杨浦区2012年学年度第一学期期中质量抽测

杨浦2012学年度第一学期期末质量抽测初一年级数学试卷一、选择题（每题2分，共10分） 1、下列各式计算正确的是（ ）A 、1)1(22+=+a aB 、532a a a =+C 、628a a a =÷D 、12322=-a a 2、下列说法中正确的是（ ）A 、2t 不是整式 B 、y x 33-的次数是3 C 、12222-+y x x 是四次三项式 D 、y1是单项式 3、下列各式不能用平方差公式计算的是（ ）A 、))((y x x y +-B 、)2)(2(x y y x ---C 、)3)(3(x y y x +--D 、)45)(54(x y y x +- 4、计算201420122013)1(5.1)32(-⨯⨯的结果是（ ）A 、32 B 、23 C 、32- D 、23- 5、下列图行政，既是轴对称图形又是中心对称图形的是（ ）A 、B 、C 、D 、二、填空题（每小题3分，共36分）6、长方形的一边长为3a ，另一边比它小b ，则其周长为 。

7、已知31332y x m -与12541-n y x 是同类项，则m+n= 。

8、计算：b a c b a 435155÷-= 。

9、计算：)2)(3(2xy y x -+= 。

10、某种细菌的长约为0.0000032厘米，用科学记数法表示这个数为 厘米。

11、当x= 时，分式xx --112的值为零。

13、要使多项式202--ax x 在整数范围内可因式分解，给出整数a= 。

（一个即可）14、当m= 时，方程111-=+-x m x x 无解。

15、在①矩形、②等腰梯形、③线段、④平行四边形这四种图形中，是轴对称图形但不是中心对称图形的是 。

（填序号）16、如图，将长方形纸片ABCD 按图中方式折叠，其中EF 、EC 为折痕，折叠后A ’、B ’、E 在一条直线上，已知∠BEC=54度，那么∠A ’EF= 度。

