23-24高一上·广东深圳·期中
名校
1 . 设不等式
的解集为
,关于x的不等式
的解集为
.
(1)求集合
;
(2)若“
”是“
”的必要不充分条件,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/703d1cafa1b570863ba1fff00a7cd7cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a833e0cdfba360da41d17aaf3d55cad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
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2 . (1)判断并证明集合
和集合
之间的关系;
(2)判断并证明
是
的什么条件.(“充分非必要、必要非充分、充要、既非充分又非必要”中选择)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092cc2154c7145667f6f4b59442b94d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce8f18aaf85c45e75e713aaf8ee96f68.png)
(2)判断并证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1040c79a8b3bc0b9edd718b41a2512c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95c82faf1f70c84931e62756b9cd73b8.png)
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3 . 若实数
、
、
满足
,则称
比
接近
,
(1)
比
接近
,求
的取值范围;
(2)判断:“
比
接近
”是“
”的什么条件(充分不必要条件,必要不充分条件,充要条件,既不充分又不必要条件),并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b2f36a11b3ee72115629252bcdbe61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0a89e3c30f6e4d4c5db4378b05d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)判断:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8fdcc662343b986bed79e4efb9319ff.png)
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2023高一·江苏·专题练习
4 . 指出下列各题中,
是
的什么条件:
(1)
数
能被6整除,
数
能被3整除;
(2)
,
;
(3)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51441c8788ff11be766766227793246d.png)
有两个角相等,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce20ef9c08e82df8c7f45bac6dd31d36.png)
是正三角形;
(4)
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51441c8788ff11be766766227793246d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce20ef9c08e82df8c7f45bac6dd31d36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3567dcfdb7139dde2ec0ef0670136132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/457185351773eeb5d216b3e8726acbbe.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51441c8788ff11be766766227793246d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce20ef9c08e82df8c7f45bac6dd31d36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97cc93a719bed81790e2d440aa40503a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6adbcb574dccb9d347938124d62cba1c.png)
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5 . 对于定义在
上的函数
和
,若对任意给定的
,不等式
都成立,则称函数
是函数
的“从属函数”.
(1)若函数
是函数
的“从属函数”,且
是偶函数,求证:
是偶函数;
(2)设
,求证:当
时,函数
是函数
的“从属函数”;
(3)若定义在
上的函数
和
的图像均为一条连续曲线,且函数
是函数
的“从属函数”,求证:“函数
在
上是严格增函数或严格减函数”是“函数
在
上是严格增函数或严格减函数”的必要非充分条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.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/9b60c23824b5013819120c3ee26d0b52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ec6c7a1da7ecaef51a3d08fbcdf2821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f02d899093d01d2e45a1a0b2402560c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ede78fd7ac619ea597856254bb5d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(3)若定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.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/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.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/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
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2023-10-26更新
|
280次组卷
|
2卷引用:上海市曹杨第二中学2023-2024学年高二上学期10月月考数学试题
名校
解题方法
6 . 已知全集
,集合
,
.
(1)当
时,求
;
(2)若
是
的必要不充分条件,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860ebb6f76cd3cb9a265dfc233002a13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/424a9f2e78cd53443a15b11ff1f8c18c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b996c27e8e35d981eb916f9dcf8d4d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5207a956f783588ad0f1df179de2dc46.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
7 . 证明:
(1)“
”是“
有两个不相等实数根”的充分不必要条件;
(2)设集合
,对集合A中的每一个
,不等式
均成立的一个必要不充分条件为
.
(1)“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6803e06223269e79138ac240d2d2f57f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4c714411bfd70c6e1629da44953c590.png)
(2)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca3a8ec8d0fc97bbbb2e81ed9e4600a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38052c45891d59e55514a7794c74d47b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ab6b598834b7cca86ed338dfbeea929.png)
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8 . 判断下列命题的真假,并说明理由.
(1)“
”是“
”的必要不充分条件;
(2)“
”是“
”的充要条件.
(1)“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9630146cd0a0cc10c8c1b50c78b18e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d4ef0f572819319adf0ea206b3fbc7.png)
(2)“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec5df5af1fdc5f838ce9573e5fabcfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca82fe36f0e894536b34c71a0a96b82.png)
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2023-10-12更新
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78次组卷
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2卷引用:陕西省部分学校2023-2024学年高一上学期10月选科调考数学试题
9 . 已知集合
,
.设p:
,q:
,试判断p是q的什么条件,q是p的什么条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80d641a3a113e9454f9531736d99178.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e0ca05efabd2c52471182ff0de315d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
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2023-10-07更新
|
27次组卷
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3卷引用:北师大版(2019)必修第一册课本习题第一章2.1 必要条件与充分条件
10 . 下列各题中,试判断p是q的什么条件.
(1)p:
,q:
;
(2)对于反比例函数
,
,p:
,q:y值随x值的增大而减小;
(3)p:函数的图象关于y轴对称,q:函数
.
(1)p:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/430d3c2114f7ae1122ef4f6a70fdc90d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/988b7e964e313579ab8869d67d5be007.png)
(2)对于反比例函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07854693dd2e33f66030d6106eb6e0ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
(3)p:函数的图象关于y轴对称,q:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
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2023-10-07更新
|
58次组卷
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4卷引用:北师大版(2019)必修第一册课本习题第一章2.1 必要条件与充分条件