1 . 如图是函数
的部分图象,其中点
在
轴上且过
点的竖直线经过图象的最高点,
是图象上一点,
是线段
与图象的交点,且
,则
点的纵坐标是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f552dba7c0d8c1038a91ba98fa9aa6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b19c3dc7d68e709093f2b1aeea4ebb54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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2 . 已知实数
满足:①
;②存在实数
,使得
,
,
是等差数列,
,
,
也是等差数列.则实数
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e633d15ed77937c15180d0593fabde03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7931c14dc4e055e3d0b709b9c080b6df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e68a9723a0e94b16a6019a2494f103f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02fc27f36003850ea40fb1d9cf18d462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebea760067502e24ddf3d1e541be36ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
3 . 将边长
的矩形
按如图所示的方式折叠,折痕过点
,折叠后点
落在边
上,记
,则折痕长度![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd1846e964fd60c54888a3c706a97442.png)
______ .(用
表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de49f19ea0a087c50d9a1b3409403693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd1846e964fd60c54888a3c706a97442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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4 . 如图,某市在两条直线公路
上修建地铁站
和
,为了方便市民出行,要求公园
到
的距离为
.设
.
的长度
关于
的函数关系式;
(2)问当
取何值时,才能使
的长度最短,并求其最短距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f47ddc7c9fb41942160e3cafcf756776.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960bdf943b1f405a12152f5520dae359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1890f0b4e81634bb7e013412698640f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588688304039065c026f2e12bd81b680.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)问当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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解题方法
5 . 已知
为坐标原点,
点在第一象限,
的内切圆
的方程为
,分别以
为圆心作圆,且
两两相外切,则
的标准方程为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd22409d1cdcf2c0a23c03957e9475c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90037b49d0338c5370e31dd957a02f87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06f5e21d225bf3c159ddf3876fbb8fb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b18609d95266520784db4c48df549fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6f6558fef858bf27e9811c2d9426fe7.png)
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23-24高二上·上海·课后作业
6 . 求证:直线
(
且不是
的整数倍)和两坐标轴围成图形的面积是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cfc7f4e0dfa43ff2a0a40f3a341b580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ae470980d6e3b53c65b9d42d1f011c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
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解题方法
7 . 已知下列是两个等式:
①
;
②
;
(1)请写出一个更具一般性的关于三角的等式,使上述两个等式是它的特例;
(2)请证明你的结论;
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e61a7dce3c7e918ff69c59921cfa0575.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc641c9bd2e45220dfc53a3994ed33ce.png)
(1)请写出一个更具一般性的关于三角的等式,使上述两个等式是它的特例;
(2)请证明你的结论;
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名校
解题方法
8 . 已知直角梯形
,
,
,
,扇形圆心角
,
,如图,将
,
以及扇形
的面积分别记为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36477401af8ec19b82d682ab184753a2.png)
的表达式,并指出其大小关系(不需证明);
(2)用
表示梯形
的面积
;并证明:
;
(3)设
,
,试用代数计算比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36572a10fcb483a9abb63a5039e09ec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/201339005285d682fbc2cf65fbabddd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4138f6987cd2ee9e56b2ac80e84f9e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ac5396c5ea442e0364b50c1db3d2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ba3f676fda6a2aaaa55c9f32874a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36477401af8ec19b82d682ab184753a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36477401af8ec19b82d682ab184753a2.png)
(2)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fec41d46ca97d3e900ef1db5a1f002c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6cc4a85bbf152031dc8ebd182e44ead.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be31dfad4f16cf1f2158b3011e3b68b9.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e8d7d33749979b7d7acc17532d86b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7787a01998f68ccc931c00ccb475f6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1ba6b6ee00c4b2763cb3fa59caa69f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3bf4af3d4543cada4b52871ac9dfb1a.png)
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2023-07-09更新
|
608次组卷
|
6卷引用:上海市复旦大学附属中学2022-2023学年高一下学期期末数学试题
上海市复旦大学附属中学2022-2023学年高一下学期期末数学试题(已下线)6.2 常用三角公式-高一数学同步精品课堂(沪教版2020必修第二册)上海市华东师范大学第二附属中学2023-2024学年高一下学期3月月考试题(已下线)专题06 期末解答压轴题-《期末真题分类汇编》(上海专用)(已下线)专题04 三角-《期末真题分类汇编》(上海专用)(已下线)高一上学期期末考试解答题压轴题50题专练-举一反三系列
解题方法
9 . 某小区围墙一角要建造一个水池和两条小路.如图,四边形
中,
,
,以
为圆心、
为半径的四分之一圆及
与
圈成的区域为水池,线段
和
为两条小路,且
所在直线与圆弧相切.已知
米,设
(
),那么当
为多少时,才能使两条小路长之和
最小?最小长度是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9536a2be7b84612f45cc875a00c5a5d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe2f6543e06a25493855fbbc648be6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f26ad70d2b3aac8604834d57dfc59bb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8cc5e8fc797a3a45c253b783631d4e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee86fc3cc1700452e83ca45bccb9c55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a80f9688e03874804defebed1db50c1b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/10/7075cd7a-74be-4925-abab-0316441128b0.png?resizew=142)
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