名校
解题方法
1 . 如图,在坡面
与水平面
所成二面角为
的山坡上,有段直线型道路
与坡脚
成
的角,这段路直通山顶
,已知此山高
米,若小李从
沿着这条路上山,并且行进速度为每分钟30米,那么小李到达山顶
需要的时间是_____ 分钟.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55669bf3ec98170c9cdda6d3df746e09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/4/b5015490-89ee-4cd7-b5b8-0c6ffbcc68f4.png?resizew=181)
您最近一年使用:0次
2023-02-03更新
|
561次组卷
|
5卷引用:上海外国语大学附属外国语学校2021-2022学年高二上学期期中数学试题
名校
解题方法
2 . 我们用
表示某个关于
的代数式,现在有如下两个关于
的真命题:
①对任意的实数
、
,都有
;
②对任意的实数
、
,都有
成立;
其中
是大于
的常数.设实数
、
、
满足条件
且
.
(1)证明:
;
(2)证明:
;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
①对任意的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffb13c8f221c87d9e6eae949405d835d.png)
②对任意的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c2f1ca03ade14de6711c85de8fc5df0.png)
其中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.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/a17884a2d114eee89f3def58398d2e48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ceb39aa5c2421cb43735afeed2f216c.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8c6d2d0d52b0ff7e63d3cfe089786e4.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83e1f02fad18a316c0514520db1d774a.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eea2a01f7c009f7bb2e82086a906640.png)
您最近一年使用:0次
3 . 函数
的定义域为D,若
存在反函数,且
的反函数就是它本身,则称
为自反函数.有下列四个命题:
①函数
是自反函数;
②若
为自反函数,则对任意的
,成立
;
③若函数
为自反函数,则
的最大值为1;
④若
是定义在R上的自反函数,则方程
有解.
其中正确命题的序号为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91ac94163e32419d17a6f0fbf5d32141.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/801d492de7ae12be2bf576f25c4f1ceb.png)
③若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23acfba90781084f10fa1999a750e651.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13502d46b8563c54c09b29b20b3006a4.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
其中正确命题的序号为( )
A.①②③ | B.①②④ | C.②③④ | D.①②③④ |
您最近一年使用:0次
名校
解题方法
4 . 设集合A、B、C、D是全集X的子集,
,
,则下列选项中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96f1ba0a1129741502600e47bf058c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/959f3c514abb15185a429e1b2f1674e5.png)
A.如果![]() ![]() ![]() |
B.如果![]() ![]() ![]() |
C.如果![]() ![]() ![]() |
D.上述各项都不正确 |
您最近一年使用:0次
2021-11-10更新
|
215次组卷
|
3卷引用:上海市复兴高级中学2021-2022学年高一上学期期中数学试题
5 . 我们知道,在平面几何中,已知
三边边长分别为
,面积为
,在
内一点到三条边的距离相等设为
,则有
.现有三棱锥
的两条棱
,其余各棱长均为5,三棱锥
内有一点
到四个面的距离相等,则此距离等于___________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f5573b30734d65648f61c0a94c98de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e57d327b4a4c779ba700bb979468966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8893e696893ba57318c8c0225b80db1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
您最近一年使用:0次
名校
6 . 已知实数
满足
,集合
,则A的长度的取值范围是__________ .(集合
的长度定义为
,其中
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce613eaa5df46a50174085ef5d1087fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e56f4504e0f80fd031c8b5f41832e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a39a7ed1db9ac0272e640ae31b46eeec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43cd905027227a9d6a60421f763d16e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe04409b13fe225707665309adb4cdde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a3a501856caf1b50008f196a31c7213.png)
您最近一年使用:0次
名校
7 . 2021年10月13日第18号台风“圆规”在海南某地登陆,最大风力达到12级.路边一棵参天大树在树干某点B处被台风折断且形成120°角,树尖C着地处与树根A相距10米,树根与树尖着地处恰好在路的两侧,设
(A,B,C三点所在平面与地面垂直,树干粗度忽略不计)
![](https://img.xkw.com/dksih/QBM/2021/11/2/2842828345049088/2845467378778112/STEM/86b9288b228c43e1b2e15b2b6a95baac.png?resizew=346)
(1)若
,求折断前树的高度(结果保留一位小数)
(2)问一辆宽2米,高2.5米的救援车能否从此处通过?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30e586a8505faad251cc182676e0390.png)
![](https://img.xkw.com/dksih/QBM/2021/11/2/2842828345049088/2845467378778112/STEM/86b9288b228c43e1b2e15b2b6a95baac.png?resizew=346)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c42206793edde00d2d43cd07adf78366.png)
(2)问一辆宽2米,高2.5米的救援车能否从此处通过?并说明理由.
