Quiz — 324744387_3115068305449946_1297687843535275619_n.pdf

Question 1 sur 10 20:00

[{"id":46918,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) quand x tend vers +∞ ?","option_a":"A. 3","option_b":"B. 0","option_c":"C. +∞","option_d":"D. -∞","option_e":"","option_f":"","bonne_reponse":"a","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\": \"a\", \"options\": {\"a\": \"A. 3\", \"b\": \"B. 0\", \"c\": \"C. +∞\", \"d\": \"D. -∞\"}}","_debug_options_count":4},{"id":46919,"question":"Soit une suite géométrique de premier terme u₀ = 2 et de raison q = -1\/2. La suite est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite géométrique converge si et seulement si |q| \u003C 1. Ici, |-1\/2| = 1\/2 \u003C 1, donc la suite converge.","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":46920,"question":"Quel est le déterminant de la matrice A = [[2, 1], [3, 4]] ?","option_a":"A. 5","option_b":"B. 11","option_c":"C. 8","option_d":"D. -5","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le déterminant d'une matrice 2x2 [[a, b], [c, d]] est ad - bc. Ici, (2*4) - (1*3) = 8 - 3 = 5.","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. 5\", \"b\": \"B. 11\", \"c\": \"C. 8\", \"d\": \"D. -5\"}}","_debug_options_count":4},{"id":46921,"question":"La fonction f(x) = x³ - 3x² + 4 est-elle croissante sur l'intervalle [0, 2] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = 3x² - 6x = 3x(x - 2). Sur [0, 2], f'(x) ≤ 0, donc la fonction est décroissante 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":46922,"question":"Quelle est la valeur de l'intégrale ∫₀¹ (2x + 1) dx ?","option_a":"A. 1","option_b":"B. 2","option_c":"C. 3","option_d":"D. 4","option_e":"","option_f":"","bonne_reponse":"c","explication":"L'intégrale de 2x + 1 est x² + x. Évaluée entre 0 et 1 : (1² + 1) - (0² + 0) = 2.","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\", \"b\": \"B. 2\", \"c\": \"C. 3\", \"d\": \"D. 4\"}}","_debug_options_count":4},{"id":46923,"question":"Le nombre complexe z = 3 + 4i a-t-il un module égal à 5 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le module de z = a + bi est √(a² + b²). Ici, √(3² + 4²) = √(9 + 16) = √25 = 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":46924,"question":"Quelle est la solution de l'équation différentielle y' + 2y = 0 avec y(0) = 1 ?","option_a":"A. y = e^(-2x)","option_b":"B. y = e^(2x)","option_c":"C. y = 2e^(-x)","option_d":"D. y = e^(-x)","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation différentielle linéaire du premier ordre a pour solution générale y = Ce^(-2x). Avec y(0) = 1, on trouve C = 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. y = e^(-2x)\", \"b\": \"B. y = e^(2x)\", \"c\": \"C. y = 2e^(-x)\", \"d\"","_debug_options_count":4},{"id":46925,"question":"Soit une variable aléatoire X suivant une loi normale N(0, 1). P(X ≤ 1) est-il supérieur à 0,5 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi normale centrée réduite, P(X ≤ 0) = 0,5. Comme 1 \u003E 0, P(X ≤ 1) \u003E 0,5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":46926,"question":"Quelle est la valeur de la somme S = 1 + 2 + 3 + ... + n (pour n entier naturel) ?","option_a":"A. n(n+1)","option_b":"B. n(n+1)\/2","option_c":"C. n²","option_d":"D. (n+1)²","option_e":"","option_f":"","bonne_reponse":"b","explication":"La somme des n premiers entiers naturels est donnée par la formule n(n+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. n(n+1)\", \"b\": \"B. n(n+1)\/2\", \"c\": \"C. n²\", \"d\": \"D. (n+1)²\"}","_debug_options_count":4},{"id":46927,"question":"La fonction f(x) = ln(x) est-elle définie sur l'intervalle ]0, +∞[ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction logarithme népérien ln(x) est définie uniquement pour x \u003E 0, donc sur l'intervalle ]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}]