2013年1海淀、西城区丰台、昌平初二期末数学试题及答案 下载本文

∴OD=OH,∠5=∠6. ··························································································· 7分 ∵?AOB??5??DOB?90?, ∴?DOH??6??DOB?90?. ∴在等腰直角三角形△DOH中, ∵DP=HP, ∴OP⊥DP,?7?12?DOH?45?.

∴?ODP??7. ∴OP=PD. ············································································································ 8分

C 3.(1)证明:在Rt△ABC中,∠ACB=90°,∠A=30°, D ∴?ABC?60?, BC=AB.

211 ∵BD平分∠ABC, ∴?1??DBA??A?∴DA=DB. ∵DE⊥AB于点E. ∴AE=BE=AB.

2130?.

A

E 图1

B

∴BC=BE. ·············································································································· 1分 ∴△BCE是等边三角形. ························································································· 2分

C

M (2)结论:AD = DG+DM. D

B A E

G

图2

······························································································································3分 (3)结论:AD = DG-DN. 理由如下:

延长BD至H,使得DH=DN . ·············································································4分 由(1)得DA=DB,?A?30?. ∵DE⊥AB于点E. ∴?2??3?60?. ∴?4??5?60?. ∴△NDH是等边三角形. ∴NH=ND,?H∴?H??2. ∵?BNG?60?, ∴?BNG??7??6?即?DNG??HNB.

?7??6?60?.

H

A N C 5 4 6 2 3 7 D 1 E B .

在△DNG和△HNB中,

G

图3

21

?DN?HN,???DNG??HNB,???H??2,

∴△DNG≌△HNB(ASA). ∴DG=HB. ∵HB=HD+DB=ND+AD,

∴DG= ND+AD. ∴AD = DG-ND. ···································································································· 6分

北京市朝阳区2012~2013学年第一学期期末统一考试

八 年 级 数 学 试 卷 2013.1

(考试时间90分钟 满分100分) 成绩 一、选择题:(本题共24分,每小题3分)

以下每个题中,只有一个选项是符合题意的.请把符合题意的选项的英文字母填在下面相应的表格中.

题号 答案 1 2 3 4 5 6 7 8 1.下列图形中,不是轴对称图形的是

A. B. C. D. 2.点M(3,-4)关于x轴的对称点的坐标是

A.(3, 4) B.(-3,-4) C.(-3, 4) D.(-4,3) 3.下列命题中,正确的是

A.三条边对应相等的两个三角形全等 B.周长相等的两个三角形全等 C.三个角对应相等的两个三角形全等 D.面积相等的两个三角形全等

22

4.如图,AD是△ABC的角平分线,从点D向AB、AC两边作垂线段,垂足分别为E、F,那么下列结论中错误的是 .. A.DE=DF B.AE=AF C.BD=CD D.∠ADE=∠ADF 5.下列各式从左边到右边的变形中,是因式分解的是

AEBDF(第4题)

C A. a(x?y)?ax?ay B. x2?4x?4?x(x?4)?4 C. x2?16?3x?(x?4)(x?4)?3x D. 10x2?5x?5x(2x?1)

x?1x?1

2

6.若分式的值为0,则应满足的条件是

A. x≠1 B. x=-1 C. x=1 D. x=±1

7.已知一次函数y=kx+b,y随着x的增大而减小,且kb>0,则这个函数的大致图象是

A. B. C. D.

8.如图,点P是等边△ABC边上的一个作匀速运动的动点,它由点A开始沿AB边运动到点B,再沿BC边运动到点C为止,设运动时间为t,△ACP的面积为S,则S与t的函数关系式的大致图象是

A P C B

A. B. C. D. 二、填空题:(本题共21分,每小题3分)

9.一种细菌半径是0.000 012 1米, 将0.000 012 1用科学记数法表示为 . 10.计算: ?6a?2a??2a= .

211.如果等腰三角形的一个内角是80°,那么它的顶角的度数是_______________.

23

12.函数y?1x?2中,自变量x的取值范围是 .

13.若一次函数y?(m?2)x?(m?1)的图象与y轴正半轴相交,则m的取值范围是 . 14.如图,在△ABC中,∠C=90°,∠B=30°,AB的垂直平分线交BC于点D,交AB于点E,CD=2,则BC= . 15.观察下列各式:

C2?2?2?2, 324354?3??4??5?324354?3, ?4, ?5,

DABE(第14题)

……

用含有字母n (其中n为正整数)的等式表示你发现的规律: . 三、作图题: (本题4分)

16.电信部门要修建一座电视信号发射塔.如图,按照设计要求,发射塔到两个城镇A,B的距离必须相等,到两条高速公路m和n的距离也必须相等.发射塔应修建在什么位置?在图中标出它的位置.(要求:尺规作图,不写作法,但要保留作图痕迹,并写出结论)

mBAn

四、解答题:(本题共51分,第17、18题每小题4分,第19-24题每小题5分,第25题7分,第26题6分)

17.分解因式:am?2amn?an.

22

(第16题)

24