Quiz — C-EX06-TRM-CA.pdf

Question 1 sur 10 20:00

[{"id":79534,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) quand x tend vers l'infini ?","option_a":"A) 0","option_b":"B) 3","option_c":"C) -∞","option_d":"D) 1","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. Ici, 3x²\/x² = 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) 1\"}}","_debug_options_count":4},{"id":79535,"question":"La fonction f(x) = x³ - 3x² + 2x est strictement croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 3x² - 6x + 2 s'annule en x = 1 ± √(1\/3), donc la fonction n'est pas strictement croissante sur tout ℝ.","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":79536,"question":"Quelle est la solution de l'équation ln(x) + ln(x-1) = ln(6) ?","option_a":"A) x = 2","option_b":"B) x = 3","option_c":"C) x = -2","option_d":"D) x = 4","option_e":"","option_f":"","bonne_reponse":"b","explication":"ln(x(x-1)) = ln(6) ⇒ x(x-1) = 6 ⇒ x² - x - 6 = 0 ⇒ x = 3 (solution positive).","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) x = 2\", \"b\": \"B) x = 3\", \"c\": \"C) x = -2\", \"d\": \"D) x = 4\"}}","_debug_options_count":4},{"id":79537,"question":"La suite définie par uₙ = (2n + 1)\/(n + 3) est convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La limite de uₙ quand n tend vers l'infini est 2, donc la suite est convergente.","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":79538,"question":"Quel est le déterminant de la matrice A = [[1, 2], [3, 4]] ?","option_a":"A) -2","option_b":"B) 2","option_c":"C) 5","option_d":"D) -5","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le déterminant est calculé par ad - bc = (1×4) - (2×3) = 4 - 6 = -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) -2\", \"b\": \"B) 2\", \"c\": \"C) 5\", \"d\": \"D) -5\"}}","_debug_options_count":4},{"id":79539,"question":"La fonction f(x) = e^(2x) est solution de l'équation différentielle y' = 2y.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de e^(2x) est 2e^(2x) = 2f(x), donc c'est bien une solution.","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":79540,"question":"Quelle est la probabilité d'obtenir un double 6 en lançant deux dés équilibrés ?","option_a":"A) 1\/6","option_b":"B) 1\/12","option_c":"C) 1\/36","option_d":"D) 1\/18","option_e":"","option_f":"","bonne_reponse":"c","explication":"Il y a 36 issues possibles, et une seule favorable (6-6), donc P = 1\/36.","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) 1\/6\", \"b\": \"B) 1\/12\", \"c\": \"C) 1\/36\", \"d\": \"D) 1\/18\"}}","_debug_options_count":4},{"id":79541,"question":"La suite uₙ = n² - 5n + 6 est minorée.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La suite tend vers +∞ quand n tend vers l'infini, donc elle n'est pas minorée.","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":79542,"question":"Quel est le coefficient directeur de la tangente à la courbe de f(x) = x² - 3x + 2 au point d'abscisse x = 1 ?","option_a":"A) -1","option_b":"B) 1","option_c":"C) -2","option_d":"D) 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 2x - 3, donc f'(1) = -1 (coefficient directeur de la tangente).","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) -1\", \"b\": \"B) 1\", \"c\": \"C) -2\", \"d\": \"D) 2\"}}","_debug_options_count":4},{"id":79543,"question":"L'équation x³ - 6x² + 11x - 6 = 0 admet trois solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le polynôme se factorise en (x-1)(x-2)(x-3), donc trois solutions réelles distinctes.","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}]