23-24高三上·北京·期中
名校
1 . 已知
,若实数
,则
在区间
上的最大值的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b62271358df0edc9a22635e3fafecc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ae16b8d4ca61fc29075c6e6968255bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf0e0cb1af4509966c57b99fe1d6ad7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c91b3592e2dce9cc8639ca9d30e12bf5.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
2 . 已知焦距为2的椭圆
:
,
,
分别为其左右焦点,过点
的直线
与椭圆交于
,
两点,
的周长为8.
(1)求椭圆
的方程;
(2)若过点
的直线
与椭圆交于
,
两点且满足
,求四边形
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.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/2e9b0f5f44abbc6544a2f672b025b013.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/d3c07ebcbfacda073208d483c58e8a84.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce08b357f11ef44c3e8207ac574422a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c593ebdb2f1934a0cb56f8c44f454f8.png)
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2023-11-19更新
|
468次组卷
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4卷引用:江西省上饶市广丰一中2024届高三上学期12月月考数学试题
名校
解题方法
3 . 已知焦点分别在
轴上的两个椭圆
,且椭圆
经过椭圆
的两个顶点与两个焦点,设椭圆
的离心率分别是
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.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/21e9feabc99f62ee569b460e61526e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f994a876391534efe497dc115a53e3fa.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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1319次组卷
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5卷引用:江苏省扬州市扬州中学2024届新高考一卷数学模拟测试一
江苏省扬州市扬州中学2024届新高考一卷数学模拟测试一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河北省邯郸市永年区第二中学2023-2024学年高二上学期12月月考数学试题(已下线)模块三 专题3 小题满分挑战练(1) 期末终极研习室(高二人教A版)(已下线)专题03 圆锥曲线方程(3)
4 . 已知双曲线
:
(
,
)与椭圆
有公共焦点,
的左、右焦点分别为
,
,且经过点
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/d80b861ba40387cb2bcd04945f5a371a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/de6140983d54ff07307ec65bddd7320e.png)
A.双曲线![]() ![]() |
B.若直线![]() ![]() ![]() |
C.设![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
D.若动直线![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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5 . 已知函数
(e是自然对数的底数)在定义域R上有三个零点,则实数m的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39160ffd99ea2ee151db7c917f57707e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
6 . 已知函数
.
(1)当
时,求过原点且与
的图象相切的直线方程;
(2)若
有两个不同的零点
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29b95e9e3e4eac2f3bb889a3bdd9a917.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e18216101435d6e82b06fcb03340bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2aabc96b7433bba077ceac76d8f0d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5936864e58831016d085424db60c7d12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-11-18更新
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6卷引用:四川省成都市石室中学2023-2024学年高三上学期期中考试理科数学试卷
四川省成都市石室中学2023-2024学年高三上学期期中考试理科数学试卷四川省成都市石室中学2023-2024学年高三上学期期中考试文科数学试卷重庆市九龙坡区四川外国语大学附属外国语学校2024届高三上学期期中数学试题四川省南充市白塔中学2024届高三上学期12月月考数学(文)试题(已下线)专题04 导数及其应用(4大易错点分析+解题模板+举一反三+易错题通关)(已下线)特训03 一元函数的导数及其应用 压轴题(七大母题型归纳)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)
名校
解题方法
7 . 已知椭圆
的离心率为
,左、右焦点分别为
,直线
与椭圆
交于
两点,且
的周长最大值为8.
(1)求椭圆
的标准方程;
(2)已知点
是椭圆
上一动点(不与端点重合),
分别为椭圆
的左右顶点,直线
交
轴于点
,若
与
的面积相等,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0e8e4c7dc8f333aa38dc8d69673c545.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d71f015144ffaf1faec94a259b4a06.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/d3c07ebcbfacda073208d483c58e8a84.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](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/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc48974114e23f5a801843710c7ae21.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/c8ef68c72248af27e3b83b4ee5fdeb51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7128a302aa5ac137ce48ebdf2c1dc87f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc48974114e23f5a801843710c7ae21.png)
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3卷引用:四川省成都市石室中学2023-2024学年高三上学期期中考试理科数学试卷
8 . 已知函数
.
(1)讨论
的单调性;
(2)若当
时,
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89602013629c67e1a25e3c1dd6257e58.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01a4a68d235453ad0c10402a1f6d0173.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
9 . 已知函数
.
(1)当
时,求函数
的极值;
(2)若
有两个极值点
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/323cc43871632c457d615a0d89066014.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e9222ffc26c0e6bfbf252ab5d8a520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd8ca3aa2d1ba52e82613d0d65d800e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c44ef0dbea2fef6e4dbf5352009c1725.png)
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3卷引用:江苏省南通市海门中学2024届高三上学期第一次调研考试数学试题
10 . 已知点在椭圆
上,椭圆
的离心率为
.
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
①若,求直线
的方程;
②求的面积的取值范围.
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2卷引用:江苏省南通市海门中学2024届高三上学期第一次调研考试数学试题