杨浦区2012学年度第一学期期末质量调研初三英语练习卷(满分150分) 2013.1(完卷时间：100分钟，答案一律写在答卷纸上)Part 1 Listening (第一部分听力)I. Listening Comprehension (听力理解): (共30分)A. Listen and choose the right picture (根据你听到的内容，选出相应的图片): （6分）A B CD E F G1. ________2. _______3. _________4. __________5. __________6. _________B. Listen to the dialogue and choose the best answer to the question you hear (根据你听到的对话和问题，选出最恰当的答案): (共10分)7. A) By bike. B) By train. C) By car. D) By bus.8. A) Hainan. B) Beijing. C) Paris. D) London.9. A) 8:45. B) 9:15. C) 8:30. D) 9:00.10. A) Pink. B) Black. C) White. D) Red.11. A) Rainy. B) Cloudy. C) Snowy. D) Sunny.12. A) Shop assistant and customer. B) Teacher and student.C) Hostess and guest. D) Repairman and customer.13. A) 100 yuan. B) 900 yuan.C) 920 yuan. D) 1,000 yuan.14. A) From newspapers. B) From a message.C) From ads on the train. D) From the woman.15. A) Have a party on Friday. B) Have a party on Saturday.C) Look for another restaurant. D) Book a more expensive room.16. A) Geography. B) Chinese. C) History. D) Science.C. Listen to the passage and tell whether the following statements are true or false (判断下列句子是否符合你听到的短文内容, 符合的用“T”表示，不符合的用“F”表示):(共7分)17. A charity worker phoned the richest man in the town for a survey.18. The man had a yearly income of at least $500,000.19. The man‘s mother died for lack of medicine and food.20. The man‘s brother could not see and walk.21. A traffic accident left the man‘s sister with a broken family.22. The charity worker was moved by the man‘s story and didn‘t know what to say.23. The rich man had his own way to give back to his town.D. Listen to the passage and complete the following sentences (听短文，完成下列内容，每空格限填一词): (共7分)24. The ―Walk to School Week‖ activity, a national and international event, began in __________.25. The activity aims to _________ the number of cars on the road during the rush hour.26. In its __________ year, the week had the theme ―Step Forward in Time‖.27. The 2012 theme encouraged children to develop the habit of __________ travel.28. Walking to school saves money and makes the traffic better around school __________.29. It was hoped that the activity would make travel to and from school safer and more __________.30. In fact, __________ of people around Northern Ireland use a car to pick up theirchildren after school.Part 2 Vocabulary and Grammar（第二部分词汇和语法）Ⅱ. Choose the best answer (选择最恰当的答案): (共20分)31. Medical teams are travelling to the disaster area to care for ______ wounded.A) a B) an C) the D) /32. _______ at the memorial service stood silent for one minute to remember those who died in theearthquake.A) Everyone B) Someone C) Anyone D) No one33. International Pen Friends has over 300,000 members in different countries. Their ______ member is only eight years old.A) young B) younger C) youngest D) the youngest34. Motorists woke up to find that their cars were covered ______ an inch of ice.A) in B) on C) for D) with35. My friend took her own life. Nobody can understand why she killed ______.A) she B) her C) hers D) herself36. Water is so important that ______ everyday tasks can be completed without it.A) few B) a few C) little D) a little37. Twenty people died and over ______ were injured in the accident.A) hundred B) hundred of C) a hundred D) hundreds of38. All the guests seemed ______ and no one was complaining.A) happy B) happily C) happiness D) unhappy39. The ______ one draws, or writes, or does anything, the ______ the end result will be.A) much … good B) more … betterC) most … best D) many … well40. We listened eagerly and carefully, ______ he brought news of our families.A) and B) but C) so D) for41. ______ it is to shop on the Internet!A) What easy B) What an easy C) How easy D) How easily42. Passengers ______ stay seated during the take-off and landing.A) can B) may C) should D) must43. In recent years, natural disasters ______ great damage to many tourist attractions.A) will cause B) have caused C) had caused D) were causing44. Twenty children aged between 5 and 10 ______ in a campus shooting last month.A) kill B) killed C) are killed D) were killed45. Some road workers ______ up the road outside my house, so I can‘t get my car back into the garage (车库).A) dig B) are digging C) were digging D) will dig46. Researchers at Xerox designed an icon system. But Apple was the first ______ it popular.A) make B) to make C) making D) made47. We hadn‘t seen each other for ages, so we spent the evening ______ up on each other‘s news.A) to catch B) catch C) catching D) to catching48. ______ he was tired after the daily hard work, Mo Yan was hungry for books.A) Since B) As soon as C) Although D) Until49. A: Sorry, Jack isn‘t here right now. Can I take a message?B: ______ I‘ll call back later.A) That‘s kind of you. B) No, thanks.C) Yes, please. D) I‘m afraid you can‘t.50. A: Someone stole my new iPhone5 last week.B: ______ Did you tell the teacher about it?A) That‘s OK. B) How awful!C) Take care. D) You should be more careful.Ⅲ. Complete the following passage with the words or phrases in the box. Each word or phrase can only be:（共8分）VSO stands for Voluntary Service Overseas. It is the largest independent volunteer 51 in the world with offices in many different countries. Since 1958, it has sent more than 30,000 volunteers to work 52 in Africa and Asia.Tom Harahan is Irish and trained as a doctor. After he graduated from a 53 school in Britain, he spent two years as a VSO volunteer in Malawi, East Africa. The following is an entry from his diary.Ⅳ. Complete the sentences with the given words in their proper forms （用括号中所给单词 的适当形式完成下列句子，每空格限填一词): (共8分) 59. More and more underground __________ are being built or willbe built in our city. (line)60. Jackson has been named as the biggest selling artist in the UK since his __________ in 2009. (die)61. The automobile industry played an important role in America throughout the __________ century. (twenty)62. “Life of Pi” is considered to be one of the most __________ films of the year. (power)63. The government hasn‘t reached a final __________ on the funding yet. (decide)64. The medicine is known to __________ side effects on children. (production)65. ―The end of the world‖rumor (谣言) was __________ reported on newspapers and the Internet some time ago.(wide)66. After World War II, some European countries worked together to __________ Europe and to prevent anotherwar. (build)Ⅴ. Rewrite the following sentences as required（根据所给要求，改写下列句子。

