{"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":"46d58ae4-a28f-57df-b117-8f635a68abed","task_key":"precalculus--test--46d58ae4-a28f-57df-b117-8f635a68abed","task_revision_id":"1","upstream_id":"","short_description":"Let $P$ be the convex polygon in the complex plane whose vertices are the roots…","config":"precalculus","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"Let $P$ be the convex polygon in the complex plane whose vertices are the roots of\\n\\\\[z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1 = 0.\\\\]The area of $P$ can be expressed in the form $\\\\frac{a + b \\\\sqrt{c}}{d},$ where $a,$ $b,$ $c,$ $d$ are positive integers, in simplest form.  Find $a + b + c + d.$\",\"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":[]}