1 . 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)
您最近一年使用:0次
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2 . 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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3 . 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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4 . 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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5 . 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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6 . ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bbe73ebce101a2ea687e3289d689b2.png)
_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bbe73ebce101a2ea687e3289d689b2.png)
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7 . 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)
您最近一年使用:0次
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
8 . 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)
您最近一年使用:0次
名校
9 . 阅读理解:为了解决负数开平方问题,数学家大胆的引入一个符号
,把
叫做虚数单位,并且规定
,我们把形如
(
、
为实数)的数叫做复数.复数的四则运算与整式的四则运算类似.例如:
;
.
根据以上信息,
的运算结果是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73be79c02db553929619d957187e2077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc228995efbba2e64d7f1de747024cc4.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/e1e3ffd3caa59783050525409875f940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c15d4c8543bf19526804b2ebefe3470.png)
根据以上信息,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db061ecfeadf7f7d84e3fd79d6c231c5.png)
A.21 | B.29 | C.![]() | D.![]() |
您最近一年使用:0次
2024-05-06更新
|
159次组卷
|
2卷引用:2024江苏省无锡市梁溪区中考一模数学试题
名校
10 . 计算:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd62331aed35edc5b2bca3ebbd2fc33.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b15cbde6a5298b5964cb3ec87af7d728.png)
您最近一年使用:0次
2024-05-06更新
|
136次组卷
|
2卷引用:2024江苏省无锡市梁溪区中考一模数学试题