1 . 若
,则
的大小关系是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829e7144ad645a398280aa4c14e9f119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2 . 【阅读材料】已知
是关于
的多项式,记为
.我们规定:
的导出多项式为
,记为
.例如:若
,则
的导出多项式
;若
,则
的导出多项式
.
【类比探究】(1)
,则它的导出多项式
___________;
【拓展应用】(2)设
是
的导出多项式.若
,求关于
的方程
的解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c964e149ebd8bd5b2307f9b9e803caf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826308511448f7b791edf4199c690768.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826308511448f7b791edf4199c690768.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa3a3fc366487b798363daeeb3643ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11a22c453d9041febde25582b463e642.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/046b388177cf781f9a1418c0cc971ece.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826308511448f7b791edf4199c690768.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711ea620e3108f5dc10b0f9d91ec96d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84bd2e39d145f598e41d2bbff0e94f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826308511448f7b791edf4199c690768.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f056d73b20957d14c3290b5c97f24eb6.png)
【类比探究】(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7604e6e8e1da83ef655af7f3a18b7823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588056ae7548b5743371671a0162a83f.png)
【拓展应用】(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11a22c453d9041febde25582b463e642.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826308511448f7b791edf4199c690768.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1df64d9daf1cb231eadbfb907f57e023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29ac95d3e3ed182968bc20a499ac0064.png)
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3 . 一个四位自然数
,若个位数字与十位数字的平方和恰好等于去掉
的十位数字与个位数字后剩余部分形成的两位数与个位数的和,则这个四位数称为“平方和数”,比如:1314,满足
,则1314为“平方和数”;比如:1234,由于
,则1234不是“平方和数”,那么最小的“平方和数”是______ .如果一个“平方和数”
的千位数字为
,百位数字为b,十位数子为c,个位数字为
,记
,且
,当F(M),G(M)均为整数时,则满足条件的M最大值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ca8ad3f3b9d727d752af50406dd8d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e218da32ef6dbee7b9e58655f0783d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f49f4df5d965298a19a333c762a5f4cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53204f149fa997004b8a90058e5f7c0f.png)
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4 . 对于一个四位正整数
,若它的各位上数字均不为零且互不相等,千位数字与个位数字之和为9,十位数字比百位数字大2,则称这个四位正整数A是“优胜数”.则符合条件的A的最大数与最小数的差为__________ ,
,
,若
能被7整除,则所有满足条件的四位正整数A的和为_________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8c73ef92e812960e7838a68958b328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0db52ed453e857ebbc14d9d1afea490f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70372b4abd3ca3b1bd299f6de40b9c7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b755944ad6b30561a31bb5c6b0d183.png)
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5 . 已知两个整式
,
,用整式A与整式B求和后得到整式
,称为第一次操作;将第一次操作的结果
加上
结果记为
,称为第二次操作;将第二次操作的结果
加上
,结果记为
,称为第三次操作;将第三次操作的结果
,加上
,结果记为
,称为第四次操作,…,以此类推.以下四个说法正确的个数是( )
①当
时,则第5次操作的结果
;
②当
时,则有
;
③
;
④当
,
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a690cc152a8406df881716032340acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c17b9e4c265244558e66dd21fc3d62b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bab3f6faa12b17f48db231e34a742d19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b104090ea2ac34be58a76a4e0e95cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e769ec7d298d92206c7c5c92b2f487.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df1d9b712b639c8b6809c9f3ae03706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df1d9b712b639c8b6809c9f3ae03706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b2da554a36939bafd8d099ab116de30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32efe4eff75508cb93e828c735dcb695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32efe4eff75508cb93e828c735dcb695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143e2061bec301ea5baffb3ca229d542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fa71450b470cb7d6464339873d74b8.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b104867a12d24a353d94858c2fa17c8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd10cd01cbf05d542bba9eb17bea7979.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6175fd4f4a9e9f4f8d76d04364bfaaec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04aec1a551c6d2a70459e553741cfb0c.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f9444c74cfd12229e6867bf8c05ca9.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/457726cd3cf3550ca5db4c2069c2140b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddd56276f743d2c2643182cc4db6f4bb.png)
A.1个 | B.2个 | C.3个 | D.4个 |
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6 . 若一个四位数
的百位数字是千位数字的3倍,十位数字是个位数字的2倍,则称这个四位数
为“幸福数”.对于一个“幸福数”
(
,
,
,
是整数,且
,
,
,
),它的千位数字和个位数字组成的两位数为
,百位数字和十位数字组成的两位数为
,将这两个两位数求和记作
;它的千位数字和百位数字组成的两位数为
,十位数字和个位数字组成的两位数为
,将这两个两位数求和记作
.规定:
.若四位数
,
均为“幸福数”,
的个位数字为1,当
能被7整除时,
的千位数字为______ ,且满足条件的最小四位数
