{"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":"93566dcf-f578-5a53-bf7d-aacf60447b9d","task_key":"precalculus--test--93566dcf-f578-5a53-bf7d-aacf60447b9d","task_revision_id":"1","upstream_id":"","short_description":"Let $\\bold{a}$ and $\\bold{b}$ be three-dimensional vectors. Then","config":"precalculus","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"Let $\\\\bold{a}$ and $\\\\bold{b}$ be three-dimensional vectors.  Then\\n\\\\[(5 \\\\bold{a} + 7 \\\\bold{b}) \\\\times (-\\\\bold{a} + 3 \\\\bold{b}) = k \\\\bold{a} \\\\times \\\\bold{b}\\\\]for some scalar $k$.  Find $k$.\",\"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":[]}