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2010大兴二模数学试题及答案
大兴区2009-2010学年度第二学期模拟试卷（二）
初三数学
考生须知 1．本试卷共6页，共五道大题，25个小题，满分120分。考试时间120分钟。
2．在试卷和答题卡上认真填写学校名称、姓名和准考证号。
3．试题答案一律书写答题纸上，在试卷上作答无效。
4．考试结束，请将本试卷答题卡和草稿纸一并交回。
第I卷（选择题，共32分）
一、选择题（本题共32分，每小题4分）
在下列各题的四个备选答案中，只有一个是正确的，请将正确答案前的字母写在答题纸上。
1. -8的绝对值等于（ ）
A. 8 B. -8 C. D.
2.如果一个角等于56°，那么它的余角等于（ ）
A. 24° B. 56° C. 34° D. 36°
3．如图1， 是⊙O的弦， 于
点 ，若 ， ，则⊙O的半径为（ ）cm．
A. 10 B. 5 C.16 D.9
4．下列运算正确的是（ ）
A． B．
C． D．
5．为了备战2010年冬奥运会，周洋刻苦进行短道1500米速滑训练，为判断她的成绩是否稳定，教练对她10次训练的成绩进行统计分析，则教练需了解这10次成绩的（ ）
A．众数 B．方差 C．平均数 D．频数
6．若一个多边形的内角和等于它的外角和的2.5倍，则这个多边形的边数是 （ ）
A．4 B．5 C．6 D．7
7．如图2，AB是⊙O的直径，点D、E是半圆的三等分点，AE、BD的延长线交于点C，若CE=2,则⊙O中阴影部分的面积之和是（ ）
A． B．
C． D．
8.如图3-6，把一张长方形纸片对折，折痕为AB，以AB的中点O为顶点，把平角∠AOB三等分，沿平角的三等分线折叠，将折叠的图形剪出一个以O为顶点的等腰三角形，那么剪出的平面图形一定是（ ）
A．正三角形 B．正方形 C．正五边形 D．正六边形
第II卷（共88分）
二、填空题（本题共16分, 每小题4分）
9．若分式 的值为0，则a的值为 .
10．在函数y= 中, 自变量x的取值范围是 .
11.代数式 的最小值是 .
12．如图7，在平面直角坐标系xOy中，等腰梯形ABCD
的顶点坐标分别为A（1，1），B（2，－1），C（－2，－1），
D（－1，1）．y轴上一点P（0，2）绕点A旋转180°
得点P1，点P1绕点B旋转180°得点P2，点P2绕点C
旋转180°得点P3，则点P3的坐标是（ , ）．
三、解答题（本题共30分, 每小题5分）
13. 计算： .
14. 解方程： ．
15. 已知：如图8，在平行四边形ABCD中，点E、F分别在
AB、DC上，AE = CF.
求证：∠ADE=∠CBF．
16．若 , 求代数式 的值.
17.在平面直角坐标系 中，一次函数 的图象与一次函数 的图象关于 轴对称，又与反比例函数 的图象交于点 ，试确定n的值．
18． 如图9，线段 分别表示甲、乙两建筑物的高， ，从 点测得 点的仰角 为60°，从 点测得 点的仰角 为30°，已知甲建筑物高AB为36米．求乙建筑物的高DC.
四、解答题（本题共20分, 第19题5分，第20题5分，第21题4分，第22题6分）
19. 某汽车制造厂决定招聘一些新工人，他们经过培训后上岗. 调研部门发现：1名熟练工人和2名新工人每月可安装8辆电动汽车，2名熟练工人和3名新工人每月可安装14辆电动汽车. 求每名熟练工人和新工人每月分别可以安装多少辆电动汽车？
20．.如图10， 是 的外接圆， 过 点作 ，交 的延长线于点 ．
（1）求证： 是 的切线；
（2）若 的半径R为5，BC=8，求线段 的长．
21．随着网络的普及，越来越多的人喜欢到网上购物。某公司对某个网站2005年到2008年网上商店的数量和购物顾客人次进行了调查。根据调查结果，将四年来该网站网上商店的数量和每个网上商店年平均购物顾客人次分别制成了折线统计图（如图11）和条形统计图（如图12）.请你根据统计图提供的信息完成下列填空：
（1）2005年该网站共有网上商店 个；
（2）2008年该网站网上购物顾客共有 万人次.
22.图13是一张宽与长之比为 的矩形纸片,我们称这样的矩形为黄金矩形.同学们都知道按图14所示的折叠方法进行折叠，折叠后再展开，可以得到一个正方形ABEF和一个矩形EFDC,那么EFDC这个矩形还是黄金矩形吗? 若是，请根据图14证明你的结论；若不是，请说明理由.