为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6274ea991349d91390e3883211f6eca4.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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a6fe0a044511f71c14c4a710f358581.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3cb8cb634644553ad16a44e4ea840b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03bab33097e190d6169262a00d23939b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46b98b963adb86a9d5943e3bfeb7052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3e285b9b7c5d56fda67f2545d9eafcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54cbdd32c22ec3b95b2db156ae28dfd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23606fe6d2b81e7b9b21dec4cc5f04b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2f22e40f4c8f12ab3d167a5c3762fce.png)
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c562cac0dcadb66803870fa005547570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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名校
7 . 一个四位自然数
的各个数位上的数字互不相等且都不等于0,如果前两位数字所组成的两位数与后两位数字所组成的两位数的和等于100,那么就称这个数为“奋进数”.把“奋进数”
的前两位数字和后两位数字整体交换得到新的四位数
.并且规定:
.例如:一个四位数3268,因为
,所以3268是“奋进数”,且
.如果四位自然数
(
,且
为整数)是一个“奋进数”,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a973ad8516cd7318adc3b1929989f502.png)
______ (用含
的代数式表示),另外规定
等于
的前两位数字之和.如果
是一个“奋进数”,
为偶数,且
(
为整数),则满足条件的
的最小值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da895d8bd043625a0839128252130d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383cdac2832f19158b2a9b2ba15468a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf059956415ef20228fe325f16fee49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28ee9af8d07a22f54b5b26f72a1b5816.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6274ea991349d91390e3883211f6eca4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a2002d8ae467f25a05c7bf179c018c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d10449bc77d692a7270e0f20a68cdf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a973ad8516cd7318adc3b1929989f502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b6fe330bde0f6f42db509765655e19c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ba84b48eceb67da48cf06599f0b7719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9a2ccb2fbbd085b04902ecb4ea0b8c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
8 . 已知
,在多项式
中任意选择相邻
(
)个字母,在不包含其中第一个字母前的符号的情况下添加一个绝对值符号,然后进行去绝对值运算,例如:
,
,下列说法:①至少有一种情况化简后与原式相等;②在所有化简结果中,不能得到“
”这一项;③化简后一共有6种不同的结果.其中正确的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d2e4f823e535e34ea4707fc1fdbcac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50555326478eb9bb1fd43ee4b5e8c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf5523598aa6fe711e726fe3ffd8d741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80de51c389fca29f01638f119ad2d52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d604b73075a673417e598357e69716f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d2cb112ba3b1b933e03206963163b9.png)
A.0 | B.1 | C.2 | D.3 |
您最近一年使用:0次
9 . 阅读下面内容,并解决问题:用求差法比较大小
学习了不等式的知识后,我们根据等式和不等式的基本性质,可知比较两个数或数量的大小可以通过它们的差来判断.例如,如果两个数或数量为
和
,那么,当
时,一定有
;当
时,一定有
;当
时,一定有
.反过来也正确,即当
时,一定有
;当
时,一定有
;当
时,一定有
,因此,我们经常把要比较的对象先数量化,再求它们的差,根据差的正负判断对象的大小.这种比较大小的方法称为“求差法比较大小”.
请解决以下问题:
(1)用“
”,“
”或“
”填空:
;
(2)制作某产品有两种用料方案:方案一用3块
型钢板,7块
型钢板:方案二用2块
型钢板,8块
型钢板.
型钢板的面积比
型钢板的面积大.若
型钢板的面积为
,
型钢板的面积为
,从省料的角度考虑,应选哪种方案?说明理由.
学习了不等式的知识后,我们根据等式和不等式的基本性质,可知比较两个数或数量的大小可以通过它们的差来判断.例如,如果两个数或数量为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7091d529281abff275ef19b9197445a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ac24f76da1470be3fd17d03812d1149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a4480988244a9d04ec293975db2cc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75a48d51b31779c62539b9642c6e3809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7961cbe98aac6a5fdee94582c341b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eec2b78fa6113466bb68e1fe67dfc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ac24f76da1470be3fd17d03812d1149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7091d529281abff275ef19b9197445a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75a48d51b31779c62539b9642c6e3809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a4480988244a9d04ec293975db2cc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eec2b78fa6113466bb68e1fe67dfc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7961cbe98aac6a5fdee94582c341b4.png)
请解决以下问题:
(1)用“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392cdb9d30684cce244bef94b8d861b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff7942da6c3fc4005256fb1458557c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1b1ce092493086f74481b7d6dd9434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1df3e8e495bae3941e3b6b03ae54f7a7.png)
(2)制作某产品有两种用料方案:方案一用3块
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/5963abe8f421bd99a2aaa94831a951e9.png)
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10 . 对于任意一个三位正整数m,如果m满足百位上的数字小于个位上的数字,且百位上的数字与个位上的数字之和等于十位上的数字,那么称这个数m为“两头和数”.
(1)最小的“两头和数”是_______ ;
(2)用“两头和数”m的十位数字的平方减去个位数字的平方再减去百位数字的平方,得到的结果记为
.若t是“两头和数”,且t的4倍与t的十位数字的2倍之和是5的倍数,则
的最大值为______ .
(1)最小的“两头和数”是
(2)用“两头和数”m的十位数字的平方减去个位数字的平方再减去百位数字的平方,得到的结果记为
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