1 . 已知直线
:
,圆
:
.
(1)若
,求直线
被圆
截得的弦长;
(2)当直线
被圆
截得的弦长最短时,求
的值及
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/695a98262ce07847698bbf60e05d434d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41ee745282e1b47f06074eac4bfa70a5.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当直线
![](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/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fcd3cea5f5e2fe943490dcb65d74c73.png)
的图象过点
,
,其部分图象如图所示,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fcd3cea5f5e2fe943490dcb65d74c73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c507dffee9a240f64cbded2cd2af0d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7fa0f62c12868d79cfa3c9b6353a0cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f742c4307718daaba81ccecb6eabacc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/31/eec2cccd-2be6-4efb-8b8b-96761fb8022a.png?resizew=150)
A.![]() |
B.![]() ![]() |
C.![]() ![]() |
D.将![]() ![]() |
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解题方法
3 . 函数
的所有零点之和为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e4ba9fe86a8dc7cc2084b12a14ce87.png)
A.-2 | B.-1 | C.1 | D.2 |
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4 . 若双曲线的同一支上存在两点A,B,使得
(O为原点)为等边三角形,则称双曲线为“优美双曲线”,已知双曲线C是“优美双曲线”,则C的离心率的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
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解题方法
5 . 如图,在四棱锥
中,底面ABCD为平行四边形,
为等边三角形,
,
,
,点E满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/79724376-1af7-4662-87f1-a44e656b276a.png?resizew=162)
(1)证明:平面
平面ABCD;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbfcae2cecc98e2d6c16dde6d3ec1c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d58da37b3d1dbd2fee75089d5ba28134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafa8c14100a4f847b41b9148954116c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f44bec66934dd2d35ffbf7d863892ed.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/79724376-1af7-4662-87f1-a44e656b276a.png?resizew=162)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
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6 . 在二项式
的展开式中,若常数项恰是所有奇数项的二项式系数之和的5倍,则实数a的值为______ .(用数字作答)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f0be4e40f301a018f03bd9236af1b7d.png)
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7 . (1)求值:
;
(2)已知
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b919c472836bad3e2de76650bce0fc.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ebe6a6476bc99d568e2844d32fee8d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/710095f0dc5bab494846fdda9db2dfb1.png)
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解题方法
8 . 已知数列
是递增的等差数列,
,若
,
,
成等比数列.
(1)求数列
的通项公式;
(2)求数列
的前
项和为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba57c83d526ac308d1461e80fcca9f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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9 . 圆
:
和圆
:
的位置关系是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8464bb7caf9d2badd4bd2dc3b4f9cebf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c5e1ef7e9acd22710f81ea859070f8.png)
A.外离 | B.相交 | C.外切 | D.内含 |
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解题方法
10 . 已知函数
(
)在区间
有且仅有2个零点,则
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df43b374df3326a3a6ccac1b73be288c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b04cfb1e8aced35dff721cdcf0b7386.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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