五、解答题（本题共22分, 第23题7分，第24题7分，第25题8分）
23．如图15，在Rt△ABC中，∠C＝90°，BC＝8厘米，点D在AC上，CD＝3厘米．点P、Q分别由A、C两点同时出发，点P沿AC方向向点C匀速移动，速度为每秒k厘米，行完AC全程所用时间是8秒；点Q沿CB方向向点B匀速移动，速度为每秒1厘米．设运动的时间为 秒 ，△DCQ的面积为 平方厘米，△PCQ的面积为 平方厘米．
⑴求 与 的函数关系，并在图16中画出 的图象；
⑵如图16， 的图象是抛物线的一部分，其顶点坐标是（4，12），求点P运动的速度 及AC的长；
⑶在图16中，点G是 轴正半轴上一点 ，过G作EF垂直于 轴，分别交 、 的图象于点E、F．
①说出线段EF的长在图15中所表示的实际意义；
②当0＜ ＜6时，求线段EF长的最大值．
24. 在平面直角坐标系中，已知直线 和抛物线 交于点B（0，4），C（5，9），直线BC与x轴交于点A.
（1）求出 A点的坐标和抛物线的对称轴；
（2）D（1，y）在抛物线上，在抛物线的对称轴上是否存在两点M、N，且MN=2 ，点M在点N的上方，使得四边形BDNM的周长最小，若存在，求出M 、N两点的坐标，若不存在，请说明理由.
（3）请求出抛物线上所有满足到直线BC距离为 的点P．
25. 如图17、18是两个相似比为 ： 的等腰直角△DMN和△ABC，将这两个三角形如图19放置，△DMN的斜边MN与△ABC的一直角边AC重合.
⑴ 在图19中，绕点 旋转△DMN，使两直角边DM、DN分别与 交于点 ，如图20. 求证： ；
⑵ 在图19中，绕点 旋转△DMN，使它的斜边CM、直角边 的延长线分别与 交于点 ，如图21，此时结论 是否仍然成立？若成立，请给出证明；若不成立，请说明理由.
⑶ 如图22，在正方形 中， 分别是边 上的点且满足 的周长等于正方形 的周长的一半， 分别与对角线 交于点 . 线段 、 、 恰能构成三角形. 请指出线段 、 、 所构成的三角形的形状，并给出证明.
大兴区2009~2010学年度第二学期模拟试卷（二）
初三数学参考答案及评分标准
一、选择题（本题共32分，每小题4分）
1．A 2． C 3． B 4. A 5．B 6．D 7． A 8．D
第II卷（共88分）
二、填空题（本题共16分, 每小题4分）
9. 2 10. 11． 12. （-6，0）
三、解答题（本题共30分, 每小题5分）
=10. ………………………………………………………………………………………5分
14. 解：去分母，得
……………………………………………………………2分
解得 ………………………………………………………………………………4分
经检验， 是原方程的解．
所以原方程的解为 ……………………………………………………………5分
15．证明：∵ 四边形ABCD为平行四边形，
∴ AD=CB, ………………………………………………………………………………1分
∠A=∠C. ………………………………………………………………………………2分
在△AED和△CFB中，
∴ △AED≌△CFB. ………………………………………………………………………4分
∴ ∠ADE=∠CBF．…………………………………………………………………………5分
16. 解：
……………………………………………………2分
……………………………………………………………………3分
……………………………………………………………………………4分
由 , 得
原式 ……………………………………………………………………5分
17. 依题意得，
一次函数 的解析式为 ………………………………………………2分
因为点A（m，3）在一次函数 的图像上，
所以 ……………………………………………………………………………………3分
即点A的坐标为（-3，3）
∵点A（-3，3）在
∴ …………………………………………………………………………………5分
18．解：（1）过点 作 于点 ，
∴ ， 2分
设 ，则 ，
在 中，
，
x,
. 3分
在 中，
四、解答题（本题共20分, 第19题5分，第20题5分，第21题4分，第22题6分）
19.解：（1）设每名熟练工人和新工人每月分别可以安装 辆电动汽车………………1分
…………………………………………………………………………………3分
解之得 …………………………………………………………………………………4分
答：每名熟练工人和新工人每月分别可以安装4辆、2辆电动汽车………………………5分
20. 解：（1）证明：
∴∠ADB=90°
，
∴∠ADB=∠PAD=90°．
∴AO⊥AP
∵AO为 的半径，
为 的切线． ……………………2分
（2）∵AO⊥BC, BC=8
∴BD=DC=4.
