{"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":"456b066e-ae97-54bc-87fc-96fad8a0a310","task_key":"precalculus--test--456b066e-ae97-54bc-87fc-96fad8a0a310","task_revision_id":"1","upstream_id":"","short_description":"Let $w$ and $z$ be complex numbers such that $|w| = 1$ and $|z| = 10$. Let…","config":"precalculus","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"Let $w$ and $z$ be complex numbers such that $|w| = 1$ and $|z| = 10$. Let $\\\\theta = \\\\arg \\\\left(\\\\frac{w-z}{z}\\\\right)$. Find the maximum possible value of $\\\\tan^2 \\\\theta.$  (Note that $\\\\arg(w),$ for $w \\\\neq 0,$ denotes the measure of the angle that the ray from 0 to $w$ makes with the positive real axis in the complex plane.)\",\"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":[]}