Quiz — ex 4 dv.pdf

Question 1 sur 10 20:00

[{"id":117253,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"2x + 3","option_b":"x² + 3","option_c":"2x + 5","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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"2x + 3\", \"b\": \"x² + 3\", \"c\": \"2x + 5\", \"d\": \"x + 3\"}}","_debug_options_count":4},{"id":117254,"question":"Une suite géométrique de raison q = 2 et de premier terme u₀ = 3 a pour expression uₙ = 3 × 2ⁿ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule générale d'une suite géométrique est uₙ = u₀ × qⁿ. Ici, u₀ = 3 et q = 2, donc l'expression est correcte.","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":117255,"question":"Quel est le résultat de l'intégrale ∫(2x + 1) dx ?","option_a":"x² + x + C","option_b":"x² + C","option_c":"2x² + x + C","option_d":"x² - x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale d'une fonction polynôme se calcule en augmentant l'exposant de 1 et en divisant par le nouvel exposant. ∫2x dx = x² et ∫1 dx = x, d'où x² + x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x² + x + C\", \"b\": \"x² + C\", \"c\": \"2x² + x + C\", \"d\": \"x² - x ","_debug_options_count":4},{"id":117256,"question":"Si P(A) = 0,3 et P(B) = 0,4 avec A et B indépendants, alors P(A ∩ B) = ?","option_a":"0,12","option_b":"0,7","option_c":"0,07","option_d":"0,1","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour deux événements indépendants, P(A ∩ B) = P(A) × P(B) = 0,3 × 0,4 = 0,12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0,12\", \"b\": \"0,7\", \"c\": \"0,07\", \"d\": \"0,1\"}}","_debug_options_count":4},{"id":117257,"question":"La fonction f(x) = 1\/x est décroissante sur son ensemble de définition.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de f(x) = 1\/x est f'(x) = -1\/x², qui est toujours négative (sauf en x=0 où elle n'est pas définie). Donc la fonction est décroissante sur ]-∞,0[ et ]0,+∞[.","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":117258,"question":"Quel est le terme général d'une suite arithmétique de premier terme u₀ = 5 et de raison r = -2 ?","option_a":"uₙ = 5 - 2n","option_b":"uₙ = 5 + 2n","option_c":"uₙ = -2 + 5n","option_d":"uₙ = 5n - 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule d'une suite arithmétique est uₙ = u₀ + n × r. Ici, u₀ = 5 et r = -2, donc uₙ = 5 - 2n.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"uₙ = 5 - 2n\", \"b\": \"uₙ = 5 + 2n\", \"c\": \"uₙ = -2 + 5n\", \"d\":","_debug_options_count":4},{"id":117259,"question":"Soit X une variable aléatoire suivant une loi normale N(μ=10, σ=2). Quelle est la probabilité P(X ≤ 12) ?","option_a":"0,8413","option_b":"0,1587","option_c":"0,5","option_d":"0,6915","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi normale N(μ, σ), P(X ≤ μ + σ) ≈ 0,8413. Ici, 12 = μ + σ, donc P(X ≤ 12) ≈ 0,8413.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0,8413\", \"b\": \"0,1587\", \"c\": \"0,5\", \"d\": \"0,6915\"}}","_debug_options_count":4},{"id":117260,"question":"La fonction f(x) = eˣ 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 eˣ est strictement positive pour tout x réel, car eˣ \u003E 0 quel que soit x.","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":117261,"question":"Quel est le résultat de la limite lim (x→+∞) (3x² + 2x - 1)\/(x² + 5) ?","option_a":"3","option_b":"2","option_c":"+∞","option_d":"0","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour les limites à l'infini de fonctions rationnelles, on compare les degrés des polynômes. Ici, les degrés sont égaux (2), donc la limite est le rapport des coefficients dominants : 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"3\", \"b\": \"2\", \"c\": \"+∞\", \"d\": \"0\"}}","_debug_options_count":4},{"id":117262,"question":"Si une variable aléatoire X suit une loi binomiale B(n=10, p=0,3), alors E(X) = ?","option_a":"3","option_b":"7","option_c":"0,3","option_d":"10","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'espérance d'une loi binomiale B(n, p) est E(X) = n × p = 10 × 0,3 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"3\", \"b\": \"7\", \"c\": \"0,3\", \"d\": \"10\"}}","_debug_options_count":4}]