您最近一年使用:0次
2021-11-06更新
|
492次组卷
|
4卷引用:上海市复兴高级中学2022届高三上学期期中数学试题
名校
8 . 将一段长12
的铁丝折成两两互相垂直的三段,使三段长分别为3
、4
、5
,则原铁丝的两个端点之间的距离为___________
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
您最近一年使用:0次
2021-10-21更新
|
514次组卷
|
6卷引用:上海市复兴高级中学2021-2022学年高二上学期10月质量检测数学试题
上海市复兴高级中学2021-2022学年高二上学期10月质量检测数学试题上海市复兴高级中学2021-2022学年高二上学期期中数学试题(已下线)第09讲 空间几何体的结构与直观图(核心考点讲与练)(1)上海市川沙中学2022-2023学年高二上学期期中数学试题上海市嘉定区第一中学2023-2024学年高二上学期12月月考数学试题(已下线)上海市高二上学期【第一次月考卷】(测试范围:第10章-第11章)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)
9 . 在平面直角坐标系
中,抛物线
,点
,
,
为
上的两点,
在第一象限,满足
.
(1)求证:直线
过定点,并求定点坐标;
(2)设
为
上的动点,求
的取值范围;
(3)记△
的面积为
,△
的面积为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1354240a807d0da2b51a19e055140165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37df9dad3961893b22d6639c4311e267.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/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46cd485957ac7c628785ca04a60e1aaf.png)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e368d77f94bb058d2480f122f44ea366.png)
(3)记△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa3a310c1f8a5af35dc3328d874e18e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c21cbb1c2bcbcb8391ac5a879f2ae0.png)
您最近一年使用:0次
2021-10-08更新
|
995次组卷
|
7卷引用:上海外国语大学附属外国语学校2022届高三上学期期中数学试题
上海外国语大学附属外国语学校2022届高三上学期期中数学试题上海市控江中学2022届高三上学期开学考数学试题上海市杨浦区控江中学2022届高三上学期第一次月考(9月)数学试题上海市控江中学2021届高三上学期12月月考数学试题(已下线)专题9.7 圆锥曲线综合问题 2022年高考数学一轮复习讲练测(新教材新高考)(讲)(已下线)9.6 三定问题及最值(精练)-【一隅三反】2022年高考数学一轮复习(新高考地区专用)(已下线)模块12 圆锥曲线-2022年高考数学一轮复习小题多维练(上海专用)
10 . 在△
中,三内角
、
、
的对边分别为
、
、
,满足
.
(1)证明:△
为直角三角形;
(2)当
,
时,设
表示成
的形式,并写出定义域;
(3)对(2)中函数
,当
为何值时,
有最值?并求出最值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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/c5db41a1f31d6baee7c69990811edb9f.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99cd2d7526d3b67d3e4c51a14fc7182c.png)
(1)证明:△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104e4c6253dac1d2ceb5376aa060433a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2df011456dcd279d5228c6707facb24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(3)对(2)中函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
您最近一年使用:0次
2021-07-24更新
|
317次组卷
|
2卷引用:上海市复兴高级中学2020-2021学年高一下学期期中数学试题