名校
1 . 如图,设
,且
,当
时,定义平面坐标系
为
的斜坐标系,在
的斜坐标系中,任意一点
的斜坐标这样定义:设
,
是分别与
轴,
轴正方向相同的单位向量,若
,记
,则下列结论中正确的是( )
![](https://img.xkw.com/dksih/QBM/2021/6/2/2734198164643840/2782411138621440/STEM/7a966c42-9f40-489f-8185-b79fe6283248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f55b8836b41be612a52ca9caf97006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d26c9fc8cfa002f40ea3908575c8ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58ca0fbe6fbda5d57855ee78caa84bf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b28baf17059c56ee9ad1ae4814acd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b04618e5b2db68f2de6ba68972c505c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b257fe21a91d22e853b1642c9d44647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beeef1949e7c1280442c22fb01dd8e75.png)
![](https://img.xkw.com/dksih/QBM/2021/6/2/2734198164643840/2782411138621440/STEM/7a966c42-9f40-489f-8185-b79fe6283248.png)
A.设![]() ![]() ![]() ![]() ![]() |
B.设![]() ![]() |
C.设![]() ![]() ![]() ![]() |
D.设![]() ![]() ![]() ![]() ![]() ![]() |
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3卷引用:山东省潍坊市2020-2021学年高一下学期期中考试数学试题
2 . 已知
,
,
,
是平面上四个点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82cb6b440405e6e7774ae5449aca8b80.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82cb6b440405e6e7774ae5449aca8b80.png)
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解题方法
3 . 在日常生活中,我们常常会看到两个人共提一个行李包的情景,若行李包所受的重力为
,两个拉力分别为
,
,且
,
与
夹角为
,当两人拎起行李包时,下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/fd84dc8b-3982-4035-b6c5-062f3843305b.png?resizew=145)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefbf34ef220b74613f1b2daa522c74d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/fd84dc8b-3982-4035-b6c5-062f3843305b.png?resizew=145)
A.![]() | B.当![]() ![]() |
C.当![]() | D.当![]() ![]() |
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解题方法
4 . 已知向量
,向量
,向量
(其中
),且
.
(1)求
的值和
;
(2)若
,
,且
、
、
三点共线,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fee11a449e8e98bef785ba333baf099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90cb7508d9c38e4847bd0853cf770ddb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a49ceaebcb3b126da175e107e97b16b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2725a89d93c791f7a0098f4964587905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00e13dedea6141c353ac153aa40a1f0e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b0fe4d834e8eaca89ceaf9c64cdabd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc7b78b446c05c9aea5bf87c7b17258a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e2715dd9d0ec90bbe2291ee8ad4526e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc965d5374f406bcc800d140830c0d23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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5 . 斐波那契螺旋线被誉为自然界最完美的“黄金螺旋”,它的画法是:以斐波那契数1,1,2,3,5,8…作为正方形的边长拼成长方形,然后在每个正方形中画一个圆心角为90°的圆弧,这些圆弧所连起来的弧线就是斐波那契螺旋线.如图这些圆弧所连成的弧线就是斐波那契螺旋线的前一部分,则阴影部分的面积与矩形
的面积之比为( )
![](https://img.xkw.com/dksih/QBM/2021/6/2/2734198164643840/2782411138383872/STEM/7dc1665e-39bc-4c26-85f1-1ba35ea02364.png?resizew=333)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2021/6/2/2734198164643840/2782411138383872/STEM/7dc1665e-39bc-4c26-85f1-1ba35ea02364.png?resizew=333)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
6 . 如图,在矩形
中,
,
,
为
的中点,
与
交于点
,则
( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/6a43d8c2-7aa2-4cfa-98f7-5d0f74219f11.png?resizew=173)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7a93a1399ff7a2bde342652479241b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b54aa2b7f9adf409f0ce8e00615432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3874cfb92230922f405524750c7c61e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/6a43d8c2-7aa2-4cfa-98f7-5d0f74219f11.png?resizew=173)
A.![]() | B.![]() | C.![]() | D.![]() |
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4卷引用:山东省潍坊市2020-2021学年高一下学期期中考试数学试题
山东省潍坊市2020-2021学年高一下学期期中考试数学试题(已下线)6.1.5向量的线性运算-2021-2022学年高一数学同步知识梳理+考点精讲精练(人教B版2019必修第二册)山东省潍坊市高密市第一中学2022-2023学年高一下学期4月月考数学试题陕西省西安市周至县第六中学2022-2023学年高一下学期第一次月考数学试题
名校
解题方法
7 . 函数
的定义域为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0c2e872f11ffbf1d6bf6fbf50639ae.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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5卷引用:山东省潍坊市2020-2021学年高一下学期期中考试数学试题
山东省潍坊市2020-2021学年高一下学期期中考试数学试题(已下线)专题5.5 正切函数的图象与性质-《聚能闯关》2021-2022学年高一数学提优闯关训练(人教A版2019必修第一册)黑龙江省大庆市大庆中学2021-2022学年高一上学期期末数学试题广西钦州市第四中学2022-2023学年高一下学期3月月考数学试题(已下线)第12讲 三角函数的图像与性质(13大考点)(3)
8 . 2021°角的终边所在的象限是( )
A.第一象限 | B.第二象限 | C.第三象限 | D.第四象限 |
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4卷引用:山东省潍坊市2020-2021学年高一下学期期中考试数学试题
山东省潍坊市2020-2021学年高一下学期期中考试数学试题(已下线)第1课时 课后 任意角(已下线)5.1任意角和弧度制(课堂探究+专题训练)-2021-2022学年高一数学课堂精选(人教A版2019必修第一册)江苏省百校大联考2021-2022学年高一上学期12月阶段测试数学试题
9 . 如图所示,在直角坐标系
中,角
的顶点与坐标原点
重合,始边落在
轴的正半轴上,终边与单位圆的交点为
,其中
.
![](https://img.xkw.com/dksih/QBM/2021/6/2/2734198164643840/2782411138768896/STEM/042dfe4c-f333-4a63-8222-6bd2ad8c5c3b.png?resizew=276)
(1)求
和
,
,
的值;
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ba700869f642c69bafadde89179f9bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b170470d02c85c1be9a3faff5eca0de.png)
![](https://img.xkw.com/dksih/QBM/2021/6/2/2734198164643840/2782411138768896/STEM/042dfe4c-f333-4a63-8222-6bd2ad8c5c3b.png?resizew=276)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8112f9185c7d48b015d9cd0525616b31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4179e1ab8705cf19ea7aaf48888843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d66c03d4ca06819a6ce7fc8ea6de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc9750c313ee972124cb62c4a6fb7ea.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5004a2aa94a7a520dcb51d374b751684.png)
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2卷引用:山东省潍坊市2020-2021学年高一下学期期中考试数学试题
解题方法
10 . 潍坊的传统民间工艺有着悠久的历史和深厚的文化底蕴.为弘扬民族文化,潍坊某中学开展劳动实习,学生到一个铸造厂学习铁皮裁剪技术,如图所示,铁皮原料的边界由一个半径为
的半圆弧(点
为圆心)和直径
围成,甲班学生决定将该铁皮原料裁剪成一个矩形
,则当该矩形
的周长最大时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e304cf018473bb54edb166fcd6502b.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e304cf018473bb54edb166fcd6502b.png)
![](https://img.xkw.com/dksih/QBM/2021/6/2/2734198164643840/2782411138752512/STEM/a3908195-637d-4fc6-b4c5-d432eddc578b.png?resizew=283)
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