2020高三上·全国·专题练习
名校
1 . 某农家小院内有一块由线段OA,OC,CB及曲线AB围成的地块,已知
,点A,B到OC所在直线的距离分别为1 m,2 m,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914d61e5f5f0c15f6981c41dfe8e3255.png)
,建立如图所示的平面直角坐标系xOy,已知曲线OAB是函数
的图象,其中曲线AB是函数
图象的一部分.
![](https://img.xkw.com/dksih/QBM/2021/4/14/2699811665330176/2699862770778112/STEM/52282b5d-52ca-40d4-9625-06ead518db53.png?resizew=240)
(1)求函数
的解析式;
(2)P是函数
的图象上的动点,现要在如图所示的阴影部分(即平行四边形PMCN及其内部)种植蔬菜,求种植蔬菜区域的最大面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd92d14b1a3a2f4be4cfa7bcc148cdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3dc14923ef3c7b89d45c3bc288d0cf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914d61e5f5f0c15f6981c41dfe8e3255.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/993da367a953a504df8255604ed63ba3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee3cbc5bd8c191b020f90da71a14f2d.png)
![](https://img.xkw.com/dksih/QBM/2021/4/14/2699811665330176/2699862770778112/STEM/52282b5d-52ca-40d4-9625-06ead518db53.png?resizew=240)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)P是函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
您最近一年使用:0次
2021-04-14更新
|
958次组卷
|
7卷引用:理科数学-学科网2020年高三11月大联考(新课标Ⅱ卷)
(已下线)理科数学-学科网2020年高三11月大联考(新课标Ⅱ卷)(已下线)数学-学科网2020年高三11月大联考(广东卷)(已下线)专题05函数的概念及表示-2022年(新高考)数学高频考点+重点题型江苏省苏州中学2020-2021学年高二下学期期中数学试题(已下线)热点03 求解函数解析式-2022年高考数学核心热点突破(全国通用版)【学科网名师堂】2023版 苏教版(2019) 选修第一册 名师精选卷 高考水平模拟性测试卷(二)(已下线)专题05 函数的概念及表示
2020高三·全国·专题练习
2 . 如果一个棱锥底面为正多边形,且顶点在底面的射影是底面的中心,这样的棱锥称为正棱锥.已知正四棱锥
内接于半径为
的球,则当此正四棱锥的体积最大时,其高为_____
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
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解题方法
3 . 如图,已知边长为2的正方形材料
,截去如图所示的阴影部分后,可焊接成一个正四棱锥的封闭容器.设
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/201001b3-a388-4571-a504-479bc3dab7da.png?resizew=427)
(1)用
表示此容器的体积;
(2)当此容器的体积最大时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5552174b50bf0445b66c0d475a27b647.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/201001b3-a388-4571-a504-479bc3dab7da.png?resizew=427)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)当此容器的体积最大时,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
您最近一年使用:0次
4 . 如图所示,等边三角形
的边长为2,
,
分别是
,
上的点,满足
,将
沿直线
折到
,则在翻折过程中,下列说法正确的个数是( )
①
;
②
,使得
平面
;
③若存在平面
平面
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e68a20c2d5b0b4238ea8b0564d044329.png)
![](https://img.xkw.com/dksih/QBM/2020/11/3/2584971638710272/2585617835597824/STEM/87729c63-06b3-4089-b40b-fafbc01d946b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e210c9698063925ad2df6b6c1749571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc7f32e4c7d1fcafc3fe0dbcf08fdd2e.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27cbdf3ac8b81542f479b8bd06df2087.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec16c7ffbe35c622363e7f09c6a23ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e60db93cd34a54c98da9ff9782656c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7495688c046142f688c822209c0e968e.png)
③若存在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d740c5dcc2122cb8767b512abb429f48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08052a312e4a29b6840a78850d666d92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e68a20c2d5b0b4238ea8b0564d044329.png)
![](https://img.xkw.com/dksih/QBM/2020/11/3/2584971638710272/2585617835597824/STEM/87729c63-06b3-4089-b40b-fafbc01d946b.png)
A.0 | B.1 | C.2 | D.3 |
您最近一年使用:0次
解题方法
5 . 如图,已知:在
中,
,
,点
是
边上异于点
,
的一个动点,
于点
,现沿
将
折起到
的位置,使
,则四棱锥
的体积的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ff60b63df46072ecba3553f6aa6cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.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/ab00e0cff0876c4183a47f1272cf9928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2ea13010e2399194be2a681310543e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b51d3992644d37dc71c9b5a97d515c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bc56fdf70e65bd88980c64af96b83da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57650963051ccb44a3cfb24f08228405.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/9d6745bd-92b6-45e9-80cd-c3c0d5ec1782.png?resizew=200)
您最近一年使用:0次
2020-09-14更新
|
570次组卷
|
3卷引用:安徽省合肥市2020-2021学年高三上学期期初调研性检测文科数学试题
安徽省合肥市2020-2021学年高三上学期期初调研性检测文科数学试题(已下线)第八单元 立体几何(B卷 滚动提升检测)-2021年高考数学(文)一轮复习单元滚动双测卷浙江省山河联盟2021-2022学年高二下学期3月联考数学试题
名校
解题方法
6 . 已知长方体
内接于半球
,且底面
落在半球的底面上,底面
的四个顶点落在半球的球面上.若半球的半径为3,
,则该长方体体积的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
A. ![]() | B. ![]() |
C.48 | D.72 |
您最近一年使用:0次
2020-09-03更新
|
639次组卷
|
4卷引用:吉林省梅河口市第五中学2020届高三第六次模拟考试数学(文)试题
吉林省梅河口市第五中学2020届高三第六次模拟考试数学(文)试题(已下线)考点12 导数的应用-备战2021年高考数学(理)一轮复习考点一遍过(已下线)考点12 导数的应用-备战2021年高考数学(文)一轮复习考点一遍过吉林省通化市梅河口五中2020届高三高考数学(文科)六模试题
名校
解题方法
7 . 如图,某公园内有一半圆形人工湖,O为圆心,半径为1千米.为了人民群众美好生活的需求,政府为民办实事,拟规划在
区域种荷花,在
区域建小型水上项目.已知
.
