名校
1 . 已知圆
,直线
,圆上恰好有两个点到直线
的距离等于1.则符合条件的实数
可以为______ .(只需写出一个满足条件的实数即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5568579340b4a3daf3f01b6dbc4048a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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名校
解题方法
2 . 已知抛物线
经过点
.
(1)求抛物线
的方程及其准线方程.
(2)设
为原点,直线
与抛物线
交于
(异于
)两点,过点
垂直于
轴的直线交直线
于点
,点
满足
.证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/603c86edc503c6a2322b286857712cc8.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ebce8b2a915356ed39f36c5bad2ebe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5e8e97c7aeabe2a1cd51c7398299663.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eef1f7b9adab87736321e30949a4d668.png)
您最近一年使用:0次
解题方法
3 . 已知正项数列
中,
,
.
(1)求数列
的通项公式;
(2)记数列
的前n项和
,求满足
的正整数n的集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db3dc3b1598a966a7aa89edb84515311.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589dd2f0fdb61a1762096a548fdeaf87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/337173d6de0d2e7861f36e29d1e9eb26.png)
您最近一年使用:0次
4 . 已知
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb90f0294dfff41f05b0fc64d7a06e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b2a7344437a5dda811f0ec372a5dd2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5262656b3496f13c2dd370da1d863e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
5 . 设A,B是一个随机试验中的两个事件,若
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/992a45dcac87eeb949b409602a95917a.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a009718e6ca1bf47b34b4a30efaea90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/974a4095bdc1de269dc72dbe0fd26945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbd58e4cf38fd29911592dbb8dfb8782.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/992a45dcac87eeb949b409602a95917a.png)
您最近一年使用:0次
6 . 如图,在四棱锥
中,底面
是直角梯形,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/22/b140676d-2c69-4654-975e-b44d2af3198f.png?resizew=154)
(1)证明:
平面
;
(2)已知
,
,
,平面
底面
,若平面
与平面
的夹角的余弦值为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e839ac941e8bf536ff35a12e56c7a400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b2768d41c12b2a8f4d1b92f50d0b96.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/22/b140676d-2c69-4654-975e-b44d2af3198f.png?resizew=154)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b6053e396df2cd152e1329fce766d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25c7ffb5540e9527451e19e477aafd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feedf3c1dee6e7befebf368c092ccd0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca48c18021e7be4bbb3e95576e1c1b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/293619c2a022f5b08f607e2f5382acf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
名校
解题方法
7 . 已知椭圆
的左右焦点为分别
为椭圆
上一点,
,则
的面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279cefeb5c389a37a71e5fd3925f5954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e046e71a5b0ac6226af6bfcbe6d621c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a238a6239b4cfca485c703523299cad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
A.![]() | B.1 | C.3 | D.![]() |
您最近一年使用:0次
名校
解题方法
8 . 已知双曲线
的左右顶点分别为
,点
均在
上,且关于
轴对称.若直线
的斜率之积为
,则该双曲线的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6bd86df0db8034b7f07eefca723ac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602baac86c2b1668ecdfadc8a5948885.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
9 . 如图,在棱长为1的正方体
中,E是线段
上的动点(不包括端点),过A,
,E三点的平面将正方体截为两个部分,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/22/2d1f51ce-9e14-4f83-945b-0f113765619b.png?resizew=161)
A.正方体的外接球的表面积是正方体内切球的表面积的3倍 |
B.存在一点E,使得点![]() ![]() |
C.正方体被平面![]() ![]() |
D.当正方体被平面![]() ![]() ![]() |
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解题方法
10 . 如图是两个底面半径都为1的圆锥底面重合在一起构成的几何体,上面圆锥的侧面积是下面圆锥侧面积的2倍,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e8b17a7840ae7b75590da92fa0965b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7330af1eaa4fbb442ebc7b47be6b6d7a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/22/3db79801-0877-4fd0-8e62-9837df87732b.png?resizew=103)
A.![]() | B.![]() | C.![]() | D.3 |
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