{"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":"9e980e35-fc46-5d89-bb9c-faf5926a14aa","task_key":"precalculus--test--9e980e35-fc46-5d89-bb9c-faf5926a14aa","task_revision_id":"1","upstream_id":"","short_description":"The parametric curve $(x,y) = (\\sin t, \\sin 2t)$ is plotted below.","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"The parametric curve $(x,y) = (\\\\sin t, \\\\sin 2t)$ is plotted below.\\n\\n[asy]\\nunitsize(2 cm);\\n\\npair moo (real t) {\\n  return (sin(t),sin(2*t));\\n}\\n\\nreal t;\\npath foo = moo(0);\\n\\nfor (t = 0; t <= 2*pi + 0.1; t = t + 0.1) {\\n  foo = foo--moo(t);\\n}\\n\\ndraw((-1.2,0)--(1.2,0));\\ndraw((0,-1.2)--(0,1.2));\\ndraw(foo,red);\\n[/asy]\\n\\nThis curve can also be expressed in the form\\n\\\\[ax^4 - bx^2 + cy^2 = 0,\\\\]where $a,$ $b,$ and $c$ are positive integers.  Find the smallest possible value of $a + b + c.$\",\"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":[]}