{"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":"deedd79d-70a8-54e0-af4f-dcdbc0b3f455","task_key":"intermediate~5falgebra--test--deedd79d-70a8-54e0-af4f-dcdbc0b3f455","task_revision_id":"1","upstream_id":"","short_description":"The equation of the hyperbola shown below can be written as","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"The equation of the hyperbola shown below can be written as\\n\\\\[\\\\frac{(y - k)^2}{a^2} - \\\\frac{(x - h)^2}{b^2} = 1.\\\\]Find $h + k + a + b.$\\n\\n[asy]\\nunitsize(0.3 cm);\\n\\nreal upperhyper (real x) {\\n  return (2*sqrt((x - 6)^2/16 + 1) - 5);\\n}\\n\\nreal lowerhyper (real x) {\\n  return (-2*sqrt((x - 6)^2/16 + 1) - 5);\\n}\\n\\nint i, n = 10;\\n\\nfor (i = -n; i <= n; ++i) {\\n  draw((i,-n)--(i,n),gray(0.7));\\n  draw((-n,i)--(n,i),gray(0.7));\\n}\\n\\ndraw((0,-n)--(0,n));\\ndraw((-n,0)--(n,0));\\n\\ndraw(graph(upperhyper,-10,10),red);\\ndraw(graph(lowerhyper,-3,10),red);\\ndraw(extension((-10,-10),(10,-10),(6,-5),(6,-5) + (4,2))--extension((10,10),(10,-10),(6,-5),(6,-5) + (4,2)),dashed);\\ndraw(extension((-10,-10),(-10,10),(6,-5),(6,-5) + (4,-2))--extension((10,10),(10,-10),(6,-5),(6,-5) + (4,-2)),dashed);\\n\\ndot((6,-5));\\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":[]}