1 . 设X,Y为任意集合,映射
.定义:对任意
,若
,则
,此时的
为单射.
(1)试在
上给出一个非单射的映射;
(2)证明:
是单射的充分必要条件是:给定任意其他集合
与映射
,若对任意
,有
,则
;
(3)证明:
是单射的充分必要条件是:存在映射
,使对任意
,有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86d7786f55f767e0a301b5032cdacc79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4645f4c284aef83b9d7edc909ce75168.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27822887caad20f3a075ca2fb74155c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
(1)试在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff048206370cd239052751e22f51089e.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d2e22788e03d6846442ce299b67bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ab73f0717678abfa9f8addc42be0c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce86cc928b228eba243c4bbfae8247ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683ee65c22bb8f6350feef3a3371a95f.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2216c6b89948de65d2e8488c2071a61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fd9b15b5cdf1c131ebf7cf2776cf7a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e0ab2f691659dfb9857e81cabc3142e.png)
您最近一年使用:0次
名校
2 . 聚点是实数集的重要拓扑概念,其定义是:
,
,若
,存在异于
的
,使得
,则称
为集合
的“聚点”,集合
的所有元素与E的聚点组成的集合称为
的“闭包”,下列说法中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f935b7601b228d3665631bf82bf03221.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51159984b2cb00f30b3986315019623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/479a4db00b70dce0c5d88715851fa564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38573dc7fb73024c610b7d123a449437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c254d67bba7f26489ff32cb12831095.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61588617d22abd00af4ca489bb3a8787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61588617d22abd00af4ca489bb3a8787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61588617d22abd00af4ca489bb3a8787.png)
A.整数集没有聚点 | B.区间![]() ![]() |
C.![]() | D.有理数集![]() ![]() |
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3 . 已知函数
,
.( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4a29fd093745c5c8602450709d66b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f9ce4e82eec17b60cc0cf34f0394e42.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.对于![]() ![]() ![]() |
D.对于![]() ![]() ![]() |
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4 . 置换是代数的基本模型,定义域和值域都是集合
的函数称为
次置换.满足对任意
的置换称作恒等置换.所有
次置换组成的集合记作
.对于
,我们可用列表法表示此置换:
,记
.
(1)若
,计算
;
(2)证明:对任意
,存在
,使得
为恒等置换;
(3)对编号从1到52的扑克牌进行洗牌,分成上下各26张两部分,互相交错插入,即第1张不动,第27张变为第2张,第2张变为第3张,第28张变为第4张,......,依次类推.这样操作最少重复几次就能恢复原来的牌型?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0364fdd3e79a0c0b61b701f9438e6eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3df27c5ca627e36f533e5c09578cf80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105cfc51f5315b2b995296b7e70d421e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/545e481ea016bf0f2ec58b26334c92ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6725d5b32aa987c64c4aaa31c78716a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/670713014d832fc20f25f47d120d0726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61eac89daa39aeea09940cb93dca734d.png)
(2)证明:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f94135872e3f37b01e0acbb144a056e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dcd78ec8777a8e6e5b32222cdb15c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc86f3506cbe0d692fcd5fc7ab7b85d0.png)
(3)对编号从1到52的扑克牌进行洗牌,分成上下各26张两部分,互相交错插入,即第1张不动,第27张变为第2张,第2张变为第3张,第28张变为第4张,......,依次类推.这样操作最少重复几次就能恢复原来的牌型?请说明理由.
您最近一年使用:0次
2024-02-27更新
|
2305次组卷
|
4卷引用:数学(九省新高考新结构卷02)
(已下线)数学(九省新高考新结构卷02)浙江省名校协作体2023-2024学年高三下学期返校考试数学试卷(已下线)第3套-期初重组模拟卷湖南省湖南省长沙市第一中学2024届高三下学期高考适应性演练(一)数学试题
5 . 水星是离太阳最近的行星,在地球上较难观测到.当地球和水星连线与地球和太阳连线的夹角达到最大时,称水星东(西)大距,这是观测水星的最佳时机(如图1).将行星的公转视为匀速圆周运动,则研究水星大距类似如下问题:在平面直角坐标系中,点A,
分别在以坐标原点
为圆心,半径分别为1,3的圆上沿逆时针方向做匀速圆周运动,角速度分别为
,
.当
达到最大时,称A位于
的“大距点”.如图2,初始时刻A位于
,
位于以
为始边的角
的终边上.
