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2016年上海市中考数学试卷及参考答案

2016年上海市中考数学试卷及参考答案
2016年上海市中考数学试卷及参考答案

2016年上海市中考数学试卷及参考答案

一、选择题(本大题共6题,每题4分,满分24分) 1、如果a 与3互为倒数,那么a 是( )

A 、3-

B 、3

C 、31-

D 、3

1 2、下列单项式中,与b a 2

是同类项的是( )

A 、b a 22

B 、22b a

C 、2ab

D 、ab 3

3、如果将抛物线22+=x y 向下平移1个单位,那么所得新抛物线的表达式是( )

A 、2)1(2+-=x y

B 、2)1(2++=x y

C 、12+=x y

D 、32+=x y

4、某校调查了20名男生某一周参加篮球运动的次数,调查结果如表所示,那么这20名男生该周参加篮球

运动次数的平均数是( )

、次 、次 、次 、次

5、已知在ABC △中,AC AB =,AD 是角平分线,点D 在边BC 上,设=,=,那么向量

用向量、表示为( )

6、如图,在ABC Rt △中,?=∠90C ,4=AC ,7=BC ,点D 在边BC 上,3=CD ,⊙A 的半径长为3,⊙D 与⊙A 相交,且点B 在⊙D 外,那么⊙D 的半径长r 的取值范围是( )

第6题

二、填空题(本大题共12题,每题4分,满分48分) 7、计算:=÷a a 3

8、函数2

3

-=

x y 的定义域是 9、方程21=-x 的解是

10、如果2

1

=

a ,3-=

b ,那么代数式b a +2的值为 11、不等式组??

?<-<0

15

2x x 的解集是

12、如果关于x 的方程032

=+-k x x 有两个相等的实数根,那么实数k 的值是 13、已知反比例函数x

k

y =

(0≠k ),如果在这个函数图像所在的每一个象限内,y 的值随着x 的增大而减小,那么k 的取值范围是

14、有一枚材质均匀的正方体骰子,它的六个面上分别有1点、2点、…6点的标记,掷一次骰子,向上的一面出现的点数是3的倍数的概率是

15、在ABC △中,点D 、E 分别是边AB 、AC 的中点,那么ADE △的面积与ABC △的面积的比 是 16、今年5月份有关部门对计划去上海迪士尼乐园的部分市民的前往方式进行调查,如图所示是收集数据后绘制的两幅不完整统计图,根据图中提供的信息,那么本次调查的对象中选择公交前往的人数

第16题 第17题

17、如图,航拍无人机从A 处测得一幢建筑物顶部B 的仰角为?30,测得底部C 的仰角为?60,此时航拍无人机与该建筑物的水平距离AD 为90米,那么该建筑物的高度BC 约为 米(精确到1米,参考数据:73.13≈)

18、如图,矩形ABCD 中,2=BC ,将矩形ABCD 绕点D 顺时针旋转?90,点A 、C 分别落在A '、C '处,如果点A '、C '、B 在同一条直线上,那么A AB '∠tan 的值为

第18题

三、解答题(本大题共7题,满分78分) 19、(本题满分10分) 计算:2

2

1

)3

1(124|13|-+---

20、(本题满分10分) 解方程:

14

4212=---x x 21、(本题满分10分,每小题满分各5分)

如图,在ABC Rt △中,?=∠90ACB ,3==BC AC ,点D 在边AC 上,且CD AD 2=,AB DE ⊥,垂足为点E ,联结CE ,求: (1)线段BE 的长 (2)ECB ∠的余切值

某物流公司引进A 、B 两种机器人用来搬运某种货物,这两种机器人充满电后可以连续搬运5小时,A 中机器人于某日0时开始搬运,过了1小时,B 中机器人也开始搬运,如图,线段OG 表示A 中机器人的搬运量A y (千克)与实践x (时)的函数图像,线段EF 表示B 中机器人的搬运量B y (千克)与时间x (时)的函数图像,根据图像提供的信息,解答下列问题: (1)求B y 关于x 的函数解析式

(2)如果A 、B 两种机器人连续搬运5个小时,那么B 种机器人比A 种机器人多搬运了多少千克

23、(本题满分12分,每小题满分各6分)

已知:如图,⊙O 是ABC △的外接圆,弧AB 等于弧AC ,点D 在边BC 上,BC AE ∥,BD AE = (1)求证:CE AD =

(2)如果点G 在线段DC 上(不与点D 重合),且AD AG =,求证:四边形AGCE 是平行四边形

如图,抛物线52-+=bx ax y (0≠a )经过点)5,4(-A ,与x 轴的负半轴交于点B ,与y 轴交于点C ,且OB OC 5=,抛物线的顶点为点D (1)求这条抛物线的表达式

(2)联结AB 、BC 、CD 、DA ,求四边形ABCD 的面积

(3)如果点E 在y 轴的正半轴上,且ABC BEO ∠=∠,求点E 的坐标

25、(本题满分14分,第(1)小题满分4分,第(2)小题满分5分,第(3)小题满分5分)

如图所示,梯形ABCD 中,DC AB ∥,?=∠90B ,15=AD ,16=AB ,12=BC ,点E 是边AB 上的动点,点F 是射线CD 上一点,射线ED 和射线AF 交于点G ,且DAB AGE ∠=∠ (1)求线段CD 的长

(2)如果AEG △是以EG 为腰的等腰三角形,求线段AE 的长

(3)如果点F 在边CD 上(不与点C 、D 重合),设x AE =,y DF =,求y 关于x 的函数解析式,并写出x 的取值范围

备用图

2016年上海市中考参考答案

三、解答题 19、原式36-=

20、原方程的解是1-=x

21、(1)22=BE (2)2

1

cot =∠ECB

22、(1)9090-=x y B (61≤≤x ) (2)150千克 23、(1)略 (2)略

24、(1)542--=x x y (2)18=ABCD S 四边形 (3))2

3,0(E

25、(1)7=CD (2)225=AE 或15=AE (3)x x y 18225-=(2

259<

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