Quiz — C-EX08-TRM-CA.pdf

Question 1 sur 10 20:00

[{"id":58626,"question":"Quelle est la limite de la fonction f(x) = (3x² - 2x + 1)\/(x² + 5) quand x tend vers +∞ ?","option_a":"A. 0","option_b":"B. 3","option_c":"C. +∞","option_d":"D. -3","option_e":"","option_f":"","bonne_reponse":"b","explication":"La limite d'un quotient de polynômes de même degré est égale au 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\": \"b\", \"options\": {\"a\": \"A. 0\", \"b\": \"B. 3\", \"c\": \"C. +∞\", \"d\": \"D. -3\"}}","_debug_options_count":4},{"id":58627,"question":"La suite définie par uₙ = (-1)ⁿ est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La suite alterne entre -1 et 1, elle n'a pas de limite finie, donc elle est divergente.","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":58628,"question":"Soit f une fonction dérivable sur ℝ. Si f'(x) \u003E 0 pour tout x ∈ ℝ, alors f est :","option_a":"A. Décroissante","option_b":"B. Croissante","option_c":"C. Constante","option_d":"D. Non monotone","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction dont la dérivée est strictement positive sur un intervalle est strictement croissante sur cet intervalle.","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. Décroissante\", \"b\": \"B. Croissante\", \"c\": \"C. Constante\", \"d\"","_debug_options_count":4},{"id":58629,"question":"L'équation x³ - 6x² + 11x - 6 = 0 admet-elle trois solutions réelles distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En factorisant, on obtient (x-1)(x-2)(x-3)=0, donc trois solutions réelles distinctes : 1, 2 et 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":58630,"question":"La probabilité d'un événement A est P(A) = 0.6. Quelle est la probabilité de l'événement contraire A̅ ?","option_a":"A. 0.4","option_b":"B. 0.6","option_c":"C. 0.3","option_d":"D. 1.6","option_e":"","option_f":"","bonne_reponse":"a","explication":"La probabilité de l'événement contraire est P(A̅) = 1 - P(A) = 1 - 0.6 = 0.4.","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. 0.4\", \"b\": \"B. 0.6\", \"c\": \"C. 0.3\", \"d\": \"D. 1.6\"}}","_debug_options_count":4},{"id":58631,"question":"Dans le plan complexe, le nombre z = 2 + 2i a pour module :","option_a":"A. 2","option_b":"B. 2√2","option_c":"C. 4","option_d":"D. √2","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le module de z = a + bi est √(a² + b²) = √(4 + 4) = √8 = 2√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. 2\", \"b\": \"B. 2√2\", \"c\": \"C. 4\", \"d\": \"D. √2\"}}","_debug_options_count":4},{"id":58632,"question":"Soit une variable aléatoire X suivant une loi normale N(μ, σ²). Si μ = 5 et σ = 2, alors P(X ≤ 7) est :","option_a":"A. Inférieure à 0.5","option_b":"B. Égale à 0.5","option_c":"C. Supérieure à 0.5","option_d":"D. Impossible à déterminer","option_e":"","option_f":"","bonne_reponse":"c","explication":"Pour une loi normale, P(X ≤ μ) = 0.5. Comme 7 \u003E μ (5), P(X ≤ 7) \u003E 0.5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A. Inférieure à 0.5\", \"b\": \"B. Égale à 0.5\", \"c\": \"C. Supéri","_debug_options_count":4},{"id":58633,"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 logarithme est définie uniquement pour x \u003E 0, donc elle n'est pas définie en x = -1.","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":58634,"question":"Quel est le produit scalaire de deux vecteurs u(1, 2, 3) et v(4, 5, 6) ?","option_a":"A. 14","option_b":"B. 32","option_c":"C. 28","option_d":"D. 20","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le produit scalaire est calculé par u·v = (1×4) + (2×5) + (3×6) = 4 + 10 + 18 = 32.","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. 14\", \"b\": \"B. 32\", \"c\": \"C. 28\", \"d\": \"D. 20\"}}","_debug_options_count":4},{"id":58635,"question":"La suite géométrique de premier terme u₀ = 3 et de raison q = 2 est-elle bornée ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite géométrique de raison |q| \u003E 1 n'est pas bornée, car ses termes tendent vers +∞ ou -∞.","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}]