{"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":"396356fc-b189-5439-a447-0b054cf98f37","task_key":"precalculus--test--396356fc-b189-5439-a447-0b054cf98f37","task_revision_id":"1","upstream_id":"","short_description":"For certain vectors $\\mathbf{p}$ and $\\mathbf{q},$ the vectors $3 \\mathbf{p} +…","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"For certain vectors $\\\\mathbf{p}$ and $\\\\mathbf{q},$ the vectors $3 \\\\mathbf{p} + \\\\mathbf{q}$ and $5 \\\\mathbf{p} - 3 \\\\mathbf{q}$ are orthogonal.  Also, the vectors $2 \\\\mathbf{p} + \\\\mathbf{q}$ and $4 \\\\mathbf{p} - 2 \\\\mathbf{q}$ are orthogonal.  If $\\\\theta$ is the angle between $\\\\mathbf{p}$ and $\\\\mathbf{q},$ then find $\\\\cos \\\\theta.$\",\"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":[]}