{"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":"fc97ac86-3036-5fb6-8002-5f80ecc5d188","task_key":"intermediate~5falgebra--test--fc97ac86-3036-5fb6-8002-5f80ecc5d188","task_revision_id":"1","upstream_id":"","short_description":"The graph of $y = \\frac{p(x)}{q(x)}$ is shown below, where $p(x)$ and $q(x)$ are…","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"The graph of $y = \\\\frac{p(x)}{q(x)}$ is shown below, where $p(x)$ and $q(x)$ are quadratic.  (Assume that the grid lines are at integers.)\\n\\n[asy]\\nunitsize(0.6 cm);\\n\\nreal func (real x) {\\n  return (-(x + 5)*(x - 4)/(x - 2)^2);\\n}\\n\\nint i;\\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));\\ndraw((0,-8)--(0,8));\\ndraw((2,-8)--(2,8),dashed);\\ndraw((-8,-1)--(8,-1),dashed);\\ndraw(graph(func,-8,1.9),red);\\ndraw(graph(func,2.1,8),red);\\n\\nlimits((-8,-8),(8,8),Crop);\\n[/asy]\\n\\nThe horizontal asymptote is $y = -1,$ and the only vertical asymptote is $x = 2.$  Find $\\\\frac{p(-1)}{q(-1)}.$\",\"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":[]}