23-24高三上·北京西城·期末
名校
解题方法
1 . 给定正整数
,已知项数为
且无重复项的数对序列
:
满足如下三个性质:①
,且
;②
;③
与
不同时在数对序列
中.
(1)当
,
时,写出所有满足
的数对序列
;
(2)当
时,证明:
;
(3)当
为奇数时,记
的最大值为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2477167a02872167b2a3760f09d6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc25d4213ca2eadce49e6d8ba805e15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b730e2023809495f2bd7fbf48f07a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca986e62ec3a6e50e4e2cad639aa9201.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd869b784314b8278f5d144b2d3a9fb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698c4d4e50062b4a7dd70fe1b4ab4fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/302391681aa37ac20d6f533dbae9e137.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a215612787e43d28bfebc840c3903b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a60302649eb940748da818199e55da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/241d587c2e6f2f109a4e41b79f1c800f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926c16dd072c9ff8a560b003cfb47053.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4546b12ff89d1599427da82294afc09b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4546b12ff89d1599427da82294afc09b.png)
您最近一年使用:0次
2024-01-19更新
|
2045次组卷
|
6卷引用:北京市西城区2024届高三上学期期末数学试题
(已下线)北京市西城区2024届高三上学期期末数学试题北京市西城区2024届高三上学期期末数学试题(已下线)高三数学开学摸底考 (北京专用)2024年普通高等学校招生全国统一考试数学冲刺卷二(九省联考题型)江西省南昌市第二中学2024届高三“九省联考”考后适应性测试数学试题(四)江苏省连云港高级中学2023-2024学年高二下学期第一次月考数学试卷
2 . 已知集合
.集合
含有
个元素的子集分别记为
,
,
,
,
,其中
,
,
.当
,
时,设
,且
.定义:
;
.
(1)若
,
(i)写出满足
的一个集合
,并写出
的最大值;
(ii)求
的值;
(2)若存在唯一的
,使得
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2b3a23d2f1fec50e17559f1636fc68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df852270b85104c0bd2d0de2830ffd48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/640d4cb502dfb924620e30dbf7546241.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf73e41a26910357acba6dd83b558af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b65b7b76ec96df162672fcdf653b9e9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7601dbefa6836756e3d2731b79af0126.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/694b52596fdfcc391b23b3894ad85ec6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338947df86eb08f890be799504afe309.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c43c0c1f79b6b55d45a56087f42b9aea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b07eeb1c770bde4ee79af5abfd298dbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc2021769c50f01848cb89311c71659b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ca99f1104c0f7c014ab87496a892d4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b096b7a7ab6364001a6fbc0d8b53291.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba05bc733cdab0d9fbb6ebcfcef5c011.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45cf86650443d1b86c79b1e3edc7e5c.png)
(i)写出满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6faa41c5bd313f84d10c09d19c4abc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c325086d711b98fc89fe38b65e1b0e31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
(ii)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe19c7c063c09c9c3740109ff526c757.png)
(2)若存在唯一的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1933b7c3ace69622339353431c519b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b99d124d29ec453459d80f079d9a442e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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