名校
解题方法
1 . 已知等差数列
满足,
,等比数列
的公比
,令![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b57b19c8d7ce597a64b147e06ef12c4.png)
的前
项和为
,若“
”是“
”的充分条件,则正整数
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1579e5e7d44cb8215a6d87280371be7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b1a1b910ff5ef0d244d659ccd6bc07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b57b19c8d7ce597a64b147e06ef12c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.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/84c29bfcb2e31e3c21967ede660eaa0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dd643a1cdf1bc2d2740c393746d75aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
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2 . 在平面直角坐标系中,二元方程
的曲线为
,若存在一个定点
和一个定角
,使得曲线
上的所有点以
为中心顺时针(或逆时针)旋转角
,所得到的图形与原曲线重合,则称曲线
为旋转对称曲线.给出以下方程及其对应的曲线:
; ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/199da209c1d449712901f9d8fa751d10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d69accbf3a6fb381616ae0a7c43b160.png)
其中是旋转对称曲线的是__ (填上所有符合题意的曲线).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31a6af0c85c1a59c2b77b6e550e1ef54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de72548ccc62e6e15d1be4afcdf09ad5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f036026cd92e9ad059c3f22a7658638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/199da209c1d449712901f9d8fa751d10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55411ad607653d2077c4e6ca583f985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d69accbf3a6fb381616ae0a7c43b160.png)
其中是旋转对称曲线的是
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解题方法
3 . 在
中,
,
,点
在
所在平面外,
平面
,且
,设
分别是线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/17/5c4393de-3ca6-4b65-95ad-2780d61ceb6c.png?resizew=184)
(1)求证:
是异面直线
与
的公垂线段.
(2)若过点
分别作
的垂线
,其中
分别是垂足,求四面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829f9180ddd9aa1a0ee0dc520f4e0b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3a51949f48ee8cf746851ba779b078e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cca777c664ecc22e40dff4ccae6b248.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/17/5c4393de-3ca6-4b65-95ad-2780d61ceb6c.png?resizew=184)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ace5e8c3769ad8f370c86f879246c174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b14fa212bbddd28310d463fcdef7e62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a406f24b5131eb7da9127750319e52.png)
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4 . 已知:如图在Rt△ABC中,斜边
厘米,
厘米,
厘米,
且
是方程
的两根.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/17/4761951c-26cd-4457-bf4a-8910c754afce.png?resizew=181)
(1)求
和b的值;
(2)
与
开始时完全重合,然后让
固定不动,将
以1厘米/秒的速度沿
所在的直线向左移动.
①设x秒后
与
的重叠部分的面积为y平方厘米,求y与x之间的函数关系式,并写出x的取值范围;
②几秒后重叠部分的面积等于
平方厘米?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e781a2489271bfd1597cba1bb6f5887.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df81cda12d7601d58b1d9c7c180c4d66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1deee72bceaa54534cf6735ca610159c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/17/4761951c-26cd-4457-bf4a-8910c754afce.png?resizew=181)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ee6e1d480ece7117e1f87ebf4bbeea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ee6e1d480ece7117e1f87ebf4bbeea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
①设x秒后
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ee6e1d480ece7117e1f87ebf4bbeea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
②几秒后重叠部分的面积等于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69ee3c61d2298e75fc4f1643f8ebc2e4.png)
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5 . 已知
为正整数.
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e881a784e2b5216ba5562e07c4553a4e.png)
不能 表示为两个以上连续整数的乘积;
(2)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e881a784e2b5216ba5562e07c4553a4e.png)
能 表示为两个连续整数的乘积,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e881a784e2b5216ba5562e07c4553a4e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e881a784e2b5216ba5562e07c4553a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-02-15更新
|
161次组卷
|
2卷引用:安徽省宣城市泾县中学2021年强基夏令营选拔测试数学试题
名校
6 . 有三个含30°角的直角三角形,它们的大小互不相同,但均有一条长为a的边.这三个三角形按照从大到小的顺序,求其面积比.
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7 . 如图,已知⊙
、⊙
的半径分别为
、
,⊙
经过点
,且两圆相交于点A、B,C为⊙
上的点,连接AC交⊙
于点D,再连接BC、BD、
、
、
有如下四个结论:①
, ②
, ③AD=DC, ④BC=DC,其中正确结论的序号为______________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2858005b9ae89ae080d83dcc13cf8e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3e95410f3b4fcb0cba425b521d1f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cee51552e3c12bc27cf8ab1777bf191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6973bc602348065901b58bb1b4e6bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28677c8dd8bb83b996d1d9e4fc6ef21b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45143c362aa4cdb71c347561f2455593.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/19/35a53867-c1bb-48ef-8fd9-15fd595702cc.png?resizew=187)
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8 . 一副牌共52张有4种花色,每种花色有13张,从中任意抽牌,最小要抽( )张才能保证有4张牌是同一花色的.
A.12 | B.13 | C.14 | D.15 |
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名校
解题方法
9 . 《国家学生体质健康标准》是国家学校教育工作的基础性指导文件和教育质量基本标准,它适用于全日制普通小学、初中、普通高中、中等职业学校、普通高等学校的学生.某高校组织
名大一新生进行体质健康测试,现抽查200名大一新生的体测成绩,得到如图所示的频率分布直方图,其中分组区间为
,
,
,
,
,
.则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/12/49df06b2-7b4e-475f-bd73-0202ed80991b.png?resizew=283)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1573487be070cf0847e22a2cb58064b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2cf2aad32b9540b16449481bf7b1669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066d47d226719ca80f3f24f2dde65a9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffb5b8bf335579b66fa92fa81e5fa1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34fc5b6de3512fa8569880c61bf786e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc92342c85a71e1bb90197319d288e83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b9bde9d7fe02d13ac6224d3c29a8342.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/12/49df06b2-7b4e-475f-bd73-0202ed80991b.png?resizew=283)
A.估计该样本的众数是![]() |
B.估计该样本的均值是![]() |
C.估计该样本的中位数是![]() |
D.若测试成绩达到![]() ![]() |
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2023-02-11更新
|
831次组卷
|
6卷引用:湖南省株洲市第二中学2022届高三上学期第三次月考数学试题
湖南省株洲市第二中学2022届高三上学期第三次月考数学试题浙江省温州市2023届高三下学期返校统一测试数学试题(已下线)9.2 用样本估计总体(学案)-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)(已下线)9.2 用样本估计总体(精练)-【题型分类归纳】湖南省邵阳市洞口县第二中学2023-2024学年高二上学期第一次月考数学试题广东省台山市第一中学2024届高三上学期第一次月考数学试题
名校
10 . 第14届国际数学教育大会(ICME-14)将于2021年7月11日至7月18日在上海华东师范大学中山北路校区举办,这是大会首次在中国举办,大会会标如图所示,会标右下方的符号
,是用八进制数字表示的年份,换算成十进制是2020,已知八进制的数字
换算成十进制为
,则这四个符号表示的数字依次是_______ .
![](https://img.xkw.com/dksih/QBM/2023/2/8/3170548510908416/3171074553954304/STEM/a5b7137f3d3a40d3907e1809f64d0b60.png?resizew=74)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72599717c20b9592c2c60dab16de30cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0899bd4bccbd001676f24758d7778f1a.png)
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