1 . 如图,A,B两点在河的两岸,A,C在同侧,B,D,E在同侧.已知
m,
m,
m,
,
.
![](https://img.xkw.com/dksih/QBM/2022/2/19/2873956543578112/2947269415993344/STEM/2beb552b-4637-4f61-8d96-5693efc734f5.png?resizew=181)
(1)求
的面积;
(2)求A,B两点间的距离.(精确到1m,参考数据:取
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88b6b9d14dc089d3b86c858d8549adb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa3cc7fef59f3d8ca607a2bcebfe9746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f10e05483bb1ed1f896d910f46e3a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63b45a709b95a1dea6ed07d44787cb1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1295be8e311b0f064b9a4c3f0c4570d.png)
![](https://img.xkw.com/dksih/QBM/2022/2/19/2873956543578112/2947269415993344/STEM/2beb552b-4637-4f61-8d96-5693efc734f5.png?resizew=181)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15514bc735fe4b744672edefe00009c.png)
(2)求A,B两点间的距离.(精确到1m,参考数据:取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a4f35a29caedab22fa64b34eb3f20b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06bd44085afb9d2981606a2d88694910.png)
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名校
解题方法
2 . 已知函数
.
(1)若
在
上单调递增,求正数
的取值范围;
(2)在
中,内角A,B,C的对边分别为a,b,c.若
,
,
,D、E、H为
边上的点.从以下给出的3个条件中选择其中1个条件,并根据所选择的条件判断是否存在满足条件的三角形?若存在,求出
的周长;若不存在,请说明理由(若多种选择作答,则按第一种解答给分).①
边的中线
;②A角的角平分线
;③
边的垂线
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c9cc4503b249cf07a89e170c2ac440d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05c43d70e8356b9c6b4eb78df00fddcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c05a467ddaa138590b3b56615c2c42a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98504cbcfcbb4489244cf3969a7e76a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66657ffdb8fd7a8ef2f4ac3579437130.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b73d73869615fbaef5bf4fed0b2209c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/405f376facfc857f536701ee5d280b44.png)
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2022-03-18更新
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5卷引用:安徽省合肥市第一中学2021-2022学年高二下学期3月测试数学试题
安徽省合肥市第一中学2021-2022学年高二下学期3月测试数学试题重庆市育才中学2022届高三下学期3月月考数学试题(已下线)押全国卷(理科)第17题 解三角形与数列-备战2022年高考数学(理)临考题号押题(全国卷)(已下线)江苏省南通市如皋市2022-2023学年高三上学期期初调研考前冲刺卷数学试题江苏省丹阳高级中学、常州高级中学、南菁高级中学2022-2023学年高三上学期10月联考数学试题
名校
解题方法
3 . 如图,已知某社区内有一个圆形绿化区,经规划调研确定,将
区域修建成居民休闲区.为方便居民通行,在圆上选取一点A,修建两条小路AB,AD(不考虑小路的宽度).已知
,
.
![](https://img.xkw.com/dksih/QBM/2022/2/19/2874384640622592/2929594155081728/STEM/88172092a53040769ea02b663d408080.png?resizew=134)
(1)若
,
,求居民休闲区的面积;
(2)若
,求修建的小路长度之和(即
)的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca7e1a727ba332984ad857b3d25344d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://img.xkw.com/dksih/QBM/2022/2/19/2874384640622592/2929594155081728/STEM/88172092a53040769ea02b663d408080.png?resizew=134)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d649afbddd907f0dfec1420f02f82fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267ace52b64e1e7dfc5211e033255b7d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/032ee24d2f1bd17afda6676eabcf82c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c760db19b0826e4542f132adeabae414.png)
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2022-03-05更新
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5卷引用:河南省2021-2022学年高二上学期阶段性检测(三)理科数学试题
21-22高二·江苏·课后作业
4 . 证明:如果两条直线斜率的乘积等于
,那么它们互相垂直.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
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21-22高二·全国·课后作业
5 . 如图,已知
在平面
内,D是斜边
的中点,
,且O到平面
的距离为
,
,
,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8807117d0d649419fdda04c531cdc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d31b274c4f82533ea4454388ed4f7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/689ff84e2d7f52c7446ef789a54557da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dafddfd80f69337909f6eac0f0dbfd59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432043f79e122f291c47453013042704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07fc6b6fa72d2af776a69c54fc6440f4.png)
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2022-02-28更新
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265次组卷
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4卷引用:第一章 空间向量与立体几何 1.2 空间向量在立体几何中的应用 1.2. 5 空间中的距离
(已下线)第一章 空间向量与立体几何 1.2 空间向量在立体几何中的应用 1.2. 5 空间中的距离3.2空间向量与向量运算 测试卷——2022-2023学年高二上学期数学北师大版(2019)选择性必修第一册 人教B版(2019)选择性必修第一册课本习题1.2.5 空间中的距离(已下线)第04讲 空间向量及其运算 (2)
21-22高二·全国·课后作业
6 . 已知某
标准跑道的内圈如图所示,其中左右两边均是半径为
的半圆弧.(设
标准跑道最内圈周长为
.)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/eb093189-3924-420d-bbbc-e986d633aed2.png?resizew=162)
(1)求每条直道的长度;
(2)建立平面直角坐标系
,写出该跑道内圈上半部分对应的函数解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05ba29eb90358e2211e1f7ba6423fa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f03c367201c385fcf9bdbf09d22b9e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05ba29eb90358e2211e1f7ba6423fa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05ba29eb90358e2211e1f7ba6423fa2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/eb093189-3924-420d-bbbc-e986d633aed2.png?resizew=162)
(1)求每条直道的长度;
(2)建立平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
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解题方法
7 . 在
中,
.
