名校
解题方法
1 . 设
是单位圆上不同的两个定点,点
为圆心,点
是单位圆上的动点,点
满足
(
为锐角)线段
交
于点
(不包括
),点
在射线
上运动且在圆外,过
作圆的两条切线
.
(1)求
的范围
(2)求
的最小值,
(3)若
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/7818812e33052be4de712cbbbb21e2e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec8858389f4c3156a946ba8bf0d8a7b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b8d5cf36f04941f4ad49fe4c5e26133.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d8eb37a4dd75318dcbd836395e575bd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e438bc5acc5cc10b3e7138279949a2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f63a42e22f8bc63465f595caf10e5842.png)
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2024-04-01更新
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4卷引用:浙江省精诚联盟2023-2024学年高一下学期3月联考数学试题
名校
解题方法
2 . 《几何原本》是古希腊数学家欧几里得创作的一部传世巨著,该书以基本定义、公设和公理作为推理的出发点,第一次实现了几何学的系绕化、条理化,成为用公理化方法建立数学演绎体系的最早典范.书中第Ⅰ卷第47号命题是著名的毕达哥拉斯(勾股定理),证明过程中以直角三角形
中的各边为边分别向外作了正方形(如图1).某校数学兴趣小组对上述图形结构作拓广探究,提出了如下问题,请帮忙解答.
问题:如图2,已知
满足
,
,设
(
),四边形
、四边形
、四边形
都是正方形.
时,求
的长度;
(2)求
长度的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
问题:如图2,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c14a66ed4bd66df65bc42c4ac1ed15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279085431149a62dd0927c114f9c2d3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0917d846965359153058d56498f076bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ddcd5435b39971f897210aa0b66a259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9beeedb7ddaac2cd3d37151d058ab7fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cae996f17c142d99dd990efb01c39621.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70ad7d1e3fad77908415415d6b2a90f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b15febfda66e733f14aa7115ed4343a8.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
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2023-06-30更新
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6卷引用:浙江省宁波市北仑中学2023-2024学年高二上学期期初考试数学试题
浙江省宁波市北仑中学2023-2024学年高二上学期期初考试数学试题江苏省苏州市2022-2023学年高一下学期期末学业质量阳光指标调研数学试题(已下线)模块五 专题3 全真拔高模拟3(苏教版高一)(已下线)第11讲 6.4.3 第2课时 正弦定理 (2)-【帮课堂】(人教A版2019必修第二册)江苏省南京市江宁高级中学2023-2024学年高一下学期第二次调研测试数学试题江苏省无锡市锡东高级中学2023-2024学年高一下学期5月月考数学试卷
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3 . 为了迎接亚运会, 滨江区决定改造一个公园,准备在道路AB的一侧建一个四边形花圃种薰衣草(如图).已知道路AB长为4km,四边形的另外两个顶点C, D设计在以AB为直径的半圆
上. 记
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/a642968f-5f02-4f94-a0ce-c384a1b9d696.png?resizew=177)
(1)为了观赏效果, 需要保证
,若薰衣草的种植面积不能少于
km2,则
应设计在什么范围内?
(2)若BC = AD, 求当
为何值时,四边形
的周长最大,并求出此最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8534428a3bd4b5396735e52a40c3be3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/a642968f-5f02-4f94-a0ce-c384a1b9d696.png?resizew=177)
(1)为了观赏效果, 需要保证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d1dfdfd2e2c671a71e60ea1b1630ff0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46bf936cb859f2033fcd8a68d954f0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(2)若BC = AD, 求当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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2023-02-18更新
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5卷引用:浙江省杭州第二中学2022-2023学年高一上学期期末数学试题
浙江省杭州第二中学2022-2023学年高一上学期期末数学试题浙江省宁波市余姚中学2022-2023学年高一下学期3月质量检测数学试题(已下线)模块三 专题6 大题分类练(解三角形)(拔高能力练)(人教A)(已下线)模块三 专题6 大题分类练(解三角形)(拔高能力练)(苏教版)河南省周口市太康县第二高级中学2022-2023学年高一下学期3月月考数学试题
名校
4 . 如图所示,
,
,
,四边形BEFM为正方形,
,N为BM的中点.
;
(2)若点P满足
,
①求
的取值范围;
②点
是以B为圆心,BM为半径的圆上一动点. 且在正方形BEFM的内部(包括边界),若
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42083f00cd68320e4e0275400c139551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e41404197ff62c7ce2a56153b65d31f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a6f36741b86f464be362b12bac13d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f74a4e3ca014ae1e1a005dd5bc5813a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e0987a20a5648765bce6ae78a693106.png)
(2)若点P满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d334d11f7c0da70074fdf6a653907ed6.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a302ee9825909922d7c0fa859e8735c.png)
②点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8ea79a1728d87bd7854e3fc14bed37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
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3卷引用:浙江省嘉兴八校联盟2020-2021学年高一下学期期中联考数学试题
浙江省嘉兴八校联盟2020-2021学年高一下学期期中联考数学试题(已下线)第11章 解三角形 单元综合检测(难点)--《重难点题型·高分突破》(苏教版2019必修第二册)广东省江门市第一中学2023-2024学年高一下学期第一次阶段考试数学试题
21-22高一下·浙江·期中
名校
5 . 设A,B,C是△ABC的三个内角,△ABC的面积S满足
,且
,
.
