名校
1 . 已知
分别为双曲线
的左焦点和右焦点,过
的直线l与双曲线的右支交于A,B两点(其中A在第一象限),
的内切圆半径为
,
的内切圆半径为
,若
,则直线l的斜率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2cfd997d3b66a3b8f7731b26f0ab0c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2858005b9ae89ae080d83dcc13cf8e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47444b5fbc4252516d54263062e47c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3e95410f3b4fcb0cba425b521d1f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f64d10dbae406a1a57080860e402b48.png)
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名校
2 . 某制药公司研制了一款针对某种病毒的新疫苗.该病毒一般通过病鼠与白鼠之间的接触传染,现有
只白鼠,每只白鼠在接触病鼠后被感染的概率为
,被感染的白鼠数用随机变量X表示,假设每只白鼠是否被感染之间相互独立
(1)若
,求数学期望
;
(2)接种疫苗后的白鼠被病鼠感染的概率为
,现有两个不同的研究团队理论研究发现概率
与参数
的取值有关.团队A提出函数模型为
,团队B提出函数模型为
.现将100只接种疫苗后的白鼠分成10组,每组10只,进行实验,随机变量
表示第
组被感染的白鼠数,将随机变量
的实验结果
绘制成频数分布图,如图所示.
”发生的概率表达式(用
表示,组合数不必计算);
(ⅱ)在统计学中,若参数
时使得概率
最大,称
是
的最大似然估计.根据这一原理和团队A,B提出的函数模型,判断哪个团队的函数模型可以求出
的最大似然估计,并求出最大似然估计.参考数据:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907e780479f1a9e1371b491538ace976.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b0919cf56a1b743189a019551b2d5a0.png)
(2)接种疫苗后的白鼠被病鼠感染的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1daba45353250e5d756cd483c681dbce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a2bc9afcbcb1fa2f356beb0fadecf8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d0178b72c60a4fa59a815c1d9fa995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd30ac5421bb71b65ec79d08c04ed686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd30ac5421bb71b65ec79d08c04ed686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa4355ff47d4d0206d9ab17d450c5a95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a52d31cef5bdd028641ae0ed4f3a2464.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(ⅱ)在统计学中,若参数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41ba7a71c56fe7355a2b3ad5bade55ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aedd1de682115fdc8b5107bf8f9dc60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07bf99e2f6d5c0c024c3e26a65a61b63.png)
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2024-02-23更新
|
1483次组卷
|
6卷引用:浙江省9+1高中联盟2022-2023学年高二下学期期中数学试题
3 . 设
是定义在
上的函数,若存在区间
和
,使得
在
上严格减,在
上严格增,则称
为“含谷函数”,
为“谷点”,
称为
的一个“含谷区间”.
(1)已知实数
,
是含谷函数,且
是它的一个含谷区间,求
的取值范围;
(2)设
,
.设函数
是含谷函数,
是它的一个含谷区间,并记
的最大值为
.若
,且
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1486d2ae6c7e7904ab47b909039ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adadc4c82ed03710cb917d552ac6e1c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd33dd2e1b404daf7c1cbbf147ab7f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)已知实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2739d1d7a587d0a327c5b75fcaba9d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7242b2ab643f9470da77e29d043b893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e0137d9ccd136186c2fe74a11e42376.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f86c67af4135ba55b227485de51d4ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13502d46b8563c54c09b29b20b3006a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b9c9a559b5ec35dd6bc7abf3f4c8d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c27aed40481d951cc4afd5c7c1a470d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94a112fefbaf48adf34edbf3243ee7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b9c9a559b5ec35dd6bc7abf3f4c8d6.png)
您最近一年使用:0次
4 . 已知双曲线
:
(
,
)过点
,且离心率为2,
,
为双曲线
的上、下焦点,双曲线
在点
处的切线
与圆
:
(
)交于A,B两点.
