一、选择题(本大题共8个小题,每小题4分,共32分.)
-
-
2.
“数”读二十大报告,见证中国的非凡十年.十年来,全国832个贫困县全部摘帽,基本养老保险覆盖10.4亿人,国内生产总值从54万亿增长到114万亿元,居民人均可支配收入从16500元增加到35100元等.其中,数据35100用科学记数法表示应为( )
A . 0.351×105
B . 351×102
C . 3.51×104
D . 35.1×103
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-
4.
用一个平面去截一个如图的圆柱体,截面不可能是( )
![](//tikupic.21cnjy.com/2023/01/07/1f/d6/1fd663b6583f7c9eee1b206df5e52ba8.png)
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5.
下列各对数中,相等的一对是( )
A .
与
B . -22与(-2)2
C . -(-3)与-|-3|
D . (-2)3与-23
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6.
如图,点A,B,C,D四个点在数轴上表示的数分别为a,b,c,d,则下列结论中,错误的是( )
![](//tikupic.21cnjy.com/2023/01/07/bb/fa/bbfaa778c7b318cb56bc0e4732dfdbda.png)
A . a+c<0
B . b-a>0
C . ac>0
D .
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7.
(2021七上·成都期中)
在下列说法中:①如果
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmo%3E%26gt%3B%3C%2Fmo%3E%3Cmi%3Eb%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,则有
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmo%3E%7C%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmo%3E%26gt%3B%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmo%3E%7C%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
;②0既不是正数,也不是负数;③一个有理数的绝对值是它本身,则这个数是正数;④若
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3En%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,则m、n互为相反数.正确的个数有( )
A . 4个
B . 3个
C . 2个
D . 1个
-
8.
如图,是由一些大小相同的小正方体组成的简单几何体的主视图和俯视图,若组成这个几何体的小正方体的个数最多为m,最少为n,则m-n的值为( )
![](//tikupic.21cnjy.com/2023/01/07/c6/7b/c67b6e13265b949eabd8191d2e9a5390.png)
A . 4
B . 3
C . 2
D . 1
二、填空题(本大题共5个小题,每小题4分,共20分.)
-
9.
﹣4的相反数是,﹣2﹣(+5)的绝对值是,倒数等于本身的数.
-
-
-
12.
比较大小:﹣
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
﹣
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
;(﹣2)
2﹣|﹣2﹣1|.(填“>”或“<”)
-
13.
某种无盖的长方体包装盒的展开图如图所示.根据图中数据计算,这种药品包装盒的体积是
.
![](//tikupic.21cnjy.com/2023/01/07/ad/0c/ad0c714a664f849f837f41585a996c63.png)
三、解答题(共48分,答聚写在答题卡上)
-
14.
计算:
-
(1)
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmfrac%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E2.4%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmfrac%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
;
-
(2)
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmo%3E%C3%97%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmn%3E7%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmo%3E%C3%B7%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmn%3E7%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
;
-
(3)
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmrow%3E%3Cmo%3E%5B%3C%2Fmo%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmo+stretchy%3D%22false%22%3E%28%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E7%3C%2Fmn%3E%3Cmn%3E9%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmn%3E11%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E12%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E6%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmo+stretchy%3D%22false%22%3E%29%3C%2Fmo%3E%3Cmo%3E%C3%97%3C%2Fmo%3E%3Cmn%3E36%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%5D%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmo%3E%C3%B7%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
;
-
(4)
﹣22﹣(﹣2)2﹣8÷(﹣2)3﹣42÷|﹣4|.
-
15.
若x是平方等于其本身的有理数,y2=4,且xy>0,求x-y的值.
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16.
已知|ab-2|+(b-1)2=0.
-
-
(2)
求
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmrow%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmi%3Eb%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmrow%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmrow%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmo%3E%E2%8B%AF%3C%2Fmo%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmrow%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E2022%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E2022%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的值.
-
17.
一几何体的三视图如图所示,求该几何体的体积.
![](//tikupic.21cnjy.com/2023/01/07/b3/7a/b37aa0502c8b364258ae7a293e2f1f4d.png)
-
18.
阅读理解:若A、B、C为数轴上三点,若点C到点A的距离是点C到点B的距离3倍,我们就称点C是【A,B】的金点.例如,如图1,点A表示的数为-1,点B表示的数为3.表示数2的点C到点A的距离是3,到点B的距离是1,那么点C是【A,B】的金点,但点C不是【B,A】的金点.
