名校
解题方法
1 . 已知
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0719844e0261af3b625d9673e5926.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1290917c2c835b61384480b335cc1d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1aaee2a13c6b1fd7419eed392f7766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0719844e0261af3b625d9673e5926.png)
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2 . 已知函数
.
(1)定义
,其中
且
,求
;
(2)对于(2)中的
,求证:对于任意
都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2170843053c6714cd98f5a6ad4a0334a.png)
(1)定义
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8803ba7ef10e3204d74a86578d0793f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)对于(2)中的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae373255bbe6f55879762cb4098d9094.png)
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解题方法
3 . 在
中,内角
的对边分别为
,已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f4be47664a28ff93f023918d9d954e.png)
(1)求角
的大小;
(2)若
是
边上靠近
的三等分点,且
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f4be47664a28ff93f023918d9d954e.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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4 . 如图所示,一套组合玩具需在一半径为3的球外罩上一个倒置圆锥,则圆锥体积的最小值为__________ .
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解题方法
5 . 已知函数
,正实数
满足
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b77fb0e7a553dab8fefb6e484eddc482.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23bd373e9b3ddd6f351a881ce163617c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4208a86040fd5d1fc91cc6714fb415f1.png)
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6 . 观察下表:已知表中的对数值有且只有一个是错误的,则其中错误的对数值是( )
![]() | 1.5 | 3 | 5 | 6 | 8 | 9 |
![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
7 . 在直角坐标系
中,点
到
轴的距离比点
到点
的距离小
,记动点
的轨迹为
.
(1)求
的方程;
(2)已知
的顶点
,
、
在
轴右侧的
上,且
,证明:
的面积不大于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c104b0d816b2f9a0a6a3fe5b6ae45858.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93fa279be319da8ef95c7e061faa2263.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d5416cca40a5caa71f3336dfe7e57c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6093eebca8f3ff82ce9298feb197e955.png)
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8 . 足球运动是深受中小学生热爱的体育运动项目之一.甲、乙两人进行足球点球比赛,每次由其中一人踢点球,规则如下:若点球进门,则此人继续踢点球,若点球没进门,则由另一人踢点球.无论之前点球情况如何,甲每次点球进门的概率为0.5,乙每次点球进门的概率为0.7.由抛掷一枚硬币的结果确定第1次踢点球人选,正面向上甲第1次踢点球,反面向上乙第1次踢点球.
(1)求第2次踢点球的人是甲的概率;
(2)求第
次踢点球的人是乙的概率;
(3)已知:若随机变量
服从两点分布,且
,
,则
.记前
次(即从第1次到第
次点球)中乙踢点球的次数为
,求
.
(1)求第2次踢点球的人是甲的概率;
(2)求第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
(3)已知:若随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f95e54a9b7c66c97dc6ee6161a25c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ef015dfcb4e200426d5f54ba6deec4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab46d077ba3d6e13fa1f6a5aaa0ce6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ece16154c3be9e43a5dd37a91d7d8c3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71701db4b413f2364dbcbd612fbc8a67.png)
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9 . 记
,
分别是数列
,
的前
项和,
,
是等差数列,且
.
(1)若
,
,求
的通项公式;
(2)若
为等差数列,且
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e71ea4f1cf744437f385dbb8bd420fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1381f0937c6052ce088e0eaee7df4880.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a34c463105463ba91ad2f3472ef24e82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6428dce66561419790580a8d1df5fdb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc49c7a6cf6044252bd55ee240b346e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
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解题方法
10 . 如图,在正四棱柱
中,
,E、F分别为
、
的中点,
为
上一动点.
时,证明:
;
(2)当二面角
为120°时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f21c7c194c5bc2986a21fd441c81495.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6133a2c2a50bc7a017c18d379a529ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdae8c3cb6783bb3594555915c0af5f2.png)
(2)当二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7cd213bef47cf44ff76af65fee9ea28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17c72cd74713d764fb5e8baf69de7b78.png)
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