名校
1 . 已知
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcde82aabb8f1c0761351fda95c6b012.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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名校
2 . 已知函数
,若
存在两个不相等的实数根
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f5f090340f798e2e4fb4331efde99d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338316b0fe50fdea0f2f75aec4c990dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6abf3f9b0ebcdc47a028c781b7edb9.png)
A.e | B.2e | C.![]() | D.![]() |
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3 . 已知函数
.
(1)讨论函数
的单调性;
(2)若函数
有且仅有两个零点,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a15248fda64819646fb6fc552be647d6.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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解题方法
4 . 已知函数
.
(1)若曲线
在其上一点
处的切线的倾斜角为
,求
的解析式;
(2)若
,不等式
恒成立,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/025001679461ff4242a2667ed7d0e80d.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ef7629fe45bf6af93bb0b6523e3837e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d812643e080d4d447fab7fe2ae2646.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc8010942f8ff56e4826c1e6b0abe6b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ab7024f73ff0cb7e6a48197538a91e.png)
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名校
5 . 已知函数
.
(1)判断并证明
的零点个数
(2)记
在
上的零点为
,求证;
(i)
是一个递减数列
(ii)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58ae99833cb675e5e36c58f345eb03e7.png)
(1)判断并证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d64af919a56a107e0fc0a417e481648.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d64af919a56a107e0fc0a417e481648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1fd18a909cecbaee7115d6b15631d83.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167f4f8fd4d3de714b87f05e57a3ba3b.png)
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2卷引用:河南省许昌市魏都区许昌高级中学2024届高三下学期5月月考数学试题
6 . 已知椭圆E:
,直线
与E交于
,
两点,点P在线段MN上(不含端点),过点P的另一条直线
与E交于A,B两点.
(1)求椭圆E的标准方程;
(2)若
,
,点A在第二象限,求直线
的斜率;
(3)若直线MA,MB的斜率之和为2,求直线
的斜率的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9966507baa6a49c181c2054acc36b7e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9758afe1afeb5b147510dab73c028b3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcab01b8a645f97b83766b1c44913fd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(1)求椭圆E的标准方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbcc169dd372661a2bac92a0d12a2a33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bda34489a663958d95e5960ff04d0bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(3)若直线MA,MB的斜率之和为2,求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
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名校
解题方法
7 . 已知双曲线
的左、右焦点分别为
,
,过点
的直线与双曲线的左、右两支分别交于A,B两点,若
,
,则C的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5546ac9f1ee485e6d0829c9eec8c0afc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfdc4b23cd18862260c341e7db9ff3a3.png)
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8 . 设点
分别为椭圆
的左、右焦点,点
是椭圆
上任意一点,若使得
成立的点
恰好有4个,则实数
的值可以是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a9859040e01b972363d182a9e8b68f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e3f19ff9d533161dedf49cf9a921341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.0 | B.2 | C.4 | D.6 |
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名校
9 . 已知函数
,若关于x的方程
的不同实数根的个数为6,则a的取值范围为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/489e175ef56f4e5d00f480adae5bf37f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7279bc9dd0aaad4e72bfac3fd69048b.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
10 . 已知点集
,且
,
,点O是坐标原点,其中正确结论的个数有( )
①点集M表示的图形关于x轴对称
②存在点P和点Q,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e8b17a7840ae7b75590da92fa0965b.png)
③若直线
经过点
,则
的最小值为2
④若直线
经过点
,且
的面积为
,则直线
的方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad8f0339d0b1ed15e016478ecb0c812.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99410abc1d628453cf3a0aac800bf154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2b02a4fd3d5f75496756117a420386a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0929421a6188c3122442866b0b85a5e.png)
①点集M表示的图形关于x轴对称
②存在点P和点Q,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e8b17a7840ae7b75590da92fa0965b.png)
③若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d518b321289c322803177fcb4caccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
④若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad8f0339d0b1ed15e016478ecb0c812.png)
A.1个 | B.2个 | C.3个 | D.4个 |
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