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2020年江苏省盐城中考数学试卷 含答案

2020年江苏省盐城中考数学试卷 含答案
2020年江苏省盐城中考数学试卷 含答案

盐城市二〇二〇年初中毕业与升学考试

数学试题

注意事项:

1.本次考试时间为120分钟,卷面总分为150分,考试形式为闭卷.

2.本试卷共6页,在检查是否有漏印、重印或错印后再开始答题.

3.所有试题必须作答在答题卡上规定的区域内,注意题号必须对应,否则不给分.

4.答题前,务必将姓名、准考证号用0.5毫米黑色签字笔填写在试卷及答题卡上.

一、选择题:本大题共8个小题,每小题3分,共24分.在每小题给出的四个选项中,只有一项是符合题目要求的.

1. 2020的相反数是( )

A .2020-

B . 2020

C .

1 2020 D .1

2020

- 2. 下列图形中,属于中心对称图形的是:( )

A .

B .

C .

D .

3. 下列运算正确的是:( )

A .22a a -=

B .3

2

6

a a a ?= C .3

2

a a a ÷= D .()

2526a a = 4. 实数,a b 在数轴上表示的位置如图所示,则:( )

A .0a >

B .a b >

C .a b <

D .a b < 5. 如图是由4个小正方体组合成的几何体,该几何体的俯视图是:( )

A .

B .

C .

D .

6. 2019年7月盐城黄海湿地中遗成功,它的面积约为400000万平方米,将数据400000用科学记数法表示应为:( )

A .6

0.410? B .9

410? C .4

4010? D .5

410?

7. 把19-这9个数填入33?方格中,使其任意一行,任意一列及两条对角线上的数之和都相等,这样便构成了一个“九宫格”.它源于我国古代的“洛書”(图①),是世界上最早的“幻方”.图②是仅可以看到部分数值的“九宫格”,则其中x 的值为:( )

A .1

B .3

C .4

D .6

8. 如图,在菱形ABCD 中,对角线AC BD 、相交于点,O H 为BC 中点,6,8AC BD ==.则线段OH 的长为:( )

A .

125 B .5

2

C .3

D .5 二、填空题(每题3分,满分24分,将答案填在答题纸上)

9. 如图,直线,a b 被直线c 所截,//,160A b ∠=.那么2∠= .

10.一组数据1,4,7,4,2-的平均数为_ . 11. 因式分解:2

2

x y -= .

12. 分式方程

1

0x x

-=的解为x = . 13.一只不进明的袋中装有2个白球和3个黑球,这些球除颜色外都相同,搅匀后从中任意摸出1个球.摸到白球的概率为 .

14. 如图,在O 中,点A 在BC 上,100,BOC ∠=?则BAC ∠=

15. 如图,//,BC DE 且,4,10BC DE AD BC AB DE <==+=,则AE

AC

的值为 .

16.如图,已知点()5,2,54()(),81A B C ,,,直线l x ⊥轴,垂足为点0(),M m ,

其中5

2

m <,若A B C '''与ABC 关于直线l 对称,且A B C '''有两个顶点在函数(0)k

y k x

=≠的图像上,则k 的值

为: .

三、解答题 (本大题共11小题,共102分.解答应写出文字说明、证明过程或演算步骤.)

17. 计算

:0

3223π??

- ???

.

18.解不等式组:32

134532

x x x -?≥?

??-<+?.

19.先化简,再求值:

2

3193m m m ?

?÷+ ?--??

,其中2m =-. 20. 如图,在ABC

中,90,tan 3

C A ABC ∠==∠的平分线B

D 交AC

于点.D CD =.求AB 的长?

21. 如图,点O 是正方形,ABCD 的中心.

()1用直尺和圆规在正方形内部作一点E (异于点O ),使得;EB EC =(保留作图痕迹,不写作法) ()2连接,EB EC EO 、、求证:BEO CEO ∠=∠.

22. 在某次疫情发生后,根据疾控部门发布的统计数据,绘制出如下统计图:图①为A 地区累计确诊人数的条形统计图,图②为B 地区新增确诊人数的折线统计图

.

()1根据图①中的数据,A地区星期三累计确诊人数为,新增确诊人数为;()2已知A地区星期一新增确诊人数为14人,在图②中画出表示A地区新增确诊人数的折线统计图. ()3你对这两个地区的疫情做怎样的分析,推断?

23.生活在数字时代的我们,很多场合用二维码(如图①)来表示不同的信息,类似地,可通过在矩形网格中,对每一个小方格涂加色或不涂色所得的图形来表示不同的信息,例如:网格中只有一个小方格,如图②,通过涂器色或不涂色可表示两个不同的信息.

