{"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":"9cbd2569-0bc3-5380-9ec6-449504ac112e","task_key":"intermediate~5falgebra--test--9cbd2569-0bc3-5380-9ec6-449504ac112e","task_revision_id":"1","upstream_id":"","short_description":"Let $\\lambda$ be a constant, $0 \\le \\lambda \\le 4,$ and let $f : [0,1] \\to…","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Let $\\\\lambda$ be a constant, $0 \\\\le \\\\lambda \\\\le 4,$ and let $f : [0,1] \\\\to [0,1]$ be defined by\\n\\\\[f(x) = \\\\lambda x(1 - x).\\\\]Find the values of $\\\\lambda,$ $0 \\\\le \\\\lambda \\\\le 4,$ for which there exists an $x \\\\in [0,1]$ such that $f(x) \\\\neq x$ but $f(f(x)) = x.$\",\"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":[]}