2018年4月石家庄市一模数学试卷及答案

2018年4月石家庄市一模数学试卷及答案
2018年4月石家庄市一模数学试卷及答案

2018年初中毕业班教学质量检测

数学试题参考答案及评分参考

说明:

1.在阅卷过程中,如考生还有其它正确解法,可参照评分标准按步骤酌情给分.

2.坚持每题评阅到底的原则,当考生的解答在某一步出现错误,影响了后继部分时,如果该步以后的解答未改变这一题的内容和难度,可视影响的程度决定后面部分的给分,但不得超过后继部分应给分数的一半;如果这一步后面的解答有较严重的错误,就不给分.

3.解答右端所注分数,表示正确做到这一步应得的累加分数.只给整数分数.

一、选择题(本大题有16个小题,共42分.1~10小题各3分,11~16小题各2分)

二、填空题(本大题有3个小题,共10分.17~18小题各3分;19小题有2个空,每空2分.) 19.(23,23-),(1009,0), 17.12- 18. 6π

三、解答题(本大题有7个小题,共68分)

20.解:(1)原式=ab b a ab -+++1

=1++b a …………………………………………………………(2分)

∵4=+b a ,∴原式=4+1=5.……………………………………………………(4分)

(2)∵b a b ab a 22222+++-=)(2)(2b a b a ++-, ………………………(6分)

由题意得,42)(2?+-b a =17,∴2)(b a -=9,

∴b a -=±3.……………………………………………………………………(8分)

21.(1)40;………………………………………………………………………(1分)

补全图形如图1所示:………………………………………………………(3分)

(2)90,90;……………………………………………………………………(5分)

(3)列表法:……………………………………………………………………(7分)

∵第二象限的点有(?2,2)和(?1,2)

奖项

祖冲之奖 刘徽奖 赵爽奖 杨辉奖 0

图1

∴P (点在第二象限)=92

……………………………………………………(9分)

22.解:(1)如图2

⊥BD ,垂足为F . ……………………………………(1分) ∵AC ⊥BD ,

∴∠ACB=

FB=90°; 在Rt

中,∠1+∠3=90°;

B ⊥AB ,∴∠1+∠2=90°, ∴∠2=∠3; ……………………………………………………………………(2分)

在△ACB 和△BF 中,

∴△ACB ≌△BF (AAS ); ∴F=BC ,……………………………………………………………………(4分)

∵AC ∥DE 且CD ⊥AC ,AE ⊥DE ,

∴CD=AE=1.8;…………………………………………………………………(5分)

∴BC=BD -CD=3-1.8=1.2, ∴F=1.2

BD 的距离是1.2m .………………………………………(6分)

H

图2

(2)由(1)知:△ACB ≌△

∴BF=AC=2m ,………………………………………………………………(7分)

H ⊥DE ,垂足为H . ∵

F ∥DE

H=FD ,……………………………………………………(8分) ∴H=BD -BF=3-2=1

1m .……………………(9分) 23.解:(1)此时点A 在直线l 上; …………………………………………………(1分)

∵BC =AB =2,点O 为BC 中点,

∴点B (?1,0),A (?1,2),……………………………………………………(3分)

把点A 的横坐标x=?1代入解析式42+=x y ,得

4)1(2+-?=y =2,等于点A 的纵坐标2,

∴此时点A 在直线l 上. …………………………………………………………(5分)

(2)由题意可得,点D (1,2),及点M (?2,0),

当直线l 经过点D 时,设l 的解析式为t kx y +=(k ≠0),

∴???=+=+-202t k t k ,解得???????==3

4

32t k ,…………………………………………………(7分)

∴当直线l 与AD 边有公共点时,t 的取值范围是3

4≤t ≤4. ………………(9分) 24.解:(1)5 ………………………………(1分) (2)设AE =x ,∵AB =4,∴BE =4﹣x ,

在矩形ABCD 中,根据折叠的性质知:

Rt △FDE ≌Rt △ADE ,

∴ FE =AE =x ,FD =AD =BC =3,

∴ BF =BD ﹣FD =5﹣3=2,

在Rt △BEF 中,根据勾股定理,得FE 2+BF 2=BE 2, 即x 2+4=(4﹣x )2,解得:x =32, ∴AE 的长为32

. ……………………………………………(4分) (3)存在, ……………………………………………(5分)

如图3,延长CB 到点G ,使BG =BC ,连接FG ,交BE 于点P ,连接PC ,

则点P 即为所求(画出点P 即可). ………………………………(6分)

此时有:PC =PG ,∴PF +PC =GF .

过点F 作FH ⊥BC ,交BC 于点H ,则有FH ∥DC ,

∴△BFH ∽△BDC , A E B

C D

F G P H 图3

FH BF BH DC BD BC ==,即2453FH BH ==, ∴8655

FH BH ==,, ………………………………………………………(8分) ∴GH =BG +BH 6213,55=+= 在Rt △GFH 中,根据勾股定理,得

∴GF 5

===

即PF +PC 的最小值为 …………………………………………………(10分) 25.解:(1)设b kx q +=(k ,b 为常数且k ≠0),

当x =2时,q =12,当x =4时,q =10,代入解析式得,

?