杨浦区2011学年度高三学科测试数学试卷(理科) 2011.12考生注意:1、答卷前,考生务必在答题纸写上姓名、考号.2、本试卷共有23道题，满分150分，考试时间120分钟.一、填空题（本大题满分56分）本大题共有14题，考生应在答题纸相应编号的空格内直接填写结果，每个空格填对得4分，否则一律得零分. 1、计算：=+-∞→)321(lim n nn ____________ 2、不等式021>+-x x的解集是__________ 3、若全集R U =，函数13-=xy 的值域为集合A ，则=A C U ____________ 4、若圆锥的母线长)(5cm l =，高)(4cm h =，则这个圆锥的体积等于____________ 5、在7)2(xx -的二项展开式中，2x 的系数是_____________（结果用数字作答） 6、若)(x f y =是R 上的奇函数，且满足)()4(x f x f =+，当)2,0(∈x 时，22)(x x f =，则=)2011(f ________7、若行列式112124=-x x ，则=x ________8、在100件产品中有90件一等品，10件二等品，从中随机取出4件产品，则至少含1件二等品的概率是____________（结果精确到0.01）9、某学校对学生进行该校大型活动的知晓情况分层抽样调查，若该校的高一学生、高二学生和高三学生分别有800人、1600人、1400人.若在高三学生中的抽样人数是70，则在高二学生中的抽样人数应该是__________10、根据如图所示的某算法程序框图，则输出量y 与输入量x 之间满足的关系式是 ________________11、若直线1:=+by ax l 与圆1:22=+y x C 有两个不同的交点，且点P 的坐标为),(b a ，则点P 与圆C 的位置关系是_____________12、已知0,0>>y x 且112=+yx ，若m m y x 222+>+恒成立，则实数m 的取值范围是_____________13、设函数)12(log )(2+=x x f 的反函数为)(1x fy -=，若关于x 的方程)()(1x f m x f +=-在]2,1[上有解，则实数m 的取值范围是_____________14、若椭圆)1(12222>>=+b a by a x 内有圆122=+y x ，该圆的切线与椭圆交于B A ,两点，且满足0=⋅OB OA （其中O 为坐标原点），则22169b a +的最小值是__________二、选择题（本大题满分20分）本大题共有4题，每题有且只有一个正确答案，考生应在答案纸的相应编号上，填写正确的答案，选对得5分，否则一律得零分.15、下列函数中，既是偶函数，又是在区间),0(+∞上单调递减的函数为 （ ）（A ）xx f 10)(= （B ）3)(x x f = （C ）xx f 1lg)(= （D ）x x f cos )(= 16、若等比数列}{n a 前n 项和a S nn +-=2，则复数ia iz +=在复平面上对应的点位于（ ）（A ）第一象限 （B ）第二象限 （C ）第三象限 （D ）第四象限 17、若函数⎩⎨⎧<+≥=11log )(2x c x x x x f ，则“1-=c ”是“)(x f y =在R 上单调增函数”的（ ）（A ）充分非必要条件 （B ）必要非充分条件 （C ）充要条件 （D ）既非充分也非必要条件18、若21,F F 分别为双曲线1279:22=-y x C 的左、右焦点，点A 在双曲线C 上，点M 的坐标为)0,2(，AM 为21AF F ∠的平分线，则2AF 的值为 （ ） （A ）3 （B ）6 （C ）9 （D ）27三、解答题（本大题满分74分）本大题共5题，解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤. 19、（本题满分12分）已知在正四棱锥ABCD P -中（如图），高为)(1cm ，其体积为)(43cm ，求异面直线PA 与CD 所成角的大小.20、（本题满分14分）本题共有2个小题，第1小题满分7分，第二小题满分7分. 在ABC ∆中，角C B A ,,的对边分别为c b a ,,，已知),2(a c b m -=，)cos ,(cos C A n -= ，且n m ⊥. 1.求角A 的大小； 2.若3=a ，ABC ∆面积为433，试判断ABC ∆的形状，并说明理由.21、（本题满分14分）本题共有2个小题，第1小题满分6分，第二小题满分8分. 