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2015年深圳宝安区二模模拟测试题

2015年深圳宝安区二模模拟测试题
2015年深圳宝安区二模模拟测试题

二模模拟试卷

一、选择题(本部分共12小题,每小题3分,共36分。) 1.4的平方根是( )A .2 B .–2 C .±2 D .16 2.2011年8月12日,第26届世界大学生夏季运动会将在深圳开幕。本届大运会的开幕式举办场地和主要分会场深圳湾体育中心总建筑面积达256520m 2。数据256520m 2用科学记数法(保留三个有效数字)表示为( ) A .25m 102.565? B .26m 100.257? C .25m 102.57? D .24m 1025.7?

3.下列各图是一些常用的标志图案,其中是轴对称图形但不是中心对称图形的是( )

A .

B .

C .

D . 4.下列运算中正确的是( )

A .123=-ab ab

B .6

24x ·

x x = C .532)(x x =

D .x x x 232

5.下列说法正确的是( )

A .一个游戏的中奖概率是5

1,则做5次这样的游戏一定会中奖. B .为了解深圳中学生的心理健康情况,应该采用普查的方式.

C .事件“小明今年中考数学考95分”是可能事件.

D .若甲组数据的方差20.01S =甲,乙组数据的方差2

0.1S =乙

,则乙组数据更稳定. 6. 如图,已知BD 是⊙O 直径,点A 、C 在⊙O 上,⌒AB =⌒BC , ∠AOB =60°,则∠BDC 的度数是( ) A.20° B.25° C.30° D. 40° 7. 不等式组11112

x x +≥-???

8.一家商店将某种商品按进货价提高100%后,又以6折优惠售出,售价60元,则这种商品的进货价是( )A .120元 B .100元 C .72元 D .50元

9、若0>ab ,则函数b ax y +=与函数b

y =在同一坐标系中的大致图象可能是( )

1

2

02

- A

D

B

C D

C

B

A

O

(第6题)

10、如图,直径为10的⊙A 山经过点C(0,5)和点0(0,0), B 是y 轴右侧⊙A 优弧上一点,则∠OBC 的余弦值为( ) A.

12 B .34

C. D .45

11、如图,Rt △ABC 中,∠C=90o,∠A =30o,AB = 4,将△ABC 绕 点B 按顺时针方向转动一个角到△A ′BC ′的位置,使点A 、B 、C ′在同一条直线上,则图中阴影部分的周长是( )

A .344+π

B .π4

C .342+π

D .π2

12.如图,已知四边形OABC 是菱形,CD ⊥x 轴,垂足为D ,函数x

y 4

=

的图象经过点C ,且与AB 交于点E 。若OD =2,则△OCE 的面积为( ) A .2 B .4 C .22

D .24

二、填空题(本题共4小题,每小题3分,共12分。) 13、分解因式:3

4a a -=__________________________。

14、如图,在⊙O 中,圆心角∠AOB=120°,弦

AB=,则圆心到AB 的距离是______cm 。

15、在数据1,2,3,1,2,2,4中,众数是

16、在△ABC 中,AB =6,AC =8,BC =10,P 为边BC 上一动点,PE ⊥AB 于E ,PF ⊥AC 于F ,M 为EF 中点,则AM 的最小值为 .

三、解答题(满分52分)

17

、计算:1

01245(2 1.41)3-??

--++ ???

18、先化简,再求值:211122

x x x -?

?-÷

?++??

,其中2x =.

A B

C ′

A ′

19、宝安区教育局为了解今年九年级学生体育测试情况,随机抽查了部分学生的体育测试成绩为样本,按A 、B 、C 、D 四个等级进行统计,并将统计结果绘制成如下的统计图,请你结合图中所给信息解答下列问题:

(说明:A 级:90分~100分;B 级:75分~89分;C 级:60分~74分;D 级:60分以下) (1)请把条形统计图补充完整;

(2)样本中D 级的学生人数占全班学生人数的百分比是 ; (3)扇形统计图中A 级所在的扇形的圆心角度数是 ;

(4)若该校九年级有500名学生,请你用此样本估计体育测试中A 级和B 级的学生人数之和为

20、如图在△ABC 中,BE 是它的角平分线,∠C=900,D 在AB 边上,以DB 为直径的半圆O 经过点E 交BC 于点F. (1)求证:AC 是⊙O 的切线;

(2)已知sinA=1

2

,⊙O 的半径为4,求图中阴影部分的面积.

21. 现计划把甲种货物1240吨和乙种货物880吨用一列货车运往某地,已知这列货车挂有A 、B 两种不同规格的货车厢共40节,使用A 型车厢每节费用为6000元,使用B 型车厢每节费用为8000元.

(1)设运送这批货物的总费用为y 万元,这列货车挂A 型车厢x 节,试求出用A 型车厢节数x 表示总费用y 的公式.

(2)如果每节A 型车厢最多可装甲种货物35吨和乙种货物15吨,每节B 型车厢最多可装甲种货物25吨和乙种货物35吨,装货时按此要求安排A 、B 两种车厢的节数,用哪一种方案费用最低。

B 46%

C 24%

D A 20%

等级

5

22.如图7-1,边长为2的正方形ABCD 中,E 是BA 延长线上一点,且AE=AB ,点P 从

点D 出发,以每秒1个单位长度沿D→C→B 向终点B 运动,直线EP 交AD 于点F ,过点F 作直线FG ⊥DE 于G ,交AB 于点R 。 (1)求证:AF=AR ;(3分) (2)设点P 运动的时间为t ,

①求当t 为何值时,四边形PRBC 是矩形?(4分) ②如图7-2,连接PB 。请直接写出....

使△PRB 是等腰三角形时t 的值.(2分)

23.如图10-1,已知抛物线y = 422

+-ax ax 与x 轴交于A 、B 两点,与y 轴交于点C ,

且OB=OC .

(1)求抛物线的函数表达式;(3分)

(2)若点P 是线段AB 上的一个动点(不与A 、B 重合),分别以AP 、BP 为一边,在直线AB 的同侧作等边三角形APM 和BPN ,求△PMN 的最大面积,并写出此时点P 的坐标; (3)如图10-2,若抛物线的对称轴与x 轴交于点D ,F 是抛物线上位于对称轴右侧的一个动点,直线FD 与y 轴交于点E .是否存在点F ,使△DOE 与△AOC 相似?若存在,请求出点F 的坐标;若不存在,请说明理由.(4分)

A B C

D E R G F P 图7-1 A B C D R G F

P 图

7-2 图10-1

图10-2

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