1 . 设
是直角坐标平面
上的一点,曲线
是函数
的图象.若过点
恰能作曲线
的
条切线
,则称
是函数
的“
度点”.
(1)判断点
是否为函数
的
度点,并说明理由;
(2)若点
是
的
度点,求
的最小值;
(3)求函数
的全体
度点构成的集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.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/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/067ea3d2afb15333c289187e3c9f3261.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)判断点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1a9821a00b71f6b7d7a76d91b3f810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12be206d66e65eb92ef08bad8cd8f71d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48890339cc88c8dd3c58754739688e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2af5cfdc65e6473a2648da0083241912.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d0660d4864c16652a6b27337462b3f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
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2 . 已知椭圆:
的离心率是
,点
是椭圆的上顶点,点
是椭圆上不与椭圆顶点重合的任意一点.
(1)求椭圆
的方程;
(2)设圆
.若直线
与圆
相切,且点
在
轴右方,求点
的坐标;
(3)若点
是椭圆
上不与椭圆顶点重合且异于点
的任意一点,点
关于
轴的对称点是点
,直线
、
分别交
轴与点
、点
,探究
是否为定值,若为定值,求出该定值,若不为定值,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fca7e0ff6a7539423620b5ecfe0ea1ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)设圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5d4d459703d0d9793b807248b874bad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ffc7d1af9053b027cf9e726f5367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5850ed6ad7d8e9652625bd03766c61df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851aa470283a8993975229cdad3021e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb74ca8fc86ddef279e33f31c1fedda.png)
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3 . 中国结是一种传统的民间手工艺术,带有浓厚的中华民族文化特色,它有着复杂奇妙的曲线.用数学的眼光思考可以还原成单纯的二维线条,其中的“
”形对应着数学曲线中的双纽线.在平面直角坐标系
中,把与定点
、
距离之积等于
的动点的轨迹称为伯努利双纽线,记为曲线
.关于曲线
,有下列两个命题:
①曲线
上的点的横坐标的取值范围是
;
②若直线
与曲线
只有一个交点,则实数
的取值范围为
.
则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/229e67dd9fe978e48c221b0b9dc57f1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcb162568cb923c31c7209c8a22e4674.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa5314fd70d2e8aeb042d308a604a2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8cc0b4997cae4d8aec791a1d3923314.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
①曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad16a9960ae9c0d968bf0651709cd5d9.png)
②若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f6f693a154b09330bad58feb9d7fd54.png)
则( )
A.①为真命题,②为假命题 | B.①为假命题,②为真命题 |
C.①为真命题,②为真命题 | D.①为假命题,②为假命题 |
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4 . 已知函数
的表达式为
,若方程
有四个不相等的实根
,且
,则
取值范围是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/664d5a568352ae5c7bb21549055ecd7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2e3397839f4b65912c2f0cfe7f05eef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd42c34b2f926f4600e8622b961e3c92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3604274ad6707a906eba371a9e884144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d4077511e2a6cd8caff76581a94b6fe.png)
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|
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2卷引用:上海市松江区2023-2024学年高一上学期期末质量监控数学试卷
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解题方法
5 . 设
为
的一个排列,满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bea2a120d0bb0d28cfaf05e69b465e8.png)
,则这样的排列的个数为_______ 个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55fc6113ce4ac2b0daa7b809c9bfb3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ed93f368c243d567a5d29ae7b9326ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bea2a120d0bb0d28cfaf05e69b465e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e32c10912f241b6f4da4486a07cf7ac2.png)
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2024-01-14更新
|
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5卷引用:上海市松江二中2023-2024学年高二上学期期末考试数学试题
上海市松江二中2023-2024学年高二上学期期末考试数学试题(已下线)专题05 计数原理(十七大题型+优选提升题)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(沪教版2020选择性必修,上海专用)(已下线)专题01 两个计数原理与排列组合(7类压轴题型)-【常考压轴题】2023-2024学年高二数学压轴题攻略(人教A版2019选择性必修第三册)(已下线)第六章 计数原理(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第二册)(已下线)第4章 数列(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)
名校
解题方法
6 . 已知
分别在直线
与直线
上,且
,点
,
,则
的最小值为__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b7f07637cafd4bdb7bc0eaa5b1eeaca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73aa23d5bae655a13ecad8f97505dbe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8966c9cc4fa4ff537a546bcd0b055554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aba5e1427340bfe2badc42b925faf6a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e07a34a83c3e712dca8952eed6f9935f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c581bdb94840715012544d1b18dc18fb.png)
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7 . 正方形
的边长为12,其内有两点
、
,点
到边
、
的距离分别为3,2,点
到边
、
的距离也是3和2.现将正方形卷成一个圆柱,使得
和
重合(如图).则此时
、
两点间的距离为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-01-04更新
|
859次组卷
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8卷引用:上海市松江二中2023-2024学年高二上学期期末考试数学试题
上海市松江二中2023-2024学年高二上学期期末考试数学试题江西省上饶市婺源天佑中学2023-2024学年高二上学期期末模拟数学试题上海市崇明中学2023-2024学年高二上学期期中考试数学试题广东省广州市广东实验中学2024届高三上学期大湾区数学冲刺卷(一)(已下线)专题2 用空间向量解决立体几何问题江西省临川第一中学2023-2024学年高二下学期第一次月考数学试卷(已下线)高二上学期期末考点大通关真题精选100题(1)(已下线)第8题 由空间距离求夹角(压轴小题)
名校
解题方法
8 . 关于曲线
,有下述两个结论:①曲线
上的点到坐标原点的距离最小值是
;②曲线
与坐标轴围成的图形的面积不大于
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93235b3c3c78325c8b58d4bb9bf9b2ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
A.①、②都正确 | B.①正确 ②错误 | C.①错误 ②正确 | D.①、②都错误 |
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2023-12-06更新
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5卷引用:上海市松江区2024届高三上学期期末质量监控数学试题
上海市松江区2024届高三上学期期末质量监控数学试题上海市通河中学2023-2024学年高二上学期期末考试数学试题上海市青浦区朱家角中学2023-2024学年高二上学期期末考试数学试题(已下线)期末真题必刷压轴60题(23个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)(已下线)期末真题必刷压轴60题(22个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)
解题方法
9 . 已知正四面体
的棱长为
,空间内任意点
满足
,则
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d88a798a3017de2cf6e2e39b8360e3d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cb420defc29953c389e10bc28f9a4c0.png)
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10 . 已知
,我们定义函数
表示不小于
的最小整数,例如:
,
.
(1)若
,求实数
的取值范围;
(2)求函数
的值域,并求满足
的实数
的取值范围;
(3)设
,
,若对于任意的
,都有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8970b99038dfdc964e26f41a1949e968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f75630540a77db49408d2c3e3b34be.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06a857be85405c5198bff2d92414a9b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec656fc93f73e7fc5971f7024612937c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd8e0e2c46e8e898749dc197d7e2e5a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10571c75b610d7506b9647cd06ddaf0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47e9521c64fdf0f72e6e7a39ab28d07d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be083b8f0bbaba3d676ef4a0f3df0222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fa12545243d18e3a66f0c277ded319a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-09-28更新
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3卷引用:上海市松江区华东政法大学附属松江高级中学2022-2023学年高一上学期期末数学试题