{"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":"c6e65a08-e32a-50a2-b714-d71bf3ccd6ac","task_key":"precalculus--test--c6e65a08-e32a-50a2-b714-d71bf3ccd6ac","task_revision_id":"1","upstream_id":"","short_description":"Given constants $C$ and $D,$ suppose that $\\tan A$ and $\\tan B$ are the…","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Given constants $C$ and $D,$ suppose that $\\\\tan A$ and $\\\\tan B$ are the solutions to\\n\\\\[x^2 + Cx + D = 0,\\\\]where $\\\\tan (A + B)$ is defined.\\n\\nSimplify\\n\\\\[\\\\sin^2 (A + B) + C \\\\sin (A + B) \\\\cos (A + B) + D \\\\cos^2 (A + B).\\\\]Your expression should contain only one of the variables $A,$ $B,$ $C,$ and $D.$\",\"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":[]}