Quiz — Copie de DC2.4.12-13C.pdf

Question 1 sur 10 20:00

[{"id":2250,"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 + 2x","option_d":"D) 6x + 2x - 5","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. Ainsi, f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A) 6x + 2\", \"b\": \"B) 3x + 2\", \"c\": \"C) 6x² + 2x\", \"d\": \"D) 6x + ","_debug_options_count":4},{"id":2251,"question":"Soit A et B deux événements indépendants avec P(A) = 0.4 et P(B) = 0.5. Quelle est P(A ∩ B) ?","option_a":"A) 0.2","option_b":"B) 0.9","option_c":"C) 0.1","option_d":"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A) 0.2\", \"b\": \"B) 0.9\", \"c\": \"C) 0.1\", \"d\": \"D) 0.45\"}}","_debug_options_count":4},{"id":2252,"question":"L'équation différentielle y' + 2y = 0 a pour solution générale y = Ce^(-2x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La solution générale de y' + 2y = 0 est bien y = Ce^(-2x), où C est une constante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":2253,"question":"Quelle est la dérivée de la fonction g(x) = ln(3x + 1) ?","option_a":"A) 3\/(3x + 1)","option_b":"B) 1\/(3x + 1)","option_c":"C) 3x\/(3x + 1)","option_d":"D) 1\/x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(u) est u'\/u. Ici, u = 3x + 1, donc u' = 3. Ainsi, g'(x) = 3\/(3x + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A) 3\/(3x + 1)\", \"b\": \"B) 1\/(3x + 1)\", \"c\": \"C) 3x\/(3x + 1)\", \"d\":","_debug_options_count":4},{"id":2254,"question":"Soit X une variable aléatoire suivant une loi binomiale B(n=10, p=0.3). Quelle est P(X=2) ?","option_a":"A) C(10,2) × (0.3)² × (0.7)^8","option_b":"B) C(10,2) × (0.3)^8 × (0.7)²","option_c":"C) (0.3)² × (0.7)^8","option_d":"D) 10 × 0.3 × 0.7","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi binomiale, P(X=k) = C(n,k) × p^k × (1-p)^(n-k). Ici, P(X=2) = C(10,2) × (0.3)² × (0.7)^8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A) C(10,2) × (0.3)² × (0.7)^8\", \"b\": \"B) C(10,2) × (0.3)^8 ×","_debug_options_count":4},{"id":2255,"question":"L'équation différentielle y'' - 4y' + 4y = 0 a pour solution générale y = (C1 + C2x)e^(2x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation caractéristique est r² - 4r + 4 = 0, soit (r-2)² = 0. La solution générale est donc y = (C1 + C2x)e^(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":2256,"question":"Quelle est la dérivée de la fonction h(x) = e^(2x + 1) ?","option_a":"A) 2e^(2x + 1)","option_b":"B) e^(2x + 1)","option_c":"C) 2x e^(2x + 1)","option_d":"D) (2x + 1)e^(2x)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de e^u est u'e^u. Ici, u = 2x + 1, donc u' = 2. Ainsi, h'(x) = 2e^(2x + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A) 2e^(2x + 1)\", \"b\": \"B) e^(2x + 1)\", \"c\": \"C) 2x e^(2x + 1)\", \"","_debug_options_count":4},{"id":2257,"question":"Soit A et B deux événements tels que P(A) = 0.6, P(B) = 0.4 et P(A ∩ B) = 0.2. A et B sont-ils indépendants ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"A et B sont indépendants si P(A ∩ B) = P(A) × P(B). Ici, 0.6 × 0.4 = 0.24 ≠ 0.2. Ils ne sont donc pas indépendants.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":2258,"question":"Quelle est la solution générale de l'équation différentielle y' - 3y = 6 ?","option_a":"A) y = Ce^(3x) - 2","option_b":"B) y = Ce^(3x) + 2","option_c":"C) y = Ce^(-3x) - 2","option_d":"D) y = Ce^(-3x) + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La solution générale de y' - 3y = 0 est y = Ce^(3x). Une solution particulière de y' - 3y = 6 est y = -2. La solution générale est donc y = Ce^(3x) - 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A) y = Ce^(3x) - 2\", \"b\": \"B) y = Ce^(3x) + 2\", \"c\": \"C) y = Ce^(","_debug_options_count":4},{"id":2259,"question":"Soit X une variable aléatoire suivant une loi normale N(μ=5, σ=2). Quelle est P(3 ≤ X ≤ 7) ?","option_a":"A) P(Z ≤ 1) - P(Z ≤ -1)","option_b":"B) P(Z ≤ 1) + P(Z ≤ -1)","option_c":"C) 2P(Z ≤ 1)","option_d":"D) P(Z ≤ 1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi normale, P(μ - σ ≤ X ≤ μ + σ) = P(Z ≤ 1) - P(Z ≤ -1), où Z suit une loi normale centrée réduite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A) P(Z ≤ 1) - P(Z ≤ -1)\", \"b\": \"B) P(Z ≤ 1) + P(Z ≤ -1)\",","_debug_options_count":4}]