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中考模拟试题四

中考数学模拟试卷（四）

一、选择题：

1、化简(－x )3·(－x )2，正确的结果是( )

A 、－x 6

B 、x 6

C 、x 5

D 、－x 5

2、不等式组?????->≤-x x x 25204的解集为(

)

A 、2＜x ≤4

B 、x ≤4

C 、x ＞2

D 、x ＜2

3、如图1，将四边形纸片ABCD 沿EF 折叠，点A 落在A 1处，若∠1＋∠2＝100°，则∠A 的度数是（）

A 、80°

B 、60°

C 、50°

D 、40°

4、一个等腰三角形的两边长分别是方程0862=+-x x 的两个根，则这个三角形的周长是（）

A 、6

B 、10

C 、6或10

D 、8或10

5、如图，王师傅在楼顶上A 点处测得楼前一棵树CD 的顶端C 的俯角为60°，若水平距离BD ＝10m ，楼高AB ＝24m ，则树CD 高约为（）

A 、5m

B 、6m

C 、7m

D 、8m

6、已知反比例函数)0(≠=k x

k y ，当x ＜0时，y 随x 的增大而增大，那么一次函数y ＝kx －k 的图象不经过（）

A 、第一象限

B 、第二象限

C 、第三象限

D 、第四象限

7、若E 、F 、G 、H 分别是等腰梯形ABCD 边AB 、BC 、CD 、DA 的中点，则四边形EFGH

一定是（

） A 、矩形 B 、等腰梯形 C 、菱形 D 、非特殊的平行四边形

8、右图是某蓄水池的横断面示意图，分深水区和浅水区，如果这个蓄水池以固定的流量注水，下面哪个图象能大致表示水的最大深度h 和时间t 之间的关系（）

二、填空题：

9、(－5)2＝。

10、一个正方体的每个面都写有一个汉字，其平面展开图如图2所示，

那么在该正方体中，和“京”相对的字是。

11、为支援南方雪灾地区，某校团委举行了“雪灾无情人有情”的损资活动，其中6个班同学的人均捐款数分别为5元、6元、8元、5元、6元、4元。则这组数据的中位数是。

12、将抛物线2x y =向左平移4个单位后，再向下平移2个单位，则所得到的抛物线的函数关系式为。

13、如图3，△ABC 的外接圆直径AD ＝2，∠ABC ＝30°，则AC 的长是。

14、已知n 12是整数，则满足条件的最小正整数n 是。

15、钟面上分针的长是6cm ，经过10分钟，分针在钟面上扫过的面积是 cm 2。

16、陈老师设计了一个计算程序，输入和输出的数据如下表：

则当输入的数据是8时，输出的数据是。

三、解答题：

17、化简：1

)12111(2-÷+-+-+a a a a a a 18、解方程：x x x -+=-3231

19、已知：如图，在平行四边形ABCD 中，E 、F 分别为边AB 、CD 的中点。

⑴求证：△ADE ≌△CBF ；

⑵在CB 的延长线上取一点G ，并能使得四边形AGBD 是矩形，则

四边形BEDF 是什么特殊四边形？证明你的结论。

20、⑴我们知道把平行四边形分成面积相等的两部分的直线有无数条，如：

这些直线都经过平行四边形的_________________________。

⑵利用上述结论，请你用两种方法画一条直线把已知的“方角形”分成面积相等的两部分。

21、桌面上放有质地均匀、反面相同的3张卡片，正面分别标有数字1、2、3，这些卡片反面朝上洗匀后放在桌面上，甲从中任意抽出1张，记下卡片上的数字后仍反面朝上放回洗匀，乙再从中任意抽出1张，记下卡片上的数字，然后将这两数相加。

⑴请用列表或画树形图的方法求两数和为4的概率；

⑵若甲与乙按上述方式做游戏，当两数之和为4时，甲胜，反之则乙胜；若甲胜一次得6分，那么乙胜一次得多少分，这个游戏才对双方公平？

22、如图，△ABC内接于⊙O，AB＝AC，过点A作BC的平行线与BO的延长线交于点P。

⑴求证：AP是⊙O的切线；⑵若⊙O的半径为5，BC＝6，求AP的长。

23、某宾馆客房部有60个房间供游客居住，当每个房间的定价为每天200元时，房间可以住满。当每个房间每天的定价每增加10元时，就会有一个房间空闲。对有游客入住的房间，宾馆需对每个房间每天支出20元的各种费用，设每个房间每天的定价增加x元。

⑴写出房间每天的入住量y（间）关于x（元）的函数关系式；

⑵写出该宾馆每天的房间收费p（元）关于x（元）的函数关系式；

⑶求该宾馆客房部每天的利润w（元）关于x（元）的函数关系式；当每个房间的定价为每天多少元时，w有最大值？最大值是多少？

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