1 . 已知方程组
的解集为
.
(1)若方程组的一个解为
,求
的值;
(2)若
时,求
;
(3)当
时,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb834a8b167f55c254e20d8f1a698be3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf04b4991cc8ef8ffb9d8ef31d54ba20.png)
(1)若方程组的一个解为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f114df5ceabdb7e5fd3fdad4eaf056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb0d7fbcc396c7b646c31f60e32d9e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6abf3f9b0ebcdc47a028c781b7edb9.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a7bb2271f0c1ae6f267beff842fcc44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88edfcabd49166a6dae74eecbdafd35f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
2 . (1)集合
,求集合
的子集个数及真子集个数;
(2)集合
.若
,
,
,求
、
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb02ea70ea7ca37e75e21bd51df0f56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7e203f994f59782d6e352c504b1f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fffebd49e69a8a984d3dd135d873556e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/343324ebf9d6e86c42fbde0fbb94689d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
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解题方法
3 . 已知函数
和
,定义集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a93a16382ef1c6e4b6eeea2909f358a7.png)
(1)设
,
,若
,求m的取值范围.
(2)设
,
,
,若
,求m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde66f0ef8ea3ac6d6ac91a93ba69ae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a93a16382ef1c6e4b6eeea2909f358a7.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7e204b1d7ee9fec55811da546bd2d9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f220ef5339248b2971cecebb6a92294b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44bac659eca0067a8f5217d0ce62c2c0.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6436413dff637d3ae243f82bd22c4f1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bbf9858659de45bd26111af7babef2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c6d4b11a69708e588e4bbac9f2b3f6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecbf3b0349dc38eb54864384c6ef043e.png)
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解题方法
4 . 下列说法正确的有( )
A.当![]() ![]() |
B.![]() ![]() |
C.已知函数![]() ![]() ![]() ![]() |
D.已知![]() ![]() ![]() ![]() |
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5 . 设集合
,称坐标
在平面直角坐标系中对应的点P为A中元素a的格点.
(1)证明:若
则
.
(2)A中的元素
所对应的格点记作
(
),现将A中所有元素进行排序,使得
,在平面直角坐标系中,求以
为顶点的三角形面积.
(3)已知集合
,若
至少有2个元素,最多有5个元素,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799adb7e4c8ebf9a30182e46e56f3192.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0203b006524305c3d8ee0b6c34cd872b.png)
(1)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91cc05fe570763e4af0ff4672e2d09e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae4202aa738ce97198687198555c84c.png)
(2)A中的元素
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf99487d7860d017c0747ff966edfd77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/019123b8c298384939e99ef5e37720d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c8c195da3f1e6e13cc9fc7aca43e17d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4a0c3c4114915039e38b671bb707c09.png)
(3)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63728e5600559674a6bb03a0f183007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fdbfa7a63fdf5717d40c8c9a73ec160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2023-10-07更新
|
201次组卷
|
2卷引用:江苏省连云港市灌南高级中学2023-2024学年高一上学期第一次月考数学试题
名校
6 . 已知全集为U,
,则其图象为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56552cb9c94f329a295d508567103f75.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2023-06-25更新
|
1705次组卷
|
4卷引用:吉林省长春市十一高中等四校联考2023-2024学年上学期第一次月考数学试题
名校
解题方法
7 . 对于非空数集A,若其最大元素为M,最小元素为m,则称集合A的幅值为
,若集合A中只有一个元素,则
.
(1)若
,求
;
(2)若
,
,求
的最大值,并写出取最大值时的一组
;
(3)若集合
的非空真子集
两两元素个数均不相同,且
,求n的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81d2ec1a5112ce091f604a70db6ff070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c91daec4d6f087fd9575aaf6556489f6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48bfdfd1a175a860a18587e4c21e04da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d70d5962157e2116e7f1a267153967.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb78779234085b9dbec4e3424a1a4971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/819a9ba7e6e80c06082fd1af18f7f43e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e45173688d37986ac521cbe53d22ed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6fa157b4f65f3a9aa1f7f82de02e99e.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a227a694dc404d1184578c7d278fd8d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c4f1149c86913354c231ad31e01fccf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/468f61b74f81868a14729e49b982246e.png)
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2023-01-04更新
|
830次组卷
|
7卷引用:北京市东城区2022-2023学年高一上学期期末统一检测数学试题
北京市东城区2022-2023学年高一上学期期末统一检测数学试题河北省邯郸市魏县2022-2023学年高一上学期期末考试数学试题(已下线)高一上学期第一次月考解答题压轴题50题专练-举一反三系列重庆市沙坪坝区部分学校2023-2024学年高一上学期9月检测(一)数学试题北京市第一零九中学2023-2024学年高一上学期12月月考数学试卷(已下线)高一上学期期末考试解答题压轴题50题专练-举一反三系列北京市第二十五中学2023-2024学年高一上学期期中过程性评价数学试题
名校
8 . 若将有限集合
的元素个数记为
,对于集合
,
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db60e5bbf9b7ccd9bcfa25b13901dc9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/397021f76cfe9b90b2289a676ccad9f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f58cd156f49a278d4805dab97f14b948.png)
A.若![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() |
D.存在实数![]() ![]() |
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2022-11-10更新
|
427次组卷
|
6卷引用:江苏省苏州市2022-2023学年高一上学期期中数学试题
解题方法
9 . 在①②两个条件中选择一个,补充在下面问题中.
①设函数
的定义域为
,且对任意
,均有
.
②设函数
的定义域为
,值域为M.集合
,
只有一个元素.
问题:设函数
满足___________.
(1)求函数
的解析式;
(2)点P是函数
图象上的一动点,由点P向y轴及直线
作垂线PA,PB,垂足为A,B,点
,求四边形PACB面积的最小值.
①设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4d0a51632e4821be8823927b56ff038.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b792991c9c5f75db404bb5f4e6d3b63d.png)
②设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccacbaeeae0e5eea57370316cefa0c7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4d0a51632e4821be8823927b56ff038.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fc3b4fa3d0f3e426281b7ce1147ddb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c81919684bc4047d376c7e57dc6c8f1c.png)
问题:设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)点P是函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c966320d637cab491c67425ef1338966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f0ec7f84f716a316ec92d133927666c.png)
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10 . 下列三个结论中所有正确结论的序号是( )
①若全集为
,集合
,则
;
②空集是任何一个集合的真子集;
③已知集合
与
,则
是
的充要条件.
①若全集为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b504c5e5a1d75d7882f8f867e7ef1cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6d403831108d8ff97494fd2e200ec58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/732f2de96c6713f2ddb0ec417cd81c33.png)
②空集是任何一个集合的真子集;
③已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2333f966f6ec29f0661f93d99b055cd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56552cb9c94f329a295d508567103f75.png)
A.① | B.③ | C.①② | D.①③ |
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