{"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":"eacaef07-0a99-5cd5-8b5b-54e6dc2a1c04","task_key":"precalculus--test--eacaef07-0a99-5cd5-8b5b-54e6dc2a1c04","task_revision_id":"1","upstream_id":"","short_description":"If $re^{i \\theta}$ is a root of","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"If $re^{i \\\\theta}$ is a root of\\n\\\\[z^8 - z^7 + z^6 - z^5 + z^4 - z^3 + z^2 - z + 1 = 0,\\\\]where $r > 0$ and $0 \\\\le \\\\theta < 2 \\\\pi,$ then find the sum of all possible values of $\\\\theta.$\",\"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":[]}