{"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":"bccb8507-699c-59f0-a181-5e734c6b4d1b","task_key":"intermediate~5falgebra--test--bccb8507-699c-59f0-a181-5e734c6b4d1b","task_revision_id":"1","upstream_id":"","short_description":"The graph of $x^2 - 2xy + 3y^2 = 5$ is an ellipse, although its axes are not…","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"The graph of $x^2 - 2xy + 3y^2 = 5$ is an ellipse, although its axes are not parallel to the coordinate axes. Two horizontal lines and two vertical lines lie tangent to the ellipse, forming a rectangle, as shown:\\n[asy]\\nsize(7cm);\\ndraw(rotate(20)*xscale(2.4)*unitcircle);\\ndraw((-3.5,0)--(3.5,0),EndArrow);\\ndraw((0,-2.5)--(0,2.5),EndArrow);\\nreal r1=2.29; draw((r1,-2.2)--(r1,2.2),dotted);\\ndraw((-r1,-2.2)--(-r1,2.2),dotted);\\nreal r2=1.26; draw((-3,r2)--(3,r2),dotted);\\ndraw((-3,-r2)--(3,-r2),dotted);\\nlabel(\\\"$x$\\\",(3.5,0),E); label(\\\"$y$\\\",(0,2.5),N);\\n[/asy]\\nWhat is the area of the rectangle?\",\"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":[]}