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2015年河南省南阳市宛城区九年级上学期期中数学试卷和解析

2015年河南省南阳市宛城区九年级上学期期中数学试卷和解析
2015年河南省南阳市宛城区九年级上学期期中数学试卷和解析

2014-2015学年河南省南阳市宛城区九年级(上)期中数学试卷

一、选择题(每小题2分,共16分)

1.(2分)一元二次方程x(x﹣2)=2﹣x的解是()

A.﹣1 B.2 C.﹣1或2 D.0或2

2.(2分)下列各式中,与是同类二次根式的是()

A.B. C. D.

3.(2分)下列运算中错误的是()

A.2×3=6B.×= C.=D.(﹣)2=2

4.(2分)若2a=3b=4c,且abc≠0,则的值是()

A.2 B.﹣2 C.3 D.﹣3

5.(2分)下列各数与相乘,结果为有理数的是()A.B.C.D.

6.(2分)点M(﹣cos60°,sin60°)关于x轴对称的点的坐标是()A.B. C. D.

7.(2分)如图,在四边形ABCD中,DC∥AB,CB⊥AB,AB=AD=2CD,点E,F 分别为AB,AD的中点,则三角形AEF与多边形BCDFE的面积之比为()

A.1:7 B.1:6 C.1:5 D.1:4

8.(2分)如图,把ABC经过一定的变换得到△A′B′C′,如果△ABC上点P的坐标为(x,y),那么这个点在△A′B′C′中的对应点P′的坐标为()

A.(﹣x,y﹣2)B.(﹣x,y+2)C.(﹣x+2,﹣y)D.(﹣x+2,y+2)

二、填空题(本大题共10小题,每小题3分,共30分)

9.(3分)化简=.

10.(3分)若方程3y2﹣4y﹣2=0可化为(y+m)2=k的形式,则m=.11.(3分)使代数式有意义的x的取值范围是.

12.(3分)近期随着国家抑制房价新政策的出台,某楼盘房价连续两次下跌,由原来的每平方米10000元降至每平方米8100元,设每次降价的百分率相同,则降价百分率为.

13.(3分)若关于x的方程(k﹣1)x2+2x﹣2=0有实数根,则k的取值范围是.

14.(3分)如图,在△ABC中,∠A=45°,∠B=30°,CD⊥AB,垂足为D,CD=1,则AB的长为.

15.(3分)已知关于x的方程(b﹣c)x2+2(a﹣b)x+b﹣a=0有两个相等的实数根,则以a、b、c为三边长的三角形的形状一定是.

16.(3分)如图,在平面直角坐标系中,矩形OABC的顶点O在坐标原点,A(﹣4,0),C(0,6),如果矩形OA′B′C′与矩形OABC关于点O位似,且矩形OA′B′C′的面积等于矩形OABC面积的,那么点B的对应点B′的坐标是.

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