1 . 某小型花圃基地计划将如图所示的一块长
,宽
的矩形空地划分成五块小矩形区域.其中一块正方形空地为育苗区,另一块空地为活动区,其余空地为种植区,分别种植
,
,
三种花卉.活动区一边与育苗区等宽,另一边长是
.
,
,
三种花卉每平方米的产值分别是100元、200元、300元.
,用含
的代数式表示下列各量:花卉
的种植面积是______
,花卉
的种植面积是______
,花卉
的种植面积是______
.
(2)育苗区的边长为多少时,
,
两种花卉的总产值相等?
(3)若花卉
与
的种植面积之和不超过
,求
,
,
三种花卉的总产值之和的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1611d15c7e1e4ab4a4a61537b3989d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167e6e41ac221847824a72e964f340f1.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585c0b361a3e508f3dbb27a40b2dad5e.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cb7404528c050f8b665081f7d6020c9.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/35c901bcdfa58f0c68ad0161b0bab269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c901bcdfa58f0c68ad0161b0bab269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c901bcdfa58f0c68ad0161b0bab269.png)
(2)育苗区的边长为多少时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)若花卉
![](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/cbc7677407a2c73ec628425f7f68f090.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/c5db41a1f31d6baee7c69990811edb9f.png)
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2 . 如图,一农户要建一个矩形鸡舍,为了节省材料,鸡舍的一边利用长为a米的墙,另外三边用长为31米的建筑材料围成,为方便进出,在垂直墙的一边留下一个宽1米的门.设
米时,鸡舍面积为S平方米.
(2)在(1)的条件下,当
为多少时,鸡舍的面积为96平方米?
(3)若住房墙的长度足够长,问鸡舍面积能否达到130平方米?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7a3d679b4dae63575903387a76ce45.png)
(2)在(1)的条件下,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
(3)若住房墙的长度足够长,问鸡舍面积能否达到130平方米?
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名校
3 . 如图1是即将建造的“碗形”景观池的模拟图,设计师将它的外轮廓设计成如图2所示的图形.它是由线段
,线段
,曲线
,曲线
围成的封闭图形,且
,
在x轴上,曲线
与曲线
关于y轴对称.已知曲线
是以C为顶点的抛物线的一部分,其函数解析式为:
(p为常数,
),现用三段塑料管
,
,
围成一个一边靠岸的矩形荷花种植区(如图3),E,F分别在曲线
,曲线
上,G,H在x轴上.
时,
①求曲线
的函数解析式.
②当
米时,求三段塑料管的长度之和.
(2)当
与
的差为多少时,三段塑料管总长度最大?请你求出三段塑料管总长度的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3182db896bc2462331796e2a6108363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/decd02bb1fd6ac5a3610a279fe96212b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3182db896bc2462331796e2a6108363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231f1df5e4970a43bb90033abc11aa72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e222f73c2dc15fa2cfd692a4293011.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0215e13a9fb5574d5194aeb9507a98aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87448e09eaa816e50ae92d111d5ded6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5481c3c38cf999b4dacada15ea517b8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b02474aa890b8bb953ea50e928f318f2.png)
①求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2afd4da1d8357df391b946052622f138.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0215e13a9fb5574d5194aeb9507a98aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
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4 . 用一段长为
的篱笆围成一个一边靠墙的菜园.
方案一:如图①,围成一个矩形菜园
,其中一边
是墙,其余的三边
,
,
用篱笆,其中
;
是墙,其余用篱笆.
①
的长可以是
;
②
的长有两个不同的值满足该矩形菜园的面积为
;
③矩形菜园
的面积的最大值为
;
④方案二围成扇形菜园的最大面积大于方案一围成矩形菜园的最大面积.
其中,正确结论的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed4998c150dcde4b3833bfe5f403da63.png)
方案一:如图①,围成一个矩形菜园
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21a98c968a7653c11f184a43851941c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e685c2fe2f54fa7947538472cd7caa9.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4fb5474bdc74da700b463eabd05bd8e.png)
③矩形菜园
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11f9ad302532cb3cfcfee6ff60fe490d.png)
④方案二围成扇形菜园的最大面积大于方案一围成矩形菜园的最大面积.
其中,正确结论的个数是( )
A.l | B.2 | C.3 | D.4 |
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5 . 根据以下素材,完成探索任务.
问题提出:根据以下提供的素材,在总费用(新墙的建筑费用与门的价格之和)不高于5900元的情况系,如何设计最大饲养室面积的方案?
素材一:如图是某农场拟建两间矩形饲养室,饲养室的一面靠现有
长的墙,中间用一道墙隔开,计划的建筑材料可建围墙的总长为
,开两个门,且门宽均为
.
素材三:与现有墙平行方向的墙建筑费用为300元/米,与现有墙垂直方向的墙建筑费用为200元/米.
问题解决:
任务1:设
,矩形ABCD的面积为S,求S关于x的函数表达式.
任务2:探究自变量x的取值范围.
