{"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":"3b5c8e51-2d73-5bb9-aa32-1661815918d6","task_key":"precalculus--test--3b5c8e51-2d73-5bb9-aa32-1661815918d6","task_revision_id":"1","upstream_id":"","short_description":"When $\\begin{pmatrix} a \\\\ b \\end{pmatrix}$ is projected onto $\\begin{pmatrix}…","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"When $\\\\begin{pmatrix} a \\\\\\\\ b \\\\end{pmatrix}$ is projected onto $\\\\begin{pmatrix} \\\\sqrt{3} \\\\\\\\ 1 \\\\end{pmatrix},$ the resulting vector has magnitude $\\\\sqrt{3}.$  Also, $a = 2 + b \\\\sqrt{3}.$  Enter all possible values of $a,$ separated by commas.\",\"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":[]}