名校
1 . 如图,边长为1正方形
,射线
从
出发,绕着点
顺时针方向旋转至
,在旋转的过程中,记
,
所经过的在正方形
内的区域(阴影部分)的面积为
,则函数
的图像是
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/111441d2-672b-47d2-9f44-72cb82c041cb.png?resizew=135)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8213df1d2811e0ec5c6d7230fabe1c28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/111441d2-672b-47d2-9f44-72cb82c041cb.png?resizew=135)
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2019-01-11更新
|
817次组卷
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5卷引用:江西省南昌市第二中学2019-2020学年高三5月模拟数学(文)试题
名校
2 . 如图,圆
与
轴的上交点为
,动点
从
点出发沿圆
按逆时针方向运动,设旋转的角度
(
),向量
在
方向的射影为
(
为坐标原点),则
关于
的函数
的图像是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/28/74876af0-04d2-4c89-a207-87ab41d5ada7.png?resizew=121)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df9e6796f834bd176928b408a6c43c32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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2卷引用:江西省九江第一中学2016-2017学年高一下学期期末考试数学(文)试题
14-15高一上·江西赣州·期末
3 . 如图,点
在半径为
的半圆上运动,
是直径,当
沿半圆弧从
到
运动时,点
经过的路程
与
的面积
的函数
的图像是下图中的( )
![](https://img.xkw.com/dksih/QBM/2014/4/2/1571596165136384/1571596170706944/STEM/0264b445970b4a3cb073dc4f67622c50.png?resizew=168)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6d7dd733fe8e8d7bdbe1b8190cfdf47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://img.xkw.com/dksih/QBM/2014/4/2/1571596165136384/1571596170706944/STEM/0264b445970b4a3cb073dc4f67622c50.png?resizew=168)
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2013·江西南昌·二模
4 . 如图,在等腰梯形
中,
,且
,设
,以
为焦点且过点
的双曲线的离心率为
,以
为焦点且过点
的椭圆的离心率为
,设
=
则
的大致图像是( )
![](https://img.xkw.com/dksih/QBM/2013/9/6/1571345106460672/1571345233289216/STEM/7a92ddda0b4545799b4b0f1452c25280.png?resizew=138)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12143a06ed24558d8cc7ad39961d3e1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac7e84e68feb8645c7f78142ae99321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://img.xkw.com/dksih/QBM/2013/9/6/1571345106460672/1571345233289216/STEM/7f81fe19fd50462aa414475a7c8f3c61.png?resizew=14)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://img.xkw.com/dksih/QBM/2013/9/6/1571345106460672/1571345233289216/STEM/7804cf2280994b6f9dd2a70e790700ce.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2013/9/6/1571345106460672/1571345233289216/STEM/ea50ad92062648088573091fb7633bc6.png?resizew=15)
![](https://img.xkw.com/dksih/QBM/2013/9/6/1571345106460672/1571345233289216/STEM/2237166cf1d4462faf0d2726b1de0d22.png?resizew=112)
![](https://img.xkw.com/dksih/QBM/2013/9/6/1571345106460672/1571345233289216/STEM/248fe77891ae4d5388586151325f9ca7.png?resizew=69)
![](https://img.xkw.com/dksih/QBM/2013/9/6/1571345106460672/1571345233289216/STEM/7a92ddda0b4545799b4b0f1452c25280.png?resizew=138)
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2013·江西南昌·二模
5 . 如图正四棱锥
的底面边长为
,高
,点
在高
上,且
,记过点
的球的半径为
,则函数
的大致图像是( )![](https://img.xkw.com/dksih/QBM/2013/5/7/1571205295046656/1571205300576256/STEM/cd3778eab51b43ba807904384125a3cb.png?resizew=120)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6420a99e3cbb9b591f8387f87c8dcff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34c157ff302a881c17514534903c575f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a798ed78ab21442b414f8b1b5510ccef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fcd39af23c7f431de48947f3f34f5ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9966dfe9109671c587892bd32f0b6699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9966dfe9109671c587892bd32f0b6699.png)
