名校
解题方法
1 . 已知
为实数集
的非空子集,若存在函数
且满足如下条件:①
定义域为
时,值域为
;②对任意
,
,均有
. 则称
是集合
到集合
的一个“完美对应”.
(1)用初等函数构造区间
到区间
的一个完美对应
;
(2)求证:整数集
到有理数集
之间不存在完美对应;
(3)若
,
,且
是某区间
到区间
的一个完美对应,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933093b52cca887f597cbe22a5467b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.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/dd4c42648f413abc4ec6b042f0924e1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e7ee80da08376cb9a6f0ac641b2d1f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)用初等函数构造区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f14df2d8d1fea71da4197e81b6ee3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d65bdc820ab87b9a7909d2be591abec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)求证:整数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/067802ecb7978511f798ef27d02e890b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/316ecb1589c3cc179e2f62507020771e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e8835e96965b13d49dd1481403eb997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aff8d9b6533ff319420cdc5e8740b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e2bb6cfd4b2fa49622dc9b7c39b62b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
2 . 已知函数
的部分图象如图所示,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49e1b36b91ee845efe122a5035172fdb.png)
A.函数![]() ![]() |
B.![]() |
C.函数![]() ![]() |
D.方程![]() ![]() ![]() |
您最近一年使用:0次
3 . 已知
,
,
,则
,
,
的大小关系为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abfbbcb874aacdb04d5af2cd4c4bac3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5048c8b2dfb367d4d01aef311e0c8b54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0308c14a89ebc6fb2a589d2502859902.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
4 . 已知
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64541d7f445079207b6f671adc7d662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b21208364124b5c477b2ff8df1c2e8f.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-06-11更新
|
607次组卷
|
3卷引用:北京市中国人民大学附属中学2024届高三下学期5月热身练习数学试题(三模)
5 . 已知角
,则数据
的中位数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a837149d753a3457daeb1eef3a90f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ada10e8bc79ded0427036fea861e4f58.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024·江苏连云港·模拟预测
6 . 已知函数
,若
且函数
在
,
,
处的切线均经过坐标原点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7f9b35017daa8b524c5717a355834a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647fea48d2c186050a67e82b57d461a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff8b1535f227e0ec975578f0200fcba2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024高三下·全国·专题练习
解题方法
7 . 正三棱锥
和正三棱锥
共底面
,这两个正三棱锥的所有顶点都在同一个球面上,点
和点
在平面ABC的异侧,这两个正三棱锥的侧面与底面
所成的角分别为
,则当
最大时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea16125a2b2462fc9a5d8e943c32cda.png)
______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7edc2e23df190c35aafad93410a05b8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/474929dd8e89d9ce37448ae72b48d04f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dc4c63a548b91061528aa11058de75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea16125a2b2462fc9a5d8e943c32cda.png)
您最近一年使用:0次
8 . 已知函数
且
在区间
上单调递减,则函数
在
上的最大值与最小值的和为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1039f324dcb31ff7393cda1d3e778117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b98b0ed5ba108a8b54af7bcbcb07986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6400ec27a77d671d1fcc1d883d525dd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09af94fc73db7a2420e7d09f3f21423a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d51992c05a557cf6058664f1f8961e.png)
您最近一年使用:0次
9 . 函数
的部分图象如图所示,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aceb6ed0e9c94c21417ba0be0a9ae237.png)
A.![]() |
B.![]() ![]() ![]() |
C.函数![]() ![]() |
D.若函数![]() ![]() ![]() ![]() |
您最近一年使用:0次
10 . 已知定义在
上的函数
的表达式为
,其所有的零点按从小到大的顺序组成数列
(
).
(1)求函数
在区间
上的值域;
(2)求证:函数
在区间
(
)上有且仅有一个零点;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7d9eebb0705256305ab3bf28898fffc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df075cd20f79486d88d80ee12fc897d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0b6a6e136f1f05417c93473d27a5efe.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71163f419555f2ed76075c8ff659fbfc.png)
(2)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85fa35905c7193c20799ed7b925b358a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0b6a6e136f1f05417c93473d27a5efe.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0710952d6f8d8f6c0de73c42f4301c79.png)
您最近一年使用:0次