Quiz — 5.Série n°4.pdf

Question 1 sur 10 20:00

[{"id":53367,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 5)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"A. 0","option_b":"B. 2","option_c":"C. -∞","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"La limite d'un rapport de polynômes de même degré est égale au rapport des coefficients dominants. Ici, 2x²\/x² = 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. 0\", \"b\": \"B. 2\", \"c\": \"C. -∞\", \"d\": \"D. +∞\"}}","_debug_options_count":4},{"id":53368,"question":"Soit une variable aléatoire X suivant une loi normale N(μ, σ²). Si σ augmente, que se passe-t-il pour l'intervalle [μ - σ, μ + σ] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Si σ augmente, l'intervalle [μ - σ, μ + σ] s'élargit, car l'écart-type mesure la dispersion autour de la moyenne.","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":53369,"question":"Quelle est la dérivée de la fonction f(x) = ln(x² + 1) ?","option_a":"A. 2x\/(x² + 1)","option_b":"B. 1\/(x² + 1)","option_c":"C. 2x","option_d":"D. x\/(x² + 1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant la règle de dérivation des fonctions composées, f'(x) = (2x)\/(x² + 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. 2x\/(x² + 1)\", \"b\": \"B. 1\/(x² + 1)\", \"c\": \"C. 2x\", \"d\": \"D. x","_debug_options_count":4},{"id":53370,"question":"Le nombre complexe z = 3 - 4i a pour module :","option_a":"A. 5","option_b":"B. 7","option_c":"C. √7","option_d":"D. 25","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le module d'un nombre complexe z = a + bi est √(a² + b²). Ici, √(3² + (-4)²) = √(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\": \"A. 5\", \"b\": \"B. 7\", \"c\": \"C. √7\", \"d\": \"D. 25\"}}","_debug_options_count":4},{"id":53371,"question":"Soit une suite géométrique de raison q = 2 et de premier terme u₀ = 3. Quelle est la valeur de u₃ ?","option_a":"A. 6","option_b":"B. 12","option_c":"C. 24","option_d":"D. 48","option_e":"","option_f":"","bonne_reponse":"c","explication":"La formule d'une suite géométrique est uₙ = u₀ × qⁿ. Donc u₃ = 3 × 2³ = 3 × 8 = 24.","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. 6\", \"b\": \"B. 12\", \"c\": \"C. 24\", \"d\": \"D. 48\"}}","_debug_options_count":4},{"id":53372,"question":"La fonction f(x) = x³ - 3x² + 2 est convexe sur l'intervalle :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La convexité d'une fonction est déterminée par le signe de sa dérivée seconde. f''(x) = 6x - 6. f''(x) \u003E 0 pour x \u003E 1, donc la fonction est convexe sur ]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":53373,"question":"Quel est le résultat de l'intégrale ∫(2x + 1)dx entre 0 et 2 ?","option_a":"A. 4","option_b":"B. 6","option_c":"C. 8","option_d":"D. 10","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'intégrale de 2x + 1 est x² + x. Évaluée entre 0 et 2, on obtient (4 + 2) - (0 + 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. 4\", \"b\": \"B. 6\", \"c\": \"C. 8\", \"d\": \"D. 10\"}}","_debug_options_count":4},{"id":53374,"question":"Soit un triangle ABC rectangle en A. Si AB = 3 et AC = 4, quelle est la longueur de BC ?","option_a":"A. 5","option_b":"B. 7","option_c":"C. √7","option_d":"D. 25","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après le théorème de Pythagore, BC² = AB² + AC² = 9 + 16 = 25, donc BC = 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. 25\"}}","_debug_options_count":4},{"id":53375,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est :","option_a":"A. 1\/6","option_b":"B. 1\/3","option_c":"C. 1\/2","option_d":"D. 2\/3","option_e":"","option_f":"","bonne_reponse":"c","explication":"Un dé a 6 faces. Les nombres pairs sont 2, 4 et 6, soit 3 faces. 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\": \"c\", \"options\": {\"a\": \"A. 1\/6\", \"b\": \"B. 1\/3\", \"c\": \"C. 1\/2\", \"d\": \"D. 2\/3\"}}","_debug_options_count":4},{"id":53376,"question":"Soit une suite arithmétique de premier terme u₀ = 5 et de raison r = -2. Quelle est la valeur de u₅ ?","option_a":"A. -5","option_b":"B. 5","option_c":"C. -3","option_d":"D. 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule d'une suite arithmétique est uₙ = u₀ + n×r. Donc u₅ = 5 + 5×(-2) = 5 - 10 = -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. 5\", \"c\": \"C. -3\", \"d\": \"D. 3\"}}","_debug_options_count":4}]