{"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":"39b57731-09c0-5965-92ed-09a9d054c8d6","task_key":"precalculus--test--39b57731-09c0-5965-92ed-09a9d054c8d6","task_revision_id":"1","upstream_id":"","short_description":"There are real numbers $a$ and $b$ such that for every positive number $x$, we…","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"There are real numbers $a$ and $b$ such that for every positive number $x$, we have the identity\\n\\\\[\\n  \\\\tan^{-1} \\\\left( \\\\frac{1}{x} - \\\\frac{x}{8} \\\\right) + \\\\tan^{-1}(ax) + \\\\tan^{-1}(bx) \\n    = \\\\frac{\\\\pi}{2} \\\\, .\\n\\\\](Throughout this equation, $\\\\tan^{-1}$ means the inverse tangent function, sometimes written $\\\\arctan$.)  What is the value of $a^2 + b^2$?\",\"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":[]}