在Rt△BDO中，
∵OB=5，
∴ ． ………………………………………………………………………3分
又∵∠BDO=∠OAP=90°．
∠AOP=∠BOD
∴△AOP∽△DOB 4分
．
即 ．
． …………………………………………………………………………………5分
21. （1） 20 ………………………………………………………………………2分
（2） 3600 …………………………………………………………………………4分
20. 解: 矩形EFDC是黄金矩形………………………………………………………………1分
证明：∵四边形ABEF是正方形
∴A B=DC=AF ………………………………………………………………………………2分
又∵
∴
即点F是线段AD的黄金分割点. ……………………………………………………………3分
∴ ………………………………………………………………………4分
∴ ………………………………………………………………………………5分
∴矩形CDFE是黄金矩形 ……………………………………………………………………6分
五、解答题（本题共22分, 第23题7分，第24题7分，第25题8分）
23. 解：⑴∵ ，CD＝3，CQ＝x，
∴ ．……………………………………1分
图象如图16所示 ………………………………2分
⑵ ，CP＝8k－xk，CQ＝x，
∴ ．……3分
∵抛物线顶点坐标是（4，12），
∴ ．解得 ．
则点P的速度为每秒 厘米，AC＝12厘米．…………………………………………4分
⑶①观察图象，知
线段的长 ，表示△PCQ与△DCQ的面积差（或△PDQ面积） ……5分
②由⑴得 ，由⑵得 .
∵EF＝y2－y1，
∴EF＝ . ……………………………………………6分
∵二次项系数小于0，0＜x＜6，
∴当 时， 时最大…………………………………………………………7分
24.解：（1）
抛物线的对称轴为：直线 ……………………………………………………………1分
（2）∵若四边形 的周长最短，求出 最短即可
∵点D抛物线上，
∴ D（1，1）
∴点D关于直线 的对称点是
∵B（0，4）
∴将B点向下平移2个单位得到 （0，2）
∴直线 交直线 于点N ,
∵ （0，2），
∴直线 的解析式为： ……………………………………………………2分
∴N
∵MN=2
∴M ………………………………………………………………………………………3分
（3）设点P到直线BC的距离为h，故P点应在与直线BC平行，且相距 的上下两条平行直线 和 上．………………………………………………………………………………4分
由平行线的性质可得：两条平行直线与y轴的交点到直线BC的距离也为 ．
如图，设 与y轴交于E点，过E作EF⊥BC于F点，
在Rt△BEF中，
，
，
∴
∴可以求得直线 与y轴交点坐标为
同理可求得直线 与y轴交点坐标为 …………………………………………………5分
∴两直线解析式 ； ．
根据题意列出方程组： ⑴ ；
⑵ ………………………………………………6分
∴解得： ； ； ；
∴满足条件的点P有四个，它们分别是 ， ， ， ……7分
25.⑴ 证明：如图20，延长ED至E′，使ED=DE′，连结E′B.
∵D是AB中点,
∴ ，
∵∠EDA=∠BDE′
∴ ≌ .
…………………………………………………………………………………1分
∠A=∠ABE′
连接
在 中
∵
又 ⊥ ，ED=DE′
……………………………………………………………………2分
(2)如图21，
，
将 绕点 逆时针旋转 ，得
，∠CBE′= ∠CAB
连接
在 中有 ………………………………………………3分
∵△CDM是等腰直角三角形，
∴∠FCE′=∠MCE′-∠MCF=45°
∴∠MCF=∠FCE′
∵CE=CE′ CF=CF
∴△CEF≌△CE′F
在 中,
………………………………………………………………………4分
(3)线段BM、MN、DN能构成直角三角形.
延长
∵ABCD是正方形
∴∠ADF=∠ABE=∠ABG=90°
AD=AB
∴ ≌
∴AG=AF
因为 的周长等于正方形 周长的一半，
∴EF=FD+BE，
EF=GB+BE
…………………………………………………5分
∵AE=AE
≌ ，
………………………………6分
∵∠GAF=∠GAB+∠BAF=∠DAF+∠BAF=90°
由（2）的结论可知：在等腰直角 中，
∵∠MAN=∠EAF=45°
，
线段BM、MN、DN可构成直角三角形 ………………………………………………………8分
[img]西安小升初2021还有DK和xk
西安小升初2021还有DK和xk。
在小升初DK/XK时，除了高新一中的高新系校考外，学校都是分了AB卷进行考试的，也就是在同一个考场，一部分孩子考的是A卷，一部分孩子考的是B卷，这是为了防止作弊和抄袭现象。
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2017年苏州市中考英语模拟试题
第一卷 选择题(74分)
一.单项选择 从各题的四个选项中选出一个最佳答案，将所选答案的字母标号写在题号前的相应位置上。(共16分，每小题1分)
1. He’s got a lovely garden. ____ flowers are really beautiful.
A. A B. An C. The D. /
2. Tony and his friends will go to the Great Wall next week and ____ will have a great time.
A. he B. she C. they D. we
3. –-Which school is better, our school or Park School?
