{"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":"e72711bd-febd-54ee-8fad-0597aca63259","task_key":"precalculus--test--e72711bd-febd-54ee-8fad-0597aca63259","task_revision_id":"1","upstream_id":"","short_description":"Line segment $\\overline{AB}$ is extended past $A$ to $P$ such that $AP:PB =…","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Line segment $\\\\overline{AB}$ is extended past $A$ to $P$ such that $AP:PB = 1:4.$  Then\\n\\\\[\\\\overrightarrow{P} = t \\\\overrightarrow{A} + u \\\\overrightarrow{B}\\\\]for some constants $t$ and $u.$  Enter the ordered pair $(t,u).$\\n\\n[asy]\\nunitsize(1 cm);\\n\\npair A, B, P;\\n\\nA = (0,0);\\nB = (5,1);\\nP = interp(A,B,-1/3);\\n\\ndraw(B--P);\\n\\ndot(\\\"$A$\\\", A, S);\\ndot(\\\"$B$\\\", B, S);\\ndot(\\\"$P$\\\", P, S);\\n[/asy]\",\"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":[]}