{"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":"8c0b1c8b-6491-5c2b-85d9-0e9ea348352a","task_key":"precalculus--test--8c0b1c8b-6491-5c2b-85d9-0e9ea348352a","task_revision_id":"1","upstream_id":"","short_description":"Let $\\mathbf{M} = \\begin{pmatrix} 0 & -5 \\\\ -2 & 4 \\end{pmatrix}.$ There exist…","config":"precalculus","split":"test","body":"{\"level\":\"Level 2\",\"problem\":\"Let $\\\\mathbf{M} = \\\\begin{pmatrix} 0 & -5 \\\\\\\\ -2 & 4 \\\\end{pmatrix}.$  There exist scalars $p$ and $q$ such that\\n\\\\[\\\\mathbf{M}^2 = p \\\\mathbf{M} + q \\\\mathbf{I}.\\\\]Enter the ordered pair $(p,q).$\",\"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":[]}