--- ____ schools are very nice.
A. Both B. Either C. Neither D. None xK b1 . Co m
4. It’s true that schoolchildren today work _____ than they did in the past, and they don’t have too much free time.
A. hard B. harder C. hardly D. hardest
5. --- How long have you studied in No.61 Middle School? ---- ____ 2008.
A. For B. In C. Since D. At
6. --- It’s getting late, Betty.
---____, I’m going to bed soon.
A. Good idea B. What’s it like C. bad luck D. Nearly finished
7. Today is ____ for married women to go out to work, but it was less common in the past.
A. unusual B. useless C. difficult D. normal
8. Study hard and you will _____ at last.
A. lose B. fail C. succeed D. make
9. I will fly to Beijing this afternoon, and now I’m getting ready to _____.
A. get off B. set off C. take off D. turn off
10. Most young people ______ the way they look.
A. think about B. care about C. talk to D. take care
11. Companies give their products to film stars ____ fans will buy them.
A. because B. because of C. so that D. in order to
12. People now don’t take as much exercise _____ they did in the past.
A. than B. as C. like D. and
13. I _____ like the trainers with the logo “Nike”
A. fortunately B. freshly C. successfully D. really
14. He is making a ____ on how to protect the environment.
A. speech B. project C. subject D. problem
15. We should give love to the children ____ lost their parents in the accidents.
A. / B. which C. who D. whom
16.My parents -------Shangdong for ten years.
A. have been in B. have been to C. have gone to D. have been at
二 完形填空(一)(10分)
阅读下列短文，从文后各题所给的四个选项中选出一个最佳答案。
Many young people today care about the way they 16 . They often buy “designer” clothes 17 they think they look cool. Then the18 well-known companies make clothes which look the same. But they don’t sell 19 well because they don’t have the 20 .
People 21 think designer clothes are better made. For example, many people think the right running shoes will make you run faster or play better. Of course, this is not always 22 . It’s the23 – not the trainers – that improves your speed or your score. 24 that’s not the point. People believe that it’s true … and then 25 the shoes. The big companies only want to make a lot of money.
17 A. look B. work C. speak D. wear
18 A. that B. because C .though D. unless
19 A. most B. less C. more D. least
20 A. as B. quite C .too D. rather
21 A. design B .time C. idea D. logo
22 A. even B. also C .always D. still
23 A. good B. true C .expensive D. wrong
24 A. logo B. quality C. training D. luck
25 A. But B. And C. So D. Then
26 A . like B refuse C make D. buy
三 阅读下列短文，从所给的A、B、C、D四个选项中选出最佳答案(每小题2分，共38分)
Passage 1
A Trip to the Forest
One day Bob took two of his friends into the mountains. They put up their tents (帐篷) and then rode off to a forest to see how the trees were growing.
In the afternoon when they were about ten kilometers from their camp(营地), it started to snow. More and more snow fell. Soon Bob could hardly see his hands before his face. He could not find the road. Bob knew there were two roads. One road went to the camp, and the other went to his house. But all was white snow. Everything was the same. How could he take his friends back to the camp?
Bob had an idea. The horses! Let the horses take them back! But what would happen if the horses took the road to his house? That would be a trip of thirty-five kilometers in such cold weather!
It was getting late. They rode on and on. At last the horses stopped. Where were they? None of them could tell. John looked around. What was that under the tree? It was one of their tents!
27. John and his two friends went to the forest to ____.
A. build their camp B. find their way home
C. enjoy the mountains in the snow D. watch the trees in the forest
28. They could not find their way back because ____.
A. there was only one road to their camp
B. they couldn't decide which of the two roads led to their tents
C. there were no roads in the mountains at all
D. everything was covered by the white snow
29. It is clear that they wanted the horses to take them to ____.
A. John's house B. the camp C. the forest D. the mountains
30. The horses stopped because____.
A. it was getting late B. they were tired after running for a long way
C. they knew that they had got to the camp D. they had seen John's house
31. The story happened ____.
A. on a cold winter day B. on a dark snowy evening
C. in a cold camp far from villages D. at night when nothing could be seen
Passage 2
Here is some news from Dalian Daily.
