1 . 如图,一个棱长为6的透明的正方体容器(记为正方体
)放置在水平面
的上方,点
恰在平面
内,点
到平面
的距离为2,若容器中装有水,静止时水面与表面
的交线与
的夹角为0,记水面到平面
的距离为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7253ffd3fc633d861810ee2e872188b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
A.平面![]() ![]() |
B.点![]() ![]() |
C.当![]() |
D.当![]() ![]() |
您最近一年使用:0次
2 . 设抛物线
的焦点为
,
是
上的一个动点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc7ad3432ac96b0a38beaa7f2edc3499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.点![]() ![]() ![]() |
B.点![]() ![]() ![]() |
C.以![]() ![]() |
D.记点![]() ![]() ![]() ![]() |
您最近一年使用:0次
解题方法
3 . 已知正实数
满足
(
是自然对数的底数,
),则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba412d4d07c2b6203b52ce006f1728ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e25da8298b6a96d627f3e8c990e55f0c.png)
A.![]() | B.![]() |
C.![]() ![]() | D.方程![]() |
您最近一年使用:0次
解题方法
4 . 在数列
的第
项与第
项之间插入
个1,称为变换
.数列
通过变换
所得数列记为
,数列
通过变换
所得数列记为
,以此类推,数列
通过变换
所得数列记为
(其中
).
(1)已知等比数列
的首项为1,项数为
,其前
项和为
,若
,求数列
的项数;
(2)若数列
的项数为3,
的项数记为
.
①当
时,试用
表示
;
②求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b00f4eb7f1bd2ccefbabf0c1dfa8f69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fd6f81b87ebc6a949329520a6e42ed8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fd6f81b87ebc6a949329520a6e42ed8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b536225194ade4db8e99df253041e034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/819f6ef3827f73ee7dea7883be3bdfdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3788785078f4cbc29eb4b3c202d1587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
(1)已知等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1752474698cd5466dd180df0a00ba9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e5577ef4b9b5764af5e21eef60ebca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fd6f81b87ebc6a949329520a6e42ed8.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3788785078f4cbc29eb4b3c202d1587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e9d41db805f5235ec4b69e436690222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147a33b715da5466c2d4f9b18cb925d7.png)
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解题方法
5 . 已知抛物线
,动直线
与抛物线
交于
,
两点,分别过点
、点
作抛物线
的切线
和
,直线
与
轴交于点
,直线
与
轴交于点
,
和
相交于点
.当点
为
时,
的外接圆的面积是
.
(1)求抛物线
的方程;
(2)若直线
的方程是
,点
是抛物线
上在
,
两点之间的动点(异于点
,
),求
的取值范围;
(3)设
为抛物线
的焦点,证明:若
恒成立,则直线
过定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf92a1ba410263d4f68b7e0432b19aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.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/bf5f0df2579e567038baa206cb0b016f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed283a253b61df01f2a1cdc0cd8003f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20b3a91ccf6028608cd03df7072f6536.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/912bae66a2b7cc1caa4cd0333796ec41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59880e470359d8e9faf6ae5ce155cf2a.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32a07da1731feb22da90850241b3580f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
解题方法
6 . 已知圆
,直线
,直线
和圆交于A,B两点,过A,B分别做直线
的垂线,垂足为C,D.
(1)求实数b的取值范围;
(2)若
,求四边形ABDC的面积取最大值时,对应实数
的值;
(3)若直线AD和直线BC交于点
,问是否存在实数
,使得点
在一条平行于
轴的直线上?若存在,求出实数
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13b673b7961af5c4b51e67d6ffe00912.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa941aa5d428f5d78ec3f281464f826.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(1)求实数b的取值范围;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdbf6506e9de40da0f3c51b81b35a901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)若直线AD和直线BC交于点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
解题方法
7 . 对于有穷数列
,从数列
中选取第
项、第
项、
、第
项
,顺次排列构成数列
,其中
,则称新数列
为
的一个子列,称
各项之和为
的一个子列和.规定:数列
的任意一项都是
的子列.则数列
的所有子列和的和为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/8dcb1ddb73e4087f8cfcc40eead8b893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533484c347e86e6bb635006a94530dc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dcb1ddb73e4087f8cfcc40eead8b893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dcb1ddb73e4087f8cfcc40eead8b893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa301d4a86341fd749f1f8c72c970565.png)
您最近一年使用:0次
8 . 某高校统计的连续5天入校参观的人数(单位:千人)如下:
并计算得,
.
(1)求
关于
的回归直线方程,并预测第10天入校参观的人数;
(2)已知该校开放1号,2号门供参观者进出,参观者从这两处门进校的概率相同,且从进校处的门离校的概率为
,从另一处门离校的概率为
.假设甲、乙两名参观者进出该校互不影响,已知甲、乙两名参观者从1号门离校,求他们从不同门进校的概率.
附:回归直线方程
,其中
.
样本号 | 1 | 2 | 3 | 4 | 5 |
第 | 1 | 2 | 3 | 4 | 5 |
参观人数 | 2.4 | 2.7 | 4.1 | 6.4 | 7.9 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985f1673ddf7ed5872c91f01ba8eef01.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)已知该校开放1号,2号门供参观者进出,参观者从这两处门进校的概率相同,且从进校处的门离校的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
附:回归直线方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1db6103cb0f1d2bd6b19235d53ee7e98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446c21b8025405469a473aa0b32f9373.png)
您最近一年使用:0次
解题方法
9 . 截面惯性矩
是衡量截面抗弯能力的一个几何参数,若截面图形为矩形,则
,其中
为矩形的宽,
为矩形的高.某木器厂要加工如图所示的长方体实木梁,已知该实木梁的截面图形为矩形
,且矩形
外接圆的直径为
,要使该截面的惯性矩最大,则矩形
对应的高应为______
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910c6cc1a6e5f6f601f9336d5f08c7a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe9f7abf7bcf4e1aa2579cd191d7761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
您最近一年使用:0次
解题方法
10 . 已知
是函数
有四个零点,记
的导函数为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ccd22fd0ca1a8e1468329284f91b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51fb3ef65a6ee809219a3f9f78d127fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
A.![]() | B.![]() |
C.![]() ![]() ![]() | D.存在![]() ![]() |
您最近一年使用:0次