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1 . 已知
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f094503733211ca30c7f50c872b01f87.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-06-05更新
|
485次组卷
|
2卷引用:黑龙江省大庆市实验中学实验二部2023-2024学年高三下学期阶段考试数学试题
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2 . 在平面内有三个互不相交的圆,三个圆的半径互不相等.三个圆的方程分别为
.其中圆
与圆
的两条外公切线相交于点
,圆
与圆
的两条外公切线相交于点
,圆
与圆
的两条外公切线相交于点
,
表示直线AB的斜率,
表示直线AC的斜率,
表示直线BC的斜率.下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/298d4f4782916ab6c13f27ac0d024054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
A.存在![]() ![]() |
B.对任意![]() ![]() |
C.存在点![]() |
D.直线![]() ![]() ![]() |
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3 . 若实数a,b分别是方程
的根,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0db7eb0183e807d8aae676dbd17bd508.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cff5ac0f3425f69ed7bafaf2f03dacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0db7eb0183e807d8aae676dbd17bd508.png)
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4 . 设点
是抛物线外一点,过点
向拋物线
引两条切线TM,TN,切点分别为M,N,焦点
,
(1)若点
的坐标为
,证明:以TM为直径的圆过焦点;
(2)若点
的坐标为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc30165c18de623d0a3efb961e606d1c.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e91676c7adfd65a76f56a0c1d4bbe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af0b2d49e1c706a9d29c4baef99aafa.png)
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解题方法
5 . (1)若
,
,求
的取值范围;
(2)证明:
;
(3)估计
的值(保留小数点后3位).
已知
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fad1dd76d5b72f10f5bb62693a2996f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c37e166515544d73dfcf03cdc084d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d3a73ba5ea3b9218649d350387a3f83.png)
(3)估计
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e24d42f61784c642e9eb1316afdd2ad.png)
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/695450724faafa68f7acabe8a3b504b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d230beb82a9f553b1e3e7cc7cd15d7f1.png)
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6 . 已知曲线
与曲线
恰有三个不同的公共点,则实数
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f02a99d78183de60029207af06a1e16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c07f6be6ad68e5c0a037be11d325bfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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7 . 设无穷等差数列
的公差为
,集合
.则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd0293f84a777e84c6438a4bcbeace75.png)
A.当且仅当![]() ![]() |
B.当![]() ![]() |
C.当![]() ![]() |
D.当![]() ![]() ![]() ![]() |
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8 . 下列命题中,正确的有( )
A.![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.已知![]() ![]() |
D.![]() |
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9 . 如图,正方形ABCD的边长为1,P,Q分别为边BC,CD上的点,且
;
的大小;
(2)求
面积的最小值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3e40a98f31996bc2ebae1cacdf3ade.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff7023ec0f513c7d0ef86859a5ede54.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
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解题方法
10 . 已知
,在平面直角坐标系
中有一个点阵,点阵中所有点的集合为
,从集全
中任取两个不同的点,用随机变量
表示它们之间的距离.
(1)当
时,求
的分布列及期望.
(2)对给定的正整数
.
(ⅰ)求随机变量
的所有可能取值的个数(用含有
的式子表示);
(ⅱ)求概率
(用含有
的式子表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de4106b72d9ff4c841746cbe6c15dfa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38190853164dc9267330efc108b83344.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaa1906383f7fb6132f07851fa62e764.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)对给定的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c6de3eb14038fda245ab1485463c8b.png)
(ⅰ)求随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(ⅱ)求概率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc616348e4213468155c5764585cfc77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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