1 . 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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2 . 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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3 . 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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4 . 已知长方形
的周长为
,其中一条边长为
,面积为
,则
与
之间的关系式为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84755b560534a4cab0c57e1a31cb656c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee3160fce05b551569b8c7b5de6dd8b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d740004cfdade4c185f722dadc27e15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 某公司计划用一种长为
,宽为
的长方形铁片制作无盖盒子.如图,在铁片的四个角各截去一个边长相同的小正方形,剩下的材料制作一个无盖盒子.
,制作的无盖盒子的侧面积为
,写出
与
之间的关系式,并描述盒子的侧面积随小正方形边长的变化而变化的情况;
(2)已知该种长方形铁片的成本为每块40元,当制成的无盖盒子的销售单价为70元时,每天可以售出140个,经调查发现,这种盒子的销售单价每降低1元,其销售量相应增加10个.不考虑其他因素,公司将销售单价
(元)定为多少时,每天销售无盖盒子所获利润
(元)最大?最大利润是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e651babde701d43faadf589dd4e14c72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9871f2a312aaf3a19b40e4fb1a7693b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee3160fce05b551569b8c7b5de6dd8b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d740004cfdade4c185f722dadc27e15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)已知该种长方形铁片的成本为每块40元,当制成的无盖盒子的销售单价为70元时,每天可以售出140个,经调查发现,这种盒子的销售单价每降低1元,其销售量相应增加10个.不考虑其他因素,公司将销售单价
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/595044a7750ab4f84519041979c3d780.png)
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2024-05-29更新
|
227次组卷
|
2卷引用:2024年山东省青岛市李沧区中考二模数学试题
6 . 某居民小区要在一块一边靠墙(墙长
)的空地上修建一个矩形花园
,花园的一边靠墙,另三边用总长
的栅栏围成(如图所示).若设花园的
边长为
,花园的面积为
.
与
之间的函数关系式,并写出自变量
的取值范围;
(2)满足条件的花园面积能否达到
?若能,请求出
的值;若不能,请说明理由;
(3)当
是多少时,矩形场地面积
最大?最大面积是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba3d1f49f620bf2d54a67ba2df3f65f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808ef53202ee31f95494ab431eeb179c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c2b70e3270ca69a01d442ec0840ed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a20728e9a9e3018723f2a86f24f332.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/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)满足条件的花园面积能否达到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b21ffa028aedbe1220cd9baecc48595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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7 . 在锐角
中,
,
,矩形
的两个顶点
,
分别在
,
上,另两个顶点
,
均在BC上,高
交
于点
,设
的长为
,矩形
的面积为
.
的长,并用含
的式子表示线段
的长;
(2)请求出
关于
的函数解析式;
(3)试求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07160f14b3b453bebb64cb2bf96dc85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4066ed8dde07a00665ad52a5d15c7531.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db1e5bbf051d2feb8f123c3ca05b5fa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db1e5bbf051d2feb8f123c3ca05b5fa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
(2)请求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)试求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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8 . 如图,正方形纸片
的边长为4,将它剪去四个全等的直角三角形,得到四边形
.设
的长为x,四边形
的面积为y.
(2)四边形
的面积是否存在最小值?若存在,求出最小值;若不存在,请说明理由.
![](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/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
(2)四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
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9 . 校园内有一块三角形空地(如图中的
),经测量
米,边
上的高
米.某综合实践小组要在这块空地上规划出一个区域(如图中的
)种植月季花,其余部分种植牡丹花.根据设计要求,点E,F分别在边
,
上,且
.已知种植月季花和牡丹花每平方米分别需要50元、80元.设
,
的面积为S.
(2)种植月季花和牡丹花的总费用是否存在最小值?若存在,求出最小值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65e34f3fbb1adf23cf81d7005f4387a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8feb9fdc5582ad3e9853890ac2738d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65b191522ca0314621f99753cce07d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f7c3b7126cf88089169528b7ff49551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81d6990ae9517922338103a5a02f0ec7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0436efefa53aad714565ab2ba7ff90fa.png)
(2)种植月季花和牡丹花的总费用是否存在最小值?若存在,求出最小值;若不存在,说明理由.
您最近一年使用:0次
名校
10 . 如图,在边长为4的正方形
,点
为边
靠近点
的四等分点.点
为边
上一动点,将线段
绕点
顺时针旋转90°得到线段
.连接
,则
的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
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