![](https://img.xkw.com/dksih/QBM/2013/5/7/1571205295046656/1571205300576256/STEM/cd3778eab51b43ba807904384125a3cb.png?resizew=120)
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2013·江西吉安·一模
6 . 如图,在等腰梯形
中,
,且
,设
=
,
∈(0,
),以
为焦点且过点
的双曲线的离心率为
,以
为焦点且过点
的椭圆的离心率为
,设
的大致图像是
![](https://img.xkw.com/dksih/QBM/2013/7/18/1571291601772544/1571291607252992/STEM/fb4cd6805a1d4d568a7fc09d907de274.png?resizew=132)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37591109b0a0ec5ffe2133f83310eca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12143a06ed24558d8cc7ad39961d3e1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4189a0821a0ffab9dc171ecd279ba442.png)
![](https://img.xkw.com/dksih/QBM/2013/7/18/1571291601772544/1571291607252992/STEM/168bc2207b1d4fccb2705a8a4bcf110d.png?resizew=13)
![](https://img.xkw.com/dksih/QBM/2013/7/18/1571291601772544/1571291607252992/STEM/168bc2207b1d4fccb2705a8a4bcf110d.png?resizew=13)
![](https://img.xkw.com/dksih/QBM/2013/7/18/1571291601772544/1571291607252992/STEM/b6d20102b2fd43bb9d3ce03523a5d031.png?resizew=17)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33558881906c228c262ff8024dcfc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
![](https://img.xkw.com/dksih/QBM/2013/7/18/1571291601772544/1571291607252992/STEM/f558fc36879840f49e866344d5346611.png?resizew=229)
![](https://img.xkw.com/dksih/QBM/2013/7/18/1571291601772544/1571291607252992/STEM/fb4cd6805a1d4d568a7fc09d907de274.png?resizew=132)
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7 . 圭表(如图1)是我国古代一种通过测量正午日影长度来推定节气的天文仪器,它包括一根直立的标竿(称为“表”)和一把呈南北方向水平固定摆放的与标竿垂直的长尺(称为“圭”).当正午太阳照射在表上时,日影便会投影在圭面上,圭面上日影长度最长的那一天定为冬至,日影长度最短的那一天定为夏至.图2是一个根据北京的地理位置设计的圭表的示意图,已知北京冬至正午太阳高度角(即
)为
,夏至正午太阳高度角(即
)为
,圭面上冬至线与夏至线之间的距离(即DB的长)为a,则表高(即AC的长)为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/081bedfbdfc071fb0f38fc41969f77b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3981e7286d41960daf4e110c1c84e03a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df51595f64ab3545d5ccfb8e6bcca23d.png)
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2020-11-06更新
|
2607次组卷
|
21卷引用:江西省景德镇一中2020-2021学年高二上学期期中考试数学(理)试题
江西省景德镇一中2020-2021学年高二上学期期中考试数学(理)试题北京市朝阳区2020届高三年级下学期二模数学试题2021届高三高考必杀技之信息阅读题--类型3 三角函数与解三角形吉林省长春市第二实验中学2020-2021学年高一下学期4月月考数学试题北京市八一学校2020-2021学年高一下学期期末数学试题山西省怀仁市第一中学2020-2021学年高一下学期期中数学试题福建省厦门市集美中学2020-2021学年高一4月月考数学试题北京市育英学校2020-2021学年高一下学期期末数学试题江苏省南通市海安市南莫中学2020-2021学年高一下学期期中数学试题江苏省盐城市滨海县东元中学2020-2021学年高一下学期期中数学试题湖南省常德市第二中学2020-2021学年高一下学期期中数学试题陕西省汉中市2022届高三下学期教学质量第二次检测考试文科数学试题陕西省汉中市2022届高三下学期教学质量第二次检测考试理科数学试题江苏省江浦高级中学2021-2022学年高一下学期期中数学试题广东省佛山市第一中学2021-2022学年高一下学期期中数学试题河北省石家庄市2021-2022学年高一下学期期末数学试题广西壮族自治区南宁市第三中学2023届高三模拟数学(理)试题(二)(已下线)模块四 专题1 期末重组综合练(河北)河北省石家庄市第一中学2022-2023学年高一下学期期末数学试题(已下线)高一下期中真题精选(常考60题专练)-【满分全攻略】2022-2023学年高一数学下学期核心考点+重难点讲练与测试(人教A版2019必修第二册)北京市汇文中学2023-2024学年高一下学期期中考试数学试卷
名校
解题方法
8 . 已知四棱锥
(图1)的三视图如图2所示,
为正三角形,
底面
,俯视图是直角梯形.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/5a697955-c9ca-493f-94d9-95f4c799e63c.png?resizew=311)
(1)求正视图的面积;
(2)求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/5a697955-c9ca-493f-94d9-95f4c799e63c.png?resizew=311)
(1)求正视图的面积;
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
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9 . 某校全体教师年龄的频率分布表如表1所示,其中男教师年龄的频率分布直方图如图2所示.已知该校年龄在
岁以下的教师中,男女教师的人数相等.
