{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"64952667-46a4-5682-acde-690dcb1470db","task_key":"precalculus--test--64952667-46a4-5682-acde-690dcb1470db","task_revision_id":"1","upstream_id":"","short_description":"If $w=\\cos40^\\circ+i\\sin40^\\circ $, then","config":"precalculus","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"If $w=\\\\cos40^\\\\circ+i\\\\sin40^\\\\circ $, then\\n\\\\[|w+2w^2+3w^3+ \\\\dots +9w^9|^{-1}\\\\]can be expressed in the form $\\\\frac{a}{b} \\\\sin n^\\\\circ,$ where $a$ and $b$ are relatively prime positive integers, and $n$ is a positive integer smaller than 90.  Find $a + b + n.$\",\"type\":\"Precalculus\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}