名校
1 . 已知
为实数集的一个非空子集,称
是一个加法群,如果
连同其上的加法运算满足如下四条性质:
①
,
;
②
,
;
③
,
,使得
;
④
,
,使得
.
例如
是一个无限元加法群,
是一个单元素加法群.
(1)令
,
,分别判断
,
是否为加法群,并说明理由;
(2)已知非空集合
,并且
,有
,求证:
是一个加法群;
(3)已知非空集合
,并且
,有
,求证:存在
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd242f355d5128425429a83e4b6632c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8362f15e544684164f38ff9ad7c38ac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ea5a550b5452df9abdbca776c2ff500.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/509a09a7391de2cc86e5e44ccccc981b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8236622218d4d4012d8637538ac9032.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bef35ae51107e991163ea418c8dec53a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebf00e8864c86c3ce8118ea76bf69773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc118659264aca9e263cb8edc41e9c44.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebf00e8864c86c3ce8118ea76bf69773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f0119b6de9149150071fe7ed848aa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a065a5ddaa18900ee15a8b436f0fcb95.png)
例如
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/178e8cc61b87b4dc63105ab4fca8680c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7cb4e4e98b375294dc1dccbeebbd6c2.png)
(1)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/809b2e00ab8e43a0f886c7f83846d3d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b113752e4f989a338747b95a40cf386.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d18f9bbb6b9feb166f7ecfb49013262d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64ee969e5c3d880e0209235bb9cfc49f.png)
(2)已知非空集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a02a810b3332821bc444f215183c9e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7d3e3d84e1fdee95574817741d731e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08152bab36dca188978d125e4b7a935a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/489ea5a5f5b5de37e238cbfbb4a01143.png)
(3)已知非空集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d28cc3165eef94c22c442b2f30c87cc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4034552829008c1daaee2701d2afe8dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e0f9ba8419972cff845bfd91f64297.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93ddc4872d58eaa6bcc432b7b94939f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd5eb4f6f84d264f3403eece1e7c37b7.png)
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2 . 设A,B为两个非空有限集合,定义
其中
表示集合S的元素个数.某学校甲、乙、丙、丁四名同学从思想政治、历史、地理、物理、化学、生物这6门高中学业水平等级性考试科目中自主选择3门参加考试,设这四名同学的选考科目组成的集合分别为
,
,
,
.已知
{物理,化学,生物},
{地理,物理,化学},
{思想政治,历史,地理},给出下列四个结论:
①若
,则
{思想政治,历史,生物};
②若
,则
{地理,物理,化学};
③若
{思想政治,物理,生物},则
;
④若
,则
{思想政治,地理,化学}.
其中所有正确结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069ec439d599e7989e74f4c4ac91d65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/911cdb689ca80557ce076cb49b3ee498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f30f56664446f32dbbc2c5f12a99374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3dabace330ccdd9755fbcf32d5d6343.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1b625192d7398634a02ea24fa78ed87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef354e5c5ff828cc8d27c71badd40f98.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d10b9f228c9a255aca3ace899db760d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9620357ea5be4037cfdccd09a27d3862.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b4f81050636eac5b4f064fa0f06313.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9620357ea5be4037cfdccd09a27d3862.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9620357ea5be4037cfdccd09a27d3862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a41bbaf9ee8f16ee2ab343dc164a8e48.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231bca548a6ffe3013474743e1b5d039.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9620357ea5be4037cfdccd09a27d3862.png)
其中所有正确结论的序号是
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3 . 按国际标准,复印纸幅面规格分为
系列和
系列,其中
系列以
,
,…等来标记纸张的幅面规格,具体规格标准为:
①
规格纸张的幅宽和幅长的比例关系为
;
②将
(
)纸张平行幅宽方向裁开成两等份,便成为
规格纸张(如图).
