1 . 如图,一块斜边长为
的直角三角尺,其中一个内角为
,把该角立在桌面上,使得斜边所在的直线与桌面所在的平面所成的角为
,再绕其斜边旋转,则直角顶点到桌面距离的最大值为______
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86cacebfac933f2d9894147286bdd4a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/85482535-6f9f-4120-ac44-44c9ea1dcd60.png?resizew=176)
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2 . 向量是解决数学问题的一种重要工具,我们可以应用向量的数量积来解决不等式等问题.
(1)(ⅰ)若
,
,比较
与
的大小;
(ⅱ)若
,
,比较
与
的大小;
(2)
,
为非零向量,
,
,证明:
;
(3)设
为正数,
,
,
,求
的值.
(1)(ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fecf76d71aed3b37bd48550bf48c1086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f683269ae8936d010ba111e9c9be5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a8f20036b1e7cfb0800f141d843718.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f01e75d42bcb00df9c20734d9f3c547.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fecf76d71aed3b37bd48550bf48c1086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012b990e9c0d9f8da823df2ef36b26dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a8f20036b1e7cfb0800f141d843718.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f01e75d42bcb00df9c20734d9f3c547.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae98586d80f892771c90ab39eaced90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee437e6ff470c2f67b8429f57b90ae37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0118005d052d96ec2490facb71145b05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b04e531f59cead9c6f1017dbf1c953f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79e891ae2a63b7c20e00cb05e9acb71.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a93b98eef83e6b1b364a4cd6c55148ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e37739c262e686df999f5b89595c264.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc786b1cdc9c0bf814f43abdb1d2ad67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5b9c5de247a0aef2e56f58a88a8698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7f4495f96d35d8cb294a872223b923a.png)
您最近一年使用:0次
名校
解题方法
3 . 在
中,角A,B,C所对的边分别为
,
,
,
为
的外接圆,
,给出下列四个结论:
①若
,则
;
②若P在
上,则
;
③若P在
上,则
的最大值为2;
④若
,则点P的轨迹所对应图形的面积为
.
其中所有正确结论的序号是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e1bd4f72b3edd9647378d1191857fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c0d9a3528b2f78a30afc3a8ad7ed2e.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821fa0301d20076ad2e541f8c4a86231.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab3b7abd49187243f54931a8e2ae3e7.png)
②若P在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2c545a5e92b066cb21323367640090.png)
③若P在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd1f0ace9ca0b79929e73af6c201c2e.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2efbf5b18492c75432b0b0189df7262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
其中所有正确结论的序号是
您最近一年使用:0次
2021-07-29更新
|
325次组卷
|
2卷引用:四川省凉山彝族自治州2020-2021学年高一下学期期末数学试题
解题方法
4 . 写出一个同时具有下列性质①②③,且定义域为实数集
的函数
:______.
①最小正周期为2 ②
③无零点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①最小正周期为2 ②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf116ecbdb894c1d05d5b3b5203c10a6.png)
您最近一年使用:0次
2021-07-27更新
|
420次组卷
|
2卷引用:辽宁省锦州市2020-2021学年高一下学期期末数学试题
名校
解题方法
5 . 如图,风景区的形状是如图所示的扇形ABC区域,其半径为2千米,圆心角为
,点P在弧BC上.现欲在风景区中规划三条商业街道
,要求街道PQ与AB垂直(垂足Q在AB上),街道PR与AB平行,交AC于点R.
![](https://img.xkw.com/dksih/QBM/2021/5/1/2711564111142912/2772377853075456/STEM/01b4186de288417badbd3a71d1f4f6aa.png?resizew=227)
(1)如果P为弧BC的中点,求三条商业街道围成的△PQR的面积;
(2)试求街道RQ长度的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e93c98be6da91f6a1a39d3bf88f0301.png)
![](https://img.xkw.com/dksih/QBM/2021/5/1/2711564111142912/2772377853075456/STEM/01b4186de288417badbd3a71d1f4f6aa.png?resizew=227)
(1)如果P为弧BC的中点,求三条商业街道围成的△PQR的面积;
(2)试求街道RQ长度的最小值.
您最近一年使用:0次
2021-07-26更新
|
534次组卷
|
5卷引用:江苏省扬州市邗江中学2020-2021学年高一下学期期中数学试题
江苏省扬州市邗江中学2020-2021学年高一下学期期中数学试题广东省广州市铁一中学2022-2023学年高一上学期期末数学试题江苏省南通市通州区金沙中学2022-2023学年高一下学期4月质量监测数学试题(已下线)第五章 三角函数(32类知识归纳+38类题型突破)(6) -速记·巧练(人教A版2019必修第一册)江苏省苏州市桃坞高级中学校2023-2024学年高一下学期3月自学能力测试数学试卷
名校
6 . 如图,在四边形
中,
为对角线
与
中点连线
的中点,
为平面上任意给定的一点.
![](https://img.xkw.com/dksih/QBM/2021/6/18/2745403371003904/2768546705989632/STEM/46cde7beb3864628b0df3a3de5e77c2e.png?resizew=93)
(1)求证:
;
(2)若
,
,
,
,点
在直线
上运动,当
在什么位置时,
取到最小值?
