{"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":"982830a7-34f7-5f29-9b66-9e80cb95a6b8","task_key":"precalculus--test--982830a7-34f7-5f29-9b66-9e80cb95a6b8","task_revision_id":"1","upstream_id":"","short_description":"Given that","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Given that\\n\\\\begin{align*}\\n\\\\cos x + \\\\cos y + \\\\cos z &= 0, \\\\\\\\\\n\\\\sin x + \\\\sin y + \\\\sin z &= 0,\\n\\\\end{align*}find\\n\\\\begin{align*}\\n&\\\\tan^2 x + \\\\tan^2 y + \\\\tan^2 z - (\\\\tan^2 x \\\\tan^2 y + \\\\tan^2 x \\\\tan^2 z + \\\\tan^2 y \\\\tan^2 z) \\\\\\\\\\n&\\\\quad  - 3 \\\\tan^2 x \\\\tan^2 y \\\\tan^2 z.\\n\\\\end{align*}\",\"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":[]}