{"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":"060ea21e-708c-5f14-aed7-7e7cc8aa24d9","task_key":"precalculus--test--060ea21e-708c-5f14-aed7-7e7cc8aa24d9","task_revision_id":"1","upstream_id":"","short_description":"A line passes through the distinct vectors $\\mathbf{a}$ and $\\mathbf{b}.$ Which…","config":"precalculus","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"A line passes through the distinct vectors $\\\\mathbf{a}$ and $\\\\mathbf{b}.$  Which of the following are valid parameterizations of the line?\\n\\n(A) $\\\\mathbf{a} + t (\\\\mathbf{a} - \\\\mathbf{b})$\\n\\n(B) $\\\\frac{3}{4} \\\\mathbf{a} + t \\\\cdot \\\\frac{\\\\mathbf{b}}{4}$\\n\\n(C) $\\\\frac{\\\\mathbf{a} + \\\\mathbf{b}}{2} + t \\\\cdot \\\\frac{\\\\mathbf{b} - \\\\mathbf{a}}{2}$\\n\\n(D) $\\\\mathbf{a} + 2 \\\\mathbf{b} + t (2 \\\\mathbf{b} - 3 \\\\mathbf{a})$\\n\\n(E) $-\\\\mathbf{b} + t (\\\\mathbf{a} + \\\\mathbf{b})$\\n\\n(F) $\\\\mathbf{b} + \\\\frac{t}{3} (2 \\\\mathbf{a} - 2 \\\\mathbf{b})$\\n\\nEnter the letters of the correct options, separated by commas.\",\"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":[]}