1 . 命题
:直线
与圆
有公共点,命题
:双曲线
的离心率
.
(1)若
均为真命题,求实数
的取值范围;
(2)若
一真一假,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f257b2c95f1935920f05d159b08a9a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8785046420bdd426bbd7a26041ff214.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc3de2a92f1ce64ad41243f39fbc4756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4612a3d0ca32bdc27e1656f9c55ee7b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2 . 设函数
,集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c563b30e0b214a3f2996e6c4c1d5ccf.png)
(1)证明:
.
(2)当
时,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82978e25c21f5153ffe233a2720880c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c563b30e0b214a3f2996e6c4c1d5ccf.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ad78dc8b8aed907b4fe9640c997454.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37d648d3fa1544e9de76c9d0ff3b021a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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|
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黑龙江省哈尔滨市第九中学校2023-2024学年高三上学期开学考试数学试题黑龙江省哈尔滨市第九中学校2024届高三上学期开学考试数学试题(已下线)第一章 集合与常用逻辑用语(单元测试)(能力卷)--高一数学同步精品课堂(人教B版2019必修第一册)
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3 . 已知
.定义
,设
.
(1)若
,画出函数
的图象并直接写出函数
的单调区间;
(2)定义区间
的长度
.若
,则
.设关于
的不等式
的解集为
.是否存在实数
,且
,使得
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a17d2ccced13f776eb6911cabd60f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3a77c9f505457fcc43429765a261529.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647a44d40e8b50a9c308541bbe646dd8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/19/fddffcca-47af-422d-8752-13d61253fc87.png?resizew=260)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66884efff7400f92b530d69d029778d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
(2)定义区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a421dcdff3dff08169805bfa9743b6f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae6ef9c3a133abc84cce48028dc61c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd6446851fd995644e727b29d40f5c2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf49915e28fa17749c4346fe9c825d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ed2fb4a6389a9994694ba9aa5e6422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d13abf7c869cb23f3e3898cce919d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d008aab3aadca7fb9ba7400f3121542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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名校
解题方法
4 . 已知全集
,集合
,集合
.
(1)当
时 ,求
;
(2)若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860ebb6f76cd3cb9a265dfc233002a13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a6c2f43fde3f76e6b61117487f1d0de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f6fd5ed246988cc93751f840195a2ce.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711b21672fd907c5c92fee1d649e7003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd9ee4df3cd0c5982eec8be19e136130.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ae3bb39a224d9d8149f7a259ab4765.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
5 . 已知集合
,
.
(1)若
,求
;
(2)
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b00a32be1457fbae408fdf23eed802ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dd4cc34925b574f59629ce0dc1f3e7a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ad78dc8b8aed907b4fe9640c997454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
6 . 给出以下命题,其中真命题有( )
A.若函数![]() ![]() ![]() ![]() |
B.若“![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.函数![]() ![]() ![]() ![]() |
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解题方法
7 . 若
分别为
的三个内角,则“
”是“
”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b610c855735a35d4168ac6a0f72ef904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d911ef06e403e4a1059a54526edb74.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充分必要条件 | D.既不充分也不必要条件 |
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解题方法
8 . 下列命题正确的是( )
A.“![]() ![]() |
B.“![]() ![]() ![]() |
C.“![]() ![]() |
D.“![]() ![]() |
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解题方法
9 . 已知集合
,
.
(1)求集合
;
(2)已知命题
:
,命题
:
,若
是
的充分不必要条件,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d4358315f066e761779a13dc85f03f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a39af6602d5c4a13f95e9ee17a0e1a88.png)
(1)求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)已知命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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10 . 已知a、b均为正数,不等式
成立是不等式
成立的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8ddaeda747dd928213f6e6392902ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74e2031df853535e4b8edcf41ee5eb8a.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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