名校
解题方法
1 .
的内角
的对边分别为
,已知
.
(1)求角
的大小;
(2)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b5c164f58a436b75026c228fea64e1.png)
,求
的面积;
(3)若角
为钝角,直接写出
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e0e02f7687d06562f4f65be3f4cee9e.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b5c164f58a436b75026c228fea64e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d447455ca3fa23710faaa4bd6b5d7c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(3)若角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99ea513ef4c8fc4d8c31eff498740680.png)
您最近一年使用:0次
2024-06-03更新
|
1825次组卷
|
3卷引用:北京市顺义区杨镇第一中学2021-2022学年高一下学期期中考试数学试卷
名校
解题方法
2 . 如图,在正方体
中,
为棱
的中点.动点
沿着棱
从点
向点
移动,对于下列三个结论:
①存在点
,使得
;
②
的面积越来越大;
③四面体
的体积不变.
所有正确的结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
①存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/656aceec19543470bd58ed3d304d155d.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c1b7f8c6e4793af4336d02addfbfbb.png)
③四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6738d05f0c7e4f0076fd5c094a4fb51c.png)
所有正确的结论的序号是
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/30/ca35a6aa-47b2-4355-a4df-1c9917f72bdf.png?resizew=163)
您最近一年使用:0次
3 . 已知数集![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea7fcdb5423c1c8c032a3efcf245682.png)
具有性质P:对任意的k
,
,使得
成立.
(1)分别判断数集
与
是否具有性质P,并说明理由;
(2)若
,求A中所有元素的和的最小值并写出取得最小值时所有符合条件的集合A;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea7fcdb5423c1c8c032a3efcf245682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40dc6d234f7984333f33d89de05e7ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/110ef251c0b9cf48fb94c928ad95e36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/412f8627babba57acd06ed10f4292210.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1e76d1341e8e6bd89b7075150536bd.png)
(1)分别判断数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/997bbd93dff19a5dba79bcd9d92f3129.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13470c4e9665748fdd20d0b181abc8e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91a94ec87afbc073e077f2c453a304b.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e73d1fc9adb4448fd245f9bbf3d3ed0.png)
您最近一年使用:0次
名校
解题方法
4 . 已知数集
具有性质
:对任意的
,
,
,使得
成立.
(1)分别判断数集
与
是否具有性质
,并说明理由;
(2)若
,求
中所有元素的和的最小值并写出取得最小值时所有符合条件的集合
;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc95c7daae935cccf8666865cba9eea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd446b1c54b898bba5260537f1b30db8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d48d21d10197c3d078db9d1ac9293e79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce133aca7a46be0dd5e055096addebac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1e76d1341e8e6bd89b7075150536bd.png)
(1)分别判断数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/997bbd93dff19a5dba79bcd9d92f3129.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13470c4e9665748fdd20d0b181abc8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91a94ec87afbc073e077f2c453a304b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91fcc8350d2ed52931f48b8b5ca11215.png)
您最近一年使用:0次
2024-02-24更新
|
150次组卷
|
2卷引用:北京市第十九中学2022-2023学年高一上学期(10月月考)期中练习(一)数学试题
5 . 如图,在棱长为2的正方体
中,
,
分别是棱
,
的中点,点
在
上,点
在
上,且
,点
在线段
上运动,给出下列四个结论:
![](https://img.xkw.com/dksih/QBM/2024/2/3/3425106637709312/3430232655585280/STEM/6a2e8f2b25ea4ba38813b3d8db0782ea.png?resizew=162)
①当点
是
中点时,直线
平面
;
②直线
到平面
的距离是
;
③存在点
,使得
;
④
面积的最小值是
.
