解题方法
1 . 《易经》是阐述天地世间关于万象变化的古老经典,如图所示的是《易经》中记载的几何图形——八卦图.图中正八边形代表八卦,中间的圆代表阴阳太极图,其余八块面积相等的图形代表八卦田.已知正八边形
的边长为
,点P是正八边形
边上的一点,则
的最大值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17d4a6cf11cda87b3dfafaecdec683f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17d4a6cf11cda87b3dfafaecdec683f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e83b9f01e806bf74042ba41b26423022.png)
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2 . 函数
的图象如图所示,图中阴影部分的面积为
,则函数
的解析式为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473c9fea4cdded9be6f12958770c0cf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/997b5842f3d4eae1989debee9ae41b9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
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3 . 如图是我国古代米斗,米斗是称量粮食的量器,是古代官仓,粮栈,米行及地主家里必备的用具.为使坚固耐用,米斗多用上好的木料制成.加上米斗有着吉祥的寓意,是丰饶富足的象征,带有浓郁的民间文化韵味,如今也成为了一种颇具意趣的藏品.已知一个斗型(正四棱台)工艺品上,下底面边长分别为2和4,侧棱长为
(其厚度忽略不计),则其外接球的表面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a68c1d20a422a363e356a160f096503c.png)
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4 . 函数
相邻的两个零点分别为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc574389b74c0e846657b2e24ffe115f.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fd5543f6cc0a25deb6410dd48cce9cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d3c0e7508ff7fd36faba07a0aa41ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc574389b74c0e846657b2e24ffe115f.png)
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5 . 已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161d39fa1cb0e994941c02bd4ab971b1.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8529a52e32b12244bd535641221e83e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161d39fa1cb0e994941c02bd4ab971b1.png)
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6 . 已知
,
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a9fcaa804011c37873b03ee284504fe.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef966cdd137b3b10e290201b4d17542e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95c98ce1bd8a5ffe3e18b4033d4ade5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc282dae4ac9132196ac5d13f63b901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f836697b6e7daec4ab093779fff51923.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a9fcaa804011c37873b03ee284504fe.png)
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7 . 函数
在
上单调递减,且
的图象向左平移
个单位后与原来的图象重合.若方程
在
上的解为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/176939fbe2a6f8285cc934781693b311.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b2bb7354fb64b7bf5ae232a93747955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b46e371d805f68a3d5210501f494d227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9bf0adbe45ec2819dbe8cf4ec99008f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf79351686762c4c82f5ac2240f84011.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/176939fbe2a6f8285cc934781693b311.png)
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8 . 函数
的部分图象如图所示,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8356710d07bb201cb58622bddb7780b2.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5325022a0f4edebcd89b4b1f861fee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8356710d07bb201cb58622bddb7780b2.png)
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9 . 已知向量
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
______ ;若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d33ee1f52775bf9ba66e0fdf0ecbb35.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3effb8e124f2aff06abd49e2cdcf426.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7dced91de1b8c38aa95ffee0e5dc202.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7901fc86cb98cdb030d6ee72816dc14a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d33ee1f52775bf9ba66e0fdf0ecbb35.png)
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10 . 我国汉代数学家赵爽为了证明勾股定理,创造了一幅“勾股圆方图”,后人称其为“赵爽弦图”.类比赵爽弦图,用3个全等的小三角形拼成了如图所示的等边
,若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a71a9d21f77e9535de152bb33f802bb.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/221a091e823526ce02a78be01068c01d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c0ba1776a7c0bac5141407836e12153.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a71a9d21f77e9535de152bb33f802bb.png)
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