1 . 若不等式
的最小整数解是关于
的方程
的解,求式子
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d12a7324c8fcb83b69ef0f15b742485.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4922d299be8988b040c6c97b2de73cdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4131c78f6f46032e2142353c11a7d6f9.png)
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2 . 在平面直角坐标系
中,对于不同的两点
,若点
到
轴,
轴的距离的较大值等于点
到
轴,
轴的距离的较大值,则称点
互为“最距等点”.例如:点
,
互为“最距等点”;点
,
互为“最距等点”.已知点
与点
互为“最距等点”,则
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.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/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97fe88412da03cc114f2250593293217.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20660e49954f09601cbf528a7f436fca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c59a593a0dd02859364a57fd100c55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcbcd0aebdd8bd688d108834747009f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b676f0c25a2c157472836924ff17322b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5f7447a1d2a826f1b1c0430029dd08d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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3 . 如图,是一个“因变量随着自变量变化而变化”的示意图,下面表格中,是通过运算得到的几组
与
的对应值.根据图表信息解答下列问题:
(1)直接写出:
,
,
;
(2)当输入
的值为
时,求输出
的值;
(3)当输出
的值为12时,求输入
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
输入 | … | 0 | 2 | … | |
输出 | … | 2 | 18 | … |
(1)直接写出:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
(2)当输入
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(3)当输出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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4 . 解下列方程(组):
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/535c843c2a9130dc3c01776a652d0d53.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/898b7d6662bb25cb88b4afb1fed06ec7.png)
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名校
5 . 阅读材料:定义:若关于
的一元一次方程的解及解的二倍都在一元一次不等式组的解集范围内,则称这个方程为该不等式组的“完全子方程”.例如:方程
的解为
,则
;不等式组
的解集是
,可以发现方程的解
及
都在不等式组的解集
的范围内,则称方程
是不等式组
的“完全子方程”.
请根据以上材料回答下面问题:
(1)在方程①
;②
中,是不等式组
的“完全子方程”的是______;(填序号)
(2)若方程
是不等式组
的“完全子方程”,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0c8851ec6a8b97591bd0062a136090f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d599059e6b2c918ab15ee22611b6962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54533da5f7c7ec315f6b6eb26fde90e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f405075181c7d3cdcd0715bcf93fc451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35655254f5b7b6f3d0ec32b4d8729c0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1d2e5599453f8d4c04369bc8f79962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35655254f5b7b6f3d0ec32b4d8729c0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0c8851ec6a8b97591bd0062a136090f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f405075181c7d3cdcd0715bcf93fc451.png)
请根据以上材料回答下面问题:
(1)在方程①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1067d53a8214920e539872ba1306f5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75c45b8b059f632c90ab88dc7259e295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1b27947153828d0502a04676095a1b0.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9315373d5d819790a9f90112b00d6d14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602fe010bf4a8fc251b41c3f4928b8cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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6 . 对于任意有理数
,规定:当
时,
;当
时,
.
(1)填空:
______,
______,
______;
(2)若
,求
的值;
(3)若两个有理数
,
,且
异号,满足
,请直接写出
之间可能存在的数量关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92ca3ac04a2bdc12bceee4dfc986054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c278ec775de4a238353c29359c2c4b54.png)
(1)填空:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0632bc67a48ee16de53fe7e19ec3328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be4e3838d6e4ea8e3defd8401b305774.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c289a19bccd3b1783fe9d6c1b7f1516.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31d5a0d87d64f56ffd93e463b87d6612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若两个有理数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03b011f69dfc5262a3d82f64676739b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6395d94d68cb6c6fdeeb6290334f0f59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
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7 . 在平面直角坐标系中,已知点
,点
.
(1)若点M的横坐标比纵坐标大2,求点M的坐标;
(2)若
轴,且
,求n的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/997742cb388b52166e7ba8145049d63c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84805088d8361257b2771e2975b6177d.png)
(1)若点M的横坐标比纵坐标大2,求点M的坐标;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce5c0cf64a0d41ba16c26338fb2a993.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e5c289b8aabdbfba95c7fd1e1842f4.png)
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8 . 若关于x的方程
和
的解相同,则m的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de1f7a1877330bd231069eb98c580fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96c131017392d6f7f1e3368ee3342b4b.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 若关于x的不等式组
有解且最多有3个整数解,且关于y的方程
的解为非负整数,则符合条件的所有整数a的和为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1130db525c65aff001f8aca534ada34e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e73a2a5b7270e3d692a9e9a7025d728.png)
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名校
10 . 新定义:若某一元一次方程的解在某一元一次不等式组解集范困内,则称该一元一次方程为该不等式组的“关联方程”,例如:方程
的解为
,而不等式组
的解集为
,不难发现
在
的范围内,所以方程
是不等式组
的“关联方程”.
(1)在方程①
;②
;③
中,关于x的不等式组
的“关联方程”是____________;(填序号)
(2)若关于x的方程
是不等式组
的“关联方程”求k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb8e4bbc9f6c98374f360c90f4cc8940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e08f6e95871ff15c56043f4693ee352c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43e23732770d5299908da955cd216a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43e23732770d5299908da955cd216a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb8e4bbc9f6c98374f360c90f4cc8940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e08f6e95871ff15c56043f4693ee352c.png)
(1)在方程①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fd8969496c94c5385420c16c40fcf31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/346d0dd15fd936e928520fec760790fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30e26e0110b8c84d1e02f4284f6a4de2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4842561aebe5b27c4afb68bc210bd4bc.png)
(2)若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b570bf9cb393fb6152a885e39f5b9d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8f76c1c1ce312268b193532e6ed302b.png)
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