{"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":"59d648c9-06bb-5e05-addf-ca69949b9e7a","task_key":"precalculus--test--59d648c9-06bb-5e05-addf-ca69949b9e7a","task_revision_id":"1","upstream_id":"","short_description":"The following line is parameterized, so that its direction vector is of the form…","config":"precalculus","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"The following line is parameterized, so that its direction vector is of the form $\\\\begin{pmatrix} -7 \\\\\\\\ b \\\\end{pmatrix}.$  Find $b.$\\n\\n[asy]\\nunitsize(0.4 cm);\\n\\npair A, B, L, R;\\nint i, n;\\n\\nfor (i = -8; i <= 8; ++i) {\\n  draw((i,-8)--(i,8),gray(0.7));\\n  draw((-8,i)--(8,i),gray(0.7));\\n}\\n\\ndraw((-8,0)--(8,0),Arrows(6));\\ndraw((0,-8)--(0,8),Arrows(6));\\n\\nA = (-5,4);\\nB = (-1,3);\\nL = extension(A, B, (-8,0), (-8,1));\\nR = extension(A, B, (8,0), (8,1));\\n\\ndraw(L--R, red);\\n\\nlabel(\\\"$x$\\\", (8,0), E);\\nlabel(\\\"$y$\\\", (0,8), N);\\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":[]}