1 . 运用整体思想解决数学问题,有时会使我们的解题更加简便快捷.例如:已知
,求
的值.解:
,当
时,原式
.请你借鉴上面的解题经验,解决下列问题:
(1)若
,则
______;
(2)若关于x,y的方程组
的解为
现有关于m,n的方程组
,求代数式
的值;
(3)如图,将
纸片沿
折叠,使点
落在点
的位置.
①如图1,点
在
内部,请你猜想
与
之间有怎样的数量关系,并说明理由;
②如图2,点
在
外部,再将
纸片沿
折叠,点C恰好也落在点N的位置,若
,
,则
____________(用m、n的代数式表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ba8a4b6fbfa194a07c0d5f0b1bd1ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46ebd1734ead1220ff0d0612da32d5e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3871379335c3c9409c7369abbba586c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ba8a4b6fbfa194a07c0d5f0b1bd1ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e11a2420bcb32522881aaeddb404f3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d873405c90a3e9bc1b8f52bcd2852e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90fc65dd9360c2ded167df709b047ca.png)
(2)若关于x,y的方程组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18a72c1f09c4b571d6f261f86f9d3b39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/485874402b318268aa6ef0eadf270a40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af4df998f4e31d587f10e9304a74f73b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34b2029464b8dac1e192ccfa5e9c0266.png)
(3)如图,将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
①如图1,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3818a2c9919d358b4c3713396093822b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e1abfc5f8a68337146228441531d442.png)
②如图2,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a0a79991aec8c223a3220f3631e8ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f3c9b63df0ce09985f60de859b55a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e7cbe31f9c11d236c7c9611f207f465.png)
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2 . 现规定:若m、n满足
,则称m、n为“固距组合”,记为
;若a、
满足
,则称a、b为“合拍组合”,记为
.
(1)在
中
的值为______;
(2)在
中,
______;(用含
的代数式表示)
(3)若a、b、m、n四个数满足
、
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ca9c6eae89ae8052c5d7aa34357cddb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd8466b576ad34d6ef492599940f4b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/126db3b9c2f680708b41aae3ae1a1c21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a3ea9f0c75151f40abcc558569e209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e014d3b55d220104538deebe7aba3b.png)
(1)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f3c451e591e1613012bac2b32b7848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e014d3b55d220104538deebe7aba3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)若a、b、m、n四个数满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd8466b576ad34d6ef492599940f4b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e014d3b55d220104538deebe7aba3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42732663d71d6e9ca4d40f1a114e81d5.png)
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名校
3 . 如果一个正整数能表示为两个连续正奇数的平方差,那么称这个正整数为“正巧数”.例如:
,
,
,因此8,16,24都是“正巧数”.
(1)写出一个30到50之间的“正巧数”;
(2)设两个连续正奇数为
和
(其中k是正整数),由它们构成的“正巧数”能被8整除吗?如果能,请说明理由;如果不能,请举例说明.
(3)m,n为正整数,且
,若
是“正巧数”,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6596702d0c35fec938e159c7b4702ae0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe86423fa7639e143883a4a4e02a7a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800cbf30ddc20b1bda7445957a0e33b5.png)
(1)写出一个30到50之间的“正巧数”;
(2)设两个连续正奇数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/897d8f6cf00391f1b3ff70432f0121b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394aee19f94c2b70fcce1d69b31dc7fd.png)
(3)m,n为正整数,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7091d529281abff275ef19b9197445a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5e4aeb59a89a39f04e23a43f18cf56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72850427e83ff19a24305783e080b280.png)
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4 . 计算:
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47c9523776c0d19c5a6bc8b4585ce236.png)
(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f16f620712917e33b8c0a3d10f2a6080.png)
(3)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/780dc3ce2e461c628e8a24b967b8d41e.png)
(4)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47c9523776c0d19c5a6bc8b4585ce236.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f16f620712917e33b8c0a3d10f2a6080.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/780dc3ce2e461c628e8a24b967b8d41e.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8d0eb73062bb1a505e168db2ca3357f.png)
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5 . 从前,一位庄园主把一块边长为
的正方形土地租给租户李老汉.第二年,他对李老汉说:“我把这块地的一边增加
,相邻的另一边减少
,变成长方形土地继续租给你,租金不变,你也没有吃亏,你看如何?”如果这样,你觉得李老汉的租地面积会( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134fafc62eb2d0a0ad2622bce9126675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff14b9614e593d12aa18b4dadb2fbbe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75dcc12aa278db5bf3da96b11cc9db51.png)
A.减少![]() | B.减少![]() | C.增加![]() | D.保持不变 |
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6 . 先化简,再求值:
,其中
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56fdf45a0977490ec08d8b37a891ba98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6afef4584542103a3a08a5fe0edae9b.png)
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7 . ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bbe73ebce101a2ea687e3289d689b2.png)
_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bbe73ebce101a2ea687e3289d689b2.png)
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8 . 先化简,再求值:
,其中
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c98f382251c505848aaed0d55aa6776a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
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2024-05-07更新
|
185次组卷
|
3卷引用:江苏省连云港市新海初级中学2023-2024学年七年级下学期期中数学试题
江苏省连云港市新海初级中学2023-2024学年七年级下学期期中数学试题广东省佛山市禅城区第三中学初中部2023-2024学年七年级下学期月考数学试题(已下线)暑假作业13+七年级下学期90道计算题专训1(8大题型)
名校
9 . 已知最外圈的小正方形个数分别为:
,
,
;
个图形最外圈的小正方形个数是: ;
(2)写出第
个等式:( )
-( )=( ),并证明其正确性;
(3)利用(2)中的规律计算:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1c64abb5fc9a8b474dfb10bf9607b78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/670ed907c479a020836bcd9bd58b64fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95c5b874055ea47f73d4a2864889bc34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)写出第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/921ef5abce73648e3834140df9a72aa8.png)
(3)利用(2)中的规律计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72d578104ae34d5d8ed0d1c348eede99.png)
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2024七年级下·全国·专题练习
名校
10 . 计算:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28dc4be671637fcfcd18a996d01371ef.png)
_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28dc4be671637fcfcd18a996d01371ef.png)
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