其中所有正确结论的序号是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3182db896bc2462331796e2a6108363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b20bec6da0e92b220021ab497e1ccc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3adea2cdc3b64f1bf79265d4cb1425ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://img.xkw.com/dksih/QBM/2024/2/3/3425106637709312/3430232655585280/STEM/6a2e8f2b25ea4ba38813b3d8db0782ea.png?resizew=162)
①当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b54387f870ae37f7951b253665d64f6.png)
②直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70db40c42655327adee01caedfc9d50c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
③存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae1adc3dbbcbb2571fe2900fd3c5be1.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ba2d49042c812a164167a8e42fde290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be3740691124a5ed24347bffe5d55af3.png)
其中所有正确结论的序号是
您最近一年使用:0次
解题方法
6 . 如图,在棱长为1的正方体
中,点
是对角线
上的动点(点
与
不重合),则下面结论中正确的是__________ .(填序号)
①存在点
,使得平面
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0a582c36d62d83c16425b2f54b4354.png)
②存在点
,使得
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6e96872af0f0b341835576c407e364.png)
③对任意点
的面积都不等于![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0467b0675c3ecfb282cc88255284d3e1.png)
④
分别是
在平面
,平面
上的正投影图形的面积,对任意点
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b04d6165b18f1a031b2a137961832491.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/14/2a051d9a-16b1-48f1-ab42-79751f3d8dba.png?resizew=163)
①存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1671cc93b233d6e52529a50c1a622ce3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0a582c36d62d83c16425b2f54b4354.png)
②存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d1d2e0f281222a5f289ea4008370aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6e96872af0f0b341835576c407e364.png)
③对任意点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc1c46130944027b9c2a39b77927269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0467b0675c3ecfb282cc88255284d3e1.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd5683dba7d9f29d643e9a3e3204fa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3928d0c519a9e198a0313c75147f6ca.png)
您最近一年使用:0次
2023-08-10更新
|
651次组卷
|
2卷引用:北京市育英学校(四年制高三)2021-2022学年高二下学期期中练习数学试题
7 . 已知函数
,下列命题正确的是( )
①
是奇函数;
②方程
有且仅有1个实数根;
③
在
上是增函数;
④如果对任意
,都有
,那么
的最大值为2.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707dd66e0d6f8c33c6e05b4555f12c31.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/becd598a11b876d858728161a7a09705.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
④如果对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8800c695cb799480fe1eb3859868e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
A.①②④ | B.①③④ | C.①②③ | D.②③④ |
您最近一年使用:0次
2023-08-10更新
|
833次组卷
|
3卷引用:北京市育英学校(四年制高三)2021-2022学年高二下学期期中练习数学试题
名校
解题方法
8 . 已知椭圆
.过点
作圆
的切线
交椭圆
于
两点.将
表示为
的函数,则
的最大值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f0748ec234ec293d31b395d0549016e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f9c0002b13f6cae093cd9dc9f19941b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
2023-08-10更新
|
842次组卷
|
4卷引用:北京市育英学校(四年制高三)2021-2022学年高二下学期期中练习数学试题
北京市育英学校(四年制高三)2021-2022学年高二下学期期中练习数学试题北京市育英学校2023届高三6月统一练习(一) 数学试题江西省丰城拖船中学2024届高三上学期开学测试数学试题(已下线)考点18 解析几何中的范围、最值问题 2024届高考数学考点总动员
9 . 对任意正整数n,记集合
,
.
,
,若对任意
都有
,则记
.
(1)写出集合
和
;
(2)证明:对任意
,存在
,使得
;
(3)设集合
.求证:
中的元素个数是完全平方数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a39352d44787ecda055946f530893f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5359f5f086b89cc656cdd4f79a3b7baa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5df0913f90131b298c8f6f57437f69b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c1352dca7dc3caf67c1cb937d52795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d35755ad07f05e7bfe00176d6334389f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75a28908216e6879a09b372d957be1e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90df641ab645927ee577e79faf18dcdd.png)
(1)写出集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
(2)证明:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e840ba7606959ccea36793f3ef0775d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b576952835af1f3492f0f3e6d00093e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90df641ab645927ee577e79faf18dcdd.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/112d102cbe7ce2bebe0c76e87e89a00c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2023-11-15更新
|
158次组卷
|
4卷引用:北京市朝阳区2022届高三上学期期末统一检测数学试题
10 . 已知函数
,
.
(1)求
的单调区间;
(2)若存在
(
是常数,
)使不等式
成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c7ed99a74e126a05cb520f19c094020.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/464a313c64632e7740a1578812996761.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9b81feb84ce1523ae97d5bff2c4072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
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6卷引用:北京市平谷区北京实验学校2021-2022学年高二下学期期中数学试题
北京市平谷区北京实验学校2021-2022学年高二下学期期中数学试题北京实验学校2022-2023学年高二下学期期中数学试题(已下线)模块二 专题2 《导数》单元检测篇 A基础卷(人教A)(已下线)模块二 专题5 《导数及其应用》单元检测篇 A基础卷(北师大2019版)(已下线)模块二 专题4 《导数及其应用》单元检测篇 A基础卷(人教B)(已下线)第七章 专题一 单变量不等式能成立(有解)之参变分离法 微点2 单变量不等式能成立(有解)之参变分离法综合训练