名校
解题方法
1 . 平面向量是数学中一个非常重要的概念,它具有广泛的工具性,平面向量的引入与运用,大大拓展了数学分析和几何学的领域,使得许多问题的求解和理解更加简单和直观,在实际应用中,平面向量在工程、物理学、计算机图形等各个领域都有广泛的应用,平面向量可以方便地描述几何问题,进行代数运算,描述几何变换,表述物体的运动和速度等,因此熟练掌握平面向量的性质与运用,对于提高数学和物理学的理解和能力,具有非常重要的意义,平面向量
的大小可以由模来刻画,其方向可以由以
轴的非负半轴为始边,
所在射线为终边的角
来刻画.设
,则
.另外,将向量
绕点
按逆时针方向旋转
角后得到向量
.如果将
的坐标写成
(其中
,那么
.根据以上材料,回答下面问题:
,求向量
的坐标;
(2)用向量法证明余弦定理;
(3)如图,点
和
分别为等腰直角
和等腰直角
的直角顶点,连接DE,求DE的中点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91174b2336306191ba275a87864172b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91174b2336306191ba275a87864172b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4293abac93e7633dc4c0fef321347e72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8a3b1b11c77ceb7ece55f76d2cd4618.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/873c064546108a5bce78bb71bc1e4a1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea99a712a0891faf366d4fec4dde5869.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/941b0d76d7b3108df49af338c989dc4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e32257bac4199820ccae5e7bd8377cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0849dbfc3775627925de0fe2e89c1692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb50427d2e8a7c605bbd18ea8e0c3b79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5f1b06a56fc382feed28e01f1ad102.png)
(2)用向量法证明余弦定理;
(3)如图,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd99c5000629d7f49499d666e68f40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852b303689c31189cd47bb4a3220f9fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfa1a2af7e38d33634c462300df381f.png)
您最近一年使用:0次
7日内更新
|
404次组卷
|
3卷引用:安徽省芜湖市第一中学2023-2024学年高一下学期期中考试数学试卷
安徽省芜湖市第一中学2023-2024学年高一下学期期中考试数学试卷(已下线)高一下学期期末模拟卷(范围:必修第二册全册)-同步题型分类归纳讲与练(人教A版2019必修第二册)湖南省永州市部分学校2023-2024学年高一下学期6月质量检测卷数学试题
名校
解题方法
2 . 如图,在边长为4的正三角形
中,
分别为
上的两点,且
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d03acb29a5812acad760d564d6c84be.png)
,
相交于点P.
的值;
(2)试问:当
为何值时,
?
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cca04b2a2b61d62a809776670a60c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc553ab786de1d90a1883911ada167ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d03acb29a5812acad760d564d6c84be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/699f8cdb31abb7223e6c46a4363fc691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/268544817735d20ffbceef3b26db5dde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5f1c2b555afad1437765d55746c1924.png)
(2)试问:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4e22ba3e6e1c1d6b12d9b8baa8d1f02.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eb330cc355b80d5f299a41f1a7e4e81.png)
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2024-06-08更新
|
256次组卷
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2卷引用:安徽省金榜教育2023-2024学年高一下学期5月阶段性大联考数学试题
名校
解题方法
3 . 如图,正方形ABCD的边长为1,P,Q分别为边BC,CD上的点,且
;
(2)求
面积的最小值;
(3)某同学在探求过程中发现PQ的长也有最小值,结合(2)他猜想“
中PQ边上的高为定值”,他的猜想对吗?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e50966267b44a653055ab15c490536.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
(3)某同学在探求过程中发现PQ的长也有最小值,结合(2)他猜想“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
您最近一年使用:0次
2024-03-29更新
|
534次组卷
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2卷引用:安徽省县中联盟2023-2024学年高一下学期3月联考数学试卷
名校
4 . 已知函数
.
(1)若
为偶函数,求函数
的定义域;
(2)若
过点
,设
,若对任意的
,
,都有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83ce606738f49f3a6441d23c70079584.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bac0d5896f4c9950e377c5d937ba98e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8485bb1fcd0253b8a3bd8003e7d40686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8bf3ba57cbcc9a63dd0b823d7c96ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ee656419648839813fdb5ee99b743d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc25aeda3577367df5acfc238c07293.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80b3882c672d7051e4ab251ebb95844d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-02-29更新
|
1129次组卷
|
4卷引用:安徽省宿州市省、市示范高中2023-2024学年高一上学期期末教学质量检测数学试题
安徽省宿州市省、市示范高中2023-2024学年高一上学期期末教学质量检测数学试题辽宁省实验中学2023-2024学年高一下学期第一次月考数学试题辽宁省沈阳市第二中学2023-2024学年高一下学期第一次月考数学试题(已下线)专题02三角函数的图像与性质期末10种常考题型归类-《期末真题分类汇编》(人教B版2019必修第三册)
5 . 对于函数
,
为函数定义域,若存在正常数
,使得对任意的
,都有
成立,我们称函数
为“
同比不增函数”.
