{"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":"1b826861-70d4-59c2-a09b-e396a8900034","task_key":"precalculus--test--1b826861-70d4-59c2-a09b-e396a8900034","task_revision_id":"1","upstream_id":"","short_description":"Find the smallest positive real number $C$ for which","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Find the smallest positive real number $C$ for which\\n\\\\[\\\\left\\\\| \\\\begin{pmatrix} 2 & 3 \\\\\\\\ 0 & -2 \\\\end{pmatrix} \\\\bold{v} \\\\right\\\\| \\\\le C \\\\|\\\\bold{v}\\\\|\\\\]for all two-dimensional vectors $\\\\bold{v}.$\\n\\nNote that for a two-dimensional vector $\\\\mathbf{a},$ $\\\\|\\\\mathbf{a}\\\\|$ is the magnitude of $\\\\mathbf{a}.$\",\"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":[]}