(1)求
的大小;
(2)条件①:
;条件②:
;条件③:
.
从条件①、条件②、条件③这三个条件中选择两个作为已知,使得
存在,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d98375aa8859a501558efccd1815698.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3818a2c9919d358b4c3713396093822b.png)
(2)条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f4f8020bef636dcb3b8dc5fa2bdbb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7806bf3865558f820a9bace47198fc41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8120119749d4bc28067e73fca7d46cd.png)
从条件①、条件②、条件③这三个条件中选择两个作为已知,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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解题方法
8 . 如图,点
分别在射线
,
上运动,且
.
![](https://img.xkw.com/dksih/QBM/2022/1/12/2893125535801344/2920021347868672/STEM/691cb6bf-e101-4059-b8ac-f58e22eaa11e.png?resizew=161)
(1)求
;
(2)求线段
的中点M的轨迹C的方程;
(3)直线
与
,轨迹C及
自上而下依次交于D,E,F,G四点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3a1467ecf286e3cadaf5aa006606f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de1c6fab6e983cef28bac0c301bba74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80b943cc778ac193b44e95803c2f6be9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6046bd4bf51a69b21ec583b6021ea545.png)
![](https://img.xkw.com/dksih/QBM/2022/1/12/2893125535801344/2920021347868672/STEM/691cb6bf-e101-4059-b8ac-f58e22eaa11e.png?resizew=161)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28b6ab702f8e93cc1e680a7d7af06786.png)
(2)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(3)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d1ad64a30b228781e1f4d8d338e74e8.png)
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9 . 我们知道,装同样体积的液体容器中,如果容器的高度一样,那么侧面所需的材料就以圆柱形的容器最省.所以汽油桶等装液体的容器大都是圆柱形的,某卧式油罐如图1所示,它垂直于轴的截面如图2所示,已知截面圆的半径是1米,弧
的长为
米
表示劣弧
与弦
所围成阴影部分的面积.
![](https://img.xkw.com/dksih/QBM/2022/1/21/2899421508214784/2918248211890176/STEM/9ffcef77fc4f45e2aa5f8dadadbeeeef.png?resizew=277)
(1)请写出
的函数表达式;
(2)用求导的方法证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daeb5d7250f887d97c9a6ce94a417b42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2022/1/21/2899421508214784/2918248211890176/STEM/9ffcef77fc4f45e2aa5f8dadadbeeeef.png?resizew=277)
(1)请写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)用求导的方法证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
您最近一年使用:0次
2022-02-17更新
|
143次组卷
|
2卷引用:山西省晋中市2021-2022学年高二上学期期末数学试题
名校
解题方法
10 . 已知两定点
,
,动点
与两定点的斜率之积为
.
(1)求动点M的轨迹方程;
(2)设(1)中所求曲线为C,若斜率为
的直线l过点
,且与C交于P,Q两点.问:在x轴上是否存在一点T,使得对任意
且
,都有
(其中
,
分别表示
,
的面积).若存在,请求出点T的坐标;若不存在,请说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc269fc04b75a3b88715a30fe9c080fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d850f8e63fdf3861d2aa77cd5da2812.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d259822ab64b8626f3893b8432673358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f30d314a642667fef559032264647366.png)
(1)求动点M的轨迹方程;
(2)设(1)中所求曲线为C,若斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2799abb64fd7bfce9dfa7228aa460564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724e11601d3807c120713018d3405d65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37b97b295f88972ba1c7e3cefda0885d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b331262ce68c03daa803a0eedfcf4ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3adf03de34b28009480e39e8d6efc0b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f32a02f53354993007080ec596fb7041.png)
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2022-01-28更新
|
219次组卷
|
2卷引用:四川省宜宾市2021-2022学年高二上学期期末数学理科试题