1 . 已知一个三角形的三边长分别为
,
,
,则这个三角形外接圆的直径为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
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2 . 已知等差数列
满足
,
.
(1)求
的通项公式;
(2)设数列
前
项和为
,且
,若
,求正整数
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1928c254cfada1f75a5cd1e34db5a63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf77c2056d5955cdd27a0f892369f84d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a49a13006ad16dd9d20a31b05f24ab87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c49d3dcc17bf0d6891c34afc32ffb031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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3 . 已知等比数列
是严格减数列,其前
项和为
,若
成等差数列,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbb708a25d30954a0a50b01d59453bbe.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3768db0f2e2881b810d44ddc39ff295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccadf5fe0d8a09ac97324ad2d9f60f69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbb708a25d30954a0a50b01d59453bbe.png)
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4 . 给出下列4个命题:
①若事件
和事件
互斥,则
;
②数据
的第
百分位数为10;
③已知
关于
的回归方程为
,则样本点
的离差为
;
④随机变量
的分布为
,则其数学期望
.
其中正确命题的序号为( )
①若事件
![](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/516cc3b619715f0309749aaed4fd2e66.png)
②数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e22d37bfc7b992a08acfa415bcd46677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aa86faa9bfef703aead8c2606684dc5.png)
③已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b0e64e3c752d3ef6501692e4fd6bcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8833ba3833480237f47774984958c01d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9862b46c3ae76bb684a7e534f97eefad.png)
④随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2dbae74a31ee10b99b31ec01bd35b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433c7aab3056671b683c392db76117c7.png)
其中正确命题的序号为( )
A.①② | B.①③ | C.②③ | D.②④ |
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5 . 若函数
满足:对任意
,都有
,则称函数
具有性质
.
(1)设
,
,分别判断
与
是否具有性质
?并说明理由;
(2)设
函数
具有性质
,求实数
的取值范围;
(3)已知函数
具有性质
,且图像是一条连续曲线,若
在
上是严格增函数,求证:
是奇函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47501e15929024c12d5ad671902b2ef2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d813b99569b5439d685be73ac11cb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff6838d84b68c6f0d3b93b196d9b08d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/841d74a21ac16e7ae3ef811d931de69d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ff9cda1684eaf1a0debe28b5b8f18a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
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6 . 已知椭圆
的焦距为
,点
在椭圆
上,动直线
与椭圆
相交于不同的两点
,且直线
的斜率之积为1.
(1)求椭圆
的标准方程;
(2)若直线
为的法向量为
,求直线
的方程;
(3)是否存在直线
,使得
为直角三角形?若存在,求出直线
的斜率;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a74e28144cbed9111d17dd239136f80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200c60216e924848b12c0e6a22d42a01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)是否存在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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7 . 3个男孩和3个女孩站成一排做游戏,3个女孩不相邻的站法种数为__________ .
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8 . 已知集合
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b9b470218359a4a47be9244980489e.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf1b618c75f86f05641b17c3286651f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b9b470218359a4a47be9244980489e.png)
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9 . 已知平面向量
满足
,若平面向量
满足
,则
的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d1bd7cb9d85f58d30f298ed2c092e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5c9f0830047cd49c467f2b1c34c6dbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f8b9855e198e41065f4408a18e6531b.png)
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解题方法
10 . 已知随机变量
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c0cd2d7ae8394a0fd6977c3e59401f.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7072f6e659388ccc62afd5831dc4fb1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684d48323e7df4fa3b551485bf096f8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c0cd2d7ae8394a0fd6977c3e59401f.png)
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