Quiz — 44.DOC

Question 1 sur 10 20:00

[{"id":16639,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) lorsque x tend vers +∞ ?","option_a":"A. 0","option_b":"B. 3","option_c":"C. +∞","option_d":"D. -∞","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. -∞\"}}","_debug_options_count":4},{"id":16640,"question":"La fonction f(x) = x³ - 3x + 2 est-elle 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 - 3 s'annule en x = ±1, donc la fonction n'est pas strictement croissante sur 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":16641,"question":"Quel est le module du nombre complexe z = 3 - 4i ?","option_a":"A. 5","option_b":"B. 7","option_c":"C. √7","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le module de z = a + bi est √(a² + b²). Ici, √(3² + (-4)²) = √(9 + 16) = 5.","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. 5\", \"b\": \"B. 7\", \"c\": \"C. √7\", \"d\": \"D. 1\"}}","_debug_options_count":4},{"id":16642,"question":"La suite définie par uₙ = (2n + 1)\/(n + 1) est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En calculant la limite de uₙ lorsque n tend vers +∞, on obtient 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":16643,"question":"Quelle est la primitive de la fonction f(x) = e^(2x) ?","option_a":"A. e^(2x) + C","option_b":"B. (1\/2)e^(2x) + C","option_c":"C. 2e^(2x) + C","option_d":"D. e^(x) + C","option_e":"","option_f":"","bonne_reponse":"b","explication":"La primitive de e^(kx) est (1\/k)e^(kx) + C. Ici, k = 2, donc la primitive est (1\/2)e^(2x) + C.","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. e^(2x) + C\", \"b\": \"B. (1\/2)e^(2x) + C\", \"c\": \"C. 2e^(2x) + C\",","_debug_options_count":4},{"id":16644,"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":"L'équation différentielle linéaire du premier ordre y' + ay = 0 a pour solution y = Ce^(-ax). Ici, a = 2, donc la solution est y = Ce^(-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":16645,"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 6 × 6 = 36 issues possibles. Un seul cas favorable (6,6), donc la probabilité est 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":16646,"question":"La fonction f(x) = ln(x) est-elle définie sur ℝ⁻ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction ln(x) est définie uniquement pour x \u003E 0, donc elle n'est pas définie sur ℝ⁻.","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":16647,"question":"Quel est le produit scalaire de deux vecteurs u et v de coordonnées respectives (1, 2, 3) et (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":"c","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\": \"c\", \"options\": {\"a\": \"A. 14\", \"b\": \"B. 32\", \"c\": \"C. 28\", \"d\": \"D. 20\"}}","_debug_options_count":4},{"id":16648,"question":"La fonction f(x) = sin(x) + cos(x) est-elle périodique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les fonctions sin(x) et cos(x) sont périodiques de période 2π, donc leur somme est aussi périodique de période 2π.","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}]