1 . 阅读理解:我们把
称作二阶行列式,规定它的运算法则为
,例如
,请根据阅读理解解答下列各题:
(1)
______;
(2)计算:
;
(3)已知实数a,b满足行列式
,则代数式
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5440a1b5d9338efd6976a56432e100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c8894e0b37af5da23a1c1bffb32017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a802b3a4b3431196c23424e972de8e33.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8505c612b1c949ad76e3af4ec996afff.png)
(2)计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8948fb83a83bf2a626b94a1c7002a581.png)
(3)已知实数a,b满足行列式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43079db582537e280f7014cecdb22c4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8b776ed793293bfbd518658b6bbc639.png)
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2 . 如果分式M与分式N的差为常数k,且k为正整数,则称M为N的“差整分式”,常数k称为“差整值”.如分式
,
,
,故M为N的“差整分式”,“差整值” .
(1)以下各组分式中,A为B的“差整分式”的是__________(填序号);
①
,
, ②
,
, ③
,
;
(2)已知分式
,
,C为D的“差整分式”,且“差整值” ,
①求G所代表的代数式;
②若x为正整数,且分式D的值为负整数,求x的值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd6aa151495e744e4242575edb9c1136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9542f873b695974b930683705c1298b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e07c4a3596c1ec2c11304b648ebfd04b.png)
(1)以下各组分式中,A为B的“差整分式”的是__________(填序号);
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c4437fe51c3eb3bb89b5a5725b805fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/008950c75c3fc622e416c7d314c280ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04fb193040d04c1cef13676f5a740c0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9774a3f55760fc3b72192b3dfa3896e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9716bbbf8ecfc9c4b8b28d1c36749cb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c688a4eec914e665634b60f096393744.png)
(2)已知分式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e277b0ec845f55c4466bbc2d569961be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/483190ffda1c70d4ebc901c97f9b28f9.png)
①求G所代表的代数式;
②若x为正整数,且分式D的值为负整数,求x的值;
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3 . 如果一个正整数可以表示为两个连续奇数的立方差,则称这个正整数为“和谐数”.如:
,则2和26均为“和谐数”.在不超过2024的正整数中,所有的“和谐数”之和为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c40bc4f5508e67034b3dc3508b3de60.png)
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4 . 定义运算
;当
时,
;当
时,
;如:
;
;
,根据该定义运算完成下列问题:
(1)
______,当
时,
______;
(2)若
,求x的取值范围;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6323f3d42a8c329f1231a4183cca21c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1132de2e8913dba9c5cc2396ecb09fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d4e40d8a516cfac555fd238041a8a78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb877714a572222f19758923620208c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58467a93f0fa687a88d59e3aa48b3d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd18f75453fb59d961f1fd5f5d90546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27fd9f24c598796f3c2859ab5ffb28e9.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97d0f11e565e4afb06db0ce84d056fbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f417f76e2e7eb5231d8e90fb85c5b17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3086da2211ec337fea66e18acd018d11.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5705097a6199e40400a4a19148999958.png)
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5 . 数学教育家波利亚曾说:“对一个数学问题,改变它的形式,变换它的结构,直到发现有价值的东西,这是数学解题的一个重要原则”.
材料一:平方运算和开方运算是互逆运算.
,那么
.如何将双重二次根式
化简?我们可以把
转化为
完全平方的形式,因此双重二次根式
得以化简.
材料二:在直角坐标系
中,对于点
和
给出如下定义:若
,则称点Q为点P的“横负纵变点”,例如:点
的“横负纵变点”为
,点
的“横负纵变点”为
.请选择合适的材料解决下面的问题:
(1)点
的“横负纵变点”为______,点
的“横负纵变点”为______;
(2)化简:
;
(3)已知
为常数
,点
,且
,点
是点M的“横负纵变点”,则点
的坐标是______.
