{"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":"41175514-9237-5966-8d8b-26f39b1ed378","task_key":"intermediate~5falgebra--test--41175514-9237-5966-8d8b-26f39b1ed378","task_revision_id":"1","upstream_id":"","short_description":"Let $T = (a, 9 - a^2)$ be a point on the parabola $y = 9 - x^2,$ for some…","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"Let $T = (a, 9 - a^2)$ be a point on the parabola $y = 9 - x^2,$ for some positive rational number $a.$\\n\\n[asy]\\nunitsize(1 cm);\\n\\nreal parab (real x) {\\n  return(4 - x^2);\\n}\\n\\npair T, X, Y;\\nreal m, t;\\n\\nt = 0.8;\\nm = -2*t;\\nT = (t,parab(t));\\nX = extension(T, T + (1,m), (0,0), (1,0));\\nY = extension(T, T + (1,m), (0,0), (0,1));\\n\\ndraw(graph(parab,0,2));\\ndraw(X--Y);\\ndraw((0,0)--(4,0));\\ndraw((0,0)--(0,5));\\n\\ndot(\\\"$T = (a, 9 - a^2)$\\\", T, NE);\\n[/asy]\\n\\nThe tangent to the parabola at $T$ and the coordinate axes form a triangle with area 25.  Find $a.$\",\"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":[]}