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2008年广东省广州市中考试题答案

2008年广东省广州市中考试题答案
2008年广东省广州市中考试题答案

广东省广州市中考数学试题

一、选择题(每小题3分,共30分) 1、(2008广州)计算3

(2)-所得结果是( ) A 6- B 6 C 8- D 8

2、(2008广州)将图1按顺时针方向旋转90°后得到的是( )

3、(2008广州)下面四个图形中,是三棱柱的平面展开图的是( )

4、(2008广州)若实数a 、b 互为相反数,则下列等式中恒成立的是( ) A 0a b -= B 0a b += C 1ab = D 1ab =-

5、(2008广州)方程(2)0x x +=的根是( )

A 2x =

B 0x =

C 120,2x x ==-

D 120,2x x == 6、(2008广州)一次函数34y x =-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、(2008广州)下列说法正确的是( )

A “明天降雨的概率是80%”表示明天有80%的时间降雨

B “抛一枚硬币正面朝上的概率是0.5”表示每抛硬币2次就有1次出现正面朝上

C “彩票中奖的概率是1%”表示买100张彩票一定会中奖

D “抛一枚正方体骰子朝正面的数为奇数的概率是0.5“表示如果这个骰子抛很多很多次,那么平均每2次就有1次出现朝正面的数为奇数

8、(2008广州)把下列每个字母都看成一个图形,那么中心对成图形有( ) O L Y M P I C

A 1个

B 2个

C 3个

D 4个

9、(2008广州)如图2,每个小正方形的边长为1,把阴影部分剪下来,用剪下来的阴影部分拼成一个正方形,那么新正方形的边长是( ) A 3

B 2

C 5

D 6

10、(2008广州)四个小朋友玩跷跷板,他们的体重分别为P 、Q 、R 、S ,如图3所示,则他们的体重大小关系是( )

A P R S Q >>>

B Q S P R >>>

C S P Q R >>>

D S P R Q >>>

二、填空题(每小题3分,共18分) 11、(20083的倒数是

12、(2008广州)如图4,∠1=70°,若m ∥n ,则∠2= 13、(2008广州)函数1

x

y x =

-自变量x 的取值范围是 14、(2008广州)将线段AB 平移1cm ,得到线段A ’B ’,则点A 到点A ’的距离是 15、(2008广州)命题“圆的直径所对的圆周角是直角”是 命题(填“真”或“假”) 16、(2008广州)对于平面内任意一个凸四边形ABCD ,现从以下四个关系式①AB=CD ;

②AD=BC ;③AB ∥CD ;④∠A=∠C 中任取两个作为条件,能够得出这个四边形ABCD 是平行四边形的概率是

三、解答题(共102分)

17、(2008广州)(9分)分解因式3

2

a a

b -

图2

图3

图4

18、(2008广州)(9分)小青在九年级上学期的数学成绩如下表所示

测验类别

平时

期中 考试 期末

考试

测验1 测验2 测验3 课题学习 成绩

88

70

98

86

90

87

(1)计算该学期的平时平均成绩;

(2)如果学期的总评成绩是根据图5所示的权重计算, 请计算出小青该学期的总评成绩。

19、(2008广州)(10分)如图6,实数a 、b 在数轴上的位置,

化简2

2

2

()a b a b -

20、(2008广州)(10分)如图7,在菱形ABCD 中,∠DAB=60°,过点C 作CE ⊥AC 且与AB 的延长线交于点E ,求证:四边形AECD 是等腰梯形

21、(2008广州)(12分)如图8,一次函数

图5

图6

图7

y kx b

=+的图象与反比例函数

m

y

x

=的图象相交于A、B两点

(1)根据图象,分别写出A、B的坐标;

(2)求出两函数解析式;

(3)根据图象回答:当x为何值时,

一次函数的函数值大于反比例函数的函数值

22、(2008广州)(12分)2008年初我国南方发生雪灾,某地电线被雪压断,供电局的维修队要到30千米远的郊区进行抢修。维修工骑摩托车先走,15分钟后,抢修车装载所需材料出发,结果两车同时到达抢修点。已知抢修车的速度是摩托车速度的1.5倍,求两种车的速度。

图8

23、(2008广州)(12分)如图9,射线AM 交一圆于点B 、C ,射线AN 交该圆于点D 、E ,且BC DE = (1)求证:AC=AE

(2)利用尺规作图,分别作线段CE 的垂直平分线与∠MCE 的平分线,两线交于点F (保留作图痕迹,不写作法)求证:EF 平分∠CEN

24、(2008广州)(14分)如图10,扇形OAB 的半径OA=3,圆心角∠AOB=90°,点C 是AB 上异于A 、B 的动点,过点C 作CD ⊥OA 于点D ,作CE ⊥OB 于点E ,连结DE ,点G 、H 在线段DE 上,且DG=GH=HE (1)求证:四边形OGCH 是平行四边形

(2)当点C 在AB 上运动时,在CD 、CG 、DG 中,是否存在长度不变的线段?若存在,请求出该线段的长度 (3)求证:2

2

3CD CH +是定值

图9

图10

25、(2008广州)(14分)如图11,在梯形ABCD中,AD∥BC,AB=AD=DC=2cm,BC=4cm,在等腰△PQR 中,∠QPR=120°,底边QR=6cm,点B、C、Q、R在同一直线l上,且C、Q两点重合,如果等腰△PQR 以1cm/秒的速度沿直线l箭头所示方向匀速运动,t秒时梯形ABCD与等腰△PQR重合部分的面积记为S 平方厘米

(1)当t=4时,求S的值

≤≤10,求S与t的函数关系式,并求出S的最大值

(2)当4t

图11

2008年广东省广州市中考试题答案

1-10 填空CAABC BDBCD11.33, 12.700

, 13.1≠x , 14.1cm, 15.真命题,16.3

1 17.))((b a b a a -+

18.(1)

5.854

86

987088=+++(2)75.87%6087%3090%105.85=?+?+? 19.-2b

20.提示:0

302

1=∠=∠DAB CAE 得DAB E ∠==∠060,由DC//AE,AD 不平行CE 得证

21.(1)y =0.5x +1,y =x

12

(2)-64

22. 40和60千米/小时

23.(1)作OP ⊥AM ,OQ ⊥AN 证AQO APO ???由BC =CD ,得EQ CP =得证 (2)同AC =AE 得CEN ECM ∠=∠,

由CE =EF 得CEN MCE FEC FCE ∠=∠=

∠=∠2

1

21得证 24.(1)连结OC 交DE 于M ,由矩形得OM =CG ,EM =DM

因为DG=HE 所以EM -EH =DM -DG 得HM =DG

(2)DG 不变,在矩形ODCE 中,DE =OC =3,所以DG =1

(3)设CD =x ,则CE =2

9x -,由EC CD CG DE ?=?得CG =3

92

x x -

所以3

)39(2

22x x x x DG =--=2

所以HG =3-1-36322x x -=

所以3CH 2

=22

22212))3

9()36((3x x x x -=-+- 所以121232

222=-+=+x x CH CD 25.(1)t =4时,Q 与B 重合,P 与D 重合, 重合部分是BDC ?=

323222

1

=??

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