名校
解题方法
1 . 记全集
,已知集合
,
.
(1)若
,求
;
(2)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/442be389c6471b36eff2652b75beb114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/126129b13dc3e8817eb0eb2de6dd1cf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/672388bcf46a971284cd2f4763bd37e6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a69c58edb641bdf02f3685d4f36d793.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7d6537709d1ab4bec43bd14c9ba696.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
2 . 已知函数
.
(1)若
,求不等式
的解集;
(2)若
时,
的最小值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b23fabe4b8c9810a3e043dfc27ffc7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a81e971f501d78f5560c0c3d42f0f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f1a722a2595fdc71462654b764ee49d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24aa16b780156e18f12baa2b8ee0f9a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
3 . 用篱笆在一块靠墙的空地围一个面积为
的等腰梯形菜园,如图所示,用墙的一部分做下底
,用篱笆做两腰及上底,且腰与墙成
,当等腰梯形的腰长为多少时,所用篱笆的长度最小?并求出所用篱笆长度的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c8fbf64cd29a08ae703e9fa2035f3c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
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4 . 解答以下两个小题:
(1)求
的值;
(2)若
,求
的值.
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6306f753fe8458efe5cf9887b64c4422.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a8c9f990fc696c4b27d02cb9e92fe9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46c1f68a5bc3695f488c3c9249ac77ea.png)
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解题方法
5 . 已知直棱柱
中,
,
,
,
,D为线段
上任一点,E,F分别为
,
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/15/27476bc5-8235-4722-94e4-cb9c91641405.png?resizew=133)
(1)证明:
;
(2)当
为何值时,平面
与平面
的二面角的正弦值最小,并求出最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c14a66ed4bd66df65bc42c4ac1ed15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41fd676c41d2d644928f014b0fea4689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f81e24376a13d648c2ed0dc73bc710e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/15/27476bc5-8235-4722-94e4-cb9c91641405.png?resizew=133)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0be099a94f553b5c982d705cc2123e43.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27daee2bab56f1808877c2e2594f8324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
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解题方法
6 . 已知斜棱柱
中,
,
.设
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/15/2f22d8ff-5b0c-4715-9280-98af323f674c.png?resizew=136)
(1)用基底
,
,
表示向量
,并求
;
(2)求向量
与向量
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cead0e8eadfdcefa334953e88864f424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4d13ecb54b1006051d2561327aa4755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3adc4ed291596abf3bb93ae7a075d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e984585ddf28c039219afcebf229de7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8780f5b68f8907a57c1c2f96233a78c5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/15/2f22d8ff-5b0c-4715-9280-98af323f674c.png?resizew=136)
(1)用基底
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/053c0f6846f2bf8671b351a4263a0270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2854c67a40773c10bf0a89479d36a0df.png)
(2)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/053c0f6846f2bf8671b351a4263a0270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5f1b06a56fc382feed28e01f1ad102.png)
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名校
解题方法
7 . 已知函数
是奇函数,当
时,
.
(1)求
的解析式;
(2)判断函数
的单调性;
(3)若方程
有三个不同的根,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8672676e9dd12438f37584512c6380c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be315e528951120e7d551f654d2a1f5e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c0d827ef8598ba6b70b34b2bdcd1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
8 . 已知椭圆T以坐标原点O为对称中心,以坐标轴为对称轴,且过
,
.
(1)求椭圆T的标准方程;
(2)若A、B为椭圆上两点,且以线段AB为直径的圆经过O点.
①求证:
为定值;
②求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f839491380e131c801e2c3c4a75bcdfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f854bbda125255ac766343c1caa71ec.png)
(1)求椭圆T的标准方程;
(2)若A、B为椭圆上两点,且以线段AB为直径的圆经过O点.
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/785fc822e5e30c0a9b7fa56d7306809a.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
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名校
解题方法
9 . 已知集合
,
.
(1)当
时,求
;
(2)若
,求实数的
取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe32720530093c2193a6104b6f98b478.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c755f76b40955d0c303d9bef3a170e7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
10 . 已知
、
分别是双曲线C:
(
,
)的两个焦点,若双曲线的一条渐近线与直线
恰好平行.
(1)求双曲线C的离心率;
(2)若
,M为双曲线上一点,且
,求
的值﹒
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af449f710cdcbb849672b3dcc2c84bb7.png)
(1)求双曲线C的离心率;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4428ec56246b35cb87bfe7ed50f0ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a22cc73ff3f197568b1de60f31c0d845.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2675e721a547386255bae4dfdca9ff2.png)
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