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2005年11月28日,清华大学在华东师范大学二附中举行了面向苏浙沪考生的自主招生考试,这是清华大学首次在京外地区进行自主招生,考试分笔试和面试两部分,笔试试题的难度略难于高考,其中不少试题还是很有意思的,值得玩味.我们下面就其中的几道数学试题做一些分析,愿与读者一起分享.例1 已知 a,6 为非负数,M=a~4+b~4,a+b=1,求 M 的最值.(2006届清华大学自主招生数学试题第2题).
On November 28, 2005, Tsinghua University held an independent entrance examination for candidates from Jiangsu, Zhejiang and Shanghai on the Second Affiliated to East China Normal University. This is the first time that Tsinghua University conducts self-enrollment, written examination and written interview in the out-of-Beijing area. A lot of questions is still very interesting, it is worth pondering. Below we do some analysis on a few maths questions among them and would like to share with readers. Example 1 Known a, 6 is non-negative, M = a ~ 4 + b ~ 4, a + b = 1, Find the most value of M. (2006 Tsinghua University independent enrollment math test question 2).