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(北师大版)2013—2014学年第一学期期中考试八年级数学试卷

发布时间:2013-11-20 09:38:24  

桥东区2013—2014学年第一学期期中考试

八年级数学试题

一、选择题(本大题共10个小题,每小题3分,共30分.在每小题

给出的四个选项中,只有一项是符合题目要求的)

1.下列关于无理数的说法中,正确的是 ( ) A.无理数不是实数 B.无理数包括正无理数、0和负无理数 C.无理数是带根号的数 D.无理数是无限不循环小数 2.满足下列条件的三角形中,不是直角三角形的是 ( )

A.三内角之比为1∶2∶3 B.三边长的平方之比为1∶2∶3 C.三边长之比为3∶4∶5 D.三内角之比为3∶4∶5 3.若a-2有意义,则a的取值范围是

A.a>2

B.a<2

C.a≥2

D.a≥-2

( )

'

4.如图,正方体盒子的棱长为2,AB中点为M,一只蚂蚁从点M沿正 方体的表面爬到点D′,蚂蚁爬行的最短距离是

A.

B.

C.

D.2?5

( )

5.下列说法中,错误的是 ( )

( ) ( )

A.4的算术平方根是2 B.81的平方根是±3

C.8的立方根是±2 D.立方根等于-1的实数是-1 6.已知点A(a-2,a+1)在x轴上,则a等于

A.1 B.0 C.-1 D.-3 7.下列二次根式中,与27合并的二次根式的是 A.64

B.

2

D.10

C

.18

8.若a-3 +|b+2|=0,则点M(a,b)在 ( ) A.第一象限 B.第二象限 C.第三象限 D.第四象限

9.李老师骑自行车上班,最初以某一速度匀速行进,?中途由于自行车发生故障,停下修车耽误了几分钟,为了按时到校,李老师加快了速度,仍保持匀速行进,如果准时到校.在课堂上,李老师请学生画出他行进的路程y?(千米)与行进时间t(小时)的函数图象的示意图,同学们画出的图象如图所示,你认为正确的是 ( )

八年级数学试题 第1页 共6页

A. B. C. D. 10.如图,把Rt△ABC放在直角坐标系内,其中∠CAB=90°,BC=5,

点A、B的坐标分别为(1,0)、 (4,0),将△ABC沿

x轴向右平移,当

点C落在直线y=2x-6上时,线段BC扫过的面积为 A.4

B.8 C.16 D.82 二、填空题(本大题共10个小题,每小题2分,共20分.把答案填在题中横线上.)

115-3绝对值是__________.

12.点A(a,2)和点B(3,b)关于x轴对称,则ab=_____.

13.一个正数x的平方根是2a?3与5?a,则a=_________.

14.把2

13化成最简二次根式为 .

15.写出一个具体的y随x的增大而减小的一次函数解析式.

163<a<5的所有整数a的和为.

17.若 x +-x有意义,则2013x+1 =____________.

18.如图,在长方形ABCD中,AB=3,BC=4,若将它折叠使点A

与点C重合,则折痕EF的长为 . 19.有这样一段材料:“一根弹簧原长10cm,在弹性限度内最多可挂质量为5kg的物体,挂上物体后弹簧伸长的长度与所挂物体的质量成正比,。由上述条件可求出:弹簧的总长度y(cm)与所挂物体质量x(kg)之间的函数关系式是y=10+0.5x (0≤x≤5).”

王刚同学在阅读上面材料时就发现部分内容被墨迹污染,被污染部分是确定函数关系式的一个条件,你认为该条件可以是: (只需写出一个).

20.如图,定义变换:将边长为1的等边△OPQ绕右下角顶点旋转,使右面的边落在x轴上称为一次变换,等边三角形连续进行2013次变换,点P依次落到点P1、P2、P3、?、

P2013,则点P2013的纵坐标是 .

八年级数学试题 第2页 共6页

三、解答题(本大题共6个小题,共50分.解答应写出文字说明.证明过程或演算步骤)

21.计算:(本题共2个小题,每题4分,满分8分)

(1)32 +3

(本题满分8分) 22.

如图,一架长2.5 m的梯子,斜靠在一竖直的墙上,这时,梯底距墙

底端0.7 m,如果梯子的顶端沿墙下滑0.4 m,则梯子的底端将滑出多少米?(8分)

(6-215)3-2-2; 2)12

八年级数学试题 第3页 共6页

23.(本小题满分8分) 我国著名的数学家秦九韶在《数书九章》提出了“三斜求积术”

即:给出已知三角形三边求三角形面积的公式,公式如下:

122a+b-c2] 4[ab-2设一个三角形的三边分别为a、b、c,S=

7,8,3,试求这个三角形的面积

(本小题满分8分) 24.

