名校
1 . 已知椭圆
:
的右焦点为
,过点
作
轴的垂线交椭圆
于点
.过点
作椭圆
的切线,交
轴于点
.
(1)求点
的坐标;
(2)过点
的直线(非
轴)交椭圆
于
、
两点,过点
作
轴的垂线与直线
交于点
,求证:线段
的中点在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0dfb290b1a84f670549554a0c988593.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
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解题方法
2 . 有
个编号分别为1,2,…,
的盒子,第1个盒子中有3个白球1个黑球,其余盒子中均为1个白球1个黑球,现从第1个盒子中任取一球放入第2个盒子,再从第2个盒子中任取一球放入第3个盒子,以此类推,从第
个盒子中取到白球的概率是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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解题方法
3 . 已知
,直线
为平面内的一个动点,过点
作
的垂线,垂足为
,且
,动点
的轨迹记为曲线
.
(1)求
的方程;
(2)若直线
交
于
两点,交圆
于
两点,且
,当
的面积最大时,求
的倾斜角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d2f61620e2b2cca65f8e581909658d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dd29e35cee24a67a35c043d7b87b654.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b33328faae2d2d4921900e97424de5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17ad7e0e730caaebab54e28873c38543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
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2卷引用:河北省南宫市私立丰翼中学2023-2024学年高二下学期第三次月考(5月)数学试卷
名校
4 .
.
(1)讨论
的单调性;
(2)
,恒有
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ea98f8c7e4073a785cf1c0e10eaa808.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ab7024f73ff0cb7e6a48197538a91e.png)
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5 . 设函数
,若
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6062d1a6ecfc72ae6689a08419982738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c925be255ca736a53b24d13ddede1a86.png)
A.![]() | B.![]() | C.![]() | D.1 |
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5779次组卷
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5卷引用:福建省泉州市安溪铭选中学2023-2024学年高二下学期6月份质量检测数学试题
福建省泉州市安溪铭选中学2023-2024学年高二下学期6月份质量检测数学试题2024年新课标全国Ⅱ卷数学真题(已下线)2024年高考数学真题完全解读(新高考Ⅱ卷)专题02函数(已下线)2024年新课标全国Ⅱ卷数学真题变式题6-10
名校
解题方法
6 . 已知函数
,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db0107fb8d4cb3a9b6311fa639ca514b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f76f05cfe51ad2ef235afc588e61db.png)
A.![]() ![]() |
B.若函数![]() ![]() ![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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解题方法
7 . 已知抛物线
和
的焦点分别为
,动直线
与
交于
两点,与
交于
两点,其中
,且当
过点
时,
,则下列说法中正确的是 ( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd002e4153239401cbe0d56ab1164b9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677e43bb9b3ff712aeea6a52cea9e25f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f98254a6193566587a70c7d95fdabf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1459402f901edc7c3bd6993b15be2805.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf328ef13181498b339a6c9b9af0eb0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910215944e29fcfe2d439b7191192cb8.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/6179bd1936944d2977cab330e0e351ca.png)
A.![]() ![]() | B.已知点![]() ![]() ![]() |
C.![]() | D.若![]() ![]() ![]() |
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解题方法
8 . 如图,已知正方体
顶点处有一质点
,点
每次会随机地沿一条棱向相邻的某个顶点移动,且向每个顶点移动的概率相同,从一个顶点沿一条棱移动到相邻顶点称为移动一次,若质点
的初始位置位于点
处,记点
移动
次后仍在底面
上的概率为
.
;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc3612ef4132dfef2f8a4f5af22e89d8.png)
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9 . 已知实数
,对
恒成立,则
的取值范围为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b44ff75c0a450bd10443d9e5a19e4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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10 . 已知抛物线
的焦点为
,
,
为
上的两点,过
,
作
的两条切线交于点
,设两条切线的斜率分别为
,
,直线
的斜率为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e1ba94066bb15ce4f20d8990885d18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
A.![]() ![]() |
B.![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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4卷引用:河南省部分重点高中(金科未来)2023-2024学年高二下学期5月大联考数学试题
河南省部分重点高中(金科未来)2023-2024学年高二下学期5月大联考数学试题河南省部分重点高中2023-2024学年高二下学期5月质量检测数学试题(已下线)湖南省岳阳市第一中学等多校2023-2024学年高二下学期5月月考数学试题山西省临汾市部分学校2023-2024学年高二下学期5月质量检测数学试题