1 . 为了加强劳动教育,我校在校园开辟了一块劳动教育基地:一面利用学校的墙(墙的最大可用长度为28米),用长为39米的篱笆,围成中间隔有一道篱笆的矩形菜地,在菜地的前端及中间篱笆上设计了三个宽1米的小门,便于同学们进入.
的长;
(2)若每平方米可收获2千克的菜,问该片菜地最多可收获多少千克的菜?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)若每平方米可收获2千克的菜,问该片菜地最多可收获多少千克的菜?
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2 . 如图,正方形
的边长为10,点G在边
上,
,E是边
上一动点,连接
,过点E作
交直线
于点F,则线段
长度的最大值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7543caff2e99f3fa6da9db9ba16cf15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f3956f008cc29ca4bae44a087d5427.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e458dd1ce1c8dcdc2becac146d9dc231.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
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2024-06-18更新
|
75次组卷
|
2卷引用:2024年黑龙江省绥化市中考三模数学试题
3 . “幂势既同,则积不容异”是我国古代数学家祖暅提出的体积计算原理,称作祖暅原理.利用祖暅原理可以得到一种求面积的方法:“夹在两条平行直线之间的两个平面图形,被平行于这两条平行线的任意直线所截,如果被截得的两条线段长总相等,那么这两个平面图形的面积相等”.
与
之间的矩形
与曲边形
满足:
,
.一平行于
的直线
交矩形
于M,N,交曲边形
的曲边于
,
,且无论
在何位置都有
,则曲边形
的面积为 _____ .
(2)如图2,记函数
的图象在第一象限围成的曲边形(阴影部分)为Ω,则Ω的面积为 _____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da895d8bd043625a0839128252130d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28b1ba4307cfde9b424d468bfcdf6c5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d163ce79fd73978bef417c672ec49e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
(2)如图2,记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6087a51f0e11663f56b783d09767d646.png)
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4 . 已知抛物线
与
轴交于
,
两点,与
轴交于点
.
(1)求抛物线
的表达式;
(2)若抛物线
关于
轴对称的抛物线为
,抛物线
上是否存在一点
,使得
?若存在,请求出点
的坐标,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d608c5f64c39fa364a8dd4e3c090441.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0929421a6188c3122442866b0b85a5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ef03f452410ab19c6246567c427178.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
(2)若抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcf90af48c665ee801c05cc55914b8fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcf90af48c665ee801c05cc55914b8fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59f7abf31402fcfd6f86fb434adc37d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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2024-06-18更新
|
35次组卷
|
2卷引用:2024年陕西省西安新城区爱知初级中学九年级第一次全仿真测试数学试题
真题
5 . 如图,在平面直角坐标系中,一次函数
的图象与
轴交于点
,与
轴交于点
,抛物线
经过
、
两点,在第一象限的抛物线上取一点
,过点
作
轴于点
,交
于点
.
(2)是否存在点
,使得
和
相似?若存在,请求出点
的坐标,若不存在,请说明理由;
(3)
是第一象限内抛物线上的动点(不与点
重合),过点
作
轴的垂线交
于点
,连接
,当四边形
为菱形时,求点
的横坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c60ecd5f53b3469726c8cb09e86ff20b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d88bbd34102b55fa928e8ff83f0d52.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70986d34cfbb5f7711e504e0f92f9ad9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2281cb6df0c3c518ce5ed19a02b57e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb49df05f2e31d005735c3f14a21d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49cd8576a1aaed7e787af3f5b19822a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
您最近一年使用:0次
6 . 陕北的窑洞是依山势开凿出来的这样一个拱顶的窑洞.由于黄土高原的黄土本身具有直立不塌的性质,而拱顶的承重能力又比平顶要好,所以窑洞一般都是采取拱顶的方式来保证了它的稳固性.如图为某窑洞门的示意图,如右图建立平面直角坐标系,窑洞的下半部分四边形
为矩形,且
窑洞的上半部分的拱形近似为抛物线的一部分,窑洞门的最高点距地面为 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ef0a33d8ad24d854292ce0cb928742.png)
(2)窑洞主人对窑洞的拱形部分进行设计,设计图如图所示,其中,点M,N在抛物线上,
,
,
,
,
均垂直于
,
,
交
于点Q,R,已知.
