1 . 在边长为1的正方形
中,点
为线段
上一动点,连接
.
作
于点
,交直线
于点
.以点
为直角顶点在正方形
的外部作等腰
,连接
.求证:
是等腰直角三角形;
(2)如图②,在(1)的条件下,记
分别交
于点
,连接
.
①试探究
之间的数量关系;
②设
,
中边
上的高为
,请用含
的代数式表示
.并求
的最大值.
![](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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb91cb9a5a14169845d700fbd95890ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362a2d1b0c5d90ad19827049c31d65a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccdf364a0e37a15893a96bbe17a2e264.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ded15467b6a0d3b56fd1cdf5a41a5122.png)
(2)如图②,在(1)的条件下,记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e98addf4639134b18a8ffdb46436854e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b1b15a4605fce993cb13aefbf40360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
①试探究
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b4d9e95fcb01d403090a2a97699302.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc2d9d9adad09281ca67132bdce523fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5845d0b7ca6980eea65473c0de995de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
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2 . 综合应用
如图,等边三角形
的边长为a,点D,E,F分别是边
,
,
上的动点,且满足
,连接
,
,
.
;
(2)设
的长为x,
的面积为y,求出y与x的函数表达式(用含a的式子表示);
(3)在(2)的条件下,当
时,y有最小值,画出y与x的函数图象.
如图,等边三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bcb4e1c3913b81c0096f1a14096d677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d09645ecedf397df03aa258a5bb14d83.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
(3)在(2)的条件下,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
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3 . 如图1,抛物线
与
轴交于点
和点
,与
轴交于点
,且
,抛物线的对称轴为直线
.
(2)若
是该抛物线的对称轴,点
是顶点,点
是第一象限内对称轴右侧抛物线上的一个动点.
(ⅰ)如图2,连接
,若
的面积为3,求点
的坐标;
(ⅱ)如图3,连接
,与
交于点
,连接
,
,
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.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/f36488f7dff759ace2a27e56c3857056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49c8dbc31b2e14067ef2f34b4e25f114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(ⅰ)如图2,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08fa5b7ee3c02add5668fcdfd13e4b6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(ⅱ)如图3,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4505508b3e36db64a207dcdaf8eb22dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a72823b5c0705214c9a5b5fc026ba643.png)
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2024-05-13更新
|
180次组卷
|
2卷引用:2024年安徽省阜阳市名校中考数学二模试题
4 . 如图,矩形
中,点
在
上.动点
以每秒1个单位的速度从点
出发,沿折线段
运动.连接
,过点
作
,交矩形
的边于点
,连接
.已知
,
,
.经探究,动点
的运动路程为
,线段
与矩形
的边围成三角形面积为
,它们之间满足二次函数关系.
沿
运动的过程中,
与
的关系如图2所示,求此时
关于
的函数解析式;
(2)在动点
由点A→D运动的过程中,当
时,点
停止运动,如图3,求此时
关于
的函数解析式;
(3)在(1)与(2)的条件下,是否存在3个路程
,
,
,(
且
),使得3个路程对应的面积S均相等,请说明理由.
![](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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31bdca09e6d95f46e427e2df3f92b39c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d84756764173829ecd7d0272785c7e19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b03bb56c7e76954b192bd8595a0865a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7cbfaec1d9dcaaf159b060163436113.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/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ba837391bb4af88a9a5042248b81e2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)在动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc90fee532e50d319081d571410421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)在(1)与(2)的条件下,是否存在3个路程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cece8a1073b11eb11aed88ae1fc5b365.png)
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5 . 在综合实践课上,数学兴趣小组用所学的数学知识来解决实际问题,实践报告如下:
请你帮助兴趣小组解决以上问题.
活动课题 | 设计围篱笆的方案 |
活动工具 | 直角三角板、量角器、皮尺、篱笆等 |
活动过程 | 【了解场地】如图,测出墙AD与墙AB的夹角是135°; 【设计图纸】用篱笆围成一个梯形的菜园,梯形满足 ![]() ![]()
![]() |
解决问题 | 如何围篱笆才能使其所围梯形的面积最大?最大面积是多少平方米? |
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6 . 【生活情境】
为美化校园环境,某学校根据地形情况,要对景观带中一个长
,宽
的长方形水池
进行加长改造(如图①,改造后的水池
仍为长方形,以下简称水池1).同时,再建造一个周长为
的矩形水池
(如图②,以下简称水池2).