![](//tikupic.21cnjy.com/2023/01/07/85/1b/851b76f33457c5f9ef22177d9f6a5fc8.png)
-
(1)
如图1,点B【D,C】的金点(填“是”或“不是”);点D是【,】的金点.
-
(2)
如图1,若点G是【A,C】的金点,则点G在数轴上表示的数是多少?
-
(3)
如图2,A、B为数轴上两点,点A所表示的数为-8,点B所表示的数为20.现有一点P从点B出发,向左运动,若点P运动到A点停止,点P在数轴上某处时,此时点P、A和B中恰有一个点为其余两点的金点,则点P表示的数是多少?(直接写出答案)
四、填空题(本大题共5个小题,每小题4分,共20分.)
-
19.
(2019七上·青羊期中)
已知a,b为有理数,且a>0,b<0,a+b<0,将四个数a,b,﹣a,﹣b按由大到小的顺序排列是
.(用“>”号连接)
-
-
21.
如果规定符号“*”的意义是
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmo%3E%2A%3C%2Fmo%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%7B%3C%2Fmo%3E%3Cmtable+columnalign%3D%22left%22%3E%3Cmtr%3E%3Cmtd%3E%3Cmsup%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmo%3E%E2%89%A5%3C%2Fmo%3E%3Cmi%3Eb%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmsup%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmi%3E%26lt%3B%3C%2Fmi%3E%3Cmi%3Eb%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 比如3*1=3
2-1=8,2*3=3
2+2=11,求(-3)*(-2)+4
*(-1)=
.
-
22.
图中的大矩形长8厘米、宽6厘米,小矩形长4厘米、宽3厘米,以长边中点连线(图中的虚线)为轴,将图中的阴影部分旋转一周得到的几何体的表面积为
平方厘米.
![](//tikupic.21cnjy.com/2023/01/07/1f/49/1f4985313723116a0fe239893feb312f.png)
-
23.
我们常用的数是十进制的数,而计算机程序处理中使用的是只有数码0和1的二进制数.这两者可以相互换算,如将二进制数101换算成十进制数应为1×22+0×21+1×20=4+0+1=5,将1101换算成十进制数应为1×23+1×22+0×21+1×20=13,按此方式,则将十进制数25换算成二进制数应为.
五、解答题(本大题共3个小题,共30分,解答过程写在答题卡上)
-
24.
小尚的妈妈在某玩具厂工作,厂里规定每周工作五天,该厂实行工资“日结算制”:每天的基本工资为200元,每天基本任务量为40个,若超额完成任务,则超出部分每个按7元奖励;若未完成任务,则未完成部分每个按8元扣除.由于种种原因,实际每天生产量与计划量相比有出入,本周五小尚妈妈刚好完成基本任务.下表是小尚妈妈本周的生产情况(比前一个工作日多记为正,比前一个工作日少记为负):
星期
|
一
|
二
|
三
|
四
|
五
|
增减产值
|
+5
|
-7
|
+1
|
+1
|
+4
|
-
(1)
根据记录的数据可知小尚妈妈星期三生产玩具个;本周实际生产玩具个;
-
-
(3)
若将工资“日结算制”改为“周结算制”,即每周的基本工资为1000元,每周基本任务为200个;若超额完成任务,则超出部分每个按7元奖励;若未完成任务,则未完成部分每个按8元扣除,在此方式下小尚妈妈本周的工资与“日结算制”的工资哪一个更多?请说明理由.
-
25.
如图,在平整的地面上,用10个棱长都为2cm的小正方体堆成一个几何体.
![](//tikupic.21cnjy.com/2023/01/07/cf/db/cfdb54356f3f14e2bcdca516d08daf16.png)
-
-
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(3)
如果现在你还有一些棱长都为2cm的小正方体,要求保持俯视图和左视图都不变,最多可以再添加个小正方体.
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26.
(2018七上·深圳期中)
如图,将一条数轴在原点O和点B处各折一下,得到一条“折线数轴”.图中点A表示﹣10,点B表示10,点C表示18,我们称点A和点C在数轴上相距28个长度单位.动点P从点A出发,以2单位/秒的速度沿着“折线数轴”的正方向运动,从点O运动到点B期间速度变为原来的一半,之后立刻恢复原速;同时,动点Q从点C出发,以1单位/秒的速度沿着数轴的负方向运动,从点B运动到点O期间速度变为原来的两倍,之后也立刻恢复原速.设运动的时间为t秒.问:
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(2)
P、Q两点相遇时,求出相遇点M所对应的数是多少;
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(3)
求当t为何值时,P、O两点在数轴上相距的长度与Q、B两点在数轴上相距的长度相等.