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寒假补课模拟测试二

寒假补课模拟测试二 数 学

本试卷分选择题和非选择题两部分,共三大题25小题,共4页,满分150分,考试用时120分钟 4.考生必须保持答题卡的整洁,考试结束后,将本试卷和答题卡一并交回。

第一部分 选择题 (共30分)

一、选择题(本大题共10小题,每小题3分,满分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. 实数3的倒数是( )

A .3

1-

B .

3

1 C .3- D .3

2. 将二次函数2x y =的图像向下平移1个单位,则平移后的二次函数的解析式为( )

A .12-=x y

B .12+=x y

C .2)1(-=x y

D .2)1(+=x y

3. 一个几何体的三视图如图1所示, 则这个几何体是( )

A . 四棱锥

B .四棱柱

C .三棱锥

D .四棱柱 4.下面的计算正确的是( )

A .156=-a a

B .3233a a a =+

C .b a b a +-=--)(

D .b a b a +=+22)(

5.如图2,在等腰梯形ABCD 中,BC ∥AD ,AD=5, DC=4, DE ∥AB 交BC 于点E ,且EC=3.则梯形ABCD 的周长是( )

A .26

B .25

C .21

D .20

6. 已知071=-+

-b a ,则=+b a ( )

A .8-

B .6-

C .6

D .8

7.在Rt △ABC 中,∠C=90°, AC=9 , BC=12.则点C 到AB 的距离是( )

A .

5

36 B .

25

12 C .

4

9 D .

4

33

8.已知b a >,若c 是任意实数,则下列不等式总是成立的是( )

A .c b c a +<+

B .c b c a ->-

C .bc ac <

D .bc ac >

9.在平面中,下列命题为真命题的是( )

A .四边相等的四边形是正方形

B .对角线相等的四边形是菱形

C .四个角相等的四边形是矩形

D .对角线互相垂直的四边形是平行四边形

图2

E

D

C

B

A

10.如图3,正比例函数x k y 11=和反比例函数x

k y 22=

的图象

交于)2,1(-A 、),(21-B 两点,若21y y <,则x 的取值范围是 ( )

A .1-x

B .1-

C .01<<-x 或10<

D .01<<-x 或1>x

第二部分 非选择题 (共120分)

二、填空题(本大题共6小题,每小题3分,满分18分.)

11.已知∠ABC=30°, BD 是∠ABC 的平分线,则∠ABD=_______度. 12.不等式101≤-x 的解集是_______. 13.分解因式:a a 83-=_______.

14.如图4,在等边△ABC 中,AB=6,D 是BC 上一点.且BC=3BD , △ABD 绕点A 旋转后的得到△ACE.则CE 的长为_______.

15.已知关于x 的一元二次方程0322

=--k x x 有两各项等的实数根,则k 的值为_______. 16.如图5,在标有刻度的直线l 上,从点A 开始. 以AB=1为直径画半圆,记为第1个半圆 以BC=2为直径画半圆,记为第2个半圆 以CD=4为直径画半圆,记为第3个半圆 以DE=8为直径画半圆,记为第4个半圆

……,按此规律,继续画半圆,

则第4个半圆的面积是第3个半圆面积的___倍, 第n 个半圆的面积为_______.(结果保留π)

三、解答题(本大题共9小题,满分102分,解答应写出文字说明、证明过程或演算步骤)

17.(本小题满分9分)

解方程组:?

??=+=-1238

y x y x

18.(本小题满分9分)

如图6,点D 在AB 上,点E 在AC 上,AB=AC ,∠B=∠C.求证:BE=CD

E

A

E

D

C

B

A

19.(本小题满分10分)

广州市努力改善空气质量,近年来空气质量明显好转,根据广州市环境局公布的2006~2010这五

年的全年空气质量优良的天数,绘制折线图如图7,根据图中信息回答:

(1)这五年的全年空气质量是优良的天数的中位数是_______ ;极差是_______ ;

(2) 这五年的全年空气质量优良天数与它的前一年相比较,增加最多的是______年(填写年份); (3)求这五年的全年空气质量优良天数的平均数

.

