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2011-2012学年度莒南第一学期九年级期末考试

2011-2012学年度莒南第一学期九年级期末考试
2011-2012学年度莒南第一学期九年级期末考试

第一学期九年级期末考试 数学试题

一、选择题:(每小题3分,共30分)将唯一正确答案的代号字母填在下面的方格内. 1.下列各等式成立的是

A .4)4(

2

-=-

B .

3)3(2=- C .x x =2

D .

24±=

2.方程(x 一1)(x 一2)=1的根是

A .2,121

==x x B .2,121-=-=x x C .3,021==x x

D .以上不对

3.已知矩形ABCD 的对称中心恰为原点O ,且点A 的坐标为(2,一3),则C 点的坐标为 A .(一2,3)

B .(一2,一3)

C .(2,3)

D .(一3,2)

4.下列判断错误的是

A .相等的圆周角所对的弧相等

B .相等的弦所对的圆周角相等

C .长度相等的两条弧是等弧

D .经过圆心的弦也是圆的直径

5.已知一个圆锥的侧面展开图是一个半径为9,圆心角为120°的扇形,则该圆锥底面圆的半径等于

A .3

B .9

C .10

D .27

6.已知圆锥的底面半径为1cm ,母线长为3cm ,则其全面积为 A .2

cm π

B .2

3cm π

C .2

4cm π

D .2

7cm π

7.随机掷一枚均匀的硬币两次,落地后至少有一次正面朝上的概率是 A .

2

1

B .

4

1 C .

3

2 D .

4

3

8.已知二次函数的图象如图所示,下列结论正确的是

A .b>0,c>0

B .b>0,c<0

C .b<0,c>0

D .b<0,c<0 9.二次函数y=2x 2-mx+5,当x<一2时,y 随x 的增大而减小;当x>一2时,y 随x 的增大而增大,则m 的值为 A .一4

B .一8

C .8

D .无法计算

10.如图,已知DE//BC ,CD 和BE 相交于点O ,

S △DOE :S △COB =4:9,则AE :EC 为 A .2:3 B .2:1 C .4:9

D .5:4

二、填空题:(每小题3分,共30分)将正确答案直接填在题中横

线上。

11.两个最简二次根式a

a 与

d

c 相加得6

5

,则

a+b+c=________.

12.已知关于x 的一元二次方程(a 一2)x 2+3x+a 2-3a+2=0有一个根为0,则a 的值为______ 13.如图,AB 是半圆O 的直径,D 是弧AC 的中点,∠B=50°。则∠A 等于_______度.

14.已知圆锥的底面周长为4πcm ,母线长为3cm .则它的侧面展开图的圆心角为______度.

15.某同学的文具盒中有两支蜡笔,一支红色的,另一支绿色的,还有三支水彩笔,颜色分别是黄色、黑色、红色.从中任意拿出一支蜡笔和一支水彩笔,这两支笔正好都是红色的概率为____________.

16.已知抛物线y=x 2+bx+2的顶点在x 轴上,则b 的值为__________. 17.用一根长为8cm 的细铁丝围成一个矩形,则矩形的最大面积是_________.

18.一根2米长的标杆直立在水平地面上,它在阳光下的影子长为1.5米,有一根垂直于地面的旗杆,此时测得其影长为3米,那么这根旗杆的高度为________米.

19.如图,已知△ABC 与DEF 是位似图形,它们的位似中心恰好为原点。已知A 点坐标为(2,0),D 点坐标为(5,0),若BC=1.6,则EF=________.

20.已知抛物线y=ax 2+bx+c (a<0)过A (一2,0)、O (0,0)、B (-3,y 1)、C (3,y 2)四点,则y l 与y 2的大小关系是_____________.

第一学期九年级期末测试 数学试卷 姓名 分数

一选择:

二填空:

11 12 13 14 15 16 17 18 19 20

三、计算题:(共22分)

21.已知三角形的三边长分别是2cm ,5cm ,acm .且a 是一元二次方程x 2—9x+18=0的一个根,求此三角形的周长.(6分)

22.如图,PA 、PB 切OO 于A 、B 两点,∠APB=60°⊙O 的半径为3cm ,求阴影部分的面积.(7分)

23.已知二次函数y=x 2—8x+15的图象与x 轴交于A 、B 两点,点C 在该抛物线上移动,若△ABC 的面积为1,求此时点C 的坐标.(9分)

四、证明题:(共14分)

24.如图,已知AB 是⊙O 的直径。弦AC//OD ,求证:弧BD=弧CD .(6分)

25.如图,在口ABCD 中,E 是BC 边上的一点,连结DE ,F 是DE 上的一点,连结AF 且∠AFE=∠B .又知AB=2,BC=3,AF=1.5.

(1)求证:△AD

F

∽△

DEC

;(2)求DE 的长.(8分)

五、应用题:共l9分)

26.如图,路灯S 距地面4米,身高1.6米的小明从距离路灯的底部(点O )6米的点A 处,沿DA 所在的直线行走6米到达点B 时,人影的长度增加了几米?(9分)

27.某公司经销一种产品,每千克的成本价为50元.通过市场调查发现,每天的销售量W (千克)随销售单价x (元/千克)的变化而变化,具体关系式为2002+-=x ω,设销售利润为y (元).解

答下列问题:

(1)求y 与x 的关系式;

(2)当x 取何值时,y 的值最大?最大利润是多少?

(3)物价部门规定销售单价每千克不得高于75元,公司要想每天获得1200元的利润,销售单价应定为多少元?(每千克利润=每千克销售单价一每千克成本价)(10分)

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