{"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":"4cf6a34e-9870-552e-b5a2-af0d77f04c64","task_key":"precalculus--test--4cf6a34e-9870-552e-b5a2-af0d77f04c64","task_revision_id":"1","upstream_id":"","short_description":"One line is parameterized by","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"One line is parameterized by\\n\\\\[\\\\begin{pmatrix} 2 - 3t \\\\\\\\ -5 - 2t \\\\\\\\ 1 - 6t \\\\end{pmatrix}.\\\\]Another line is parameterized by\\n\\\\[\\\\begin{pmatrix} -\\\\frac{3}{2} + s \\\\\\\\ 2s \\\\\\\\ -6 + 2s \\\\end{pmatrix}.\\\\]The two lines intersect at $P.$  If $\\\\theta$ is the acute angle formed by the two lines at $P,$ 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":[]}