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 . 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
3 . 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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4 . 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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5 . 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
|
77次组卷
|
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
名校
解题方法
6 . 已知
.
(1)若
,则
是
的什么条件?
(2)若
的必要不充分条件是
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af85ec373a252beb969df490c411f14d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(2)若
![](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/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
7 . 已知
:
,
:
.
(1)若
为真命题,求
的取值范围;
(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/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3d8a600e7b6a10eeb9f96c3462cf35e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be86d6e29ae536b32a6671c4593f14c7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若
![](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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8 . 指出下列各组命题中,p是q的什么条件?q是p的什么条件?(在“充分不必要”、“必要不充分”、“充要”、“既不充分又不必要”中选一种作答)
(1)p:x为自然数,q:x为整数;
(2)p:
,q:
;
(3)p:同位角相等,q:两直线平行;
(4)p:四边形的两条对角线相等,q:四边形是平行四边形.
(1)p:x为自然数,q:x为整数;
(2)p:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7cfada8fd642ddf968bfd4228d48ec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d217c7b12e12e5fb67472452518859ec.png)
(3)p:同位角相等,q:两直线平行;
(4)p:四边形的两条对角线相等,q:四边形是平行四边形.
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2023-04-14更新
|
204次组卷
|
2卷引用:山东省滨州高新高级中学2022-2023学年高二下学期3月月考数学试题(春考班)
名校
9 . 下列各题中,命题p是命题q的什么条件?(填“充分不必要条件”,“必要不充分条件”,“充要条件”,“既不充分也不必要条件”)(只写答案即可)
(1)
且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a871ef7bf13de3e15489d65b57a3cc.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8389b5845314bef7412341c36d014ce.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0f3c89e41f778ad417cc0eec1544e0f.png)
(4)
某四边形是菱形
某四边形对角线相互垂直
(5)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51441c8788ff11be766766227793246d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce20ef9c08e82df8c7f45bac6dd31d36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bc539c71b72aff71e7c8e31e74969d1.png)
(6)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51441c8788ff11be766766227793246d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce20ef9c08e82df8c7f45bac6dd31d36.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/284b3586c879f13f0ccb3319672e0f9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30ab9408d72b2185996182108575fc2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a871ef7bf13de3e15489d65b57a3cc.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf2f40a4c50312b5f18f179020ae1381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8389b5845314bef7412341c36d014ce.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efaaaf9a43f1ca71d4ab50ca94d39e78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0f3c89e41f778ad417cc0eec1544e0f.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51441c8788ff11be766766227793246d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce20ef9c08e82df8c7f45bac6dd31d36.png)
(5)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51441c8788ff11be766766227793246d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d229cbec798c9c278a9b5979cb38247.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce20ef9c08e82df8c7f45bac6dd31d36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bc539c71b72aff71e7c8e31e74969d1.png)
(6)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51441c8788ff11be766766227793246d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a479511a50da604b2fc7398617db8387.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce20ef9c08e82df8c7f45bac6dd31d36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6204ebd38f7dcba36e4086998680046c.png)
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2023-07-31更新
|
212次组卷
|
2卷引用:山东省东营市利津县高级中学2022-2023学年高一上学期10月月考数学试题
10 . 已知定义域为
的函数
,若存在实数
,使得对任意
,都存在
满足
,则称函数
具有性质
.
(1)判断函数
是否具有性质
,说明理由;
(2)若函数
的定义域为D,且具有性质
,求证:“函数
存在零点”是“
”的一个必要不充分条件;
(3)若存在唯一的实数a,使得函数
,
具有性质
,求实数t的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37cb15d282a40c780c2b68287e47867e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28e384ba050b238e11f7c74d3002aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f57537b1a7ca7e4eed38a922ac707a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbde2170c24819edd47db617810bf47.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b161347f6a2fcfd9bf0acf1e8a03fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ba837ccb2f36f9dcef19706e5a1f27.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2387880727d458702651d699e76d7d76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8becbf02ba7e4bf68241153c0bfbbbfd.png)
(3)若存在唯一的实数a,使得函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23c80e143804fcfcbbb919fbeb11bc71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790daaa89fc9d093f45023becf765697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbde2170c24819edd47db617810bf47.png)
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