math-ai/BlueMO
BlueMO 🚀 BlueMO: A Comprehensive Collection of Challenging Mathematical Olympiad Problems from the Little Blue Book Series BlueMO is a comprehensive and challenging dataset comprising mathematical olympiad problems paired with detailed solutions, meticulously curated from the esteemed "Little Blue Book" (小蓝书) series (Second Edition)—a vital resource for Chinese students training for national and international olympiad math competitions. Designed to… See the full description on the dataset page: https://huggingface.co/datasets/math-ai/BlueMO.
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1{2 "source_file": "./raw_volume-zh/volume3/exercise3.tex",3 "problem_type": "calculation",4 "problem": "问题5 在直角三角形中, $\\angle C=90^{\\circ}$, 则 $\\sin A \\cos ^2\\left(45^{\\circ}-\\frac{B}{2}\\right)-\\sin \\frac{A}{2} \\cos \\frac{A}{2}(\\quad)$.\n(A) 有最大值 $\\frac{1}{4}$ 和最小值 0\n(B) 有最大值 $\\frac{1}{4}$ 但无最小值\n(C) 既无最大值又无最小值\n(D) 有最大值 $\\frac{1}{2}$ 但无最小值",5 "solution": "B. 原式 $=\\sin A \\cdot \\frac{1+\\cos \\left(90^{\\circ}-B\\right)}{2}-\\frac{1}{2} \\sin A=\\frac{1}{2} \\sin A \\cdot \\sin B= \\frac{1}{2} \\sin A \\cos A=\\frac{1}{4} \\sin 2 A \\leqslant \\frac{1}{4}$.",6 "remark": "",7 "figures": []8}