{"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":"430c65f8-7b00-5030-a32f-ceb400c39ee4","task_key":"precalculus--test--430c65f8-7b00-5030-a32f-ceb400c39ee4","task_revision_id":"1","upstream_id":"","short_description":"Let $\\mathbf{a},$ $\\mathbf{b},$ $\\mathbf{c}$ be three vectors such that","config":"precalculus","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"Let $\\\\mathbf{a},$ $\\\\mathbf{b},$ $\\\\mathbf{c}$ be three vectors such that\\n\\\\[\\\\mathbf{a} \\\\times \\\\mathbf{b} = \\\\begin{pmatrix} 6 \\\\\\\\ -7 \\\\\\\\ 3 \\\\end{pmatrix}, \\\\quad \\\\mathbf{a} \\\\times \\\\mathbf{c} = \\\\begin{pmatrix} 4 \\\\\\\\ 7 \\\\\\\\ 2 \\\\end{pmatrix}, \\\\quad \\\\mathbf{b} \\\\times \\\\mathbf{c} = \\\\begin{pmatrix} 1 \\\\\\\\ -7 \\\\\\\\ 18 \\\\end{pmatrix}.\\\\]Compute $(2 \\\\mathbf{b} - \\\\mathbf{a}) \\\\times (3 \\\\mathbf{c} + \\\\mathbf{a}).$\",\"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":[]}