成都七中嘉祥外国语学校初三入学考试题

成都七中嘉祥外国语学校初三入学考试题
成都七中嘉祥外国语学校初三入学考试题

成都七中嘉祥外国语学校

初2009级九年级(下)数学入学考试题

(时间120分钟,满分150分) 命题人: 审题人:

A 卷 (共100分)

(注意:请将选择题和填空题的答案填在后面的表格中!)

一、选择题:(本大题共10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.)

1.2cos45°的值等于 ( )

A.2

2

B.2

C.2

4

D.22

2.计算326(3)m m ÷-的结果是( )

A.-3m

B. -2m

C.2m

D.3m

3. 在成都市晨晖路在某段时间内的车流量为30.6万辆,用科学记数法表示为( ) A .4

30.610?辆 B .3

3.0610?辆

C .43.0610?辆

D .5

3.0610?辆

4.小华拿一个矩形木框在阳光下玩,矩形木框在地面上形成的投影不可能是( )

A

B

C

D

5. 下列事件中,哪个是确定事件?答:( ) A .明日有雷阵雨

B .小明的自行车胎被扎坏

C .小红买体彩中奖

D .抛掷一枚正方体骰子,出现7点朝上

6.下列函数中,自变量x 的取值范围是x>2的函数是 ( ) A. 2y x =- B. y 21x =-

C. 12y x =

- D. 1

21

y x =- 7. 如图,△ABC 中,AB=AC ,∠A=30°,DE 垂直平分AC ,则∠BCD 的度数为( )

A. 80°

B.75°

C. 65°

D. 45°

8.将100个个体的样本编成组号为○1~○8的八个组,如下表

7题图

E

D

C

B

A

组号 ○1 ○2 ○3 ○4 ○5 ○6 ○7 ○8 频数

14

11

12

13

13

12

10

那么第○5组的频率为( )

A.14

B.15

C.0.14

D.0.15

9.一个圆锥的高为33,侧面展开图是半圆,则圆锥的侧面积是( ) A. 9π B . 18π C. 27π D.39π 10. 有下列函数:①y = 3x ;②y =-x – 1:③y =-

x

1

(x < 0);④y = x 2 + 2x + 1.其中当x 在各自的自变量取值范围内取值时,y 随着x 的增大而增大的函数有( )

(A )①②

(B )②④

(C )①③

(D )③④

二.填空题. (本大题共4小题,每小题4分,共16分)

11.现有甲、乙两个学习小组,每个小组的数学平均分都为130分,方差分别为2

甲S

=32,

2

乙S

=26,则数学成绩较整齐的学习小组是

组.

12.将抛物线23y x =-向上平移一个单位后,得到的抛物线解析式

是 .

13.如图,O 内切于△ABC,切点分别为D 、E 、F ,已知∠B=50°,∠C=70°,连结OE ,OF ,DE ,DF ,那么tan ∠EDF 等于________________.

14.如图,菱形OABC 中,120A =

∠,1OA =,将菱形OABC

绕点O 按顺时针方向旋转90

,则图中由 BB ',B A '', A C ',CB

围成的阴影部分的面积是 .

三.解答题. (第15题每小题6分,第16题6分,共18分)

15. (1) 0

1)41.12(45tan 32)3

1(-++---

(2) 化简求值)1()1

112(2-?+--a a a ,其中33-=a 。

13题

D F

E

A

B

C

B C O

A '

B '

C '

16. 解不等式组

20

5121

1

23

x

x x

->

?

?

+-

?

+

??

≥,

并把解集在数轴上表示出来.

四、(每小题8分,共16分)

17、如图,小岛A在港口P的南偏西45°方向,距离港口81

海里处,甲船从A出发,沿AP以9海里

每小时的速度驶向港口,乙船从港口P出发,沿南偏东60°方向,以18海里每小时的速度驶离港口,现两船同时出发,问出发后几小时乙船在甲船的正东方向?(结果精确到0.1小时,参考数据2 1.413 1.73

≈≈

,)

18、如图,已知A(-4,2)、B(n,-4)是一次函数y=kx+b的图像与反比例函数y=m

x

的图象的两个交点。

(1)求此反比例函数和一次函数的解析式;

(2)根据图象写出使一次函数的值小于反比例函数的值的x的取值范围。

17题

18题

D C B A E

图 1

E

D C H F G B A P y

x

图2 五、(每小题10分,共20分)

19、有三张卡片(背面完全相同)分别写在12,1

12-??

???

,3-,把它们背面朝上洗匀后,小军从中抽

取一张,记下这个数后放回洗匀,小明又从中抽出一张. (1)两人抽取的卡片上都是3-的概率是 .

(2)李刚为他们俩设计了一个游戏规则:若两人抽取的卡片上两数之积是有理数,则小军获胜,否则小明获胜.你认为这个游戏规则对谁有利?请用列表法或树状图进行分析说明.

