{"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":"d513b7b2-1823-5f45-8717-c9e642dcec47","task_key":"precalculus--test--d513b7b2-1823-5f45-8717-c9e642dcec47","task_revision_id":"1","upstream_id":"","short_description":"Let $\\mathbf{u}$ and $\\mathbf{v}$ be unit vectors, and let $\\mathbf{w}$ be a…","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Let $\\\\mathbf{u}$ and $\\\\mathbf{v}$ be unit vectors, and let $\\\\mathbf{w}$ be a vector such that\\n\\\\[\\\\mathbf{w} + \\\\mathbf{w} \\\\times \\\\mathbf{u} = \\\\mathbf{v}.\\\\]Find the largest possible value of $(\\\\mathbf{u} \\\\times \\\\mathbf{v}) \\\\cdot \\\\mathbf{w}.$\",\"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":[]}