•President’s pet.
Do you keep a pet? American President Obama does.He calls his new dog Bo.It is six months old.The president’s family like the dog very much.Look! They are having fun with Bo on the South Lawn (南草坪)of the White House.The president’s daughter, Malia ,is showing the dog off.
•Back on her feet.
Mosha is a young elephant in Thailand.She lost her right front leg after stepping on a landmine(地雷)two years ago.She was taken to a hospital and became the first elephant in the world with a prosthetic leg(假肢).
Now aged three Mosha is growing up.She is happy to have the new prosthetic leg.
•Liu Xiang
World champion Liu Xiang returned to Shanghai on March 8.The 25-year –old star had a foot operation in December in America.It took him three months to recover(康复)and train there.It is said that some doctors are ready in Shanghai to help with Liu’s recovery.Liu left the 2008 Beijing Olympics because of his foot injury(损伤)last August.
32.The name of the president’s dog is________.
A.Washington B.Bo C.Malia D.Obama
33.How old is the dog?
A.Two months old B.Three years old C.Six months old D.Six years old
34.How did the elephant lose his front leg?
A.She had a traffic accident. B.She stepped on the landmine.
C.She was ill. D.She fell into a big hole.
35.Liu Xiang had his foot operation in________.
A.China B.America C.Japan D.Australia
36.Liu Xiang left the Beijing Olympics because________.
A.he was afraid of the other players B.he was too nervous to take part in it
C.his coach told him to do that D.his foot hurt
Passage 3
Everybody can suffer from stress. No matter what your age is, you can feel stressed out by things that are happening in your life.
Teenagers, however, have many more opportunities to get stressed than people in any other age group. Being a teenager is hard. You are not a child any more, but you are not an adult, even though you have to deal with some very grown-up problems and decisions.
Families can be one of the biggest causes of stress, such as problems with parents arguing at home. or problems with brothers and sisters. Teenagers also have a lot of stress from school, either from their teachers or from their friends. Some teenagers also feel stressed about choosing their education after high school. Getting a place at university can be very difficult and some cannot afford to go to university. The stress about getting a job when finishing school is hard for some teenagers. There are so many young people finishing school and not enough jobs for them.
Sadly, there is nothing we can do to remove these causes of stress from the 1ives of teenagers, but you can learn the best way to deal with it. Talking to people is one of the best ways to deal with stress. It may sound simple, but it is true. A problem shared is a problem halved.
37. Why is being a teenager often difficult?
A. Because even though you are not an adult, you must deal with adult problems.
B. Because even though you are an adult, you must deal with children’s problems.
C. Because even though you are a teenager, you must do a lot of homework.
D. Because adults often make them feel stressed.
38. Families can add to the stress a teenager might experience ______.
A. by asking them to go to university
B. by helping them with their homework
C. as teenagers quarrel with their parents, and their brothers or sisters
D. as families never support their children enough
39. Why can leaving school be a stressful time for teenagers?
A. Because they will be leaving their favorite teachers.
B. Because many people’s favorite memories are at school.
C. Because they may worry about getting a place at university.
D. Because they may worry about becoming an adult.
40. Why can finding a job after finishing school be difficult?
A. Because there is a lot of competition for jobs.
B. Because there are no jobs.
C. Because a job is more difficult than school work.
D. Because there is a lot of competition for places at university.
41. We can deal with the stress in our life ______.
A. by not trying to find a job B. by forgetting about our problems
C. by getting a place at university D. by sharing our problems with our friends
Passage 4
When you think about running away, you probably imagine that there will be no more rules, no parent to tell you what to do, no more fights. Sounds great and exciting, right? In fact, ___42__ but fun. Kids who run away face new problems like not having any money, food to eat, a safe place to, sleep, or
anyone to take care of them.
People with no home and no money become ready to do anything just to meet their everyday needs. Because of this, ___43__ that would be terrible even for adults. Run-away kids join in dangerous crimes(犯罪) much more often than kids who live at home.
Kids who live on the streets often have to steal(偷) for a living. Many take drugs to get through the day because they become so sad and feel that ___44__. Some are forced(被迫) to do things they wouldn’t normally do to make money. The number of kids with HIV or AIDS and other diseases is higher on streets, too, because ___45__. This problem is attracting more and more attention.
A. running away is nothing
B. they often find them in risky situations
C. it may be natural
D. these kids are more easily to get affected(感染)
E. no one cares about them
F. take good care of
四、补全对话(10分)
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