{"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":"c47ff50a-b8cc-5641-a9eb-dc1a656f84c8","task_key":"precalculus--test--c47ff50a-b8cc-5641-a9eb-dc1a656f84c8","task_revision_id":"1","upstream_id":"","short_description":"Let $S$ be the set of all points $(x,y)$ in the coordinate plane such that…","config":"precalculus","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"Let $S$ be the set of all points $(x,y)$ in the coordinate plane such that $0\\\\leq x\\\\leq \\\\frac{\\\\pi}{2}$ and $0\\\\leq y\\\\leq\\n\\\\frac{\\\\pi}{2}$. What is the area of the subset of $S$ for which \\\\[\\n\\\\sin^2 x -\\\\sin x \\\\sin y +\\\\sin^2 y \\\\leq\\\\frac{3}{4}\\\\,?\\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":[]}