名校
解题方法
1 . 在凸四边形
中,
.
(1)若
,
,
,
四点共圆,
,
,
.
①求四边形
的面积;
②求
的值;
(2)若
,
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc0cedfb76e95ae3371fad58069554ea.png)
(1)若
![](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/32104791e7ef79623fe410e4f4a18bec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e39bee1445161f91213c83b498b8ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7660397da21f66377e239a57e26d1c3f.png)
①求四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8bad16b7cdf8c638cd324f5be5d834f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9536a2be7b84612f45cc875a00c5a5d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03d21d06de0d7677aaff4b395b68ef63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0341d5d97dd32312f8cbf89dfed17201.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4465b5971b4a15886bcd69eef74d0700.png)
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2卷引用:江苏省如皋中学2023-2024学年高一下学期教学质量调研(一)数学试题
名校
解题方法
2 . 锐角
的角A,B,C的对边分别为a,b,c,满足
,则
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30c52cac43f9853215319638cf13e8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11f787941cb1abfe9bb757276b765c0b.png)
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2024-04-16更新
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1131次组卷
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3卷引用:江苏省如皋中学2023-2024学年高一下学期教学质量调研(一)数学试题
名校
解题方法
3 . 已知
是单位圆上的三点,满足
,
,且
(
为非零常数),则下列正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ccfaae23a94c6f92581b5271ee7561a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7784e6c622a939f2aaa0c02afd32ac8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/974ea1c156b723429f993a6a5d714db7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e9313001be630624f28b158ee4d5445.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
A.若![]() ![]() | B.若![]() ![]() |
C.![]() | D.![]() |
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名校
解题方法
4 . 已知
与
都是非零有理数,则在
,
,
中,一定是有理数的有( )个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae3c7568ada9b818bb2a7a902f8bc62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d328ffcf1b593e1fe064b1a54e7b5931.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de7d5ef3a3d9a03be91135fc426d57cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
A.0 | B.1 | C.2 | D.3 |
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2024-04-15更新
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381次组卷
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3卷引用:专题02 三角恒等变换(2)-期末考点大串讲(苏教版(2019))
5 . 我国古代数学著作《九章算术》中记载:斜解立方,得两堑堵.其意思是:一个长方体沿对角面一分为二,得到两个一模一样的堑堵.如图,在长方体
中,
,
,
,将长方体
沿平面
一分为二,得到堑堵
,下列结论正确的序号为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f3e58edd1f900ca82bb2a3058293f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679748eab882a6be0fefd2cc300349a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b5b14d74bdf9ed7c45b2e754b7ccc4f.png)
A.堑堵![]() |
B.![]() ![]() ![]() |
C.堑堵![]() ![]() |
D.堑堵![]() |
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名校
解题方法
6 . 在
中,
是边
中点,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
A.若![]() ![]() ![]() ![]() |
B.若点Q是线段AD上的动点,且满足![]() ![]() ![]() |
C.若O为![]() ![]() ![]() |
D.若单位向量![]() ![]() ![]() ![]() |
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名校
解题方法
7 . 依次抛掷一枚质地均匀的骰子两次,
表示事件“第一次抛掷骰子的点数为2”,
表示事件“第一次抛掷骰子的点数为奇数”,
表示事件“两次抛掷骰子的点数之和为6”,
表示事件“两次抛掷骰子的点数之和为7”,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e57c789cfd4b0be7dbf63aa99435656.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c454eeaf119c8a0fc328eb64ff2dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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2024-04-13更新
|
1157次组卷
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8卷引用:专题11 概率归类(1) -期末考点大串讲(苏教版(2019))
(已下线)专题11 概率归类(1) -期末考点大串讲(苏教版(2019))(已下线)10.2?事件的相互独立性——课后作业(巩固版)(已下线)第02讲 事件的相互独立性-《知识解读·题型专练》(人教A版2019必修第二册)(已下线)专题10.8 概率全章综合测试卷(提高篇)-举一反三系列(人教A版2019必修第二册)(已下线)专题06 第十章 概率-期末考点大串讲(人教A版2019必修第二册)(已下线)高一第二学期期末模拟卷01-重难点突破及混淆易错规避(苏教版2019必修第二册)(已下线)【高一模块一】难度3 小题强化限时晋级练(基础3)广东省惠州市第一中学2023-2024学年高二下学期第一次阶段考试(4月)数学试题
8 . 在平面直角坐标系
中,利用公式
①(其中
,
,
,
为常数),将点
变换为点
的坐标,我们称该变换为线性变换,也称①为坐标变换公式,该变换公式①可由
,
,
,
组成的正方形数表
唯一确定,我们将
称为二阶矩阵,矩阵通常用大写英文字母
,
,…表示.