(1)求
的面积;
(2)点
为圆
上一动点,过
能作双曲线
的两条切线,设切点分别为
,
,记直线
和
的斜率分别为
,
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b26461529321c5e669bdf3c489c5d74.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/9fdf0b6fecd6a78bc83f42e11e60a004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/950500494c2dce2158932ed3716031e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77e4ee0d9eda21284d1c32cea08ef02d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ff8a5886e42095da57422c8777c10d.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b67528f875a6d4bac8bbf784f7b66a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d90a03b11a51bd7824aa4094526e5aec.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/b4757181824e15e0f21e5bdd55448783.png)
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5 . 人教A版选择性必修第一册在椭圆章节的最后《用信息技术探究点的轨迹:椭圆》中探究得出椭圆(
)上动点
到左焦点
的距离和动点
到直线
的距离之比是常数
.已知椭圆
:
,
为左焦点,直线
:
与
轴相交于点
,过
的直线与椭圆
相交于
,
两点(点
在
轴上方),分别过点
,
向
作垂线,垂足为
,
,则( )
A.![]() | B.![]() |
C.直线![]() ![]() | D.![]() |
您最近一年使用:0次
2023-11-26更新
|
987次组卷
|
3卷引用:浙江省9+1高中联盟2023-2024学年高三上学期期中考试数学试题
名校
解题方法
6 . 已知椭圆经过点
,焦距为
是椭圆
上不在坐标轴上的两点,且
关于坐标原点对称,设点
,直线
交椭圆于另一点
,直线
交椭圆于另一点
.
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)记直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67351fe10fcfc3f9072eec4c60bfaaa5.png)
您最近一年使用:0次
2023-11-19更新
|
467次组卷
|
2卷引用:浙江省七彩阳光新高考研究联盟2023-2024学年高二上学期11月期中联考数学试题
名校
7 . 已知函数
为常数).函数
定义如下:对每个给定的实数
.
(1)若
,求
在
上的最大值;
(2)若
且
,求函数
在区间
上的单调增区间的长度之和.(闭区间
的长度定义为
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095878335d1f0c342afc4a2a300edfe6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68f842876e8f512903598574fa62e86e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20e1c681b27df538bd4742f6cd8298ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7242b2ab643f9470da77e29d043b893.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575002003f89bc8309a2c7f206761794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa21416f901e005780f383fb029e86f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede949a2fe7bf9f1f98f5457d408b41d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
您最近一年使用:0次
2023-11-18更新
|
740次组卷
|
2卷引用:浙江省宁波市镇海中学2023-2024学年高一上学期11月期中考试数学试题
8 . 在平面直角坐标系
中,已知点
,点
满足
.记
的轨迹为
.
(1)求
的方程;
(2)已知直线
,若点
关于直线
的对称点
(与
不重合)在
上,求实数
的值;
(3)设直线
的斜率为
,且与
有两个不同的交点
,设
,直线
与
的另一个交点为
,直线
与
的另一个交点为
,若点
和点
三点共线,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c0c5a67238a7e2564f3b31af17bfe71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9091d23af8d3d6db8c7ea66128152e12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d00a5df9d281dd4e1e45bf6a4d6fb27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8678fa21a720c7c5d3a9fc132310d5bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa259cd1057a92fda6f86d7a71d25c70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e98c4b3f3fe826e124ca7d199d4ca4b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/817a419430d9951cbdb89b657b21bcf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb7094907574192cfe56ced520da6c9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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9 . 已知
,点
为圆
上一动点,过点
作圆
的切线,切点分别为
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a1aeb00e17bb5fe34dc23e42e23c76e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
A.若圆![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.直线![]() ![]() |
D.![]() ![]() |
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10 . 已知椭圆的离心率为
,左焦点F与原点O的距离为1,正方形PQMN的边PQ,MN与x轴平行,边PN,QM与y轴平行,
,过F的直线与椭圆C交于A,B两点,线段AB的中垂线为l.已知直线AB的斜率为k,且
.
(1)若直线l过点P,求k的值;
(2)若直线l与正方形PQMN的交点在边PN,QM上,l在正方形PQMN内的线段长度为s,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faa0caf10891428e45904c7c5043101c.png)
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2023-11-11更新
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508次组卷
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2卷引用:浙江省浙南名校联盟2023-2024学年高二上学期11月期中联考数学试题