??=+=+104122b k b k ,解得:???=-=141b k , …………………………………………………(2分) ∴14+-=x q . ……………………………………………………………………(3分)

(2)当产量小于或等于市场需求量时,有p ≤q , ∴82

1+x ≤14+-x ,解得x ≤4, ………………………………………………(5分) 又2≤x ≤10,∴2≤x ≤4.…………………………………………………………(6分)

(3)①当产量大于市场需求量时,可得4<x ≤10,

由题意得,厂家获得的利润是:

p qx y 2-= ………………………………………………………………………(7分)

=16132-+-x x =4

105)213(2+-

-x .……………………………………………………………(9分) ②∵当x ≤213时,y 随x 的增加而增加, 又∵产量大于市场需求量时,有4<x ≤10,

∴当4<x ≤

213时,厂家获得的利润y 随销售价格x 的上涨而增加.……(11分)

26.解:【发现】

(1)3π.………………………………………………………………………(1分) (2)设⊙P 半径为r ,则有r =4-3=1, 当t =2时,如图4,点N 与点A

∴ PA =r =1,

设MP 与AB 相交于点Q ,在Rt △∵∠OAB =30°,∠MPN =60°,

∵∠PQA =90°.∴11,22PQ PA ==

∴cos30AQ PA =?=

∴111,22228

PQA S PQ AQ ==??= 即重叠部分的面积为8

3.………………………………………………(4分) 【探究】: ① 如图5,当⊙P 与直线AB 相切于点C

连接PC ,则有PC ⊥AB ,PC =r =1,

∵∠OAB =30°,∴AP

=2,

∴OP =OA -AP =3-2=1;

∴点P 的坐标为(1,0);

…………(6② 如图6,当⊙P 与直线OB 相切于点D 连接PD ,则有PD ⊥OB ,PD =r =1,

∴PD ∥AB , ∴∠OPD =∠OAB =30°,

∴cos ∠OPD =PD OP ,OP =3

3230cos 1= ,图7

∴点P的坐标为(

33

2

,0);………(8分)③如图7,当⊙P与直线OB相切于点E时,

连接PE,则有PE⊥OB,同②可得:OP=

33

2

∴点P的坐标为(-

33

2

,0)……………………………………………(10分)

【拓展】

t的取值范围是2

(提示:当点N运动到与点A重合时,MN与Rt△ABO的边有一个公共点,此时t=2 ;当t>2 直到⊙P运动到与AB相切时(t=3 ),MN与Rt△ABO 的边有两个公共点,∴2

x

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In seventh grade,a group of my classmates fixed their cold stares on my clothes.They called out to me,"Go get your gangsta clothes." In one of my Spanish classes,the teacher asked me,"Do you like rap music or rock music more?" I replied,"Rock." The look of shock on my classmates' faces made me uncomfortable. Now I still take all Honors courses.I still wear clothes that fit me.My music library covers from rock to pop to techno,and almost everything in between.When it comes to choosing my friends,I am still colorblind.I continue to do my best to work in school in order to reach my goals;and yet,when I look in the mirror,I still see skin of that same brown. I believe in being myself.I believe that I myself should decide who I am and what actions I take in life.In high school,popularity often depends on your willingness to follow trends.And I've been told that it doesn't get much easier going into adulthood.But the only other option is to sacrifice my personality for the satisfaction and approval of others.This can be appealing,but I'm not going to do that. 4.Why did his classmates laugh at him?______ A. His fly was open. B. Something was stuck in his teeth. C. He went into the wrong classroom. D. They had prejudice against him. 5.What are black people usually believed to do?______ A. Listen to rap music. B. Wear small clothes. C. Take Honors courses. D. Attend Spanish classes. 6.What does the underlined word "colorblind" probably mean?______ A. Making friends of the same skin color. B. Having no idea what friends to make. C. Treating people equally and fairly. D. Feeling hurt and offended inside. 7.What can be a suitable title for the text?______ A. Following Popular Trends B. Being Content with Myself C. Having Faith in Skin Color D. Changing My Personality C Coca-Cola,which reportedly produced more than 3 million tons of plastic packaging in 2017,announced Thursday it wants to "help fix the world's plastic waste problem one community (社区)at a time." The soda giant is doing so by providing $5.4 million for recycling programs in cities like Atlanta,Boston,Denver and Houston.In these cities,partners,like The Green Blue Institute and The Recycling Partnership,which receive the money,will work together to improve recycling rates. "We focus on areas where we have the ability to make the biggest influence on communities through the funding and expert skills of Coca-Cola employees," Carlos Pagoagoa,Coca-Cola's group director of community partnerships,said in a statement."In each city,local partners will work together to identify barriers to recycling on a local level and test a range of solutions," he added."We hope the learnings from these ‘model markets' can offer solutions to other cities facing similar challenges." As part of the effort,The Recycling Partnership and the city of Atlanta,where the cola company's headquarters are based,will send street teams out to open recycling carts and leave citizens cards informing them what they can and can't recycle,and let them know how their efforts work. "Two of the most urgent problems with recycling in the U.S.today are lack of access,followed by pollution in recycling," Keefe Harrison,CEO of The Recycling Partnership,said in a statement."We know from the success of Atlanta in 2017 that the citizens want to recycle,and that communicating with them in the street works." Last year,Coca-Cola announced its task to collect and reuse a bottle or can for each one it sells,and increase the amount of its products out of recycled materials to 50% by 2030.The brand also aims to make all its packaging fully recyclable by 2025. 8.What does Coca-Cola company intend to do in the program?______ A. Produce less packaging. B. Help deal with plastic waste. C. Pick up waste in communities. D. Build a plant to recycle plastic waste. 9.What's Paragraph 2 mainly about?______ A. How Coca-Cola conducts its program. B. What organizations participate in the program. C. How Coca-Cola chooses cities for the program. D. What the local people do in Coca-Cola's program. 10.What do street teams do to help?______ A. Sort out various waste in the city. B. Look into the cause of pollution.

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