解题方法
1 .
的角
对应边是 a,b,c ,三角形的重心是 O.已知
.
(1)求 a 的长.
(2)求
的面积.
![](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/7f9fbd659c7e4424a2ea5a20a86c0cf7.png)
(1)求 a 的长.
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2 . 集合
,则以下可以是
的表达式的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa8dc8557c42aba626ef06c04d1a314f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 已知椭圆
:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
,左右顶点分别是
,
,椭圆的离心率是
.点
是直线
上的点,直线
与
分别交椭圆
于另外两点
,
.
(1)求椭圆的方程.
(2)若
,求出
的值.
(3)试证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f87ec1b06e89b681bdc2b4523f5f4ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38729d36302cda29e4878e9a094b65f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a64d2e963e29c2c691bb297ec30d80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c6423c70e96d862ca12998a22d676b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)求椭圆的方程.
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/830284dc0954ca6c4d7e9cd2fe239029.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf5909a2b109d048bd7c7a0377a769f.png)
(3)试证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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4 . 给定定点
,对任意可能的
,及函数
的图象上的任意可能的点
,
的最小值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71885f023172807ad43f2c9a670aa960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6499f194456d6ac45326a33c74fd781b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4323dcce28ed1206e6ff65600d0dc9e7.png)
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5 . 若
,
,则
的最小值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88758250b53fb7c638770066b3e3e1fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af06f5d56ca75cc7188ab3d542397eab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbae4853231076a1c59a0d37eeaf7469.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
6 . 若
,
,则下列说法中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88358272f25c372c5ddf625db4ec0bb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca0d92e6a1651bd2f30e222b158c39fd.png)
A.![]() | B.![]() |
C.![]() ![]() | D.![]() |
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7 .
,求
的值为 ( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de02706fe3ce4a4b3e3bf72356bc9a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2a09e4d44e894212cf7864b8ecfae5d.png)
A.922 | B.923 | C.924 | D.925 |
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8 . 已知单位向量
共面,则下列说法中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46fddc1f1c50aab4de7fff286d691b97.png)
A.若![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() | D.若![]() ![]() |
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9 . 在坐标平面内
的区域,随机生成一个横纵坐标均为整数的一个整点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aac473ddb43914f7a4a5d142dd8dfbc.png)
,记该点到坐标原点的距离是随机变量X
相关公式:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd9fe7e51b7aebba4012e077f621c02.png)
(1)当
时,写出X的分布列和期望.
(2)记随机变量
与
分别表示
的横纵坐标.
①求出
的期望 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/651127534574ec89f87fbe6223ded5bf.png)
②现在实际上选取了四个点
尝试运用样本的平均值去估计数学期望,以此来得到估计值
(四舍五入取整).
(3)记方差
,试证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231b96ac0b7b1a9500b16b6f06da6949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aac473ddb43914f7a4a5d142dd8dfbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37784c634db2a54c7f1dc6951172a29.png)
相关公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd9fe7e51b7aebba4012e077f621c02.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38c9d7f7f9a3e9ec476f5cf7fda97c88.png)
(2)记随机变量
![](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/3aac473ddb43914f7a4a5d142dd8dfbc.png)
①求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/704f858f73063183e5779257900e694d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/651127534574ec89f87fbe6223ded5bf.png)
②现在实际上选取了四个点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ea2bfe7ece5086158430c8487459f3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71dcc323aa6b7e73f92b2111cc4648be.png)
(3)记方差
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/406721302685612b54af3c223f059b8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b958aecb5dc4ed0c6475f84e7eec5ca5.png)
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解题方法
10 . 函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b13de318e4c5c80b80da664aaa9c16f.png)
(1)求
的单调区间.
(2)若
在
时恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b13de318e4c5c80b80da664aaa9c16f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bd94ebdf16cfd29953a34e866c2c416.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a154aa77357cb73cbcd37275d873a324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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