()1用树状图或列表格的方法,求图③可表示不同信息的总个数:(图中标号1,2表示两个不同位置的小方格,下同)

()2图④为22?的网格图.它可表示不同信息的总个数为;

()3某校需要给每位师生制作一张“校园出入证”

,准备在证件的右下角采用n n ?的网格图来表示各人身份信息,若该校师生共492人,则n 的最小值为 ; 24. 如图,O 是ABC 的外接圆,AB 是

O 的直径,DCA B ∠=∠.

()1求证:CD 是

O 的切线;

()2若DE AB ⊥,垂足为,E DE 交AC 与点;

求证:DCF 是等腰三角形.

25.若二次函数2

y ax bx c =++的图像与x 轴有两个交点()()()1212,0,,00M x N x x x <<,且经过点

()0,2,A 过点A 的直线l 与x 轴交于点,C 与该函数的图像交于点B (异于点A ).满足ACN 是等腰直角

三角形,记AMN 的面积为1,S BMN 的面积为2S ,且215

2

S S =

.

()1抛物线的开口方向 (填“上”或“下”); ()2求直线l 相应的函数表达式;

()3求该二次函数的表达式.

26.木门常常需要雕刻美丽的图案.

()1图①为某矩形木门示意图,其中AB 长为200厘米,AD 长为100厘米,阴影部分是边长为30厘米的正

方形雕刻模具,刻刀的位置在模具的中心点P 处,在雕刻时始终保持模具的一边紧贴木门的一边,所刻图案如虚线所示,求图案的周长;

()2如图②,对于()1中的木门,当模具换成边长为刻刀的位置仍在模具的中

心点P 处,雕刻时也始终保持模具的一边紧贴本门的一边,使模具进行滑动雕刻.但当模具的一个顶点与木门的一个顶点重合时,需将模具绕着重合点进行旋转雕刻,直到模具的另一边与木门的另一边重合.再滑动模具进行雕刻,如此雕刻一周,请在图②中画出雕刻所得图案的草阁,并求其周长.

27. 以下虚线框中为一个合作学习小组在一次数学实验中的过程记录,请阅读后完成虚线框下方的问题

1~4.

()

1在Rt

ABC 中,90,C AB ∠=?=

据如下表:(单位:厘米)

()2根据学习函数的经验,选取上表中BC 和AC BC +的数据进行分析;

①设BC x AC BC y =+=,,以(),x y 为坐标,在图①所示的坐标系中描出对应的点;

②连线;

观察思考

()3结合表中的数据以及所面的图像,猜想.当x = 时,y 最大; ()4进一步C 猜想:若Rt

MBC 中,90C ∠=?,斜边(2AB a a =为常数,0a >),

则BC = 时,AC BC +最大.

推理证明

()5对()4中的猜想进行证明.

问题1.在图①中完善()2的描点过程,并依次连线;

问题2.补全观察思考中的两个猜想:()3 _______ ()4 _______ 问题3.证明上述()5中的猜想:

问题4.图②中折线B E F G A ----是一个感光元件的截面设计草图,其中点,A B 间的距离是4厘米,

1AG BE ==厘米,90,E F G ∠=∠=∠=平行光线从AB 区域射入,60,BNE ∠=线段FM FN 、为

感光区城,当EF 的长度为多少时,感光区域长度之和最大,并求出最大值.

盐城市二O 二O 年初中毕业与升学考试

数学试卷参考答案

一、选择题

二、填空题

9.

60

10.2

11.()()x y x y +- 12.1

13.

2

5

14.130 15.2 16. 6-或4-

三、解答题

17. 解:原式821=-+

7=.

18.解不等式组:21

1,3453 2.x x x -?≥?

??-<+?

解:21

1,3453 2.x x x -?≥?

??-<+?①②

解不等式①,得2,x ≥ 解不等式②,得7,x <

在数轴上表示不等式①、②的解集如图:

∴不等式组的解集为27x ≤<.

19.

23193m m m ?

?÷+ ?--??

,其中2m =-.

解:原式2

3

3933m m m m m -??=

÷+ ?---??

2

93

m m

m m =

÷-- ()()

3

33m

m m m m

-=

?

+- 1

3

m =

+ 当2m =-时代入 原式1

123

=

=-+

20.解:在Rt ABC 中,90,C tanA ∠==

30,60,A ABC ∴∠=∠=

BD 是ABC ∠的平分线, 30,CBD ABD ∴∠=∠=?

