{"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":"6e780eee-e32b-5658-8c23-c6eb5cf185af","task_key":"intermediate~5falgebra--test--6e780eee-e32b-5658-8c23-c6eb5cf185af","task_revision_id":"1","upstream_id":"","short_description":"Tangents are drawn from $(1,3)$ to the parabola $y^2 = 4x,$ at $A$ and $B.$ Find…","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Tangents are drawn from $(1,3)$ to the parabola $y^2 = 4x,$ at $A$ and $B.$  Find the length $AB.$\\n\\n[asy]\\nunitsize(0.4 cm);\\n\\nreal upperparab (real x) {\\n  return (sqrt(4*x));\\n}\\n\\nreal lowerparab (real x) {\\n  return (-sqrt(4*x));\\n}\\n\\npair A, B, P;\\n\\nP = (1,3);\\nA = ((7 + 3*sqrt(5))/2, upperparab((7 + 3*sqrt(5))/2));\\nB = ((7 - 3*sqrt(5))/2, upperparab((7 - 3*sqrt(5))/2));\\n\\ndraw(graph(upperparab,0,10));\\ndraw(graph(lowerparab,0,10));\\ndraw(interp(A,P,-0.8)--interp(A,P,1.2));\\ndraw(interp(B,P,-1)--interp(B,P,1.5));\\n\\ndot(\\\"$A$\\\", A, N);\\ndot(\\\"$B$\\\", B, W);\\ndot(\\\"$(1,3)$\\\", P, NW);\\n[/asy]\",\"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":[]}