{"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":"a3b9aa11-8673-5877-baaa-975ce53a909d","task_key":"precalculus--test--a3b9aa11-8673-5877-baaa-975ce53a909d","task_revision_id":"1","upstream_id":"","short_description":"A line is parameterized by","config":"precalculus","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"A line is parameterized by\\n\\\\[\\\\begin{pmatrix} x \\\\\\\\ y \\\\end{pmatrix} = \\\\begin{pmatrix} 5 \\\\\\\\ -1 \\\\end{pmatrix} + t \\\\begin{pmatrix} 2 \\\\\\\\ 1 \\\\end{pmatrix}.\\\\]A second line is parameterized by\\n\\\\[\\\\begin{pmatrix} x \\\\\\\\ y \\\\end{pmatrix} = \\\\begin{pmatrix} -7 \\\\\\\\ 3 \\\\end{pmatrix} + u \\\\begin{pmatrix} -1 \\\\\\\\ 1 \\\\end{pmatrix}.\\\\]If $\\\\theta$ is the acute angle formed by the two lines, 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":[]}