1 . 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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2 . 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 |
您最近一年使用:0次
名校
3 . (1)求边长为
的等边三角形的面积;
(2)小明将一根长为
的绳子剪成2段,分别围成两个等边三角形.问:如何剪才能够使得这两个等边三角形的面积和最小?最小面积和为多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70444e3a66d1068038c5b5a77c7954aa.png)
(2)小明将一根长为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc6a8e3c0184a6f39ba69966efee510.png)
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2024-06-04更新
|
132次组卷
|
3卷引用:2024年广东省大湾区联考中考二模数学试题
名校
4 . 如图,某农场计划修建三间矩形饲养室,饲养室一面靠现有墙(墙可用长
),中间用两道墙隔开,已知计划中的修筑材料可建围墙总长为
,设饲养室宽为
,占地总面积为
,则三间饲养室总面积
有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3c6e910f598a2161e316274cbc6490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8badcdb1e5621f0ac4d9272041185a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3bde6ef2ee5b749b4d48d706543cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a20728e9a9e3018723f2a86f24f332.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
A.最小值![]() | B.最小值![]() | C.最大值![]() | D.最大值![]() |
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5 . 如图,在等边
中,
,动点P从点 B 出发,沿
方向运动,过点 P作
于点 H,设
的面积为y,点 P的运动路程为x,则y与x之间的函数关系的图象正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7012d1ff11db5e150182e19646814cd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20e64f503acd02b53ac2a26b6af3b27b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38c665061b7bbfab79f9a3a1e8a14239.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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名校
6 . 如图,在
中,
,
为边
上的中线,点
与点
关于点
对称,连接
,
,
.
为平行四边形;
(2)以
为边在四边形
同侧作等边
,
,
分别交直线
于点
,
,若
,当
的面积最小时,
的值是否也最小?如果是,求出
的面积最小值;如果不是,请说明理由;
(3)若
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1438142deeac876fc7dc50552e552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b63d2504bd3ecce8c10560b142356f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e5e61804ce550636a0354e0a78a22d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e5e61804ce550636a0354e0a78a22d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18670a76edf5a4c32a34021a4ae3feef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
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7 . 小明发现有一处隧道的截面由抛物线的一部分和矩形构成,他对此展开研究:测得矩形的宽为
,长为
,最高处点P到地面的距离
为
,建立如图所示的平面直角坐标系,并设抛物线的表达式为
,其中
表示抛物线上任一点到地面
的高度,
表示抛物线上任一点到隧道一边
的距离.
(2)为了保障货车在道路上的通行能力及行车安全,根据我国交通运输部的相关规定,普通货车的宽度应在
之间,高度应在
之间,小明发现隧道为单行道,一货车
沿隧道中线行驶,宽
为
,货车的最高处与隧道上部的竖直距离
约为
,通过计算,判断这辆货车的高度是否符合规定.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f07e72dad77519af893339b3592d71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f11849e8e91738efb18af7dee6a0586f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e17ee14bd91bfff409c06fd434f6745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dffe06e97859163655d8dbec9dfd844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835cbdbbfa0718c2f7b70cfb41ba5ad3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f193416fbd3c6270c178009aaa27c255.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
(2)为了保障货车在道路上的通行能力及行车安全,根据我国交通运输部的相关规定,普通货车的宽度应在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2718570e90b5e433c54d827c7688cb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc079d5c451b538425bface6b6d48508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/005d5a05bdbe27001212eca9a1d5f0d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6c6e7c025362c46a64a8956761f08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e5c71ba69433849c3349a5cc417ee36.png)
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2024-06-03更新
|
219次组卷
|
2卷引用:2024年河南省平顶山市九年级中考三模数学试题
8 . 如图,在平面直角坐标系
中,直线
与x轴交于点A,与抛物线
交于点B,C(点B在点C的左边).
(2)作点B关于x轴的对称点
,若以点A,
,C为顶点的三角形为直角三角形,求a的值;
(3)我们把平面直角坐标系中横坐标与纵坐标均为整数的点叫作格点,如
,
等均为格点.若直线
)与抛物线
所围成的封闭图形内部(不包含边界)的格点数有且只有6个,请直接写出a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc0a06d9aee0608772ed179dabf3cf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0ed3681b6dcd0b77e23ca71396779ff.png)
(2)作点B关于x轴的对称点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5326817f9af012432a202749d1df59f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5326817f9af012432a202749d1df59f.png)
(3)我们把平面直角坐标系中横坐标与纵坐标均为整数的点叫作格点,如
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4772c835cbe626040ecc4df30e6f0ccc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9311b13eb2baab6641da9e7b48e13e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc0a06d9aee0608772ed179dabf3cf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0ed3681b6dcd0b77e23ca71396779ff.png)
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9 . 如图,将一根长
的铁丝弯成一个长方形(铁丝正好全部用完且无损耗),设这个长方形的一边长为
,它的面积为
,则y与x之间的函数关系式为 ( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bfb5d041a5709d4d3ae8b170af9d792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274d5d66721fbc76a4420d7788e70b07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c173649973e40904f53077b66d0c57e.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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10 . 综合与实践
中式建筑中的窗户将对称美发挥得淋漓尽致.小明在旅游中看到了如图
所示的八边形窗户,发现它既是轴对称图形又是中心对称图形,这个八边形窗户各个角都相等.图
是从图
中抽象出来的几何图,其中
,
,
.八边形
的周长为
.设
,
.
的一个内角的度数为 .
(2)求
关于
的函数解析式.
(3)当
等于多少时,这个八边形窗户外框透过的光线最多?
中式建筑中的窗户将对称美发挥得淋漓尽致.小明在旅游中看到了如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a2fe17bc412220dd1f633158fb2eaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66be013a233384c2aaa41770cc0633f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9b86bbe43e5ff93228e55645d8d72f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17d4a6cf11cda87b3dfafaecdec683f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4fb316b1d85380bc1108f494571e0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/282109710bb1244cac7c934334900d14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b805f3941003d81560025ef4580d3f20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17d4a6cf11cda87b3dfafaecdec683f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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