如图, M(-3,2),N(-3,1).动点P从点O出发,沿y轴以

每秒1个单位长的速度向上移动,且过点P的直线l:y=x+b也随之移动,设移动时间为t秒.

(1)当t=3时,求l的解析式;

(2)若点M,N位于l的异侧,确定t的取值范围;

八年级数学试题 第4页 共6页

25.(本小题满分8分)

如图:图1是某公共汽车线路每月收支差额y(票价总收入减去运营

成本)与乘客量x的函数图象。目前这条线路刚好不盈利也不亏损,为了改变这种状况,制定了两种方案: 方案一:降低运营成本,实现盈利

方案二:提高票价,实现盈利

根据两种方案,制作了方案一和方案二的函数图象,如图2 (1)请说明图1中点A和点B的实际意义

(2)如图2:直线n∥AB,分别求出直线m和直线n的函数关系式,并指出直 线m和直线n分别是哪种方案的函数图象?

(3)若该线路汽车每月乘客人数不变,两种方案哪种盈利更多?

八年级数学试题 第5页 共6页

26.(本小题满分10分)

根据图形探究一次函数y=kx+b(k≠0

探究一:

(1)图1中,直线l1和直线l2关于____轴对称, 直线l1的函数关系式为:_____________________ 直线l2的函数关系式为:_____________________ (2)图1中,直线l3和直线l4函数关系式中的k、b 有何关系?_____________________

(3)一般地,若两个一次函数的图象关于y轴对称,你有怎样的猜想:_________________ ____________________________________________________________________________

探究二:用探究一中的思路研究下面问题 (1)图2中,直线

l5和直线l6关于____轴对称, 直线l5的函数关系式为:_____________________ 直线l6的函数关系式为:_____________________ (2)请在图2中任意画两条关于x轴对称的直线 l7和直线l8,并写出出他们的函数关系式的k、b 有何关系?_____________________

(3)一般地,你有怎样的猜想:________________________________________________ ____________________________________________________________________________

八年级数学试题 第6页 共6页

八年级数学试题参考答案

一、选择题 DDCAC DBDCC

二、填空

11.3-5

16.2 12.-6 17.1 13.-2 184152614.2 15.k<0即可

19.每挂1kg物理,弹簧伸长0.5cm(答案合理即可)

三、解答题 320.2

21.(122 ·············································································································· 4分

(2)-65 ··············································································································· 4分

22.解:如图:在Rt△ABO中

OA=AB-OB

=0.7m ······························································································· 2分 OC=OA-AC

=2.4-0.4=2m ················································································· 4分

在Rt△CDO中

OD=CD-OC

=1.5m ······························································································ 6分

∴BD=OD-OB=1.5-0.7=0.8m

即梯子底端将演出0.8m ·············································································· 8分

4723.2 ······················································································································ 4分

24.(1)y=x+3 ··········································································································· 2分

(2)4<t<5 ············································································································ 8分

25.(1)叙述合理即得分 ·························································································· 2分

(2)解:设直线AB的函数解析式是y=k1x-1

由已知1.5k-1=0,∴k=3 ∴AB:y=3-1

∵n∥AB

∴直线n的函数关系式是y=3-0.5 ·················································· 4分 2229

八年级数学试题 第7页 共6页

当y=0时,3x-0.5=0,解得x=0.75 ························································ 5分

设直线m的函数解析式是y=k2x-1

根据图象,当x=0.75时,k2x-1=0,∴k2=3

∴直线m的函数关系式是y=3-1 ··························································· 6分 直线n是方案一的图象,直线m是方案二的图象 ································ 7分

(3)当x=1.5时

方案一:31.5-0.5=0.7 方案二:y=31.5-1=1

∴方案二盈得更多 ································································································ 8分

26.探究一:

(1)x,y=-2x+2,y=2x+2 ······················································································· 3分

(2)b相等,k互为相反数 ····················································································· 4分

(3)两个函数关系式中的k互为相反数、b相等 ·················································· 5分

探究二:

(1)x,y3x-2,y=3+2 ························································································· 7分

(2)画图略 ·············································································································· 8分

k、b均互为相反数 ·························································································· 9分

(3)若两个一次函数的图象关于x轴对称,则两个函数关系式中的k、b均互为

相反数 ·············································································································· 10分 2224442 八年级数学试题 第8页 共6页

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