3,CD =

330

CD

BC tan ∴=

=

在Rt ABC 中,90,30C A ∠=?∠=?

630BC

AB sin ∴=

=?

.

21. 解:()1如图所示,点E 即为所求.

()2连接OB OC 、

由()1得:EB EC =

O 是正方形ABCD 中心, ,OB OC ∴=

∴在EBO 和ECO 中, EB EC EO EO OB OC =??

=??=?

(),EBO ECO SSS ∴?

BEO CEO ∴∠=∠.

22.()141,13

()2如图所示

:

()3A地区累计确诊人数可能会持续增加,B地区新增人数有减少趋势,疫情控制情况较好(答案不唯一,仅供参考).

23.()1解:画树状图如图所示:

∴图③可以表示不同信息的总数个数有4个.

()216;

()33;

24.()1证明:连接OC

,OC OA = ,OCA A ∴∠=∠

AB 为圆O 的直径, 90,BCA ∠=?∴ 90,A B ∴∠+∠=

,DCA B ∠=∠

90,OCA DCA OCD ∴∠+∠=∠=

,OC CD ∴⊥

点C 在圆O 上,

CD ∴是O 的切线.

()2证明:

90,OCA DCA ∠+∠=

,OCA A ∠=∠ 90,A DCA ∴∠+∠=? ,DE AB ⊥ 90,A EFA ∴∠+∠=? ,DCA EFA ∴∠=∠

,EFA DFC ∠=∠

,DCA DFC ∴∠=∠

DCF ∴是等腰三角形.

25. 解:()1上

()2①若90

ACN ∠=,

则C 与O 重合,直线l 与二次函数图像交于A 点 因为直线与该函数的图像交于点B (异于点A ) 所以不合符题意,舍去

②若90ANC ∠=?,则C 在x 轴下方,

因为点C 在x 轴上, 所以不合符题意,舍去

③若90CAN ∠=?

则45,2ACN ANC AO CO NO ∠=∠=?===

()20(),2,0C N ∴-,

设直线:l y kx b =+ 将(),(02,0),2A C -代入:

202b

k b ==-+??

?

解得1

2

k b ==??

?

∴直线:2l y x =+.

()3过B 点作BH x ⊥轴,垂足为,H

1211

,,22S MN OA S MN BH =

?=? 又

215

2

S S =

5

2

OA BH ∴=

2,OA =

5,BH ∴=

即B 点纵坐标为5,

将5y =代入2y x =+中,得3,x =

()3,5B ∴

将A B N 、、三点坐标代入2

y ax bx c =++中,得

24220,9325c a b a b =??

++=??++=?

解得25,2a b c =??

=-??=?

∴抛物线解析式为2252y x

x =-+.

26. 解:()1如图,过点P 作,PE CD ⊥垂足为E

P 是边长为30cm 的正方形模具的中心, 15,PE cm ∴=

同理:A B ''与AB 之间的距离为15,cm

''A D 与AD 之间的距离为15,cm

'B C '与BC 之间的距离为15,cm ''''2001515170,A B C D cm ∴==--= ''''100151570,B C A D cm ==--= ()''170702480A B C D C cm ''∴=+?=四边形.

答:图案的周长为480cm .

()2连接,PE PF PG 、、过点P 作PQ CD ⊥,垂足为Q

P 是边长为30cm 的等边三角形模具的中心, ,30PE PG PF PGF ∴==∠=? ,PQ GF ⊥

,GQ QF ∴==

3015,PQ CQ tan cm ∴=??= 3030CQ

PG cm cos =

=?

.

当三角形EFG 向上平移至点G 与点D 重合时, 由题意可得:'E F G ''绕点D 顺时针旋转30, 使得''E G 与AD 边重合

'DP ∴绕点D 顺时针旋转30至",DP 3030

5180

p p l cm ππ'''??∴=

=.

同理可得其余三个角均为弧长为5cm π的圆弧

(3030

20010024180

C π??=--?+

?

()

60020cm π=-.

答:雕刻所得图案的草图的周长为()

60020cm π-.

27. 问题1:图

问题2:()32

(

4

问题3:

法一:(判别式法)

证明:设,BC x AC BC y ===

在Rt ABC 中,

90,C AC ∠=?==

y x ∴=

y x ∴-=222224,y xy x a x -+=- 2222240,x xy y a -+-=

关于x 的元二次方程有实根,

()2222444240,b ac y x a ∴-=-??-≥

228,y a ∴≤

00,y a >>,

,y ∴≤

当y 取最大值时,

22240x a -+=

)

2

20a

-=

12x x ==

∴当BC =时,y 有最大值.