四边形
和四边形
为正方形,求点 M,N 的坐标;
(3)判断四边形
的形状并说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/862529127f259d85e366f5c31bdc3c3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dd385f31dddcd490a8e72a4a1c6237f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ef0a33d8ad24d854292ce0cb928742.png)
(2)窑洞主人对窑洞的拱形部分进行设计,设计图如图所示,其中,点M,N在抛物线上,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6cc9f041724e7fa6b08c717de02fc9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce8f887360a533f0a25b0b34fb11f0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a16f5621716bfef7a056a3f2712feb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fda40d4d62aa28f9e5f877bbea5ce511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce8f887360a533f0a25b0b34fb11f0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a16f5621716bfef7a056a3f2712feb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b326654b3cbfbbe6ef861804d59b8ead.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05250abe6da85eb0b555948d7dbaf317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe0092ffe905a4fd88e2abc1d23fbf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04baaea36511681098765a2a80d28341.png)
(3)判断四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0ab69b0ece7e75cd29cefa4b69e3842.png)
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7 . 如图,在矩形
中,
,
.设P,Q分别为
,
上的动点,点P自点D沿
方向作匀速移动的同时,点Q自点B沿
方向向点C作匀速移动,移动的速度均为
,设P,Q移动的时间为t(
).
?
(2)写出
的面积
与时间
之间的函数表达式,当t为何值时,S有最大值?最大值是多少?
(3)当t为何值时,
为等腰三角形?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b35ed92397da56c7afbd6967597a9611.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9547f6b5c7c54d216ecea72becb7d373.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/654bdcd4d474a9899693db1eec0d71e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2aa9b9894a953c812b52eba95559f33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/902f24325565a9dd95128a633a240da2.png)
(2)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c495b8fd7f7bb21c177c9d50fbf6919.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f372e567a416d3dc405b2b0d72506b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d744165d6aad705f64de41a9d931750a.png)
(3)当t为何值时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c495b8fd7f7bb21c177c9d50fbf6919.png)
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名校
8 . 如图1所示是某家具厂的抛物线木板余料,其最大高度为
,最大宽度为
,现计划将此余料进行切割:
的中点O为原点,水平向右为x轴正方向,竖直向上为y轴正方向建立平面直角坐标系,求出抛物线对应的函数表达式;
(2)工人师傅现需要一块边长为
的正方形木板,为了切割方便,要求一边在底部边缘
上,这块余料能否满足工人的需求?如果能,请说出切割方案,如果不能,请说明理由;
(3)若切割成矩形,要求一边在底部边缘
上且周长最大,求此矩形的周长;
(4)若切割成宽为
的矩形木板若干块,然后拼接成一个宽为
的矩形,如何切割才能使拼接后的矩形的长边最长?请直接写出拼接后的矩形的长边长(结果保留根号).注意:思考中可能会用到的数据
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b178474bc9008e83b4661dcfbf4e87b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a29dc67d489b45471e5179e543649e80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)工人师傅现需要一块边长为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e6cc70babacf10168a738b90a1aec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(3)若切割成矩形,要求一边在底部边缘
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(4)若切割成宽为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da9429d1238ea3e979dd0de49dd2b48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da9429d1238ea3e979dd0de49dd2b48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3180e6cef57558978128081f259bd9fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d92accf6e50007ee4b73b16487f78a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/460317e7c26f95b9b29cfe1a89b796d6.png)
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9 . 如图,某农户计划用篱笆围成一个矩形场地养殖家禽,为充分利用现有资源,该矩形场地一面靠墙(墙的长度为
),另外三面用篱笆围成,中间再用篱笆把它分成三个面积相等的矩形分别养殖不同的家禽,计划购买篱笆的总长度为
,设矩形场地的长为
, 宽为
, 面积为
.
(2)当x为何值时,矩形场地的总面积最大?最大面积为多少?
(3)若购买的篱笆总长增加
,矩形场地的最大总面积能否达到
若能,请求出x的值;若不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19d4166fee97516ad1b1d4759a8e4ce6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c857aaa8fc6074c0d499298451e4e737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3bde6ef2ee5b749b4d48d706543cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97e084ae38a5dc1db3c411b5fd3787b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7f771ee0caa0143663939cb00451de.png)
(2)当x为何值时,矩形场地的总面积最大?最大面积为多少?
(3)若购买的篱笆总长增加
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39ea92883fe24b097c9a881ef8c92eb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8efcf848e40683b1b608aac62062a09.png)
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10 . 【综合与实践】
矩形种植园最大面积探究
【解决问题】
根据分析,分别求出两种方案中S的最大值;比较并判断矩形种植园的面积最大值为多少?
矩形种植园最大面积探究
情境 | 劳动实践基地有一长为12米的墙![]() ![]() ![]() |
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分析 | 要探究面积S的最大值,首先应将另一边![]() | |
探究 | 方案一:将墙![]() 按图1的方案围成矩形种植园(边 ![]() ![]() | |
方案二:将墙![]() 按图2的方案围成矩形种植园(墙 ![]() ![]() |
根据分析,分别求出两种方案中S的最大值;比较并判断矩形种植园的面积最大值为多少?
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2024-06-16更新
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