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1 . 已知函数
.
(1)求
和
;
(2)若
,求
的值;
(3)作出函数
的图象;并根据图象写出单调区间;
(4)当方程
有3个解时,直接写出实数k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f2e92fcc7b2d36880047071a0f95e8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32a859898e9905e0524d3a982eb34b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14348dcf52b54174c7f3cecc63d69e3e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a73db674d29eae8f8921eff5944983.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)作出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(4)当方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb101c5df08aa35ae24a6416840b199b.png)
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2 . 已知关于
的函数
,其中
.
(1)若不等式
的解集是
,求
的值;
(2)当
且
时,解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3de5f87b3d136b15866b1fe9ccff3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73254f32b6da29ecc32df2e9f87a4c97.png)
(1)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea7b4b6431e5ffd783ea295c875ca895.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
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解题方法
3 . 写出一个使得命题“
恒成立”是假命题的实数
的值:_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/929b23185548d761dccc2ab9aa8d5408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4 . 如图,平行六面体
各条棱长均为1,
,
,则线段
的长度为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a674aa2ce5caabcad5abe65b5402ce6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0d7095ddd69d6ceaf1065b1bc2c79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/23/990e1874-d36e-442f-a1b6-fd390f5bf6b8.png?resizew=188)
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2023-12-22更新
|
403次组卷
|
3卷引用:北京市昌平区第一中学2023-2024学年高二上学期期中考试数学试题
名校
解题方法
5 . 设
是定义在
上的奇函数,且
时,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1893ec3241bbeb7909e5a1ecfb7c1760.png)
_____ ;当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba99a5c5661eedaef4b36ade1a7c5c5.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2372f424431ce7b547a66b7d61d75421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ef372029c8ce2b27cf47ddfd21b6f87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1893ec3241bbeb7909e5a1ecfb7c1760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2b74d89854116e411c089d053df053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba99a5c5661eedaef4b36ade1a7c5c5.png)
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6 . 已知集合
,其中
.
①集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d0d2a6750330ebe1cf1b3a65825d0e6.png)
_______________ ;
②若
,都有
或
,则c的取值范围是____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abeb837962544605c14c9338047b8ba9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686b332872c51b433befe65fbe773380.png)
①集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d0d2a6750330ebe1cf1b3a65825d0e6.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad5fe274cfc8da2dacfb65801f344ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
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7 . 函数
的最小值是 _______ ,此时![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcbf0599e319b705d9dbe6f190c02896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
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解题方法
8 . 已知全集
,若集合
,
.
(1)求
、
、
;
(2)若集合
,且
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa26ede4564b80c035c146272384bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e0155399b4bb0be98374a772cb9f73b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e5c56e26078de84e688cc828a86251.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fdbfa7a63fdf5717d40c8c9a73ec160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc89f4653a8138635a1e500a437ca860.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294757c3dd960c763d8eb325174d1f81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3961c8391f4fc03a97cf9a697d4f7efe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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9 . “
”是“
”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9568a2471720ff97a22d0b8a47420b2b.png)
A.充分不必要条件 |
B.必要不充分条件 |
C.充要条件 |
D.既不充分也不必要条件 |
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解题方法
10 . 已知函数
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b40cde1f72d8ab72201dceededac189.png)
A.![]() ![]() |
B.![]() ![]() |
C.![]() ![]() |
D.![]() ![]() |
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