20、将两块大小一样含30°角的直角三角板,叠放在一起,使得它们的斜边AB 重合,直角边不重合,已知AB=8,BC=AD=4,AC 与BD 相交于点E ,连结CD .

(1)填空:如图1,AC= ,BD= ;四边形ABCD 是 梯形. (2)请写出图1中所有的相似三角形(不含全等三角形).

(3)如图2,若以AB 所在直线为x 轴,过点A 垂直于AB 的直线为y 轴建立如图2的平面直角坐标系,保持ΔABD 不动,将ΔABC 向x 轴的正方向平移到ΔFGH 的位置,FH 与BD 相交于点P ,设AF=t ,ΔFBP 面积为S ,求S 与t 之间的函数关系式,写出t 的取值值范围.

B 卷 (共50分)

一、填空题:(每小题4分,共20分) 21、已知

113x y -=,则代数式21422x xy y

x xy y

----的值为 22. 某农场租用播种机播种小麦,在甲播种机播种2天后,又调来乙播种机参与播

种,直至完成800亩的播种任务,播种亩数与天数之间的函数关系如图所示,那么乙播种机参与播种的天数是 .

23. 已知关于x 的一元二次方程()2120x m x m --++=的一个根 大于4,另一个根小于4,则m 的取值范围为______________. 24.

二次函数

()20y ax bx c a =++≠的图象如图所示,且

OA=OC ,则

①()241b a c =+②abc>0③a-b+c>0④ac+b+1=0其中正确的是___________

25. 如图,在直角坐标系中直线分别交x 轴、y 轴于A (4,0)、B (0,-3),现有一半径为1的动圆,圆心位于B 点处,沿着BA 方向以每秒1个单位的速度作平移运动,则经过___________秒后动圆与坐标轴相切。

二、(共8分)

26.某商场销售某种品牌的纯牛奶,已知进价为每箱40元,生产厂家要求每箱售价在40元~70元之间,市场调查发现:若每箱以50元销售,平均每天可销售90箱,价格每降低1元,平均每天多销售3箱,价格每升高1元,平均每天少销售3箱。

(1)写出平均每天销售量y (箱)与每箱售价x (元)之间的函数关系式,并注明自变量取值范围; (2)求出商场平均每天销售这种牛奶的利润W (元)与每箱牛奶的售价x (元)之间的函数关系式; (3)当牛奶售价为多少时,平均每天的利润最大?最大利润为多少? 三、(10分)

27. 如下图,直线AB 经过O 上的点C ,并且OA OB =,CA CB =,O 交直线OB 于E D ,,连接EC CD ,.

(1)求证:直线AB 是O 的切线;

(2)试猜想BC BD BE ,,三者之间的等量关系,并加以证明; (3)若1

tan 2

CED ∠=

,O 的半径为3,求OA 的长. (24题图)

y

X

O B

A

(22题图)

(25题图)

四、(12分)

28.如图,在平面直角坐标系中,已知点A 坐标为(2,4),直线2=x 与x 轴相交于点B ,连结OA ,抛物线2

x y =从点O 沿OA 方向平移,与

直线2=x 交于点P ,顶点M 到A 点时停止移动. (1)求线段OA 所在直线的函数解析式; (2)设抛物线顶点M 的横坐标为m ,

①用m 的代数式表示点P 的坐标; ②当m 为何值时,线段PB 最短;

(3)当线段PB 最短时,相应的抛物线上是否存在点Q ,使△QMA

的面积与△PMA 的面积相等,若存在,请求出点Q 的坐标;若 不存在,请说明理由.

y

B

O

A P M

x

2

x =(第28题)

成都七中嘉祥外国语学校

初2009级九年级(下)数学入学考试题

数 学 答 题 卷

A 卷

一、选择题:(每小题3分,共30分)

题号 1 2 3 4 5 6 7 8 9 10 答案

二、填空题:(每小题4分,共16分)

11、 12、 13、 14、

三.解答题(第15题每小题6分,第16题6分,共18分) 15. (1) 01

)41.12(45tan 32)

3

1(-++--- (2) 化简求值)1()1

11

2(2-?+--a a a ,

其中33-=a 。

16.解不等式组20512112

3x x x ->??

+-?+??,≥,并把解集在数轴上表示出来.

四、(每小题8分,共16分) 17.

姓名_____________________ 班级_____________________ 学号____________________ ………………密………………………………………封……………………………………线……………………………………..

D C B

A

E

图 1

E D

C H

F

G B

A P y x

图2

18. 五、(每小题10分,共20分) 19.(10分)

(1)两人抽取的卡片上都是3 的概率是 . (2)

20、(1)如图1,AC= ,BD= ;四边形ABCD 是 梯形. (2)

(3)

B 卷

一.填空题.(每题4分,共20分)

21、22、23、24、25、二、

26. (8分)

27(10分)

28.(12分)

y

B

O

A

P M

x

2

x ……………………密………………………………………封……………………………………线……………………………………..

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