Quiz — Copie de DC2.4.13-14Mc.pdf

Question 1 sur 10 20:00

[{"id":36510,"question":"Soit la fonction f définie par f(x) = x² - 4x + 3. Quelle est la dérivée de f ?","option_a":"A. f'(x) = 2x - 4","option_b":"B. f'(x) = x - 4","option_c":"C. f'(x) = 2x + 3","option_d":"D. f'(x) = x² - 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme à terme : f'(x) = 2x - 4.","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. f'(x) = 2x - 4\", \"b\": \"B. f'(x) = x - 4\", \"c\": \"C. f'(x) = 2x ","_debug_options_count":4},{"id":36511,"question":"Dans une classe de 30 élèves, 18 sont des filles. Quelle est la probabilité de choisir une fille au hasard ?","option_a":"A. 0,4","option_b":"B. 0,6","option_c":"C. 0,5","option_d":"D. 0,3","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité est le rapport du nombre de cas favorables (18 filles) sur le nombre total d'élèves (30), soit 18\/30 = 0,6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. 0,4\", \"b\": \"B. 0,6\", \"c\": \"C. 0,5\", \"d\": \"D. 0,3\"}}","_debug_options_count":4},{"id":36512,"question":"Une suite est définie par uₙ₊₁ = 2uₙ + 1 avec u₀ = 0. Cette suite est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite arithmétique a une différence constante entre deux termes consécutifs. Ici, u₁ = 1, u₂ = 3, donc u₂ - u₁ = 2 ≠ u₁ - u₀ = 1. La suite n'est pas arithmétique.","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":36513,"question":"Soit la fonction g(x) = (3x + 2)\/(x - 1). Quelle est l'équation de son asymptote verticale ?","option_a":"A. x = 1","option_b":"B. x = -1","option_c":"C. y = 3","option_d":"D. y = -2","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'asymptote verticale d'une fonction rationnelle se trouve là où le dénominateur s'annule (x - 1 = 0 ⇒ x = 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. x = 1\", \"b\": \"B. x = -1\", \"c\": \"C. y = 3\", \"d\": \"D. y = -2\"}}","_debug_options_count":4},{"id":36514,"question":"On lance un dé équilibré. Quelle est la probabilité d'obtenir un nombre pair ?","option_a":"A. 1\/6","option_b":"B. 1\/2","option_c":"C. 1\/3","option_d":"D. 2\/3","option_e":"","option_f":"","bonne_reponse":"b","explication":"Un dé a 6 faces, dont 3 sont paires (2, 4, 6). La probabilité est donc 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. 1\/6\", \"b\": \"B. 1\/2\", \"c\": \"C. 1\/3\", \"d\": \"D. 2\/3\"}}","_debug_options_count":4},{"id":36515,"question":"Soit une suite géométrique de raison q = -2 et de premier terme u₀ = 3. Quel est le terme u₃ ?","option_a":"A. -24","option_b":"B. 24","option_c":"C. -12","option_d":"D. 12","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le terme général d'une suite géométrique est uₙ = u₀ × qⁿ. Donc u₃ = 3 × (-2)³ = 3 × (-8) = -24.","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. -24\", \"b\": \"B. 24\", \"c\": \"C. -12\", \"d\": \"D. 12\"}}","_debug_options_count":4},{"id":36516,"question":"La fonction h(x) = eˣ est-elle toujours croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de h(x) = eˣ est h'(x) = eˣ, qui est toujours positive sur ℝ. La fonction est donc toujours croissante.","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":36517,"question":"Soit une variable aléatoire X suivant une loi binomiale B(n=10, p=0,3). Quelle est l'espérance E(X) ?","option_a":"A. 3","option_b":"B. 0,3","option_c":"C. 7","option_d":"D. 10","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi binomiale, 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\": \"A. 3\", \"b\": \"B. 0,3\", \"c\": \"C. 7\", \"d\": \"D. 10\"}}","_debug_options_count":4},{"id":36518,"question":"Soit la suite uₙ définie par uₙ = 5 - 2n. Cette suite est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite arithmétique de raison négative (ici -2) est divergente car ses termes tendent vers -∞.","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":36519,"question":"Soit la fonction k(x) = ln(x). Quelle est la limite de k(x) quand x tend vers 0+ ?","option_a":"A. -∞","option_b":"B. 0","option_c":"C. +∞","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction ln(x) tend vers -∞ quand x tend vers 0 par la droite.","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. -∞\", \"b\": \"B. 0\", \"c\": \"C. +∞\", \"d\": \"D. 1\"}}","_debug_options_count":4}]