{"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":"78015003-8cbb-57f7-9bb3-8d80ff277300","task_key":"intermediate~5falgebra--test--78015003-8cbb-57f7-9bb3-8d80ff277300","task_revision_id":"1","upstream_id":"","short_description":"Let $A$ and $B$ be two points lying on the parabola $y^2 = 4x$ in the first…","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Let $A$ and $B$ be two points lying on the parabola $y^2 = 4x$ in the first quadrant.  The circle with diameter $\\\\overline{AB}$ has radius $r,$ and is tangent to the $x$-axis.  Find the slope of line $AB$ in terms of $r.$\\n\\n[asy]\\nunitsize(0.4 cm);\\n\\npath parab = (16,-8);\\nreal y;\\npair A, B, O;\\nreal a, b, r;\\n\\na = (10 + 2*sqrt(5))/5;\\nb = (10 - 2*sqrt(5))/5;\\nA = (a^2,2*a);\\nB = (b^2,2*b);\\nO = (A + B)/2;\\nr = a + b;\\n\\nfor (y = -8; y <= 8; y = y + 0.2) {\\n  parab = parab--(y^2/4,y);\\n}\\n\\ndraw(parab,red);\\ndraw((-2,0)--(16,0));\\ndraw((0,-8)--(0,8));\\ndraw(Circle(O,r));\\ndraw(A--B);\\n\\ndot(\\\"$A$\\\", A, N);\\ndot(\\\"$B$\\\", B, W);\\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":[]}