1 . 已知数列
中,
,
.正项等比数列
的公比
,且满足
,
.
(1)证明数列
为等差数列,并求数列
和
的通项公式;
(2)如果
,求
的前n项和为
;
(3)若存在
,使
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ac9d17bc8f166fc3894bf865ad6a53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d21cfd1ad0f4254be1d88c6577b6bbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e90d19bcd582ed71cde0f18027174459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e3824ddd2210bd1e6313ad11dc8b13.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/102abb18c888eb23d40708b97de140ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c39de50ed2f805d9c28aa7aadc46fe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066141ba294715e4e725d59acfb85caa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
2 . 如图,在△ABC中,AC⊥BC.延长BA到D,使得AD=2,且
.
,求△DBC的面积;
(2)当
时,求△ACD面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ac807d79b5a31acc6cd92514b19f3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71807a35b3170fce28ee6edf4c00d083.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83e8e9455a0b4175572a579497bd2925.png)
您最近一年使用:0次
2022-05-26更新
|
1082次组卷
|
4卷引用:四川省成都市树德中学2021-2022学年高一下学期5月阶段性测试数学试题
名校
3 . 已知函数
(其中
),且
相邻两对称轴之间的距离为
.
(1)求函数
在
上的值域;
(2)若角
,
,且
,
.求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/682ea0497d6c7f5006b8475d98daf8e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ad72d7565699d1ebb741eb0ce12bac.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fee19fef930b81f2605c4642b6211c.png)
(2)若角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8789ef11df1d17d7ea0ef6787b047094.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6617bc55beab081645eddf9a9976da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/322850dc7abad4130474c14afcd9574f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f8c2bc7747cac3f94cac7d24c89985b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7404111c48efd06a127f5b2e77f5989.png)
您最近一年使用:0次
名校
解题方法
4 . 已知数列
的前n项和为
,且满足
,
.
(1)求数列
的通项公式;
(2)若
,求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46cf5a3e7e2c314b5a48f2e974199cde.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d084bc8330546bc9387020e551e5593.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
5 . 如图,已知正四棱柱(底面为正方形的直四棱柱)内接于底面半径为1,高为2的圆锥.
![](https://img.xkw.com/dksih/QBM/2022/5/25/2986877512228864/2987585358577664/STEM/db1d6dc7-9dd3-45cd-bcc5-59b0ce36a012.png?resizew=265)
(1)求此圆锥的表面积;
(2)当正四棱柱的一个顶点B和圆锥的母线PE满足
时,求该正四棱柱的体积和表面积.
![](https://img.xkw.com/dksih/QBM/2022/5/25/2986877512228864/2987585358577664/STEM/db1d6dc7-9dd3-45cd-bcc5-59b0ce36a012.png?resizew=265)
(1)求此圆锥的表面积;
(2)当正四棱柱的一个顶点B和圆锥的母线PE满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d98a416fc94dee82e20fc1cfc9b01c80.png)
您最近一年使用:0次
名校
解题方法
6 . 已知平面直角坐标系中,点O为原点,
,
.
(1)若
,且
与
的夹角为45°,求
的值;
(2)设
为单位向量,且
,求
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fadc9a19de13ca7688ca93f0c70a8a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ea6b5f801158380a615c3f99f615e1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd18461fd9d77e6fa46a654f0ab540f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0124273936916d54882dfcc4ca698c95.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56eda4bb8604c18d0016a4377d05435a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/801376a7e55a6c65caa6860d7491e6cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56eda4bb8604c18d0016a4377d05435a.png)
您最近一年使用:0次
2022-05-26更新
|
508次组卷
|
3卷引用:四川省成都市树德中学2021-2022学年高一下学期5月阶段性测试数学试题
名校
7 . 山顶上有一座信号发射塔,塔高100米,山脚下有A,B,C三个观测点,它们两两之间的距离分别为AB=2千米,AC=3千米,BC=4千米,从这三个观测点望塔尖的仰角均为60°,则山高为______ 千米.
您最近一年使用:0次
名校
解题方法
8 . 已知正项数列
的前n项和为
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5eb9b8f893dd71876349ad40724550.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec1e07c5b19e513d4155be61cd7e6798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5eb9b8f893dd71876349ad40724550.png)
您最近一年使用:0次
名校
9 . 已知a,b,c分别是△ABC内角A,B,C所对的边.若b,c恰是方程
的两个根,且
,则a=______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fb2a637df1634242820241d425f6b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7cc0800b13f5a37a0d38ed8d66c1380.png)
您最近一年使用:0次
名校
10 . 不等式
的解集为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f600f10bf949231f74be8226b9bd6fbf.png)
您最近一年使用:0次
2022-05-26更新
|
405次组卷
|
2卷引用:四川省成都市树德中学2021-2022学年高一下学期5月阶段性测试数学试题