1 . 在①
是
和
的等差中项;②
;③
.这三个条件中任选一个,补充在下面的问题中,并解答问题.
在
中,角
、
、
所对的边分别为
、
、
,且满足条件 (填写所选条件的序号).
(1)求角
;
(2)若
,求锐角
的周长的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99ea513ef4c8fc4d8c31eff498740680.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4239165ee886662653d8da4c567a79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e7cf7bade77e7e538c9956bed4866b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c9c8a15646d31d91274517d11a4a88.png)
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8120119749d4bc28067e73fca7d46cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2022-02-17更新
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3卷引用:重庆市2022届高三下学期开学考试数学试题
名校
解题方法
2 . 将
个数排成
行
列的一个数阵,如下图:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6b42a6527d536851721e2d6d1779f40.png)
该数阵第一列的
个数从上到下构成以
为公差的等差数列,每一行的
个数从左到右构成以
为公比的等比数列(其中
).已知
,
,记这
个数的和为
.给出下列结论:①
②
③
④![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ee24cb4787a625ef896018298b3a22.png)
其中结论正确的是______ .(填写所有正确答案的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceef1abeeef220b4fe5f7d96feedd90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6b42a6527d536851721e2d6d1779f40.png)
该数阵第一列的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c20bc8da04fbb4bfea4e412274dde2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b73ec6f2aef5440b1b689fe74a8da96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceef1abeeef220b4fe5f7d96feedd90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd9f9fa5a74a471d784caf42fa662a6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0367f5f840bf6ad1c1dc94049a326e26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ee24cb4787a625ef896018298b3a22.png)
其中结论正确的是
您最近一年使用:0次
名校
3 . 如图,下面的表格内的数值填写规则如下:先将第1行的所有空格填上1;再把一个首项为1,公比为
的数列
依次填入第一列的空格内;其它空格按照“任意一格的数是它上面一格的数与它左边一格的数之和”的规则填写
(1)设第2行的数依次为
,试用
表示
的值;
(2)设第3列的数依次为
,求证:对于任意非零实数
,
;
(3)能否找到
的值,使得(2)中的数列
的前
项
成为等比数列?若能找到,
的值有多少个?若不能找到,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
第1列 | 第2列 | 第3列 | … | 第 | |
第1行 | 1 | 1 | 1 | … | 1 |
第2行 | |||||
第3行 | |||||
… | … | ||||
第 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e3d172f08313520e76b6cbc2ff9980c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05efa45c7e0cb072bc50414d5b3af20c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe3c7a8aa20a4d8f59e069331588a8bf.png)
(2)设第3列的数依次为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab48fb927796e4255ce8da7084366f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e8ca54783c66b05d71041fea750943.png)
(3)能否找到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab48fb927796e4255ce8da7084366f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca95e4940cdfab892b9f75620848852e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
4 . 以下各说法中:
①若等比数列
的前
项和为
,
,则实数
=-1;
②若两非零向量
,若
,则
的夹角为锐角;
③在锐角△ABC中,若
,则
,
④已知数列
的通项
,其前
项和为
,则使
最小的
值为5
其中正确说法的有________ (填写所有正确的序号)
①若等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97b794ed9de8e93de6e067c3d0259558.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②若两非零向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdbc0945b4e1962e66f6f7e7f6af235d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
③在锐角△ABC中,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa8d75a6638e08eedbff8662267da6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b56c0452faa9377574227c3df2b4c46.png)
④已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c4593f37ce523cfa8fb5c102240319.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
其中正确说法的有
您最近一年使用:0次
2019-05-23更新
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243次组卷
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2卷引用:湖南省长沙市麓山国际实验学校2022-2023学年高三上学期入学考试数学试题
5 . 国际象棋是国际通行的智力竞技运动.国际象棋使用
格黑白方格相间棋盘,骨牌为每格与棋盘的方格大小相同的
格灰色方格.若某种黑白相间棋盘与骨牌满足以下三点:①每块骨牌覆盖棋盘的相邻两格;②棋盘上每一格都被骨牌覆盖;③没有两块骨牌覆盖同一格,则称骨牌构成了棋盘的一种完全覆盖.显然,我们能够举例说明
格黑白方格相间棋盘能被骨牌完全覆盖.
格黑白方格相间棋盘的对角两格,余下棋盘不能被骨牌完全覆盖;
(2)请你切掉
格的黑白方格相间棋盘的任意两个异色方格,然后画出余下棋盘的一种骨牌完全覆盖方式,并证明:无论切掉的是哪两个异色方格,余下棋盘都能被骨牌完全覆盖;
(3)记
格黑白方格相间棋盘的骨牌完全覆盖方式数为
,数列
的前n项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a96e9c2e2a15130d1d56a1d0e16b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71fb79f6535ee15a3d41ca71cf72082b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a96e9c2e2a15130d1d56a1d0e16b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a96e9c2e2a15130d1d56a1d0e16b72.png)
(2)请你切掉
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a96e9c2e2a15130d1d56a1d0e16b72.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e70354d6ca5ad9f6b4592fac0b5e559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe5d94e748101eaf9aa5ae725b0040e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/485596f7fc2aa8d80466a7d02a00af15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6cfd722654be25b48b28ba0f6698e89.png)
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2024-03-06更新
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4卷引用:山东省菏泽第一中学人民路校区2024届高三下学期开学考试数学试题
山东省菏泽第一中学人民路校区2024届高三下学期开学考试数学试题(已下线)第四套 最新模拟重组卷江苏省苏州大学2024届高考新题型2月指导卷数学试题(已下线)压轴题08计数原理、二项式定理、概率统计压轴题6题型汇总
6 . 2022年北京冬奥会开幕式精彩纷呈,其中雪花造型惊艳全球.有一个同学为了画出漂亮的雪花,将一个边长为1的正六边形进行线性分形.如图,图(n)中每个正六边形的边长是图
中每个正六边形的边长的
.记图(n)中所有正六边形的边长之和为
,则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/2022/7/6/3016722249293824/3017456663044096/STEM/796b58b3864449808ec23533587929c5.png?resizew=307)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c963caefd1a314ca9641ae98ee57237f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://img.xkw.com/dksih/QBM/2022/7/6/3016722249293824/3017456663044096/STEM/796b58b3864449808ec23533587929c5.png?resizew=307)
A.图(4)中共有294个正六边形 |
B.![]() |
C.![]() |
D.记![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2022-07-07更新
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5卷引用:湖南省怀化市麻阳县第一中学2022-2023学年高三上学期开学考试数学试题