{"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":"9b31a299-6391-55ce-8365-202c37299009","task_key":"precalculus--test--9b31a299-6391-55ce-8365-202c37299009","task_revision_id":"1","upstream_id":"","short_description":"Let $z$ be a complex number with $|z|=2$. Let $P$ be the polygon in the complex…","config":"precalculus","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"Let $z$ be a complex number with $|z|=2$. Let $P$ be the polygon in the complex plane whose vertices are $z$ and every $w$ such that\\n\\\\[\\\\frac{1}{z+w}=\\\\frac{1}{z}+\\\\frac{1}{w}.\\\\]Find the area enclosed by $P.$\",\"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":[]}