中,将点
绕原点
按逆时针旋转
得到点
(到原点距离不变),求点
的坐标;
(2)如图,在平面直角坐标系
中,将点
绕原点
按逆时针旋转
角得到点
(到原点距离不变),求坐标变换公式及对应的二阶矩阵;
(3)向量
(称为行向量形式),也可以写成
,这种形式的向量称为列向量,线性变换坐标公式①可以表示为:
,则称
是二阶矩阵
与向量
的乘积,设
是一个二阶矩阵,
,
是平面上的任意两个向量,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba6e18ee381b4e43352acb377fdb4bf0.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/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ee82573986d4fa6a7ee1b5f397edae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0859290725efef72a1b04f473d07da6e.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/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c84c4a85e9f31e35bc48c15d9873a03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c84c4a85e9f31e35bc48c15d9873a03.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/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39822cb6df5463c27ac9bfed261a2ff6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/762bfc20a2da28b3c59225851ea40036.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/762bfc20a2da28b3c59225851ea40036.png)
(2)如图,在平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ee82573986d4fa6a7ee1b5f397edae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0859290725efef72a1b04f473d07da6e.png)
(3)向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4224bf1cbcd51f4cbdce93d981d65c5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c17f1f4912527319e32f60e7523c65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26b9e508047e76f3a7ad88d587702ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd47bfcd685d2466ee27c01bf286406.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c84c4a85e9f31e35bc48c15d9873a03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c17f1f4912527319e32f60e7523c65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f7a1df960feef63dec4790d63f52279.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b8a88a16125366536cb4ad658e0cf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/595e7e1d74355ac82dcfc16b3e86cf78.png)
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7卷引用:模块五 专题5 全真拔高模拟1(苏教版期中研习高一)
(已下线)模块五 专题5 全真拔高模拟1(苏教版期中研习高一)(已下线)模块五 专题5 全真拔高模拟1(高一人教B版期中)安徽省皖江名校联盟2024届高三下学期4月模拟数学试题(已下线)数学(新高考卷02,新题型结构)(已下线)压轴题02圆锥曲线压轴题17题型汇总-1湖南省湘楚名校2023-2024学年高二下学期5月月考数学试题黑龙江省实验中学2024届高三第四次模拟考试数学试题
名校
解题方法
9 . 由倍角公式
,可知
可以表示为
的二次多项式.对于
,我们有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8604f1213464671ae14ff30411929efd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b752c5b70e8bef980994bfbb88df7cbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24ac6009b4b740312dc0af7045c62549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51a08df228aef6b4c7088a9f9753e520.png)
可见
也可以表示成
的三次多项式.
(1)利用上述结论,求
的值;
(2)化简
;并利用此结果求
的值;
(3)已知方程
在
上有三个根,记为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c91d0d02d04a3f1b777b0d86e2372e46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5ff5a2e7663e6a21ccea3149a10113.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e039219978242ec380e66de6cf9bab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8604f1213464671ae14ff30411929efd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b752c5b70e8bef980994bfbb88df7cbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24ac6009b4b740312dc0af7045c62549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51a08df228aef6b4c7088a9f9753e520.png)
可见
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e039219978242ec380e66de6cf9bab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
(1)利用上述结论,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d0ac5e4a6ef4f217b2ffb08aea29489.png)
(2)化简
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f57e191a75514170400a9af7a1f28013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a88b4e0ab9e63411ab2e1ddb5dcdba6.png)
(3)已知方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b322f4b08de183d0897d4d81050d9e63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc30165c18de623d0a3efb961e606d1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc6fb329f26c7281c111e8997057cf4.png)
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2024-04-11更新
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785次组卷
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4卷引用:江苏省泰州中学2023-2024学年高一下学期期中考试数学试题
江苏省泰州中学2023-2024学年高一下学期期中考试数学试题(已下线)模块三专题2 新定义专练【高一下人教B版】江西省南昌市第五高级中学2023-2024学年高一下学期期中考试数学试卷(已下线)专题04 三角函数恒等变形综合大题归类 -期末考点大串讲(苏教版(2019))
名校
解题方法
10 . 已知锐角
三个内角
的对应边分别为
,且
.则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d54d65f4c2bfd7fc736e021643b3f0e9.png)
A.![]() ![]() |
B.![]() ![]() |
C.![]() |
D.![]() ![]() |
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