Quiz — 683201e728b04_sujet revision 3 théorique corrigé.pdf

Question 1 sur 5 10:00

[{"id":345,"question":"Quelle est la limite de la fonction f(x) = (3x² - 2x + 1)\/(x² + 1) 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":"Pour déterminer cette limite, on divise le numérateur et le dénominateur par x², ce qui donne (3 - 2\/x + 1\/x²)\/(1 + 1\/x²). Lorsque x tend vers +∞, les termes en 1\/x et 1\/x² tendent vers 0, donc la limite est 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. -∞\"}}","_debug_options_count":4},{"id":346,"question":"Soit une suite géométrique de premier terme u₀ = 2 et de raison q = 1\/2. Quelle est la valeur de u₃ ?","option_a":"A. 1\/4","option_b":"B. 1\/2","option_c":"C. 1","option_d":"D. 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule d'une suite géométrique est uₙ = u₀ × qⁿ. Ici, u₃ = 2 × (1\/2)³ = 2 × 1\/8 = 1\/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. 1\/4\", \"b\": \"B. 1\/2\", \"c\": \"C. 1\", \"d\": \"D. 2\"}}","_debug_options_count":4},{"id":347,"question":"Quelle est la dérivée de la fonction f(x) = ln(2x + 3) ?","option_a":"A. 1\/(2x + 3)","option_b":"B. 2\/(2x + 3)","option_c":"C. 1\/(x + 3)","option_d":"D. 2\/(x + 3)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de ln(u) est u'\/u. Ici, u = 2x + 3, donc u' = 2. Ainsi, f'(x) = 2\/(2x + 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. 1\/(2x + 3)\", \"b\": \"B. 2\/(2x + 3)\", \"c\": \"C. 1\/(x + 3)\", \"d\": \"","_debug_options_count":4},{"id":348,"question":"Dans un repère orthonormé, quelle est l'équation de la droite passant par les points A(1, 2) et B(3, 6) ?","option_a":"A. y = 2x","option_b":"B. y = x + 1","option_c":"C. y = 2x + 1","option_d":"D. y = x + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le coefficient directeur m = (6 - 2)\/(3 - 1) = 4\/2 = 2. L'équation est y = 2x + b. En remplaçant A(1, 2), on trouve b = 0. Donc y = 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\": \"A. y = 2x\", \"b\": \"B. y = x + 1\", \"c\": \"C. y = 2x + 1\", \"d\": \"D. y","_debug_options_count":4},{"id":349,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré à 6 faces ?","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":"Les nombres pairs sur un dé sont 2, 4 et 6, soit 3 faces sur 6. 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}]