任务3:确定设计方案:当
,
时,S的最大值为
.(直接填写结果)
问题提出:根据以下提供的素材,在总费用(新墙的建筑费用与门的价格之和)不高于5900元的情况系,如何设计最大饲养室面积的方案?
素材一:如图是某农场拟建两间矩形饲养室,饲养室的一面靠现有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb1e0bd4fe8afb14b572852121cef83d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a6d690befd9571e1cf9a80388ab2b68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f328ba89c0a92a4447788b65571f7aa.png)
素材三:与现有墙平行方向的墙建筑费用为300元/米,与现有墙垂直方向的墙建筑费用为200元/米.
问题解决:
任务1:设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66ac400e3f5ba8b945bbef83db8611b7.png)
任务2:探究自变量x的取值范围.
任务3:确定设计方案:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26a46e7879436d532af3f4b6e258a81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ca90e8a784f990c4097eec9219908d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c901bcdfa58f0c68ad0161b0bab269.png)
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6 . 以农业和农村为载体的生态农业观光园,不仅具有生产性功能,还具有改善生态环境质量,为人们提供观光、休闲、度假的生活性功能.数学探究小组以“设计矩形生态农业观光园”为主题开展数学实践活动.
①若
,
,
,请求出矩形生态农业观光园PN边的长;
②设
,点A到道路BC的距离为h,矩形观光园PEFN的面积是否存在最大值?若存在,请用含a,h的代数式表示其最大面积;若不存在,请说明理由.
(2)如图2,是一块四边形ABCD的田地,已知
.经数学探究小组测量得,
,
,
.数学探究小组在四边形ABCD田地设计了一个点E、F在BC边上且面积最大的矩形生态农业观光园PEFN,试求该矩形PEFN的面积.
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a429566515467722d2edb4ecbc81f688.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7dcc2bedc1f53ae017c1e9438940281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667c50b897a3e209018f0ee09d37e73d.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e781a2489271bfd1597cba1bb6f5887.png)
(2)如图2,是一块四边形ABCD的田地,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/592eaf4082b7ec72379f521c03f01545.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25a8afe4cff7a6dc45c84c43f2ed372e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c7dd5a53fa95e592ddcfdfae590c35c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81151b5ab9c25834a2f68027247d3924.png)
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7 . 如图,学校为美化校园环境,打造绿色校园,决定用60米长的篱笆围成一个一面靠墙(墙足够长)的长方形花园,并用一道篱笆把花园分为A、B两块长方形区域.
,花园面积是
,写出S关于x的函数表达式,并求S的最大值;
(2)在花园面积最大的条件下,A、B两块区域内分别种植牡丹和芍药,每平方米种植2株,若A区域面积不小于B区域面积的2倍,则至少要购买多少株牡丹?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3bde6ef2ee5b749b4d48d706543cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baaa2d65026770c5505f8adeb450e43b.png)
(2)在花园面积最大的条件下,A、B两块区域内分别种植牡丹和芍药,每平方米种植2株,若A区域面积不小于B区域面积的2倍,则至少要购买多少株牡丹?
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8 . 如图,抛物线
与x轴交于点
,
,与y轴交于点C,顶点为D,直线
与抛物线交于点
是线段
的中点.
(2)若点E的横坐标是
,求点M的坐标.
(3)若
,求四边形
的面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d88bbd34102b55fa928e8ff83f0d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d57173ef4cd72eb270686875dfd623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f36488f7dff759ace2a27e56c3857056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f654f238b3fc9d5078d1dcc211cc98aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(2)若点E的横坐标是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cff8fe00e5270dbc5ce9f9a5a6340781.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/660058b0809f5c91ce27534c3bcf2fb6.png)
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9 . 如图,已知抛物线
与x轴交于点
和点B,与y轴交于点C,连接
,过B、C两点作直线.
(2)将直线BC向下平移
个单位长度,交抛物线于
两点.在直线
上方的抛物线上是否存在定点D,无论m取何值时,都使点D到直线
的距离最大,若存在,请求出点D的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e71461c5134339b5b54a80e588640f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae838c1a48dfea1f44e5869fac5d2b5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)将直线BC向下平移
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb0142304c989e20f90e37c6b0a8f74e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42782ee007b97ceccafc82c205c6f4bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e737bc35da650eda3825d29799b5f86f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e10d97a96f9a3c097714694a9411176d.png)
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10 . 如图,人民医院在某流感高发时段,用防护隔帘布临时搭建了一隔离区,隔离区一面靠长为
的墙,隔离区分成两个区域,中间也用防护隔帘布隔开.已知整个隔离区所用防护隔帘布总长为
,如果隔离区出入口的大小不计,并且隔离区靠墙的一面不能超过墙长,小明认为:隔离区的最大面积为
;小亮认为:隔离区的面积可能为
.你认为他们俩的说法是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167e6e41ac221847824a72e964f340f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74dee2e8849924124cbb31f9c6f15479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b04aadf7101e832fec3dc86c2619773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3a5429f6ade39116fc3ac69f199b113.png)
A.小明正确,小亮错误 | B.小明错误,小亮正确 |
C.两人均正确 | D.两人均错误 |
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