材料一:平方运算和开方运算是互逆运算.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a7cc808e0017a45a8350ed2e511f03b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1208fde2351fab3a8d1249c8883ecbe6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7eec0a5ed8b6a0e32cb9cec193bcad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/130976294ee199a2adce7cf0a902cbf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa56089a9e58e6e4ce03d844b0186568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e10ad10b93426464834dcc678750bc.png)
材料二:在直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a737d1c87d49e5457d41b3cb247ee38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2faec1cbb0d7383aa6e9a564266b7cba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990eaf5dbba84f199bdc438da81fcfa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990eaf5dbba84f199bdc438da81fcfa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4e71593587f76bc6f8cdd3dc54e605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc2d29199d181d4edeaadcee4862eeab.png)
(1)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bdc236963e2bbe9f9780904b812f35a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03b016a2f20561616e65406a84f80008.png)
(2)化简:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7db9a75e939ca25663a9a16619a91085.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3df2b82368be4b0577c8d564bbf0cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c249c4f55cb0df4141c1384ac98191c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1775b115051900c415988cb14227564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da895d8bd043625a0839128252130d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da895d8bd043625a0839128252130d9.png)
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6 . 新定义:
是一次函数
(
,a,b为实数)的“关联数”.若“关联数”是
的一次函数是正比例函数,则点
所在的象限是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e136e7637543c8ae92c8dcd55b31924.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31d803857a10e17622a68f71826707c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b7715827f82140efb289bea2b85191.png)
A.第一象限 | B.第二象限 | C.第三象限 | D.第四象限 |
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7 . 设[x)表示大于x的最小整数,如
,则下列结论:①
;②
的最小值是0;③
的最大值是1;④存在实数x,使
成立;⑤如
,则不大于a的最大整数一定是奇数.其中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06f15593472178d8431354af99971e08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fdf9866e881112110a39f7612b7afa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bd4b31261102424c57e29f939579ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bd4b31261102424c57e29f939579ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29dc4db92eb6cee20502f8384243e976.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5579ba9b7c5d7dfae4315f3385d13fe9.png)
A.①③④ | B.②③④ | C.③④ | D.③④⑤ |
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2024-04-24更新
|
54次组卷
|
2卷引用:福建省漳州台商投资区交通中学2023-2024学年八年级下学期月考数学试题
8 . 阅读:如果两个分式A与B的和为常数k,且k为正整数,则称A与B互为“关联分式”,常数k称为“关联值”. 如分式
,
,
,则A与B互为“关联分式”,“关联值”
.
(1)若分式
,
,判段A与B是否互为“关联分式”,若不是,请说明理由;若是,请求出“关联值”k.
(2)已知分式
,
,C与D互为“关联分式”,且“关联值”
.
①
________(用含x的式子表示);
②若x为正整数,且分式D的值为正整数,则x的值等于________.
(3)若分式
,
(a,b为整数且
),E是F的“关联分式”,且“关联值”
,求c的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d564d8d623db1d218f180b53f9268f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a427db44aee1dc6ff2e95a23963fde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67dadcfd2426a28d6143c3babe34ade2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
(1)若分式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7c503ce0a35cff925d00171759cc128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb07d370b63fb64af124523b8602318.png)
(2)已知分式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abbaf1a69701f710f4cc2aebd8778346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f691e4f6fc833cc5b8a0bfe7a21fb5bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e69866076dcff686a05e9e91e61e68.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9163ebe812708ee5337d62298c2e3363.png)
②若x为正整数,且分式D的值为正整数,则x的值等于________.
(3)若分式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e602529700122ccc32313c8281a8cfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/122509d33723272a2f76f18e0c669a11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9678ae57ecdf808530b4cbc2ca0f12e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aab343f7e994c908f3cd031bb988c4a.png)
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名校
9 . 新定义:如果两个实数
使得关于
的分式方程
的解是
成立,那么我们就把实数
组成的数对
称为关于
的分式方程
的一个“关联数对”.
例如:
使得关于
的分式方程
的解是
成立,所以数对
就是关于
的分式方程
的一个“关联数对”.
(1)判断下列数对是否为关于
的分式方程
的“关联数对”,若是,请在括号内打“√”. 若不是,打“×”.
①
( );②
( );
③
( ); ④
( );
(2)若数对
是关于
的分式方程
的“关联数对”,求
的值;
(3)若数对
(
且
,
)是关于
的分式方程
的“关联数对”,且关于
的方程
有整数解,求整数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba8770ec3fd5a1ac8c5e636abe6641c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca767de75b2b8f9b04dbc1db190165af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba8770ec3fd5a1ac8c5e636abe6641c.png)
例如:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4eab7cdf5ad059b2b171a5a65e17ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/044ea58136273ecf7c9979524d6c8cec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d08d294e975df3d21155fe4ec9f340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b4178fe9a19dc0bd0e64ada35d9c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba8770ec3fd5a1ac8c5e636abe6641c.png)
(1)判断下列数对是否为关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba8770ec3fd5a1ac8c5e636abe6641c.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da0cfdeae348f10ef862e8560c46986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9f88173ef0c29bedd0155b7893d2474.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b4178fe9a19dc0bd0e64ada35d9c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40765d09390381658d5b4dc0160366cb.png)
(2)若数对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37238859b90c31e12b45c201569478db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba8770ec3fd5a1ac8c5e636abe6641c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)若数对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b59998db99c4acdb1cf032fd1706bda2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4967f87cd5be9fed1587f48324b12c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0baedc4d7e690ab3f7d80d30ba0a9efe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c525393775354325cbf7839366ca50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba8770ec3fd5a1ac8c5e636abe6641c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9122c60e2bc2c542f7f7ca2d4fcd4f65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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10 . 定义一种新运算:对于任意实数a,b,规定:
,例如:
,则
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79325cca6227afb9f52361a891f2c5ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d507f6f19fc4d87f96d6e0543ffe6ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6471cf7043f337134e973a164a22652b.png)
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