Quiz — Pratique2015 - 24.pdf

Question 1 sur 10 20:00

[{"id":36410,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 2x² + 5 ?","option_a":"3x² - 4x","option_b":"3x² - 4x + 5","option_c":"x² - 2x","option_d":"x³ - 4x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'un polynôme se calcule terme par terme. La dérivée de x³ est 3x², celle de -2x² est -4x, et celle de 5 est 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\": \"3x² - 4x\", \"b\": \"3x² - 4x + 5\", \"c\": \"x² - 2x\", \"d\": \"x³ - 4x","_debug_options_count":4},{"id":36411,"question":"La fonction f(x) = 1\/x est-elle dérivable en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction 1\/x n'est pas définie en x = 0, donc elle n'est pas dérivable en ce point.","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":36412,"question":"Quelle est la limite de (sin x)\/x lorsque x tend vers 0 ?","option_a":"0","option_b":"1","option_c":"∞","option_d":"π\/2","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est un résultat fondamental en analyse : lim (x→0) (sin x)\/x = 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\": \"0\", \"b\": \"1\", \"c\": \"∞\", \"d\": \"π\/2\"}}","_debug_options_count":4},{"id":36413,"question":"Soit une suite définie par uₙ₊₁ = 2uₙ + 3 avec u₀ = 1. Quelle est la valeur de u₂ ?","option_a":"7","option_b":"11","option_c":"13","option_d":"17","option_e":"","option_f":"","bonne_reponse":"b","explication":"u₁ = 2*1 + 3 = 5, puis u₂ = 2*5 + 3 = 13. Attention à ne pas confondre u₂ et u₁.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"7\", \"b\": \"11\", \"c\": \"13\", \"d\": \"17\"}}","_debug_options_count":4},{"id":36414,"question":"L'équation x² + 4x + 5 = 0 admet-elle des solutions réelles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le discriminant Δ = 16 - 20 = -4 \u003C 0, donc l'équation n'a pas de solutions réelles.","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":36415,"question":"Quelle est la primitive de la fonction f(x) = e^(2x) ?","option_a":"(1\/2)e^(2x) + C","option_b":"e^(2x) + C","option_c":"2e^(2x) + C","option_d":"(1\/2)e^x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La primitive de e^(kx) est (1\/k)e^(kx) + C. Ici, k = 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\": \"(1\/2)e^(2x) + C\", \"b\": \"e^(2x) + C\", \"c\": \"2e^(2x) + C\", \"d\": \"(1","_debug_options_count":4},{"id":36416,"question":"Dans un triangle rectangle, si le cosinus d'un angle est 0,5, quel est cet angle ?","option_a":"30°","option_b":"45°","option_c":"60°","option_d":"90°","option_e":"","option_f":"","bonne_reponse":"a","explication":"cos(30°) = √3\/2 ≈ 0,866, cos(45°) ≈ 0,707, cos(60°) = 0,5, cos(90°) = 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\": \"30°\", \"b\": \"45°\", \"c\": \"60°\", \"d\": \"90°\"}}","_debug_options_count":4},{"id":36417,"question":"La fonction f(x) = |x| est-elle dérivable en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction valeur absolue n'est pas dérivable en x = 0 car elle présente un point anguleux (dérivée à gauche ≠ dérivée à droite).","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":36418,"question":"Quelle est la valeur de l'intégrale ∫₀¹ (3x² + 2x) dx ?","option_a":"1","option_b":"2","option_c":"3","option_d":"4","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'intégrale se calcule terme par terme : ∫3x² dx = x³ et ∫2x dx = x². Évaluée entre 0 et 1, cela donne (1 + 1) - (0 + 0) = 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\": \"1\", \"b\": \"2\", \"c\": \"3\", \"d\": \"4\"}}","_debug_options_count":4},{"id":36419,"question":"Soit une variable aléatoire X suivant une loi normale N(μ, σ²). Que vaut P(X ≤ μ) ?","option_a":"0","option_b":"0,5","option_c":"1","option_d":"μ","option_e":"","option_f":"","bonne_reponse":"b","explication":"Dans une loi normale, la probabilité que X soit inférieure ou égale à sa moyenne μ est de 0,5 (symétrie de la courbe).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0\", \"b\": \"0,5\", \"c\": \"1\", \"d\": \"μ\"}}","_debug_options_count":4}]