规格纸张裁剪其他规格纸张.共需
规格纸张40张,
规格纸张10张,
规格纸张5张.为满足上述要求,至少提供
规格纸张的张数为( )
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fea68b25c2e09c6aa70843052e43c422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aa7e89c5d3ca8e70330ac3010005100.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fea68b25c2e09c6aa70843052e43c422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526ddee4ed97b917d9e4cc4542c72a37.png)
②将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e2edb08ade32f10e715ec57755d7d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57c4efdbc64857469c666dd78a4a7019.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90db8321e9bb3b8fdfbff204fe958c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fea68b25c2e09c6aa70843052e43c422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b553e2a281714677e29a5e97dd7d5a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f2ba909c3435f8212c1da4fae36ee19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aa7e89c5d3ca8e70330ac3010005100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fea68b25c2e09c6aa70843052e43c422.png)
A.6 | B.7 | C.8 | D.9 |
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4 . 2023年6月22日,由中国帮助印尼修建的雅万高铁测试成功,高铁实现时速
自动驾驶,不仅速度比普通列车快,而且车内噪声更小.如果用声强
(单位:
)表示声音在传播途径中每平方米上的声能流密度,声强级
(单位:
)与声强
的函数关系式为
,其中
为基准声强级,
为常数,当声强
时,声强级
.下表为不同列车声源在距离
处的声强级:
设在离内燃列车、电力列车、高速列车
处测得的实际声强分别为
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd054da0ad34c8ba01fe54179ba0a7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1db72d10094c3d5cf2cb4eaa4809a1f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca586d4c35ce52dec4b545cf13ee0721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7980ec6e0e432b23fbe3f4562848913.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/164932c352061abf01e7e3513b08229d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f0a1908e167c64684b0a50aee5ec64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e3a88ef910aa647ac022c3880262f78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c08094f72d5bd69246c453dd28e33d1.png)
声源 | 与声源的距离(单位:![]() | 声强级范围 |
内燃列车 | 20 | ![]() |
电力列车 | 20 | ![]() |
高速列车 | 20 | ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c08094f72d5bd69246c453dd28e33d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/146e570dfac0a06f1547a444808701d9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
5 . 下列关于函数
的论述中,正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ffd63eb7acd452e288c1b0adbf8a11.png)
A.是奇函数 | B.是增函数 | C.最大值为![]() | D.有一个零点 |
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6 . 使
恰有2个整数解的正整数n的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7db6187cc7a8e5c863f95fa721065f8b.png)
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7 . 某学校球类社团组织学生进行单淘汰制的乒乓球比赛(负者不再比赛),如果报名人数是2的正整数次幂,那么每2人编为一组进行比赛,逐轮淘汰.以2022年世界杯足球赛为例,共有16支队进入单淘汰制比赛阶段,需要四轮,
场比赛决出冠军.如果报名人数不是2的正整数次幂,则规定在第一轮比赛中安排轮空(轮空不计入场数),使得第二轮比赛人数为2的最大正整数次幂.(如20人参加单淘汰制比赛,第一轮有12人轮空,其余8人进行4场比赛,淘汰4人,使得第二轮比赛人数为16.)最终有120名同学参加校乒乓球赛,则直到决出冠军共需__________ 轮;决出冠军的比赛总场数是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/430fa6c9000aa7129274e4f29613ad63.png)
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8 . 一种细胞的分裂速度
(单位:个/秒)与其年龄
(单位:岁)的关系可以用下面的分段函数来表示:
其中
,而且这种细胞从诞生到死亡,它的分裂速度变化是连续的.若这种细胞5岁和60岁的分裂速度相等,则
( )
(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc13a607ac0c7f76d252d7cb1bb040fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d5ad22dca5f612a6d073d1964bdba0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73254f32b6da29ecc32df2e9f87a4c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beac718b4efd5ac6e804bf9f76de98f1.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/782320358aa1c6f48b51fb728f2936ad.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 若
为正整数,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a296772b32c3a9d0844de389327a06.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
10 . 已知
,若对任意
,均有
,则函数
可以是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7552cd1f3525a8ac34ba7fe51c225e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f95425c7f376f1d63a3e8a16f207dcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次