{"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":"1b6d4df9-432f-5299-82f6-0e37385d12da","task_key":"precalculus--test--1b6d4df9-432f-5299-82f6-0e37385d12da","task_revision_id":"1","upstream_id":"","short_description":"The expression","config":"precalculus","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"The expression\\n\\\\[\\\\sin^3 2x \\\\cos 6x + \\\\cos^3 2x \\\\sin 6x\\\\]can be written in the equivalent form $a \\\\sin bx$ for some positive constants $a$ and $b.$  Find $a + b.$\",\"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":[]}