法二:(基本不等式)

设,,BC m AC n AC BC y ==+= 在Rt ABC 中,

90,C ∠=?

2224m n a ∴+=

()

2

0,m n -≥

222m n mn ∴+≥.

当m n =时,等式成立

242,a mn ∴≥

22mn a ≤.

y m n =+=

=,

22,mn a ≤

,y ∴≤

∴当BC AC ==时,y 有最大值.

问题4:

法一:延长AM 交EF 于点,C

过点A 作AH EF ⊥于点,H 垂足为,H 过点B 作BK GF ⊥交于点,K 垂足为,K

BK 交AH 于点,Q

由题可知:在BNE 中,60,90,1BNE E BE ∠=?∠==

BE

tan BNE NE

∴∠=

1NE

=

3

NE ∴=

//,AM BN 60,C ∴∠=?

90,GFE ∠=

30,CMF ∴∠=? 30,AMG ∴∠=?

90,1,30G AG AMG ∠=?=∠=?,

∴在Rt AGM 中,

AG

tan AMG GM

∠=

1GM

=

GM ∴=

90,90,G GFH AHF ∠=∠=?∠=?

2020年盐城中考英语试题

绝密★启用前 2020年高中阶段教育招生统一考试 英语试题 注意事项: 1.本试卷包含第I卷选择题(第1 ~ 45题)、第II卷非选择题(第46 ~ 85题及书面表达题)两部分。本次考试时间为100分钟,卷面总分为120分。考试形式为闭卷。 2.本试卷中所有试题必须作答在答题卡上规定的位置,否则不给分。 3.答题前,务必将自己的姓名、准考证号用书写黑色字迹的0.5毫米签字笔填写在试卷及答题卡上。 第Ⅰ卷(选择题,共60分) 一、单项选择(共15小题,每小题1分,计15分) 从A、B、C、D四个选项中选出一个可以填入句中空白处的最佳答案。 1. Ge You is ______ popular film star in China, who likes listening to music. A. a B. an C. the D.∕ 2. ______ interesting it is to go sailing in Qingdao in summer! A. What B. What an C. How D. How an 3. —Where’s David? —He ______ be in the playground because he is fond of playing basketball. A. will B. may C. can’t D. mustn’t 4. —Can I use your e-dictionary? —Sorry. I don’t have ______. A. it B. this C. that D. one 5. Sandy feels unhappy because nobody seems to ______ her progress. A. notice B. look C. watch D. read 6. —I’ll go to Beijing for the coming summer holiday. —______. A. Thank you B. It doesn’t matter C. The same to you D. Have a good time 7. I saw Li Ming ______ near the river on my way home. A. plays B. playing C. to play D. played 8. The two cities have reached an ______ to develop science and technology. A. education B. excitement C. agreement D. invention 9. Mr. White came to our school in 2008, and since then he ______ us English. A. teaches B. taught C. has taught D. will teach 10. Many volunteers______ food and water to the local people in Japan after the tsunami. A. gave out B. cut out C. put out D. found out 11. Plan your time carefully and make sure you have some time ______ what you like every day. A. do B. to do C. doing D. done 12. I ______ along the road when I saw Peter. So we stopped and had a chat. A. walked B. was walking C. would walk D. had walked 13. —Is Mr. Black ill? —______. I think he will have to stay at home to have a good rest. A. I don’t think so B. I’m afraid not C. I hope so D. I’m afraid so 英语试题第1页(共8页)

江苏省盐城市2018中考数学试题及答案

江苏省盐城市2018年中考数学试卷 一、选择题(本大题共8小题,每小题3分,共24分.在每小题给出的四个选项中,只有一项是符合题目要求的,请将正确选项的字母代号填涂在答题卡相应位置上) 1.-2018的相反数是( ) A .2018 B .-2018 C .12018 D .12018- 2.下列图形中,既是轴对称图形又是中心对称图形的是( ) A . B . C . D . 3.下列运算正确的是( ) A .224a a a += B .33a a a ÷= C .235a a a ?= D .246 ()a a = 4.盐通铁路沿线水网密布,河渠纵横,将建设特大桥梁6座,桥梁的总长度约为146000米,将数据146000用科学记数法表示为( ) A .51.4610? B .60.14610? C .61.4610? D .314610? 5.如图是由5个大小相同的小正方体组成的几何体,则它的左视图是( ) A . B . C . D . 6.一组数据2,4,6,4,8的中位数为( ) A .2 B .4 C .6 D .8 7.如图,AB 为O 的直径,CD 是O 的弦,35ADC ∠=,则CAB ∠的度数为( )

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