2022·上海浦东新·模拟预测
名校
解题方法
1 . 已知
,函数
的图象为曲线
.
、
是
上的两点,
在第一象限,
在第二象限.设点
、
.
(1)若
到
和到直线
的距离相等,求
的值;
(2)已知
,证明:
为定值,并求出此定值(用
表示);
(3)设
,且直线
、
的斜率之和为
.求原点
到直线
距离的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d6eb8e22b38b1a1f2f4550bc8633bd0.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/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/7ae4f082771efb99874041fe9c32aa81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f02e22b0fc087bd2cbb96ec3483b58e8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79e1023c4d2941e4753560787b7a9851.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ace585d3cc2e113a0927cdf9e56756a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7acff98078cdd32804d8f1c4efbe2ddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2 . 已知点
,
和点
,
.给出下列四个结论:
①点
到直线
的最大距离为
;
②当
最大时,
=
;
③
的面积的最大值为
;
④若
,则
.
其中所有正确结论的序号是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d295a4cc3a58f9f38ee98337313c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fcf82d01c39fd2c96e1edba0ad37dd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/285f34134c43ba75b616c6591afa79c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e36c9c91220b0f2cbd4a48e8fa90e3d.png)
①点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f190b17530d81d927c358ac84757a4.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59bafaec1cbb31d644a0df6bbd4fe4f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce5dcaffd91bc44cda4a2e44000ae73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4e7d0191acd17b6a0330ed4e0682f24.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c94427559676f1e8227566d7d3ce46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eea11be684f46600795154c1ef93268.png)
其中所有正确结论的序号是
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解题方法
3 . 已知关于向量
的方程:
,其中向量
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560ee2894ba8c5cee6633430cc8b3b41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf6aa50439bcec3c4b47433fd047925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4a9a13c67e66e90411872d76507090b.png)
A.关于向量![]() ![]() ![]() |
B.向量![]() ![]() |
C.满足该方程的向量![]() |
D.![]() |
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名校
解题方法
4 . 给出以下三个条件:①
且
;②
,
; ③
;请从这三个条件中任选一个将下面的题目补充完整,并求解.
在锐角△ABC中,
,____.
(1)求角B;
(2)求△ABC的周长l的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd312e2176f93eac627e279bcd34f4ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75facc3fb154fc96f015561c6b32491f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a768baac31b6add7c08508ecd6b29abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc5698e845a50fb597c0e9ad9e3a91cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c470c0506069b4e50706b44d55a6317a.png)
在锐角△ABC中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6129fbf40a950fc8c516f0abaab21957.png)
(1)求角B;
(2)求△ABC的周长l的取值范围.
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名校
解题方法
5 . 已知四边形
和四边形
为正方形
,
,则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/13/3849bdda-2f34-43f2-b4a2-55c21c527fe1.png?resizew=145)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c10f93679abcee21bacd92c3b1552a0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef136887b0c5a7cfdb0bdb96ba2c48dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4044a32b87a1985ea40e4d57ef32015b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/13/3849bdda-2f34-43f2-b4a2-55c21c527fe1.png?resizew=145)
A.![]() | B.![]() | C.![]() | D.![]() |
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2021-08-27更新
|
739次组卷
|
5卷引用:专题23 三法破解平面向量的数量积-备战2022年高考数学一轮复习一网打尽之重点难点突破
(已下线)专题23 三法破解平面向量的数量积-备战2022年高考数学一轮复习一网打尽之重点难点突破江苏省扬州中学2022届高三下学期5月高考前调研测试数学试题(已下线)重难点04五种平面向量数学思想-1福建省漳州市第五中学2020-2021学年高一下学期月考数学试题山东济南十一校2021届高三4月诊断联考数学试题
20-21高一下·江苏南通·期中
名校
6 . 已知向量
,
,其中
.
(1)若
,且
,求
的值;
(2)设函数
,当
时,是否存在整数
使得
的值域为
?若存在,请求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f310462a3548afa750007a5614889c6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d665aac8275eb07169842ef0c4ebb55b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a4a549ed1d52de7b6b60827e3802d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4f44474f48d66d0083fcadb6222c2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d57ebb3f3887aab618920750092dd6e.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40a5be152df7a82b3d4cbc8561230a80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e62ca9beef3cf514b4f99092b70038ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b67284ca9982944fd8bbe0a49102669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
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2021-08-27更新
|
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|
3卷引用:苏教版(2019) 必修第二册 必杀技 专练2 开放题(含结构不良题)专练
苏教版(2019) 必修第二册 必杀技 专练2 开放题(含结构不良题)专练(已下线)江苏省南通市如皋市2020-2021学年高一下学期期中数学试题福建省三明市第二中学2022届高三上学期阶段2考试数学试题
名校
7 . 已知线段
的端点
,端点
在圆
上运动,线段
的中点的轨迹方程为E.
