读一读:
数形结合作为一种数学思想方法,其应用大致又可分为两种情形:或者借助于数的精确性来阐明形的某些属性,或者借助形的几何直观性来阐明数之间某种关系,即数形结合包括两个方面:第一种情形是“以数解形”,而第二种情形是“以形助数”.例如:在我们学习数轴的时候,数轴上任意两点,
表示的数为
,
表示的数为
,则
,
两点的距离可用式子
表示,例如:5和-2的距离可用
或
表示.
研一研:
如图,在平面直角坐标系中,直线
分别与
轴正半轴、
轴正半轴交于点
、点
,且
、
满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/25/e36d02c5-6307-460c-86c1-947db229348d.png?resizew=439)
(1)直接写出以下点的坐标:
(______,0),
(0,______).
(2)若点
、点
分别是
轴正半轴(不与
点重合)、
轴负半轴上的动点,过
作
,连接
.已知
(近似值),请探索
与
之间的数量关系,并说明理由.
(3)已知点
是线段
的中点,若点
为
轴上一点,且
,求点
的坐标.
数形结合作为一种数学思想方法,其应用大致又可分为两种情形:或者借助于数的精确性来阐明形的某些属性,或者借助形的几何直观性来阐明数之间某种关系,即数形结合包括两个方面:第一种情形是“以数解形”,而第二种情形是“以形助数”.例如:在我们学习数轴的时候,数轴上任意两点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.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/a13880b9454c5942f164d934b1834783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea7ba690de4bdbdceb968265181a208f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9642893060f4633b2394557fd1b61e72.png)
研一研:
如图,在平面直角坐标系中,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c240561788bc63f41a6703219fb66d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48c09615735d331befd07664aa47cb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/053b1b12ec44d44cef04920f455aaa40.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/25/e36d02c5-6307-460c-86c1-947db229348d.png?resizew=439)
(1)直接写出以下点的坐标:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若点
![](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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc962e84c6d80f0471732c3bef2fe68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48a68f5e1bc8ed3db2caa77acbe51fd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eb967f3188ad239a78047edf98458d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2225e9d4e443d81abfe1bed83ba25e9b.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0913e0c22ce025eea9a56d5c0b860063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc71bbc6fbca7f7deb0538ed6ea057a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
21-22七年级下·广东广州·期末 查看更多[2]
广东省广州市花都区2021-2022学年七年级下学期期末数学试题(已下线)第一次月考押题培优卷(1)(考试范围:第五-七章)-【微专题】2022-2023学年七年级数学下册常考点微专题提分精练(人教版)
更新时间:2022-07-24 18:09:22
|
相似题推荐
解答题-问答题
|
适中
(0.65)
【推荐1】如图,点C为线段
的中点,点E为线段
上的一点,点D为线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/20/e9b4e52b-6e0e-43bf-b70f-480fa552732a.png?resizew=227)
(1)若线段
,
,
,求m,n的值;
(2)在(1)的条件下,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/20/e9b4e52b-6e0e-43bf-b70f-480fa552732a.png?resizew=227)
(1)若线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa375c3888b332f24e7d0f9b9600c694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d748edb40aa7696f79f087d68ca4877d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db70d49ff66adb4d0af6c56503035d3d.png)
(2)在(1)的条件下,求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
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解答题-计算题
|
适中
(0.65)
【推荐2】(1)
和
互为相反数,求
的值
(2)计算:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa516c51d04d6d6a8884d04483db27fd.png)
(3)已知
,
,求a与b的乘积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70b4feb90b84eb54fe644c596f5156a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccdb09750317458d4569071da153c53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dd3117cda28bb370c787343239b8810.png)
(2)计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa516c51d04d6d6a8884d04483db27fd.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f5c2e18c76a59348dc37cf9dd2a2513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f654b5b45f1a14cfacebda83203b611.png)
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解答题-问答题
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名校
【推荐1】如图,点A、B和线段
都在数轴上,点A、M、N、B对应的数字分别为
、0、2、11. 线段
沿数轴的正方向以每秒1个单位的速度移动,移动时间为t秒.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/14/1ec73e4e-01a3-4ec9-b27d-ee29a08f1241.png?resizew=300)
(1)用含有t的代数式表示
的长为 .
