解题方法
1 . 在滨海文化中心有天津滨海科技馆,其建筑有鲜明的后工业风格,如图所示,截取其中一部分抽象出长方体和圆台组合,如图所示,长方体
中,
,圆台下底圆心
为
的中点,直径为2,圆与直线
交于
,圆台上底的圆心
在
上,直径为1.
![](https://img.xkw.com/dksih/QBM/2021/4/23/2705880246927360/2730846585544704/STEM/45b2fb4d77584581b5ffa7988d973437.png?resizew=234)
![](https://img.xkw.com/dksih/QBM/2021/4/23/2705880246927360/2730846585544704/STEM/5d45fccb0ba7472eb5b9f5ed084f1e3a.png?resizew=205)
(1)求
与平面
所成角的正弦值;
(2)求二面角
的余弦值;
(3)圆台上底圆周上是否存在一点
使得
,若存在,求点
到直线
的距离,若不存在则说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2089110ce065e01dc57e38edb840dceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/2021/4/23/2705880246927360/2730846585544704/STEM/45b2fb4d77584581b5ffa7988d973437.png?resizew=234)
![](https://img.xkw.com/dksih/QBM/2021/4/23/2705880246927360/2730846585544704/STEM/5d45fccb0ba7472eb5b9f5ed084f1e3a.png?resizew=205)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c9f260496ba23993238601a89eca5c.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae190120755c4dd7070df21dd0a90a01.png)
(3)圆台上底圆周上是否存在一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b72acd3da8b22454e5d461379f5bde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
您最近一年使用:0次
解题方法
2 . 已知中心在原点,焦点为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
的椭圆经过点
.
(1)求椭圆方程;
(2)若M是椭圆上任意一点,
交椭圆于点A,
交椭圆于点B,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e09872be2fce54e922259bde2c540bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa2e31608e60e3fd40c040cfe9d6e8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ca4733400ec78f1378dd337630babd0.png)
(1)求椭圆方程;
(2)若M是椭圆上任意一点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b67528f875a6d4bac8bbf784f7b66a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/183b6a0cef4256c9696a5bca31053da5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3248e218eef5885d063dd2866b59c6b.png)
您最近一年使用:0次
2021-05-24更新
|
1284次组卷
|
4卷引用:天津市河东区2021-2022学年高二上学期期末数学试题
天津市河东区2021-2022学年高二上学期期末数学试题四川省天府名校2021届高三5月诊断性考试文科数学试题四川省天府名校2021届高三5月诊断性考试理科数学试题(已下线)2022年高考考前20天终极冲刺攻略(四)【理科数学】(6月4日)
3 . 已知
是各项都为整数的等比数列,
是等差数列,
,
,
.
(Ⅰ)求
和
的通项公式;
(Ⅱ)设
表示数列
的前
项乘积,即
,
.
(ⅰ)求
;
(ⅱ)若数列
的前
项和为
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebaf2a2590bb84d646957f913d78f6dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b575b74af96b739ba6d8fa8088d8cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/769fe52ac96348d3b12d23d06d702595.png)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d643a5fb1c6254e1ee355872d2afc7e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f81c7dbe91ed0a67c9b98a84fb384c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d643a5fb1c6254e1ee355872d2afc7e7.png)
(ⅱ)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19a33f48bf5f6b79b601f69552c892cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de23c44e267c2bc99efc56bec3a8dac.png)
您最近一年使用:0次
4 . 已知函数
,
(
为自然对数的底数),
.
(Ⅰ)若
,求函数
的单调区间;
(Ⅱ)若
恒成立,求实数
的值;
(Ⅲ)若直线
是曲线
的一条切线.求证:对任意实数
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad406e22502cf97b27d51bb87258622c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ec6ad1c734902409ff399e95525388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa662f0273f0921c1fa4727f632395.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be812216ebb70fdf53eb519d22a6690.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a36ede780090698d1dcb4b136a90193.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(Ⅲ)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad406e22502cf97b27d51bb87258622c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35f63d0559956db2f2519dd0b23112b4.png)
您最近一年使用:0次
2021-05-12更新
|
887次组卷
|
2卷引用:天津市南开区2021届高三下学期二模数学试题
名校
解题方法
5 . 已知等差数列
中,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8c0cf480490ee96ecddc74ef0c182d9.png)
(1)求数列
的通项公式;
(2)若将数列
的项重新组合,得到新数列
,具体方法如下:
,
,
,
,
,依此类推,第
项
由相应的
中
项的和组成.