(3)在(2)的条件下,过
的直线分别交线段
、
于点
、
(不含端点),若
,
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/2021/6/18/2745403371003904/2768546705989632/STEM/46cde7beb3864628b0df3a3de5e77c2e.png?resizew=93)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5632cbd5252f07934ecdb6e6951246f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a0816f8db1e1cad53f05b8dc1837ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed8128329f973dff60d13e4039957b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7652bbae10722db2cf0458d9da4a54c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f82432e6351f381c0008e5bc6b545f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbc4a9a1594591b27b24998ea3f5a2e5.png)
(3)在(2)的条件下,过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da25790e5a2cc740b8a5ef8809dab3a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/660018ccbfd4abf386c30cad0f9ea8eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27e62ba44cbfec6823ebc1f0c7457fb.png)
您最近一年使用:0次
2021-07-20更新
|
437次组卷
|
3卷引用:上海市复兴高级中学2020-2021学年高一下学期期末数学试题
7 . 对
,定义
.
(1)求
的最小值;
(2)
,有
恒成立,求A的最大值;
(3)求证:不存在
,且m>n,使得
为恒定常数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f166b8917034ebc7522d1a160707f6a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7de87e4f04e15189c927b34b2e5afb.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde2576b383ae3c851529435805b3adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b206982b923b94befb9985e51f6499cb.png)
(3)求证:不存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c61a450b5c1c412aca3294e9eb4e9874.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c29ca729804f56f23d760ab66b79f68.png)
您最近一年使用:0次
2021-07-19更新
|
556次组卷
|
3卷引用:北京市一零一中学2020-2021学年高一下学期期末数学试题
20-21高一下·上海浦东新·期末
名校
8 . 已知
,向量
,
,
、
、
是坐标平面上的三点,使得
,
.
(1)若
,
的坐标为
,求
;
(2)若
,
,求
的最大值;
(3)若存在
,使得当
时,△
为等边三角形,求
的所有可能值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce632c0ad85f24096c0f05d5450e473e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2aa1670a597db4dcc5e481c9eb41dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27945773ec2b92d380eaddc5026836c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a9066cefc9b9b13bec0a2b62540d1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16b2299483e9e9ce35f12538e10b4ff7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a0f96c4dfd44a0412601f183a8c7443.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e3db90f04d3df749923b1763de1b58c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/312d5e0158617b367cb0fd246c83bb36.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0817e4c901a4729662505086e7ec6c69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6ea4ced7d3817604c02e8793f28ccf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c31fbfce3b4faf00ab7e4388f37ecc5d.png)
(3)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b7cbba6f130b84315180391c177d0c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d92355504a42ddba1d0f03d5db455858.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56448a74c1b8430c425d79d626764f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
您最近一年使用:0次
2021-07-12更新
|
1025次组卷
|
9卷引用:上海市华东师范大学第二附属中学2020-2021学年高一下学期期末数学试题
(已下线)上海市华东师范大学第二附属中学2020-2021学年高一下学期期末数学试题(已下线)专题13 平面向量(练习)-2上海市七宝中学附属鑫都实验中学2021-2022学年高一下学期期末数学试题(已下线)上海高二下学期期末真题精选(压轴60题35个考点专练)-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)(已下线)高一下学期期末真题精选(压轴60题20个考点专练)-【满分全攻略】2022-2023学年高一数学下学期核心考点+重难点讲练与测试(人教A版2019必修第二册)(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02 平面向量-《期末真题分类汇编》(上海专用)(已下线)上海市高一下学期期末真题必刷04-期末考点大串讲(沪教版2020必修二)上海市金山中学2023-2024学年高一下学期期末考试数学试卷
名校
9 . 如图,已知点
是边长为1的等边
内一点,满足
,过点
的直线
分别交
,
于点
,
.设
,
,则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/2021/7/9/2760355507085312/2762005288312832/STEM/e8e74121-cd2e-4fad-b0c5-ff82aad8ae16.png?resizew=264)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c41af21f3c86faeb4b18e6ba7abf67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.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/4f0d53573554894dbe3b31027d7cdfe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c9ca024d66f87e779fee3922c3b37b.png)
![](https://img.xkw.com/dksih/QBM/2021/7/9/2760355507085312/2762005288312832/STEM/e8e74121-cd2e-4fad-b0c5-ff82aad8ae16.png?resizew=264)
A.![]() | B.点![]() ![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2021-07-11更新
|
485次组卷
|
4卷引用:山东省潍坊市2020-2021学年高一下学期期末数学试题
山东省潍坊市2020-2021学年高一下学期期末数学试题湖北省黄冈市蕲春县2021-2022学年高二上学期期中数学试题广东省广州市第四十一中学2021-2022学年高一下学期4月月考数学试题(已下线)专题02 平面向量的相关计算(中档题)-【重难点突破】2021-2022学年高一数学常考题专练(人教A版2019必修第二册)
10 . 折扇是一种用竹木做扇骨,韧纸或绫绢做扇面的能折叠的扇子.用时须展开,成扇形,聚头散尾.如图,某折扇的扇骨长度
,扇面长度
,已知折扇展开所对圆心角的弧度为
,则扇面的面积为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e04c40ba8997a23293eb594fa47cea88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cd4a1c8087ef697d82b321a3331211.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/85ba1dfe-98ea-484a-b33e-9ccfdee323e7.png?resizew=180)
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6卷引用:河南省2020-2021学年下学期高一第三次联考数学试题
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