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广东省近三年中考试题和答案

广东省近三年中考试题和答案
广东省近三年中考试题和答案

2008年广东省初中毕业生学业考试数 学学参考答案

一、选择题(每小题3分) 1.B ; 2.C ; 3.D ; 4.C ; 5.B. 二、填空题(每小题4分) 6.2; 7.2

y x

=

8.9+ 9.60; 10.30. 三、解答题(一)(每小题6分)

11.解: 原式

12.解:移项,得 4x-x<6,………………1分 合并,得 3x<6,…………………2分 ∴不等式的解集为 x<2,…………4分

其解集在数轴上表示如下:

……………………6分

13.解:(1)作图正确得2分(不保留痕迹的得1分)…………2分 (2)在△ABC 中,AB=AC ,AD 是△ABC 的中线,

∴AD ⊥BC ,…………………………………………………3分 11

8422

BD CD BC ==

=?=.…………………………4分 在Rt △ABD 中,AB =10,BD =4,2

2

2

AD BD AB +=,……5分

AD ∴==…………………6分

14.解:由题意得,

45,1

4.2

y x y x =-+???=-?? ……………………………………1分 解得,2,

3.x y =??=-?

…………………………………………3分

∴ 直线1l 和直线2l 的交点坐标是(2,-3).……………4分

11

1;322

2.6=++= 分

交点(2,-3)落在平面直角坐标系的第四象限上.……6分

15.解:设小正方形的边长为xcm . …………………………1分 由题意得,2

108480%108x ?-=??.……………3分 解得,122, 2x x ==-. ………………………………4分 经检验,12x =符合题意,22x =-不符合题意舍去.

∴ 2x =.…………………………………………………5分 答:截去的小正方形的边长为2cm . ……………………6分

四、解答题(二)(每小题7分)

16.解:设抢修车的速度为x 千米/时,则吉普车的速度为1.5x 千米/时.…………1分 由题意得,

1515151.560

x x -=. ……………………………………………………3分 解得,20x =.……………………………………………………………………5分

经检验,20x =是原方程的解,并且20, 1.530x x ==都符合题意.…………6分 答:抢修车的的速度为20千米/时,吉普车的速度为30千米/时.……………7分

17.解:(1)设红球的个数为x ,………………………………1分

由题意得,

2

0.521x

=++ ………………………………2分

解得, 1x =.

答:口袋中红球的个数是1. ………………………………3分 (2)小明的认为不对. ………………………………………4分 树状图如下:

…………6分

∴ 21()42P =

=白,1()4P =黄,1()4

P =红. ∴ 小明的认为不对. ………………………………………7分

白2

白1

开始

2

1

F

E D

C

B

A

18.(1)证明:

CF ACB ∠ 平分,

∴ 12∠=∠.……………………1分 又∵ DC AC =,

∴ CF 是△ACD 的中线,

∴ 点F 是AD 的中点.…………2分 ∵ 点E 是AB 的中点, ∴ EF ∥BD,

即 EF ∥BC. …………………………3分 (2)解:由(1)知,EF ∥BD , ∴ △AEF ∽△ABD , ∴

2

()AEF ABD S AE S AB

??=.……………………………………4分 又∵ 1

2

AE AB =

, 6AEF ABD ABD BDFE S S S S ???=-=-四边形,………………5分 ∴

2

61()2

ABD ABD S S ??-= ,………………………………………6分

∴ 8ABD S ?=,

∴ ABD ?的面积为8. ………………………………………7分

19.解:过点A 作AF ⊥BC ,垂足为点F. 在Rt △ABF 中,∠B=60°,AB=6,

∴ sin AF AB B =∠

6sin 60=?

= cos BF AB B =∠ 6cos 60=?

3=.…………………2分 ∵ AD ∥BC,AF ⊥BC,DE ⊥BC, ∴ 四边形AFED 是矩形,

DE AF ==4FE AD ==.……………………………………3分

F E

B

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