,当A第一次位于
的“大距点”时,A的坐标为______ ;
(2)在
内,A位于
的“大距点”的次数最多有______ 次
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3551176fd3003244122a34612d90113c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c896216c135b8c568a5f0987c23947e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22f9341d51c827a29a4a0b0b3dded16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7c7f579d5017888a314d681fe44db8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/590e165e407098fcac9f871beb047dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf01af951cc03381ca19150c6fe5364.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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解题方法
6 . 已知
,
,
,则下列结论一定成立的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de07daa4c7c7cfcf5241726fa788e6ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/832444aae81de7f780b5e496315cc82e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d625d77f3bfadc66947098bc41233d2.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() |
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解题方法
7 . 雅各布·伯努利(Jakob Bernoulli,1654-1705年)是伯努利家族代表人物之一,瑞士数学家,他酷爱数学,常常忘情地沉溺于数学之中.伯努利不等式就是由伯努利提出的在分析不等式中一种常见的不等式.伯努利不等式的一种形式为:
,
,则
.伯努利不等式是数学中的一种重要不等式,它的应用非常广泛,尤其在概率论、统计学等领域中有着重要的作用.已知
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02fe85f6383f5b2aca40ab15ba4bc248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d4045366a437d4003259050718e244.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37510088319e438ceee842590ab6e3af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56893c747445bebabfe192eca5b9eaa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24311368ea9d298e36fdb3562093fc68.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 如图1“Omniverse雕塑”将数学和物理动力学完美融合,遵循周而复始,成就无限,局部可以抽象成如图2,点P以
为起始点,在以O为圆心,半径为2(单位:10米),按顺时针旋转且转速为
rad/s(相对于O点转轴的速度)的圆周上,点O到地面的距离为a,且
(单位:10米),点Q在以P为圆心,半径为1(单位:10米)的圆周上,且在旋转过程中,点Q恒在点P的正上方,设转动时间为t秒,建立如图3平面直角坐标系
.
(1)求经过t秒后,点P到地面的距离PH;
(2)若
时,圆周上存在4个不同点P,使得
成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2584d4e78881413d8ddd1ec84011db2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/29/02068183-41e7-46dd-8916-f69c8e00bae1.png?resizew=177)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/29/5e8787db-81e4-4dec-ac9f-5aa14404dfc1.png?resizew=250)
(1)求经过t秒后,点P到地面的距离PH;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b8a359aff6030dbfeef0f628341b07d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe8b38f88b0f72334f0530fd827fefb.png)
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9 . 设
是正整数,集合
.当
,集合
有______ 个元素;若集合
有100个元素,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a26e50631247f26a9eb51ff32493a591.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
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解题方法
10 . 已知
不是常数函数,且满足:
.①请写出函数
的一个解析式_________ ;②将你写出的解析式
得到新的函数
,若
,则实数a的值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18a8a9d79a3e0ae1ac03c874c7c6caa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cd283b96778ee18fa785383b5107e71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a880176a4707912382bccb0bdaa5ce.png)
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2024-01-21更新
|
703次组卷
|
5卷引用:黄金卷05(2024新题型)
(已下线)黄金卷05(2024新题型)贵州省六盘水市2022-2023学年高一上学期期末教学质量监测数学试题2024届高三新改革适应性模拟测试数学试卷一(九省联考题型)福建省部分优质高中2023-2024学年高一下学期入学质量抽测数学试卷(已下线)专题03y=Asin(ωx+φ)的综合性质期末8种常考题型归类-《期末真题分类汇编》(人教B版2019必修第三册)