(i)求数列
的通项公式;
(ii)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f419b37a8000307c448986e294591c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2798e1dcab1f7f0fe3b8a94b3cd6a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0ba3ab5da2ce99f0b7380c13157a48b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8c0cf480490ee96ecddc74ef0c182d9.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若将数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aaee408bdec05bbdfcd4b841a331e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4835113e51ced39acb5dc41fcb8eabcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28dffc06e1434756b05ca5dbfe12e867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1252958abd7a62018a7e4de438078029.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f1ad18371ec533aeac27cf1fad95c1.png)
(i)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(ii)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e2b696888834b0fee59a9d466ead46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
名校
解题方法
6 . 南开园自然环境清幽,栖居着多种鸟类,热爱动物的南鸢同学独爱其中形貌雅致的蓝膀香鹊,于是她计划与生物兴趣小组的同学一起在翔字楼前广场一角架设一台可转动镜头的相机,希望可以捕捉到这种可爱鸟儿的飘逸瞬间,南同学设计了以下草图,为简化模型,假设广场形状为正方形,边长为1,已知相机架设于A点处,其可捕捉到图象的角度为
,即
,其中
分别在边
上,记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db5e90d59e2f4f4663c2ed16d3a184f.png)
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/6d5ed283-11f3-488b-a2a5-735f2a1ef8f7.png?resizew=173)
(1)南鸢同学的数学老师很欣赏她的计划,并根据她的设计草图编制了此刻你正在思考的这道期中考试试题,设
与
相交于点
,当
时,请你求出:
(i)线段
的长为多少?
(ii)线段
的长为多少?
(2)为节省能源,南鸢同学计划在广场上人员较多的时段关闭相机镜头的自动转动功能,为使相机能够捕捉到的面积(即四边形
的面积,记为
)最大,
应取何值?
的最大值为多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f443e2bf7702ccde21e5a25accf45a07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/481e426224c3a3ce9bb5a731eed81c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db5e90d59e2f4f4663c2ed16d3a184f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2eabc72e24e6bb3beb4fbb815288c6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/6d5ed283-11f3-488b-a2a5-735f2a1ef8f7.png?resizew=173)
(1)南鸢同学的数学老师很欣赏她的计划,并根据她的设计草图编制了此刻你正在思考的这道期中考试试题,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74dc2063147bb66cc18c7cab905bb662.png)
(i)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3525ddc5153fada64eaf14e50b536542.png)
(ii)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6da2235c42867f9a79007c3fc83fec9.png)
(2)为节省能源,南鸢同学计划在广场上人员较多的时段关闭相机镜头的自动转动功能,为使相机能够捕捉到的面积(即四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7d81d09859b280b424855dec3c5ad99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
名校
7 . 如图,已知正方形
的边长为2,点
为正方形内一点.
![](https://img.xkw.com/dksih/QBM/2021/4/29/2710296903680000/2715216039837696/STEM/3bae4e5e8d8d4b4986a0d08c848ec8f9.png?resizew=296)
(1)如图1
(i)求
的值;
(ii)求
的值;
(2)如图2,若点
满足
.点
是线段
的中点,点
是平面上动点,且满足
,其中
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/2021/4/29/2710296903680000/2715216039837696/STEM/3bae4e5e8d8d4b4986a0d08c848ec8f9.png?resizew=296)
(1)如图1
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b397a5aac82cc59f9d189801923b0d2.png)
(ii)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c5b8c2f382a4e11f8bc17c3c425fbe7.png)
(2)如图2,若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7733d699577409c0ea047ae271a8eaa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beca16d2f8a6a1b16e78f4678e08c2c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e87088da41685cc8d433fbbe0e18d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f78d33e95e9a27695947a489ae3bf1.png)
您最近一年使用:0次
2021-05-06更新
|
1327次组卷
|
5卷引用:天津市南开中学2020-2021学年高一下学期期中数学试题
名校
解题方法
8 . 已知函数
.
(1)
,求函数
的最大值;
(2)若
恒成立,求
的取值集合;
(3)令
,过点
作曲线
的两条切线,若两切点横坐标互为倒数,求证点
一定在第一象限内.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c013a7b9d9eba700eb2c7dca0e9e2b2.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4e6eed28e95d743071cf09483bc573c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e89249f9a184300e0e278b194cf51a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4133958c09fdd82cda8838c9cf46ccda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2021-05-06更新
|
1226次组卷
|
4卷引用:天津市武清区杨村第一中学2021届高三下学期高考热身训练(二)数学试题