{"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":"20ab45e6-3ace-54ad-b03e-e41b6b46c8dc","task_key":"precalculus--test--20ab45e6-3ace-54ad-b03e-e41b6b46c8dc","task_revision_id":"1","upstream_id":"","short_description":"Consider two lines: line $l$ parameterized as","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Consider two lines: line $l$ parameterized as\\n\\\\begin{align*} \\nx &= 1 + 4t,\\\\\\\\\\ny &=  4 + 3t\\n\\\\end{align*}and the line $m$ parameterized as\\n\\\\begin{align*} \\nx &=-5  + 4s\\\\\\\\\\ny &=  6 + 3s.\\n\\\\end{align*}Let $A$ be a point on line $l$, $B$ be a point on line $m$, and let $P$ be the foot of the perpendicular from $A$ to line $m$.\\n\\nThen $\\\\overrightarrow{BP}$ is the projection of $\\\\overrightarrow{BA}$ onto some vector $\\\\begin{pmatrix} v_1\\\\\\\\v_2\\\\end{pmatrix}$ such that $v_1+v_2 = -7$. Find $\\\\begin{pmatrix}v_1 \\\\\\\\ v_2 \\\\end{pmatrix}$.\",\"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":[]}