{"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":"60f1c881-ffd8-5a60-abff-5c519cf7ba16","task_key":"intermediate~5falgebra--test--60f1c881-ffd8-5a60-abff-5c519cf7ba16","task_revision_id":"1","upstream_id":"","short_description":"Let $F_1 = (10,2)$ and $F_ 2= (-16,2).$ Then the set of points $P$ such that","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"Let $F_1 = (10,2)$ and $F_ 2= (-16,2).$  Then the set of points $P$ such that\\n\\\\[|PF_1 - PF_2| = 24\\\\]form a hyperbola.  The equation of this hyperbola can be written as\\n\\\\[\\\\frac{(x - h)^2}{a^2} - \\\\frac{(y - k)^2}{b^2} = 1.\\\\]Find $h + k + a + b.$\",\"type\":\"Intermediate Algebra\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}