ = 3 × 2ⁿ","option_d":"D. uₙ = 2 × n³","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le terme général d'une suite géométrique est uₙ = u₀ × qⁿ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":29841,"question":"Si A et B sont deux événements indépendants, alors P(A ∩ B) est égal à :","option_a":"A. P(A) + P(B)","option_b":"B. P(A) × P(B)","option_c":"C. P(A) - P(B)","option_d":"D. P(A) \/ P(B)","option_e":"","option_f":"","bonne_reponse":"B","explication":"Par définition, deux événements indépendants vérifient P(A ∩ B) = P(A) × P(B).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":29842,"question":"La fonction f(x) = x³ - 3x² + 2 est croissante sur l'intervalle [0 ; 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 6x s'annule en x=0 et x=2. Le signe de f' montre que f est décroissante sur [0 ; 2].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":29843,"question":"L'intégrale ∫₀¹ (4x³ - 2x)dx est égale à :","option_a":"A. 0","option_b":"B. 1","option_c":"C. 0.5","option_d":"D. -0.5","option_e":"","option_f":"","bonne_reponse":"C","explication":"Calcul : [x⁴ - x²]₀¹ = (1 - 1) - (0 - 0) = 0.5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":29844,"question":"Une suite arithmétique de premier terme u₀ = 5 et de raison r = -2 a pour terme u₅ :","option_a":"A. -5","option_b":"B. 5","option_c":"C. -3","option_d":"D. 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le terme général est uₙ = u₀ + n×r. Donc u₅ = 5 + 5×(-2) = -5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":29845,"question":"Si P(A) = 0.4 et P(B) = 0.5, alors P(A ∪ B) ≤ 0.9.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par la formule des probabilités totales, P(A ∪ B) = P(A) + P(B) - P(A ∩ B) ≤ 0.4 + 0.5 = 0.9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":29846,"question":"La dérivée de la fonction f(x) = e^(2x) est :","option_a":"A. e^(2x)","option_b":"B. 2e^(2x)","option_c":"C. e^x","option_d":"D. 2e^x","option_e":"","option_f":"","bonne_reponse":"B","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":29847,"question":"L'intégrale ∫₀² (3x² + 1)dx est égale à :","option_a":"A. 8","option_b":"B. 10","option_c":"C. 12","option_d":"D. 6","option_e":"","option_f":"","bonne_reponse":"B","explication":"Calcul : [x³ + x]₀² = (8 + 2) - (0 + 0) = 10.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]