(1)若函数
是“
同比不增函数”,求
的取值范围;
(2)是否存在正常数
,使得函数
为“
同比不增函数”,若存在,求
的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f69a10dd74a5189353a5db9d5828ac3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f7f1ed660ed810ad4ffd5d0a6d3762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03cddfaa4522ab14daa358d2d5af019e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)是否存在正常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8f44b70df66b4e8b1f958d1335fb83b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
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名校
解题方法
6 . 设函数
,
,
.
(1)求函数
在
上的单调区间;
(2)若
,
,使
成立,求实数a的取值范围;
(3)求证:函数
在
上有且只有一个零点
,并求
(
表示不超过x的最大整数,如
,
).
参考数据:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d89231f0078f75ad0193f9aec97b9286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9f049a5f960728c60a909821b2404b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa3e40a1b375c50331403283bfd7139b.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0167434c2c1a16e59e89d436ac0a1278.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69fc78bba43797d2f81cb912f2d05c93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac0afd127806b03435a649606544fc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe53bb5e833f83c2d8290d195fabf02b.png)
(3)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b5e51f08fcfaa95b58f3a14c8250a38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41667e2986ec718cabeeb1088794ed67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04309e875209bde5b87438535ea3b1cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/977353e0326dc27334a2940f1149e973.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dad09268b7cb8bfcbea010cb6d2a29e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e143d31a5ae4d2fb8cba2466bae1fe54.png)
您最近一年使用:0次
2024-01-06更新
|
657次组卷
|
6卷引用:安徽省合肥市合肥一中肥东分校2023-2024学年高一上学期期末数学试题
解题方法
7 . 已知函数
,
.
(1)求
的值;
(2)解关于
的不等式
;
(3)
对
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/068fe824048360fba77109636452fda8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3b302cf413a9ca1b05ab584a023cfbd.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/778779516833e28ed4096df26f90c08a.png)
(2)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02508a8389cd36c714631f4c026194d.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fecccf04d7942398c7551dc4868b2f1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-12-22更新
|
621次组卷
|
2卷引用:安徽省宿州市十三所重点中学2021-2022学年高一上学期期终质量检测数学试卷
解题方法
8 . 已知直线
经过定点
是坐标原点,点M在直线
上,且
.
(1)当直线
绕着点N转动时,求点M的轨迹E的方程;
(2)已知点
,过点T的直线交轨迹E于点
,且
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab44625790b53e57cce0478e6f0b90e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a89efb10e95245a41f6c7a80189528.png)
(1)当直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8118929231691bbaaa2f2c5976e132ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b1b15a4605fce993cb13aefbf40360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc67853693315ab6959e11cc0863581e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
您最近一年使用:0次
名校
解题方法
9 . 已知
是不共线的三点,且
满足
,直线
与
交于点
,若
.
(1)求
的值;
(2)过点
任意作一条动直线交射线
于
两点,
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06f5e21d225bf3c159ddf3876fbb8fb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d651eb2a890fd91d49e8f36a13f8b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e06ca53803f042a5eca99f56a70f05e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5a5e484dfef494d27bc35ae7b8cf75d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5381f952daa8f010cada233f1ccc34d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
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2023-10-09更新
|
638次组卷
|
2卷引用:安徽省皖江名校联盟2024届高三上学期第二次联考(10月)数学试题
10 . 如图,在梯形
中,
,点
为
的中点.
(1)求
与
夹角的余弦值;
(2)以
为圆心
为半径作圆,点
是劣弧
(包含
两点)上的一点,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d8ed97308e4fef971ddc9f03cf379b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/21/bef3b6a3-7500-48b5-9d6e-309ebf871900.png?resizew=162)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d021a5c98388463d577675e58068aa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4781e3daa2c4e018ca0ae09bb56abc0f.png)
(2)以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667349d99185bb045030b733352ff7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098a3e7d1f1890863b7483a98b618119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb1be854f041172d933c7b42602cb53.png)
您最近一年使用:0次
2023-10-05更新
|
520次组卷
|
3卷引用:安徽省铜陵市2023-2024学年高三上学期第二次联考(月考)数学试题