【建立模型】
如果设水池
的边
加长长度
为
,加长后水池1的总面积为
;设水池2的边
的长为
,面积为
.上述两个函数在同一平面直角坐标系中的图象如图③,两个函数图象的交点分别是点C和点D.
(1)分别求出
与x,
与x的函数关系式;
【问题解决】
(2)求水池2面积的最大值:
(3)当水池1的面积大于水池2的面积时,求
的取值范围;
【数学抽象】
(4)在图④的图象中,点P是此抛物线上一点,点Q是抛物线对称轴上一点,是否存在以点C、D、P、Q为顶点的四边形是平行四边形?若存在,请直接写出点P的坐标;若不存在,请说明理由.
为美化校园环境,某学校根据地形情况,要对景观带中一个长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ea5a06ae3858e78b5ae3f9d42ec095a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c01b4e82dc80021c9cfceeda4fd67992.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e53abbd672b82a02c4975f99fbbd2c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/652d9ac21e0f4af80df32e8c0d6b7e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
【建立模型】
如果设水池
![](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/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3c0ed0b68d3fa015f99cf7eeec43897.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9209b113a6fa04799965c1b15dcfcf5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0743ff4aae4d402b6b1729dc32ec40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d6b434f390fd59b5bc577aaea94b27d.png)
(1)分别求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
【问题解决】
(2)求水池2面积的最大值:
(3)当水池1的面积大于水池2的面积时,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df149da97eaa1ee5f3a793ddf33af124.png)
【数学抽象】
(4)在图④的图象中,点P是此抛物线上一点,点Q是抛物线对称轴上一点,是否存在以点C、D、P、Q为顶点的四边形是平行四边形?若存在,请直接写出点P的坐标;若不存在,请说明理由.
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7 . 阅读与思考
下面是小涵同学的数学日记,请仔细阅读并完成相应的任务.
任务:
(1)小涵同学解决矩形蔬菜基地问题中的“办法一”和“办法二”,主要体现的数学思想有______;(从下面选项中选出两个即可)
A.方程思想 B.统计思想 C.函数思想 D.数形结合思想
(2)请你直接写出“办法一”中一次函数的表达式为:______,反比例函数的表达式为:______.
(3)按照小涵日记中的“办法二”解决问题:是否存在满足上述所给条件的矩形?请说明理由.
下面是小涵同学的数学日记,请仔细阅读并完成相应的任务.
![]() ![]() ![]() “用函数思想解决生活中的实际问题” 五一假期,我班数学作业是“用函数思想解决生活中的实际问题”,并参与解决问题的全过程.今天、爸爸计划在农村老家用 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
(1)小涵同学解决矩形蔬菜基地问题中的“办法一”和“办法二”,主要体现的数学思想有______;(从下面选项中选出两个即可)
A.方程思想 B.统计思想 C.函数思想 D.数形结合思想
(2)请你直接写出“办法一”中一次函数的表达式为:______,反比例函数的表达式为:______.
(3)按照小涵日记中的“办法二”解决问题:是否存在满足上述所给条件的矩形?请说明理由.
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8 . 综合与实践
【材料阅读】我们知道,
,展开移项得
,当
时,取到等号;我们可以利用它解决形如“
(
,
为常数且
)的最小值”问题.
例如:求式子
的最小值.
解:
,当
时,即
时,式子有最小值,最小值为4
【学以致用】在一次踏青活动中,某数学兴趣小组围绕着一个有一面靠墙(墙的长度为
)的矩形篱笆花园(如图1所示)的面积
和篱笆总长
与
的长度
之间的关系进行了研究分析.
为
,篱笆总长
为
时,求
的值;
(2)当篱笆总长
为
时,
①写出
关于
的函数关系式,并写出
的取值范围;
②当
取何值时,
有最大值?最大值是多少?
