{"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":"39d82282-5e43-5ad0-afd1-1b5b366a3c6f","task_key":"intermediate~5falgebra--test--39d82282-5e43-5ad0-afd1-1b5b366a3c6f","task_revision_id":"1","upstream_id":"","short_description":"The parabola $y = ax^2 + bx + c$ crosses the $x$-axis at $(p,0)$ and $(q,0),$…","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"The parabola $y = ax^2 + bx + c$ crosses the $x$-axis at $(p,0)$ and $(q,0),$ both to the right of the origin.  A circle also passes through these two points.  Let $t$ be the length of the tangent from the origin to the circle.  Express $t^2$ in terms of one or more of the coefficients $a,$ $b,$ and $c.$\\n\\n[asy]\\nunitsize(3 cm);\\n\\npair A, O, T;\\n\\nreal func (real x) {\\n  return ((x - 1)*(x - 2));\\n}\\n\\nA = (1.5,-0.4);\\nO = (0,0);\\nT = intersectionpoint(Circle(A,abs(A - (1,0))),arc(A/2,abs(A)/2,0,90));\\n\\ndraw(graph(func,0.5,2.5));\\ndraw((-0.5,0)--(2.5,0));\\ndraw((0,-1)--(0,1));\\ndraw(Circle(A,abs(A - (1,0))));\\ndraw(O--T);\\n\\nlabel(\\\"$t$\\\", T/3, N);\\n\\ndot(T);\\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":[]}