{"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":"248ee68d-3b56-518b-b2df-be3be5dea89c","task_key":"intermediate~5falgebra--test--248ee68d-3b56-518b-b2df-be3be5dea89c","task_revision_id":"1","upstream_id":"","short_description":"The function $f : \\mathbb{R} \\to \\mathbb{R}$ satisfies","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"The function $f : \\\\mathbb{R} \\\\to \\\\mathbb{R}$ satisfies\\n\\\\[x^2 f(x) + f(1 - x) = -x^4 + 2x\\\\]for all real numbers $x.$  Then $f(x)$ can be uniquely determined for all values of $x,$ except $f(\\\\alpha)$ and $f(\\\\beta)$ for some real numbers $\\\\alpha$ and $\\\\beta.$  Compute $\\\\alpha^2 + \\\\beta^2.$\",\"type\":\"Intermediate Algebra\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}