![](https://img.xkw.com/dksih/QBM/2020/8/8/2523555747610624/2525064219410432/STEM/d43ce3b78d494e8d9fc652174a966b55.png?resizew=198)
![](https://img.xkw.com/dksih/QBM/2020/8/8/2523555747610624/2525064219410432/STEM/7afc61f9d2a94d2f938b792496feab9e.png?resizew=217)
(1)求四边形OCDB的面积(用
表示);
(2)当四边形OCDB的面积最大时,求BD的长(最终结果可保留根号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4807ca16360c0cca436e59d4be98f626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7189182cc23d759be2764d141952737b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f770124bd1d035eb83f3603e383b2e03.png)
![](https://img.xkw.com/dksih/QBM/2020/8/8/2523555747610624/2525064219410432/STEM/d43ce3b78d494e8d9fc652174a966b55.png?resizew=198)
![](https://img.xkw.com/dksih/QBM/2020/8/8/2523555747610624/2525064219410432/STEM/7afc61f9d2a94d2f938b792496feab9e.png?resizew=217)
(1)求四边形OCDB的面积(用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)当四边形OCDB的面积最大时,求BD的长(最终结果可保留根号).
您最近一年使用:0次
2020-08-10更新
|
1256次组卷
|
2卷引用:江苏省苏州市常熟中学2020届高三下学期校内适应性考试数学试题
8 . 有一矩形硬纸板材料(厚度忽略不计),一边AB长为6分米,另一边足够长.现从中截取矩形ABCD(如图甲所示),再剪去图中阴影部分,用剩下的部分恰好 能折卷成一个底面是弓形的柱体包装盒(如图乙所示,重叠部分忽略不计),其中OEMF是以O为圆心、∠EOF=120°的扇形,且弧
分别与边BC,AD相切于点M,N.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/1ac51142-ec65-4793-9414-873c9e4ebe09.png?resizew=365)
(1)当BE长为1分米时,求折卷成的包装盒的容积;
(2)当BE的长是多少分米时,折卷成的包装盒的容积最大?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8137b20811e24de7235ce5849b199c1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/1ac51142-ec65-4793-9414-873c9e4ebe09.png?resizew=365)
(1)当BE长为1分米时,求折卷成的包装盒的容积;
(2)当BE的长是多少分米时,折卷成的包装盒的容积最大?
您最近一年使用:0次
名校
9 . (本小题满分16分)
如图,某城市有一个边长为
百米的正方形休闲广场,广场中间阴影部分是一个雕塑群. 建立坐标系(单位:百米),则雕塑群的左上方边缘曲线
是抛物线
的一段. 为方便市民,拟建造一条穿越广场的直路
(宽度不计),要求直路
与曲线
相切(记切点为
),并且将广场分割成两部分,其中直路
左上部分建设为主题陈列区. 记
点到
的距离为
(百米),主题陈列区的面积为
(万平方米).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/0cd815f7-32a6-4da2-9482-c2ceb206c9ba.png?resizew=161)
(1)当
为
中点时,求
的值;
(2)求
的取值范围.
如图,某城市有一个边长为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/458b6c1f8e142098dacb00c24c76aeb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/716691d12e3c149bf9e5438bf49f0a3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/0cd815f7-32a6-4da2-9482-c2ceb206c9ba.png?resizew=161)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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10 . 如图,边长为1的正方形区域OABC内有以OA为半径的圆弧
.现决定从AB边上一点D引一条线段DE与圆弧
相切于点E,从而将正方形区域OABC分成三块:扇形COE为区域I,四边形OADE为区域II,剩下的CBDE为区域III.区域I内栽树,区域II内种花,区域III内植草.每单位平方的树、花、草所需费用分别为
、
、
,总造价是W,设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d12b555a9a3b1045138514339ec6a61.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/326069ca-5021-4972-a333-165cdfc41fa6.png?resizew=150)
(1)分别用
表示区域I、II、III的面积;
(2)将总造价W表示为
的函数,并写出定义域;
(3)求
为何值时,总造价W取最小值?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad52beba3181bfc922d5c59d73a5a11a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d2a7b13d95229e2e938514739054541.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d12b555a9a3b1045138514339ec6a61.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/326069ca-5021-4972-a333-165cdfc41fa6.png?resizew=150)
(1)分别用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa5ab3d4aa386b96560e339d8a31ecb.png)
(2)将总造价W表示为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa5ab3d4aa386b96560e339d8a31ecb.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa5ab3d4aa386b96560e339d8a31ecb.png)
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