解题方法
1 . 已知正方形
的边长为1,点
满足
.当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a171eb7987227fe033ceeb99a79321.png)
______ ;当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
______ 时,
取得最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4c58e3d93a5473d2d24dfcac856cc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1c3ea872a20fdc1843cb5ffce8a554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a171eb7987227fe033ceeb99a79321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233ba22f7ffcf96d6efe556e4c7a8edb.png)
您最近一年使用:0次
名校
2 . 已知
中,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42acd3ee01d9f843a8579ffb0b7d9d82.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69d2eec3b3ef5a2a660315db9f0feb99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42acd3ee01d9f843a8579ffb0b7d9d82.png)
您最近一年使用:0次
2024-05-29更新
|
831次组卷
|
2卷引用:北京市昌平区2024届高三第二次统一练习数学试题
3 . 已知函数
.
(1)求曲线
在点
处的切线方程;
(2)求
在区间
上的最小值;
(3)若
,当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a436bc4e31df34790a31a6de459d969.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17767bfaae48acebff5a10994d3165aa.png)
您最近一年使用:0次
4 . 已知集合
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b64582baa65eb04aa32e1efbbd0e9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b9b470218359a4a47be9244980489e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
5 . 已知数列
满足
,则数列
的前4项和等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd22079405139ae2798f7f73c939b373.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.16 | B.24 | C.30 | D.62 |
您最近一年使用:0次
6 . 在
的展开式中,常数项为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e79182f650c9b077e1d5c9162faeee.png)
A.![]() | B.15 | C.30 | D.360 |
您最近一年使用:0次
7 . 已知抛物线
的焦点和双曲线
的右顶点重合,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c477e5ade921ffa8377c4719319380ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
A.1 | B.2 | C.4 | D.6 |
您最近一年使用:0次
解题方法
8 . 如图,在棱长均为2的四棱柱
中,点
是
的中点,
交平面
于点
.
为线段
的中点;
(2)再从条件①、条件②、条件③这三个条件中选择两个作为已知,使得四棱柱
存在且唯一确定.
(i)求二面角
的余弦值;
(ii)求点
到平面
的距离.
条件①:
平面
;
条件②:四边形
是正方形;
条件③:平面
平面
.
注:如果选择的条件不符合要求,则第2问得0分;如果选择多组符合要求的条件分别解答,按第一个解答计分.
![](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/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)再从条件①、条件②、条件③这三个条件中选择两个作为已知,使得四棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
(i)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11a150b9250addf8b5dbbf8a89c61c5d.png)
(ii)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e11d3af986880db2910a92e26e0b5b.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ddbb0422a136f45653c8c369f2d75fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
条件②:四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
条件③:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a45953045e613b97eeee15ac188ae2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c52091eb745de866044477641a7c55f.png)
注:如果选择的条件不符合要求,则第2问得0分;如果选择多组符合要求的条件分别解答,按第一个解答计分.
您最近一年使用:0次
9 . 已知
为有穷正整数数列,
,且
.从
中选取第
项,第
项,
,第
项
,称数列
,
为
的长度为
的子列.规定:数列
的任意一项都是
的长度为1的子列.若对于任意的正整数
,数列
存在长度为
的子列
,使得
,则称数列
为全覆盖数列.
(1)判断数列
和数列
是否为全覆盖数列;
(2)在数列
中,若
,求证:当
时,
;
(3)若数列
满足:
,且当
时,
,求证:数列
为全覆盖数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6089fe00ae7015041da535c55ea04a25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6ea59f1c1a0d85dd6bec266e5270cc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27a0ab9b965cac0ac2bbee007b5343d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5f59bc23cf55f56312c9ed9806371f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6af9e7b1c23db5584ad8521d4444d5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/608d034715f9b1dfb306f9c89d383582.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e636879245230dd00a3ab3cbcfbfd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55b78937e77b8af5fb0fc2289aa3281f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c29c5650949891380e29f64fa64b46f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbe39a14cd55b5db170bd070b808ec63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7059e1f61ea8ec9ec3964af3ea588759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3750937ff180de90d13726ca22cc456b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60e7ec4f442ae834ca2ed9d168d7d9e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30a2a8194c260def0080f507775fc628.png)
(2)在数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47e2d4b414b02d127b831c48bb6edb0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5059e492214c793847f8a11dffff0b9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfb6929aee480560b6e53acb2e69ba8.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5059e492214c793847f8a11dffff0b9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fde80fb262f5dcb2dd5e7fcfd96d7c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
10 . 若圆
与
轴,
轴均有公共点,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9400822f1bd2f368d9f192c7575c3fa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次