1 . 在一次数学活动课上,老师要求同学们画15°、30°和60°角,小强同学身旁没有量角器,也没有圆规、三角尺,他灵机一动,想到了折纸的办法:他拿出一张矩形纸片
,先对折使
与
重合,如图一,得到折痕
,把纸片展平,再一次折叠纸片
,使点
落在
上的
处,并使折痕经过点
,得到折痕
和线段
.
(1)请直接写出
的度数,并说明理由;
(2)在图一的线段
上取一点
,将
沿着直线
折叠,如图二,使得
点恰好落在线段
上,求
;
(3)若
为
边上一点,如图三,将
沿直线
折叠,
的对应点为
,延长
交
边于点
,延长
交
边于点
,连接
.
①若
,当
时,若存在唯一的点
,使得四边形
为平行四边形,求
的值;
②在①的条件下,若
为线段
上一动点,如图四,连接
,取线段
的中点
,连接
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/8/dc966f24-8ff2-417d-8670-e6f8bdae0cfc.png?resizew=175)
(1)请直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d76e136e7df3692ae6536fc70b6961a9.png)
(2)在图一的线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1028cdd34b2ec5e663dd1f8092a32a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ad8115387158c8dda205d26968ba11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28df0b35b6afe90dcba33b09a4b9b13f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/8/8ec36c3e-4d2b-4248-adbb-853570f3befb.png?resizew=172)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a5e0a51c9e14fb246b0ba0b231c1e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/8/b3f6d92f-b8d9-4863-b6f5-1fb877d0ef77.png?resizew=160)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f6197e055a0bc8a2a0c1414026e6fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cc3dcc4325297dac77a92c0682a6cad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8412a577b2368392d634250d43c57f3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
②在①的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e4fa04825ac7d071968056322d88be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e4fa04825ac7d071968056322d88be.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/8/20dac818-63b8-481e-8185-afa70ca936de.png?resizew=160)
您最近一年使用:0次
2023-09-07更新
|
28次组卷
|
2卷引用:湖南省怀化市洪江市黔阳一中2023-2024学年高一上学期学生学科素养测试数学试题
名校
2 . 如图,在平行四边形
中,
是
的中点,则下列四个结论:
①
;
②若
,
,则
;
③若
,则
;
④若
,则
与
全等.
其中正确的结论为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/7/4db5b0f4-68d3-459f-a868-ccf3c61118ee.png?resizew=179)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/049ba02a6816033ade98e679a59a3b24.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3796f1648a3d17b0e9ff860300a5ead6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f89deb952f57f4b3fa4887b098b7b91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3d1d3c51f36c9913364a8fc8c643530.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594b800b89955d8d2e605cc7977bb75d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2f1e7b232aa818163ce24a549ce1f.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b317b54f6072b74b42e27a534eddf28c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66a5c35b41bb1a8fa59998a6dcc791f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a37ba261860ddad9d11b2e8348a8f3.png)
其中正确的结论为( )
A.① | B.② | C.③ | D.④ |
您最近一年使用:0次
2023-09-07更新
|
24次组卷
|
2卷引用:湖南省怀化市洪江市黔阳一中2023-2024学年高一上学期学生学科素养测试数学试题
名校
3 . 如图,将边长为2cm的正方形
沿其对角线
剪开,再把
沿着
方向平移,得到
,若两个三角形重叠部分的面积为
,则它移动的距离
等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ee6e1d480ece7117e1f87ebf4bbeea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168487ff53e9fb74f786a7e6e78823e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/8/c854bb17-958d-424f-bb32-21c4e3aec8b2.png?resizew=258)
A.0.5cm | B.1cm | C.1.5cm | D.2cm |
您最近一年使用:0次
2023-09-07更新
|
26次组卷
|
3卷引用:湖南省怀化市洪江市黔阳一中2023-2024学年高一上学期学生学科素养测试数学试题
4 . 已知椭圆
,
的上、下顶点是
,
,左,右顶点是
,
,点
在椭圆
内,点
在椭圆
上,在四边形
中,若
,
,且四边形
面积的最大值为
.
(1)求
的值.
(2)已知直线
交椭圆
于
,
两点,直线
与
交于点
,证明:当
变化时,存在不同于
的定点
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baff7011784b367fc9bf84e208269240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1295b852efee8d6d0a92cbe38439c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e94cea3a50438fdf994c44bb79020a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50639bca2f8b8b4f3db2ec01b1fd2ed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab8d0b87680432b4b59bde91688b833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e94cea3a50438fdf994c44bb79020a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533a7b702ada1dd80123e4041271d521.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/303094682b317daea83be885d1c7ff4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec18c028746b73be7503ff6ff458a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0db06552aa4469859f27f601d5f07536.png)
您最近一年使用:0次
2023-02-14更新
|
960次组卷
|
3卷引用:湖南省怀化市长沙市长郡中学等3校2023届高三上学期开学考试数学试题
解题方法
5 . 为有效控制我国儿童和青少年近视发病率,提高儿童和青少年的视力健康水平,教育部发文鼓励和倡导学生积极参加乒乓球、羽毛球等有益于眼肌锻炼的体育活动.某学校提倡学生利用暑期的早上和晚上参加体育锻炼活动,已知甲、乙两位同学都选择羽毛球作为暑期的体育锻炼活动,这两位同学过去30天的安排如下表:
假设甲、乙每天的选择相互独立,用频率代替概率.
