名校
解题方法
1 . 如图,在四棱锥
中,
底面
,在直角梯形
中,
,
,
,
是
中点.求证:
平面
;
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae1e04eeb4de72e5750dae77bcb6f88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fa6ea683971fa8b6299d7aab6d04092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932a04304f2d4975955d4baabb2deeea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4cd8ba7eb52e38857830162e770f534.png)
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2 . 已知数列
的前
项和为
,且满足
.
(1)求证:数列
为等比数列;
(2)已知
,求数列
的前
项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0df387df5d97ffab16c92b6f6c0f7728.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82f8b6edfb7d680d88ed991d5c552c43.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1e8a0503abebc7b0f2a60b2ec15d282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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名校
3 . “阳马”是我国古代数学名著《九章算术》中《商功》章节研究的一种几何体,即其底面为矩形,一条侧棱垂直于底面的四棱锥.如图,四边形
是边长为3的正方形,
,
.
是一个“阳马”;
(2)已知点
在线段
上,且
,若二面角
的余弦值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91d5a57d368261e7a0a61d8386459eea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8cee96ca90f9f26644860329443ed56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69e27dea946df6947fb791374c992dcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6f351b3ffc75878acdbbe4d4926524f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5930602f8d9bb301d34db872d7a3cd53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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名校
解题方法
4 . 已知函数
,则不等式
的解集为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef88bf752cda4bb15e3205d4feccff89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9652e30dad4d1ea51c10b229a10252d.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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5 . 在平面直角坐标系中,点
为坐标原点,已知
,
,
.
(1)求向量
与
夹角的余弦值;
(2)若点
满足
,
,求点
的坐标及向量
在向量
上的投影向量的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98b2cc0d2f6d3eee9a33db83e0c0830d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8159754fa962579d7dcb79da0ba1908.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02eea25799267c0a948a6a9ffab2ffd9.png)
(1)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89265cbe3abc6b966ce8967fead448b.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8978ecc859804a7c23c2cc8c9175677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1206fd4b58cd793401ef61fd2ff22ee3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f28b09c6074898b0bf992928336eb5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc9656d8286c4d6fa309d6ae347c89e.png)
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6 . 对于函数
,若存在大于零的常数
和非零常数
,使得当
取定义域中的每一个值时,都有
,那么
称为“类周期函数”,
叫做“类周期”.下列四个命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3281ac9e36c20d31cf4bc12548b46f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
A.函数![]() ![]() |
B.函数![]() |
C.函数![]() |
D.设函数![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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7 . 在
中,角
,
,
的对边分别为
,
,
,其中
,
,若
,
,则
的最小值为( )
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e842fe98ec9ded46916a7443969495e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d9ec09e1ad28e85ea0c2345127c8fff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6732580ffff616408c0985d7175a4c2.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 .
的一般结构是
.站在三角换元的角度,就是利用同角三角函数中的平方关系,对代数式中的两数和或平方和为常数的结构进行三角代换以挖掘代数式中的隐含条件来解决问题.研究函数
,求出
的值域是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2302bd8fbae724ad0aa0dd1a2c318968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d8cc033b39e6328fa6c478bdb5c7a6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51cbb353e903b72f2e59f025a8e3179f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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9 . 某同学在利用正弦定理和余弦定理解三角形的研究性学习中发现,用边角互化的思想求出以下三个式子的值都等于同一个常数.
(1)
;
(2)
;
(3)
;
这个常数为________ ,将该同学发现的结论一般化后表述出来为________ .
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af7cc3f9cdac66bfcbb4e25547a78a5a.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5741640c81fc54484403a3b1495a2f11.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcf279f5d03cf5d1abe3541fc17b77fd.png)
这个常数为
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10 . 已知函数
的一部分图象如图所示.下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6309e18f51f43800c0a16205c6a491b.png)
A.函数![]() ![]() |
B.![]() ![]() |
C.![]() ![]() ![]() |
D.当![]() ![]() |
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