20.(本小题满分10分)

已知511=

+b a )(b a ≠,求

)

()

(b a a b b a b a --

-的值.

21.(本小题满分12分)

甲、乙两个袋中均装有三张除所标数值外完全相同的卡片,甲袋中的三张卡片上的所标的数值分别为7-、1-、3,乙袋中的三张卡片上所标的数值分别为2-、1、6 ,先从甲袋中随机取一张卡片,用x 表示取出的卡片上标的数值,再从乙袋从随机取出一张卡片,用y 表示取出的卡片上标的数值.把x 、y 分别作为点A 的横坐标、纵坐标.

(1)用适当的方法写出点)(y x A ,的所有情况;

(2)求点A落在第三象限的概率 .

22.(本小题满分12分)

如图8,⊙P的圆心为)

(0,5

M且平行于y轴,点N在点M的上

P,半径为3,直线MN过点)

(2,3

方.

(1)在图中作出⊙P关于y轴的对称的⊙P’,根据作图直接写出⊙P’与直线MN的位置关系;

(2)若点N在(1)中的⊙P’上,求PN的长.

23.(本小题满分12分)

某城市居民用水实施阶梯收费.每户每月用水量如果未超过20吨,按每吨1.9元收费:每户每月用水量如果超过20吨,未超过的部分仍按每吨1.9元收费,超过的部分则按每吨2.8元收费.设某户每月用水量为x吨,应收水费为y元。

(1)分别写出每月用水量未超过20吨和超过20吨时,y与x间的函数关系式;

(2)若该城市某户5月份水费平均为每吨2.2元,求该户5月份用水多少吨?

24.(本小题满分14分)

如图9,抛物线34

38

32

+-

-=x x y 与x 轴交于A 、B 两点(点A 在点B 的左侧),与y 轴

交于点C

(1)求点A 、B 的坐标;

(2)设D 为已知抛物线对称轴上任意一点,当△ACD 面积等于△ACB 面积时,求点D 的坐标; (3)当直线l 过点)(0,4E ,M 为直线l 上的动点,当以A 、B 、M 为顶点所作的直角三角形

有且只有....

三个时,求直线l 的解析式.

25.(本小题14分)

如图10,在平行四边形ABCD 中,AB=5,BC=10,F 为AD 中点,CE ⊥AB 于点E ,

设∠ABC=a )(

9060<≤x (1)当

60=a 时,求CE 的长; (2)当

9060<

①是否存在正整数k ,使得∠EFD=k ∠AEF ?若存在,求出k 的值;若不存在,请说明理由 ②连接CF ,当2

2

CF CE -取最大值时,求tan ∠DCF 的值.

F

E

D

C

B

A

寒假补课模拟测试二 数学答案

一、选择题

1--5:BADCC 6--10:BABCD 二、填空题

11、15 12、11≤x 13、)22)(22(-+a a a 14、2 15、—3 16、4; π522-n 三、解答题 17、??

?-==3

5y x

18、证明:)(ASA ACD ABE ??

19、(1)345;24 (2)2008 (3)343.2 20、原式=

511=

+=+b a ab

b a

21、(1)、(-7,-2),(-7,1),(-7,6),(-1,-2), (-1,1),(-1,6),(3,-2),(3,1),(3,6)

(2)

9

2

22、(1)相交;(2)69

23、(1)?

??>-≤≤=)20(188.2)200(9.1x x x x y

(2)30吨

24、 (1))0,4(-A )0,2(A

(2))4

27,1(1-D )49,1(2-

-D

(3)343+-

=x y 或3-4

3x y =

25、 (1)35

(2)存在 3=k (3)3

15tan =∠DCF

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