名校
解题方法
1 . 设集合
,
,
(1)若
,求
,
;
(2)若
中只有一个整数,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff1aa2c6593b922adda24f698c682dd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f7259cb8656ee25e0cf139c5ef44bfa.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9cf8dffa529bdb60c61af0d12c7e737.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e349af7d47125d7028ee57178e199da5.png)
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名校
解题方法
2 . 已知全集为
,集合
.
(1)当
时,求
;
(2)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/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbf3d46d67ef50002ca18e04a3bb0442.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda922978abb112ea099f28ff9ec1170.png)
(2)若“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3f9e3e9114efdef663ecd60364e2c1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3 . 进位制是人们为了计数和运算方便而约定的记数系统,如果约定满二进一,就是二进制:满十进一,就是十进制:满十六进一,就是十六进制.k进制的基数就是k.我们日常生活中最熟悉、最常用的就是十进制.例如,数3721也可以表示为:
一般地,如果k是大于1的整数,那么以k为基数的k进制数可以表示为
.其中
.为了简便,也会把它写成一串数字连写在一起的形式:
,如果不加下标就默认是十进制.
(1)令集合
,将B中的元素按从大到小的顺序排列,则第100个数为多少?
(2)若
,记
为整数n的二进制表达式中0的个数,如
,求
的值.(用数字作答)
(3)十进制中的数999在其他进制中是否也可以表示成一个各位数字之和为27的三位数?如果能,请求出所有的k进制数;如果不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8e187d488943587384ba81366d7cb2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf78d6c2cd4fab5d71e969af0f530e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d47daf899fce1cb06151012a09153d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79224c6579e5f93906b81de9a7f8dbfd.png)
(1)令集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b963d591925c79c381bb8c7cf8121390.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39bc26525689d068504cd9298b19d424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c51592137a3a852f5c802be493e065a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39009f3279d0431b9b444634f18f355b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a80cc2a98cd5e91efa4169a97d4e8e1.png)
(3)十进制中的数999在其他进制中是否也可以表示成一个各位数字之和为27的三位数?如果能,请求出所有的k进制数;如果不能,请说明理由.
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名校
4 . 定义1:对于一个数集
,定义一种运算
,对任意
都有
,则称集合
关于运算
是封闭的(例如:自然数集
对于加法运算是封闭的).
定义2:对于一个数集
,若存在一个元素
,使得任意
,满足
,则称
为集合
中的零元,若存在一个元素
,使得任意
,满足
,则称
为集合
中的单位元(例如:0和1分别为自然数集
中的零元和单位元).
定义3:对于一个数集
,如果满足下列关系:
①有零元和单位元;
②关于加、减、乘、除(除数不为0)四种运算都是封闭的;
③对于乘法和加法都满足交换律和结合律,且满足乘法对加法的分配律,则称这个数集
是一个数域.
(1)指出常用数集
中,那些数集可以构成数域(不需要证明);
(2)已知集合
,证明:集合
关于乘法运算是封闭的;
(3)已知集合
,证明:集合
是一个数域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e16415b61722f9961e412386e6819f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57e35231b964e293122c4383dac2431b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bfad095b65beb6e77aee3664b0e6bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e16415b61722f9961e412386e6819f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad135b14c9dcd83eab6618d7694c7b0.png)
定义2:对于一个数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc020b0997a2f37b214718112b79d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac385ec112e6d61b90d953e3f106ee85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29df165b5fc74dcbc39df74d541148da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb9df3a17aa370eba2add2c13cfc2619.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac385ec112e6d61b90d953e3f106ee85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c4e0c03c5aef711627f1b3124d8b5fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad135b14c9dcd83eab6618d7694c7b0.png)
定义3:对于一个数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
①有零元和单位元;
②关于加、减、乘、除(除数不为0)四种运算都是封闭的;
③对于乘法和加法都满足交换律和结合律,且满足乘法对加法的分配律,则称这个数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)指出常用数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39021e0f386119bd1b5c73b843106e55.png)
(2)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37b491b231d0ff8a387813b5686579f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da4c1c450038724991d6d39ecefae405.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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2024高三·全国·专题练习
解题方法
5 . 已知
.问是否存在
,使得
若存在,求出
的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db885bcc03565aa2ad49fba46d219123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e7507801c71834002632b164138eb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac133625f32922eed106f8b50f95b705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
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2024高三下·全国·专题练习
解题方法
6 . 已知
,
,求
成立时
需满足的充要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea508345fd8d185695b0fd5cc7b1899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbebb5ce7581439e873e53d55d944c3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ba583329b831d06312a1f20edb4a81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
7 . 已知非空集合
,
.
(1)若
,求
;
(2)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55201a71f63e95aef66df1ca9e21551a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44fbb02d5a584747b4a8287c6c24e0d1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-06-10更新
|
320次组卷
|
4卷引用:甘肃省陇南市第一中学2023-2024学年高一上学期期末考试数学试题
名校
8 . 对于定义在
上的函数
,如果存在一组常数
,
,…,
(
为正整数,且
),使得
,
,则称函数
为“
阶零和函数”.
(1)若函数
,
,请直接写出
,
是否为“2阶零和函数”;
(2)判断“
为2阶零和函数”是“
为周期函数”的什么条件(用“充分不必要条件”“必要不充分条件”“充要条件”或“既不充分也不必要”回答),并证明你的结论;
(3)判断下列函数是否为“3阶零和函数”,并说明理由.
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c7eb49a823f757461cd5260757b088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd84a8f95166367063218ee03ffd5a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f7f4cc0837a4e6dcd0072887e4e2704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe6d9f54a34762aadfdf8e2bac977cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892519541cfba6f2763cd29159bf1b02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/329fb959f16f82835aa68fca9d3f08f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcda6a21da79726f8fb3ba6235b9010f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebef85c05f6d84ceb67d92abf77ba2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ace630100e64ed290d82936ad249c8.png)
(2)判断“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)判断下列函数是否为“3阶零和函数”,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab7da79b2400cf8125ef040cd056b76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/321b15db96dc89f136a7421e09fc9814.png)
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2024高三下·全国·专题练习
解题方法
9 . 已知集合
,
.若
,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c581a30d70e2894bbb93b96528996302.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51452061e672940d11737de54c806d2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
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名校
10 . 在计算机科学中,
维数组
是一种基础而重要的数据结构,它在各种编程语言中被广泛使用.对于
维数组
,定义
与
的差为
与
之间的距离为
.
(1)若
维数组
,证明:
;
(2)证明:对任意的数组
,有
;
(3)设集合
,若集合
中有
个
维数组,记
中所有两元素间的距离的平均值为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcb13ab18937e51cc842fa85defe2b2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70a5369bb892f707c3f0a2ac2fa18f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8373ec34bc1c49f29b672cec668a7189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab4a9bfa50054c808dd8190305d0abd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e1d1f71b5aee622ad3bb731172aaac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5725a091f17274ae34890339ae7178c.png)
(2)证明:对任意的数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2748d82571d4ba75ae1ebdfacc011a7a.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/727a608a5ccb82aa87e46194fe7e2fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2ea5126ca30d68cc8b70f03860ba2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae8e92f2312c156aa28806f810cc96d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3484a2499e9b47bd15e2cf721356798.png)
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