表1:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/3/87bde2e4-f486-4c3c-a167-0401c904a503.png?resizew=264)
(1)求图2中
的值;
(2)若按性别分层抽样,随机抽取16人参加技能比赛活动,求男女教师抽取的人数;
(3)若从年龄在
的教师中随机抽取2人,参加重阳节活动,求至少有1名女教师的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba505969331b28f0e2d3047d49988914.png)
表1:
年龄(岁) | [25,30) | [30,35) | [35,40) | [40,30) | [45,50) | [50,55) | [55,60) | 合计 |
人数 | 6 | 8 | 11 | 23 | 18 | 9 | 5 | 80 |
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/3/87bde2e4-f486-4c3c-a167-0401c904a503.png?resizew=264)
(1)求图2中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若按性别分层抽样,随机抽取16人参加技能比赛活动,求男女教师抽取的人数;
(3)若从年龄在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3936da712fd5463f7d7c50a5f8f449.png)
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10 . 近年来,随着我国汽车消费水平的提高,二手车流通行业得到迅猛发展.某汽车交易市场对2017年成交的二手车交易前的使用时间(以下简称“使用时间”)进行统计,得到频率分布直方图如图1.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/3/13623c64-470f-45ac-9ca6-14cdf7b1db20.png?resizew=536)
附注:①对于一组数据
,
,…,
,其回归直线
的斜率和截距的最小二乘估计分别为
,
;
②参考数据:
,
,
,
,
.
(Ⅰ)记“在2017年成交的二手车中随机选取一辆,该车的使用年限在
”为事件
,试估计
的概率;
(Ⅱ)根据该汽车交易市场的历史资料,得到散点图如图2,其中
(单位:年)表示二手车的使用时间,
(单位:万元)表示相应的二手车的平均交易价格.由散点图看出,可采用
作为二手车平均交易价格
关于其使用年限
的回归方程,相关数据如下表(表中
,
):
①根据回归方程类型及表中数据,建立
关于
的回归方程;
②该汽车交易市场对使用8年以内(含8年)的二手车收取成交价格
的佣金,对使用时间8年以上(不含8年)的二手车收取成交价格
的佣金.在图1对使用时间的分组中,以各组的区间中点值代表该组的各个值.若以2017年的数据作为决策依据,计算该汽车交易市场对成交的每辆车收取的平均佣金.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/3/13623c64-470f-45ac-9ca6-14cdf7b1db20.png?resizew=536)
附注:①对于一组数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1c6aadc0129bf86f4fff9dcfb924b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/154100371e025fffe0ffae8be9567383.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a14e40329de36fc4a1a3f8fbfafda12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b217e43590a55a9e845a98b65b6ea698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eaf14ff39b5e3d38ca14ddee5a0c21c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a04c0258b10c40100f7436e5e5a0d62.png)
②参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bb6419de115c41a268acf50d071e077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3fcfa18786446c645d1caf478ba1138.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a4addbd6d3545f73ec29faf563ac292.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6703b823c228587469d204b2d055262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b991711f6b845541210aed8f4c645a6.png)
(Ⅰ)记“在2017年成交的二手车中随机选取一辆,该车的使用年限在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e108d24b0d3cb0bd5e2c9827445eec9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(Ⅱ)根据该汽车交易市场的历史资料,得到散点图如图2,其中
![](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/2e5ae7c9c52aeb42a3647267e5f88df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4dfbde71347621b52037755c9fe9480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89c1c174744090ebde8bde8e205c6ae7.png)
![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
5.5 | 8.7 | 1.9 | 301.4 | 79.75 | 385 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
②该汽车交易市场对使用8年以内(含8年)的二手车收取成交价格
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356dd6809a78dacc01ab21226c4afc49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3de0640bc12a9b2ffd7247fa20f1dafd.png)
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