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1 . 双曲线
的渐近线方程为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dad0c75ce33673ec4c425896e8619e4.png)
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2 . 已知
是椭圆
的两个焦点,
为椭圆
上的一点,且
,若
的面积为9,则
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.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/9a2d54af835ed981959c1c6280815ece.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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3 . 在平面直角坐标系xOy中,已知双曲线C:
(
,
)的左、右焦点分别为
、
,
是双曲线C上一点,且
.
(1)求双曲线C的方程;
(2)过点P作直线l与双曲线C的两条渐近线分别交于R、S两点.若点P恰为线段RS的中点,求直线l的方程;
(3)设斜率为-2的直线l与双曲线C交于A、B两点,点B关于坐标原点的对称点为D.若直线PA、PD的斜率均存在且分别为
、
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd849d4c356a8d7d8263d78be15d1b88.png)
(1)求双曲线C的方程;
(2)过点P作直线l与双曲线C的两条渐近线分别交于R、S两点.若点P恰为线段RS的中点,求直线l的方程;
(3)设斜率为-2的直线l与双曲线C交于A、B两点,点B关于坐标原点的对称点为D.若直线PA、PD的斜率均存在且分别为
![](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/b4757181824e15e0f21e5bdd55448783.png)
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4 . 如图:双曲线
的左、右焦点分别为
,
,过
作直线
交
轴于点
.
平行于
的斜率大于
的渐近线
时,求直线
与
的距离;
(2)当直线
的斜率为
时,在
的右支上是否存在点
,满足
?若存在,求出
点的坐标;若不存在,说明理由;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a3d3fefe175906355dda6ce8a0c4bd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(2)当直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77d13740ec197a8b449614511edde9bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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5 . 已知具有线性相关关系的两个变量x、y之间的一组数据如下:
若回归方程为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
________ .
x | 0 | 1 | 2 | 3 | 4 |
y | 1 | ![]() | 2a | 5 | 7 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fef9f74aa2aee778fbc5c3c2f7070cc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
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6 . 已知椭圆
:
(
)的左、右焦点分别为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
,点P是
上一点,直线l:
(
).
(1)当
时,已知直线l恰经过
的右顶点A,求m的值;
(2)当
时,若P同时是l上一点且
,求a的值;
(3)设直线
交l于点Q,对每一个给定的
,任意满足
的实数a,都有
成立.则当m变化时,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78f9b6b54e434819f50ae1349f534abd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b7fcfde0f8949461eb9ea7af43ede8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff99ce2491f3b979cbbfbc5e9f8d9b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d670dcd0ce51abe372bc51a88ba1a7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af039cad52ca4e1f1e322277bc81afd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94a71a658362bd9faa329c3d9f6e6d2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377923225cb490323c85e4e5a12643e5.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d670dcd0ce51abe372bc51a88ba1a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697cf7097b0133b2598b697fa8470d9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ee83676fa76e3f845ab3d47ad678a8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b213e4e1164ff957df10996756912a7c.png)
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7 . 设
,
,
是互不重合的平面,
,
是互不重合的直线,给出四个命题:
①若
,
,则
②若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a93a52c2b943e4c70ace99ed802d2b5.png)
③若
,
,则
④若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4042f9c51f83e3367d496e851735d7f9.png)
其中正确命题的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4042f9c51f83e3367d496e851735d7f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79018590293277ff2d76452a50ad2dbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a93a52c2b943e4c70ace99ed802d2b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/008241f4c7f47526109c74c92ed21fdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88182084a712c7f0a34540b16b95c477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a93a52c2b943e4c70ace99ed802d2b5.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4042f9c51f83e3367d496e851735d7f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b59b1a01a6da42ff2a41e5b91ea301ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84b6e422b2e6f6dada4d8c369559a077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a93a52c2b943e4c70ace99ed802d2b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79018590293277ff2d76452a50ad2dbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4042f9c51f83e3367d496e851735d7f9.png)
其中正确命题的个数是( )
A.1 | B.2 | C.3 | D.4 |
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7卷引用:上海市晋元高级中学2023-2024学年高二上学期10月月考数学试题
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8 . 将三颗骰子各掷一次,记事件
“三个点数都不同”,
“至少出现一个6点”,则条件概率
等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f9fabbbe61a759e52ec975215e2e7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af61ac71ade09d3b07b7232065163346.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3卷引用:上海市金山中学2023-2024学年高二下学期5月月考数学试卷
上海市金山中学2023-2024学年高二下学期5月月考数学试卷广东省中山市中山纪念中学2023-2024学年高二下学期第二次月考数学试卷(已下线)专题04 高二下期末考前必刷卷02(提高卷)--高二期末考点大串讲(人教A版2019)
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9 . 从0,1,2,3这四个数字中,不放回地取两次,每次取一个.构成数对
,x为第一次取到的数字,y为第二次取到的数字.设事件
“第一次取出的数字是1”,
“第二次取出的数字是2”.
(1)写出此试验的样本空间及
的值;
(2)判断A与B是否为互斥事件,并求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17e2710e526ff3e34fc84b6867e60020.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f9fabbbe61a759e52ec975215e2e7c.png)
(1)写出此试验的样本空间及
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c11072e934cca77ef81a656af395c82.png)
(2)判断A与B是否为互斥事件,并求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e37f32bef5568fcdef4b368232b1b1.png)
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10 . 下列统计量中,不能 度量某样本离散程度的是( )
A.方差 | B.极差 | C.中位数 | D.标准差 |
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