(1)若向量
,
,求
的取值范围;
(2)求函数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e8f600a4b31918ac9b34e9616d05135.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2be49b607826b359b2d49e4bdb4d1a7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6afb7d794dccc9a4425ef7d7e9abed6.png)
(1)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/616244009cc72dbbfa655638f0667e70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be191c63539b923b64018f692b90cb97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dce19a5aa0467cb5474260b0b4d26fb.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dea327a749eadad43bb84873fec9da7.png)
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6 . 设函数
,
.
(1)求
的值;
(2)从下述问题①、问题②、问题③中选择一个进行解答.
问题①:当
时,求
的值域.问题②:求
的单调递增区间.问题③:若
,且
,试求
的值.
注:作答时首先说明选择哪个问题解答;如果选择多个问题解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19e091a92328e54f8997efb819e5cdf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b87f4ef298bdeebf59a0d850aff72c.png)
(2)从下述问题①、问题②、问题③中选择一个进行解答.
问题①:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb48434bdcafb5e084fc0b6396cb9469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bbcecfcebf4c4493e22bfb978df4c86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f55b8836b41be612a52ca9caf97006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
注:作答时首先说明选择哪个问题解答;如果选择多个问题解答,按第一个解答计分.
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名校
解题方法
7 . 正方形ABCD中,
,点O为正方形内一个动点,且
,设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96643cc016e7e68f30c445bf47936a3.png)
(1)当
时,求
的值;
(2)若P为平面ABCD外一点,满足
,记
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91934cac6477909cf68ec266f562a397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96643cc016e7e68f30c445bf47936a3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc1f08c7640e62e8717abf4d44a6c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7444214a631d3904f722bc05f07d0f0.png)
(2)若P为平面ABCD外一点,满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1909a3a6c9c51b7232cbf5acdfdc734.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c5b8a21ed3092f78d0c6c05267b635.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd288d4152caf5fc8187a1a901c8949f.png)
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2022-05-17更新
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5卷引用:浙江省杭州学军中学2022-2023学年高二上学期期中模拟数学试题
解题方法
8 . 如图,
中,
,
,
,点D是以BC为直径的半圆弧上的动点,满足
,
.过点D作
交AC于点E,作
交AB于点F.
![](https://img.xkw.com/dksih/QBM/2022/5/9/2975951414378496/2977256452653056/STEM/72a3f6a6-7ed5-41f3-a02f-72ef08c24c92.png?resizew=164)
(1)试用α表示BD的长度;
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc8c65bea2c80af038768b74250c694e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73c916d5b02f278ee842393dab6dcce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb278a1476067378944794a3933dfd6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ad3351820c5c8f468095c1b93e66c58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c0aa4c793921fdaa5d430cb90d78ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b3f839ce88bf970aceb44ab939bd5b.png)
![](https://img.xkw.com/dksih/QBM/2022/5/9/2975951414378496/2977256452653056/STEM/72a3f6a6-7ed5-41f3-a02f-72ef08c24c92.png?resizew=164)
(1)试用α表示BD的长度;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/462379369371064bca86df3d386c7c2d.png)
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解题方法
9 . 如图,某专用零件四边形ABCD由平面图是一个半圆形钢板切割而成,其中O为圆心,
,OC平分角BOD交圆于点C,D为圆弧上一点,设
.
![](https://img.xkw.com/dksih/QBM/2022/4/24/2965157107834880/2967235418718208/STEM/52ee48324c024d859e37058855110092.png?resizew=214)
(1)当
时,求该零件的面积;
(2)若该零件周长为函数
,且
恒成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11db4b9921a9fe4d5c03b17bafc852fb.png)
![](https://img.xkw.com/dksih/QBM/2022/4/24/2965157107834880/2967235418718208/STEM/52ee48324c024d859e37058855110092.png?resizew=214)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/734a6a1d319648bb969845a9159cdba7.png)
(2)若该零件周长为函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5224a7da7fe6bc28971ce4c277f88588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28337006f3588305caa22481f28c1d30.png)
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解题方法
10 . 如图,自行车前后轮半径均为rcm(忽略轮胎厚度),固定心轴间距
为3rcm,后轮气门芯P的起始位置在后轮的最上方,前轮气门芯Q的起始位置在前轮的最右方.当自行车在水平地面上往前作匀速直线运动的过程中,前后轮转动的角速度均为
,经过t(单位:s)后P,Q两点间距离为f(t).
![](https://img.xkw.com/dksih/QBM/2022/1/21/2899097242673152/2909150147477504/STEM/be339d9f-a88d-48b1-952c-1c7476e72aa3.png?resizew=230)
(1)求f(t)的解析式:
(2)求f(t)的最大值和最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20bfa7196c89d0828ba06ca3c18161a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e48d11be56a4bdf2aa8c318ba9fe3e.png)
![](https://img.xkw.com/dksih/QBM/2022/1/21/2899097242673152/2909150147477504/STEM/be339d9f-a88d-48b1-952c-1c7476e72aa3.png?resizew=230)
(1)求f(t)的解析式:
(2)求f(t)的最大值和最小值.
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