(1)求轨迹方程
;
(2)过点
的直线
与曲线E交于P,Q两点,若
,其中O为坐标原点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356547c08d2cd7ba5a6aaf412266d7b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c25b4d3207ab7c0bc74255ebb9a86f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
(1)求轨迹方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8748dc55e2f45bc37fc4d84d7310f79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5913bd66d21e7f78c7573dfef4945194.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
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2021-11-19更新
|
662次组卷
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3卷引用:第2章 直线和圆的方程(基础、典型、新文化、压轴)分类专项训练-2022-2023学年高二数学考试满分全攻略(人教A版2019选择性必修第一册)
(已下线)第2章 直线和圆的方程(基础、典型、新文化、压轴)分类专项训练-2022-2023学年高二数学考试满分全攻略(人教A版2019选择性必修第一册)(已下线)高二上学期期中【压轴60题考点专练】(选修一全部内容)-2022-2023学年高二数学考试满分全攻略(人教A版2019选修第一册)广东省湛江市第二十一中学2021-2022学年高二上学期期中数学试题
名校
解题方法
8 . 桌面上有一张边长为2的正三角形的卡纸,设三个顶点分别为
,
,
,将卡纸绕顶点
顺时针旋转
,得到
、
的旋转点分别为
、
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e48d868645df7564b567db8e859b61.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e3b9a20c31e397ae1dc8a44baf7de91.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/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e48d868645df7564b567db8e859b61.png)
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2022-01-15更新
|
440次组卷
|
4卷引用:广东省东莞市2022届高三上学期期末数学试题
广东省东莞市2022届高三上学期期末数学试题山西省吕梁市临县第一中学2022届高三上学期期末数学试题(已下线)专题03 平面向量基本定理及坐标表示-2021-2022学年高一《新题速递·数学》(人教A版2019)2023版 湘教版(2019) 必修第二册 过关斩将 第1章 1.5 向量的数量积 1.5.2 数量积的坐标表示及其计算
名校
解题方法
9 . 正多边形具有对称美的特点,很多建筑设计都围绕着这一特点展开.已知某公园的平面设计图如图所示,
是边长为2的等边三角形,四边形
,
,
都是正方形,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04171842cecdf6ca503faf888bba0106.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8eb3f27deb3ca8ee6797664bb8e50d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a0ccec3dc620a444da084dfd6a8e784.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/21/e8560814-3508-4f23-9a41-8c4ef414bafd.png?resizew=156)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-06-19更新
|
213次组卷
|
3卷引用:1号卷·A10联盟高二年级(2021级)下学期6月学情调研考试数学试题
名校
解题方法
10 . 已知
中,
在
轴上,点
是
边上一动点,点
关于
的对称点为
.
(1)求
边所在直线的方程;
(2)当
与
不重合时,求四边形
的面积;
(3)直接写出
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f30c61a02b40511af1b459f31986d56a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/520f8abda6a85e7ef6f281fc2df853fa.png)
(3)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf93c36691a6faab3e6fd40057e87a1.png)
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2021-07-09更新
|
680次组卷
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5卷引用:第07讲 直线的交点坐标与距离公式(6大考点12种解题方法)-2022-2023学年高二数学考试满分全攻略(人教A版2019选择性必修第一册)
(已下线)第07讲 直线的交点坐标与距离公式(6大考点12种解题方法)-2022-2023学年高二数学考试满分全攻略(人教A版2019选择性必修第一册)北京市第八中学2020-2021学年高二下学期期末数学试题(已下线)专题1.3 直线与方程 章末检测3(难)-【满分计划】2021-2022学年高二数学阶段性复习测试卷(苏教版2019选择性必修第一册)(已下线)第12讲 点到直线的距离公式-【帮课堂】(已下线)2.3直线的交点坐标与距离公式(专题强化卷)-2021-2022学年高二数学课堂精选(人教A版2019选择性必修第一册)