(3)当面积
为
时,
关于
的函数解析式为
,数学兴趣小组的小李同学利用数学软件作出了其函数图象如图2所示,点
为图象的最低点,观察图象并结合[材料阅读],当自变量
的取值范围为多少时,
随
的增大而减小?(直接写出
的取值范围)
【材料阅读】我们知道,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73051611311f17ba159ac4df11cad5df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/759c09917e5728d75bf5cfdb5b4a807f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f22fec5a381ae8aca93d876e54c79de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84016a43ea1d0697d33e0e29d7d7916b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8610232c77741a37463feba1a66c94.png)
例如:求式子
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baf343012f687718ed4e313b3793d23a.png)
解:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01cdc65f1068c9506046926a7724254e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41f1e3048c60441505af80599dba214f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
【学以致用】在一次踏青活动中,某数学兴趣小组围绕着一个有一面靠墙(墙的长度为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e978c77cb0d7eff794447241e9829867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6393a74bf832f7ae73c721cddffb1b78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c08094f72d5bd69246c453dd28e33d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当篱笆总长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c08094f72d5bd69246c453dd28e33d1.png)
①写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(3)当面积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6393a74bf832f7ae73c721cddffb1b78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a5a68c69e04ecc008e8b7d370e30e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
9 . 综合与实践
问题提出
中,
,
,点D在
上,
,点P沿折线
运动(运动到点C停止),以
为边作正方形
.设点P运动的线路长为x,正方形
的面积为y.
初步感悟
(1)当点P在
上运动时,若
,则
①
______,y关于x的函数关系式为______;
②连接
,则
长为______.
(2)当点P在
上运动时,求y关于x的函数解析式.
延伸探究
(3)如图2,将点P的运动过程中y与x的函数关系绘制成如图2所示的图象,请根据图象信息,解决如下问题:
①当点P的运动到使
时,图像上对应点的坐标为______;
②当
将正方形
分成面积相等的两部分时,
与正方形交于点G、H两点,请直接写出此时
的长,以及自变量和函数的值.
问题提出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d9142db4dd2ef151bf3d4a63afb61e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37750daa8ba3b3fe3e9e2092f81c848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d6138974bc163a985e4820a7e86037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b8db7b0199e77f81433d385180e01f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b8db7b0199e77f81433d385180e01f9.png)
初步感悟
(1)当点P在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4fb2e1f711d92daf9e32e669ded7d7d.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070d1ea22a92808dad7489438c239629.png)
②连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
(2)当点P在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
延伸探究
(3)如图2,将点P的运动过程中y与x的函数关系绘制成如图2所示的图象,请根据图象信息,解决如下问题:
①当点P的运动到使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e305fa6e419e4187ccecd395c9d05288.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b8db7b0199e77f81433d385180e01f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
您最近一年使用:0次
2024-05-08更新
|
236次组卷
|
3卷引用:2024年江西省吉安市青原区中考一模数学试题
10 . 在平面直角坐标系中,
为原点,
的顶点
的坐标为
,点
在第一象限,
,
,矩形
的顶点
在
轴的负半轴上,点
在
轴的正半轴上,点
坐标为
.
的坐标;
(2)将矩形
沿
轴向右平移,得到矩形
,点
,
,
,
的对应点分别为
,
,
,
.设
,矩形
与
重登部分的面积为
.
①如图②,当矩形
与
重叠部分为五边形时,
与
相交于点
,
与
相交于点
,试用含有
的式子表示
,并直接写出
的取值范围;
②当
时,求
的取值范围(直接写出结果即可).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2afd0e94837e05d0fa036432997eed8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66de81385e9afd8e180f1f156607cd01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0360abc145add7c147be3574fb682188.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f87d89b3eb0c40885f5a6f011d9171b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12d79a8155d17f030b8639cb20e1d26e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)将矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f87d89b3eb0c40885f5a6f011d9171b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b983d15e2265ea1fbe2e1b041b1865a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/12fe32dfbd66709875c5b9f79c9496da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3bd5e6bc2a0a277d279bb01af9584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b1a5427d8ff23df0f3ec194756c84c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ec5b34559d44ba345133399644b485.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b983d15e2265ea1fbe2e1b041b1865a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
①如图②,当矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b983d15e2265ea1fbe2e1b041b1865a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cece895cbddf9d1f37f75e3b6346edda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2cd93546f613f13b741ad234fbc04d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192136708cd4c7650623be29cb1e02cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次