名校
解题方法
1 . 在
中,三个内角
所对的边分别为
.已知
的面积为
,
.
(1)求
的值
(2)求
的最小值.
![](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/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf8c9594a0dc9767b5e84b9d55c5d03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24eb259fab57e11a4b98d4448a0e65fe.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6732580ffff616408c0985d7175a4c2.png)
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2 . 在四边形
中,
,则实数
的值为______ ,若
是线段
上的动点,且
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de4fec47150e684e8b270289048aff7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d92b9548115581546be6f0a3c5a7057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2ab157cd50abfa3a6de8027f3f0b424.png)
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3 . 如图所示,正方体
的棱长为1,线段
上有两个动点
,且
,则下列结论中正确的有( )
;
②三棱锥
的体积为定值;
③
的面积与
的面积相等;
④二面角
的正切值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f115f2683c0422042f1846450885e7fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589ddae20626f9aaac616d2a3b5d95bd.png)
②三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc3bf74119692ac98eb24fcfa2a3f9f.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2ea13010e2399194be2a681310543e.png)
④二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecd41f11a3360662c09b042a9f987e70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
A.1个 | B.2个 | C.3个 | D.4个 |
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解题方法
4 . 正四棱锥
的底面积为3,外接球的表面积为
,则正四棱锥
的体积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d80f16c3278cd252725625dcf253cda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
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解题方法
5 . 圆锥的母线
,高
,点
是
的中点,
(1)求圆锥的体积;
(2)有一球在该圆锥内部且与它的侧面和底面都相切,求这个球的体积;
(3)一质点自点
出发,沿侧面绕行一周到达点
,求其最短路程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c19f0fcacac715a1200770516d1e4a67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4f0f713cd40634ee6c5e075a17064eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
(1)求圆锥的体积;
(2)有一球在该圆锥内部且与它的侧面和底面都相切,求这个球的体积;
(3)一质点自点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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解题方法
6 . 在平面四边形
中,
,
,
,若
为边BC上一动点,当
取最小值时,
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae2a696b84492a736c5b444e61b7ad96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4795ee1f96b430529934e2231b38885d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab7aaa871ceb78e5b80b531a7cf4f1c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe020f2d372f3bf21c9ef5c71895132c.png)
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7 . 已知
三个内角
,
,
的对边分别为
,
,
,则下列说法正确的有( )
①若
是锐角三角形,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85b48895daa87c296d961bfd0d4fd386.png)
②若
,则
是等腰三角形
③若
,则
是等腰三角形
④若
是等边三角形,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a641da1c70d0ad481082af87e98ccbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85b48895daa87c296d961bfd0d4fd386.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e02e6946143207c276f7430942c1b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647598d9c27e8bff03fe47d84998fc73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a641da1c70d0ad481082af87e98ccbf.png)
A.1个 | B.2个 | C.3个 | D.4个 |
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8 . 在△
中,角A,B,C所对的边分别为a,b,c,若
,△
的面积为
.
(1)求
;
(2)若
,求
;
(3)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faef87744ed2a4d51009b0d52c360cbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821309f088a175c00dc0f4828334503d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03005d17bf564371ad29fea41f5c650.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2526197224eea5878e62d46952cd669.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b919f0869717376807ca5481f17412.png)
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解题方法
9 . 已知
,当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
______ 时,
取得最小值,最小值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/372fc66e4dac769ed6eaba8f030d697f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70b8eca8a27ff7b03e4f4202cf4199de.png)
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解题方法
10 . 在数列
中,
.在等差数列
中,前n项和为
,
,
.
(1)求证
是等比数列,并求数列
和
的通项公式;
(2)设数列
满足
,
的前n项和为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa960b83e70e40e60e53a6d4334c0fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fe5fa40132bde317eb91fa3a399da23.png)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d17d72d1d20d385920c3d9da6bed8bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0044e257218c2173d21a8e864680c384.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd85b79372dc6e596d465f738c3c300.png)
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