(1)在过去的30天内任取一天,求甲同学在这一天中参加了羽毛球活动的概率;
(2)只考虑早上和晚上参加体育锻炼活动的情况,且早上和晚上都参加体育锻炼活动视为参加了2次锻炼,求甲、乙两位同学在一天中参加锻炼的次数之和为2的概率.
锻炼项目(早上,晚上) | (羽毛球,休息) | (休息,羽毛球) | (休息,休息) | (羽毛球,羽毛球) |
甲 | 10天 | 10天 | 5天 | 5天 |
乙 | 8天 | 7天 | 5天 | 10天 |
(1)在过去的30天内任取一天,求甲同学在这一天中参加了羽毛球活动的概率;
(2)只考虑早上和晚上参加体育锻炼活动的情况,且早上和晚上都参加体育锻炼活动视为参加了2次锻炼,求甲、乙两位同学在一天中参加锻炼的次数之和为2的概率.
您最近一年使用:0次
6 . 小军进入高一后的12次数学考试成绩如下:
110,95,90,102,120,100,110,115,98,125,106,130,则( )
110,95,90,102,120,100,110,115,98,125,106,130,则( )
A.这12次数学考试成绩的极差为40 |
B.这12次数学考试成绩的众数为110 |
C.这12次数学考试成绩的50%分位数比40%分位数多5 |
D.在这12次数学考试成绩中,120分及以上数学成绩的标准差为![]() |
您最近一年使用:0次
名校
7 . 已知空间中三点
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fee493bf1eac50f2ae85d4f4b9e393.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d3f874bbb4536aa563f6a530934d0a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ad11597e0c15853ed65e1e5c0058b4b.png)
A.![]() | B.![]() |
C.![]() | D.A,B,C三点共线 |
您最近一年使用:0次
2022-08-30更新
|
1749次组卷
|
13卷引用:湖南省怀化市2022-2023学年高二上学期开学考试数学试题
湖南省怀化市2022-2023学年高二上学期开学考试数学试题重庆市万州清泉中学2022-2023学年高二上学期9月月考数学试题浙江省温州市平阳县万全综合高级中学2022-2023学年高二上学期10月检测数学试题重庆市涪陵第二中学校2022-2023学年高二上学期第一次月考数学试题福建省厦门第六中学2022-2023学年高二上学期期中质量检测数学试题重庆市第七中学校2022-2023学年高二上学期期中数学试题黑龙江省哈尔滨市第一中学校2022-2023学年高二上学期11月月考数学试题湖南省娄底市新化县第一中学2022-2023学年高二上学期期末线上测试数学试题河南省南阳市邓州市邓州春雨国文学校2022-2023学年高二下学期6月月考数学试题山东省枣庄市第八中学2023-2024学年高二上学期第一阶段性检测数学试题(一) 云南省昆明市云南师范大学附属中学2023-2024学年高二上学期10月月考数学试题福建省厦门外国语学校2023-2024学年高二上学期10月阶段性检测数学试题河北华北油田第五中学2023-2024学年高二上学期十月月考数学试题
解题方法
8 . 已知甲箱有2个红球和2个白球,乙箱有3个红球和3个白球,现任选1个箱子并从中任取1个球,记下球的颜色后将球放入另1个箱子内,再任选1个箱子并任取1个球,若两次取出的球的颜色相同为“成功”,则( )
A.两次都从甲箱取球时“成功”的概率最大 |
B.两次都从乙箱取球时“成功”的概率最大 |
C.先从甲箱取球再从乙箱取球时“成功”的概率最大 |
D.先从乙箱取球再从甲箱取球时“成功"”的概率最大 |
您最近一年使用:0次
名校
9 . 某位同学记录了100次上学所用时间(单位:分钟),得到如图的频率分布直方图,则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/28/fc3acfc2-cd04-4e79-a034-6374e9187fb2.png?resizew=276)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/28/fc3acfc2-cd04-4e79-a034-6374e9187fb2.png?resizew=276)
A.![]() |
B.上学所用时间平均数的估计值小于14 |
C.上学所用时间超过15分钟的概率大约为0.17 |
D.上学所用时间的众数和中位数的估计值相等 |
您最近一年使用:0次
2022-07-15更新
|
866次组卷
|
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
10 . 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
|
907次组卷
|
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