(2)当
时,求t的值;
(3)若点A、B与线段
同时移动,点A以每秒2个单位速度向数轴的正方向移动,点B以每秒1个单位的速度向数轴的负方向移动,在移动过程,
和
可能相等吗?若相等,请求出t的值,若不相等,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/14/1ec73e4e-01a3-4ec9-b27d-ee29a08f1241.png?resizew=300)
(1)用含有t的代数式表示
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9a2bfccba497481eae10020d143bbb.png)
(3)若点A、B与线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
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解答题-作图题
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适中
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【推荐1】已知:
在平面直角坐标系中的位置如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/8/b6d4c3ea-30be-461d-9d58-11a544772227.jpg?resizew=193)
(1)
的面积是 .
(2)作出
关于
轴对称的三角形
;
(3)在
轴上找到一点
,使
的值最小,在图中画出点
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/8/b6d4c3ea-30be-461d-9d58-11a544772227.jpg?resizew=193)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)作出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4310db23fc79936c7182361e652bab1a.png)
(3)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40b60a048024136e0fd06d80fc9fd58b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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解答题-问答题
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【推荐2】如图,在平面直角坐标系中,O为坐标原点,点A(a,b)在第一象限,点B(﹣b﹣1,0),且实数a、b满足
+(b﹣4)2=0
(1)求点A,B的坐标;
(2)若点P以2个单位长度/秒的速度从O点出发,沿x轴的负半轴运动,设点P运动时间为t秒,三角形ABP的面积为S,求S与t的关系式;
(3)在(2)的条件下,当t为何值时,S△ABP:S△AOP=2:3
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a68e696225e1a6f4d3475c2b19efde.png)
(1)求点A,B的坐标;
(2)若点P以2个单位长度/秒的速度从O点出发,沿x轴的负半轴运动,设点P运动时间为t秒,三角形ABP的面积为S,求S与t的关系式;
(3)在(2)的条件下,当t为何值时,S△ABP:S△AOP=2:3
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/19/c0afaeec-e5c2-4856-9e04-0448100875a5.png?resizew=308)
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解答题-证明题
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适中
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【推荐1】取一张
的纸按下图操作:
第一步:先把矩形
对折,折痕为
,如图(1)所示;
第二步:再把B点叠在折痕线
上,折痕为
,点B在
上的对应点为
,得
,如图(2)所示;
第三步:沿
线折叠得折痕
,点A在直线
上,如图(3)所示.
利用展开图(4)探究:
是什么三角形并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b553e2a281714677e29a5e97dd7d5a3.png)
第一步:先把矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
第二步:再把B点叠在折痕线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5326817f9af012432a202749d1df59f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16b4322e3be12ac26ac075b9cac0795c.png)
第三步:沿
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fcdf6433a4d158702f09391f191f5e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
利用展开图(4)探究:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/28/fb67c062-133f-4efc-b99f-a7cc90ef7bd9.png?resizew=473)
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解答题-证明题
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名校
【推荐2】已知如图1,直线
分别是直线
上的点,点
是直线
上一定点,点
是直线
上一动点,过点
作直线,点
是直线
上的动点(点
不与点
重合).设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5fe2ebefb1a233571828ec992f8e9c1.png)
(1)当点
在
点左侧运动,点
在线段
上运动时,如图
之间有什么数量关系?证明你的结论.
(2)当点
在点
左侧运动,点
在线段
外运动时,
之间有什么数量关系?直接写出你的结论:___________.
(3)当点
在点
右侧运动,点
也同时运动时,
之间有哪些数量关系?请在备用图中画出相应的图形,并直接写出结论:___________.(备用图不够时,可以自己添图形)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3942253960c528baf35318e2f7fd96c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e203b7c9a6600e0272c58a23733490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5fe2ebefb1a233571828ec992f8e9c1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/27/be107766-3071-4847-828a-9fa7f778d98d.png?resizew=827)
(1)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00de3b37f53fdc8d6c8b19c8d4fb7923.png)
(2)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b267acd63b496b5db2115f149f6cf791.png)
(3)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecfbc9d9fe354d859141145c4b6fcdc3.png)
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