{"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":"20e184bb-ef63-51f9-8697-e04ccf197c77","task_key":"precalculus--test--20e184bb-ef63-51f9-8697-e04ccf197c77","task_revision_id":"1","upstream_id":"","short_description":"Below is the graph of $y = a \\csc bx$ for some positive constants $a$ and $b.$…","config":"precalculus","split":"test","body":"{\"level\":\"Level 2\",\"problem\":\"Below is the graph of $y = a \\\\csc bx$ for some positive constants $a$ and $b.$  Find $b.$\\n\\n[asy]import TrigMacros;\\n\\nsize(500);\\n\\nreal g(real x)\\n{\\n\\treturn 2*csc(x/3);\\n}\\n\\ndraw(graph(g,-6*pi + 0.01, -3*pi - 0.01),red);\\ndraw(graph(g,-3*pi + 0.01,-0.01),red);\\ndraw(graph(g,0.01,3*pi - 0.01),red);\\ndraw(graph(g,3*pi + 0.01,6*pi - 0.01),red);\\nlimits((-6*pi,-5),(6*pi,5),Crop);\\ndraw((-3*pi,-5)--(-3*pi,5),dashed);\\ndraw((3*pi,-5)--(3*pi,5),dashed);\\ntrig_axes(-6*pi,6*pi,-5,5,pi/2,1);\\nlayer();\\nrm_trig_labels(-11, 11, 2);\\n\\nlabel(\\\"$1$\\\", (0,1), E);\\nlabel(\\\"$2$\\\", (0,2), E);\\nlabel(\\\"$3$\\\", (0,3), E);\\nlabel(\\\"$4$\\\", (0,4), E);\\nlabel(\\\"$-1$\\\", (0,-1), E);\\nlabel(\\\"$-2$\\\", (0,-2), E);\\nlabel(\\\"$-3$\\\", (0,-3), E);\\nlabel(\\\"$-4$\\\", (0,-4), E);\\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":[]}