若函数)(x f y =，如果存在给定的实数对),(b a ，使得b x a f x a f =-+)()(恒成立，则称)(x f y =为“Ω函数”.1.判断下列函数，是否为“Ω函数”，并说明理由： ① 3)(x x f = ② xx f 2)(=2.已知函数x x f tan )(=是一个“Ω函数”，求出所有的有序实数对),(b a22、（本题满分16分）本题共有3个小题，第1小题满分3分，第二小题满分6分，第三小题满分7分. 已知函数323)(+=x x x f ，数列}{n a 满足11=a ，)(1n n a f a =+，*N n ∈， 1.求432,,a a a 的值； 2.求证：数列⎭⎬⎫⎩⎨⎧n a 1是等差数列； 3.设数列{}n b 满足)2(1≥⋅=-n a a b n n n ，31=b ，n n b b b S +++= 21，若22012-<m S n 对一切*N n ∈成立，求最小正整数m 的值.23、（本题满分18分）本题共有3个小题，第1小题满分3分，第二小题满分6分，第三小题满分9分.已知ABC ∆的三个顶点在抛物线y x =Γ2:上运动， 1.求Γ的焦点坐标；2.若点A 在坐标原点，且2π=∠BAC ，点M 在BC 上，且满足0=⋅，求点M 的轨迹方程；3.试研究：是否存在一条边所在直线的斜率为2的正三角形ABC ，若存在，求出这个正三角形ABC 的边长，若不存在，说明理由.杨浦区2011学年度高三学科测试参考答案及评分标准一．填空题（本大题满分56分） 2011.12.31 1. 1-；2. 理()1,2-，文()1,0； 3. 理(]1,-∞-，文(]0,∞-；4. π12；5. 理14-，文4；6.2-；7.理0，文1；8.理0.35，文0.30； 9. 80；10.()⎩⎨⎧≤>-=1,21,2x x x x f x； 11.理 P 在圆外，文1；12. 理()2,4-，文⎥⎦⎤⎢⎣⎡5,22；13. 理⎥⎦⎤⎢⎣⎡53log ,31log 22 ，文()2,4-； 14. 理49，文⎥⎦⎤⎢⎣⎡53log ,31log 22二、选择题（本大题满分20分）本大题共有4题 15. C ； 16. A ； 17. A ； 18.B ；三、解答题（本大题满分74分）本大题共5题19. 【解】 设异面直线PA 与CD 所成角的大小θ， 底边长为a ,则依题意得 41312=⋅⋅a ……4分故32=a ， 62=∴AC()76122==+=∴PA ……7分CD ∥AB ，故直线PA 与AB 所成角的大小θ为所求 ……9分 721cos =∴θ721arccos=θ ． ……12分（其他解法,可根据上述【解】的评分标准给分） 20.理: （1）【解1】.由⊥ 得 0=⋅ ，故()0cos cos 2=--C a A c b , ……2分 由正弦定理得()0cos sin cos sin sin 2=--C A A C B ……4分()0sin cos sin 2=+-∴C A A B ……5分3,21cos ,0sin ,0ππ=∴=≠<<A A B A ……7分【解2】. 由()0cos cos 2=--C a A c b ，余弦定理得()0222222222=-+--+-ab c b a a bc a c b c b 整理得bc a c b =-+222，212cos 222=-+=∴bc a c b A3,21cos ,0ππ=∴=<<A A A ．（其他解法,可根据【解1】的评分标准给分）（2）433sin 21==∆A bc S ABC 即34333sin 21=∴=bc bc π ……10分又A bc c b a cos 2222-+=, 622=+∴c b ……12分故()302==∴=-c b c b 所以，ABC ∆为等边三角形． ……14分文:【解1】. 由 ()0cos cos 2=--C a A c b ,由正弦定理得()0cos sin cos sin sin 2=--C A A C B ……4分()0sin cos sin 2=+-∴C A A B ……5分3,21cos ,0sin ,0ππ=∴=≠<<A A B A ． ……7分【解2】. 由()0cos cos 2=--C a A c b ，余弦定理得()0222222222=-+--+-ab c b a a bc a c b c b 整理得bc a c b =-+222，212cos 222=-+=∴bc a c b A3,21cos ,0ππ=∴=<<A A A ．（其他解法,可根据【解1】的评分标准给分）21. （1）【解】①（理）若()3x x f =是“Ω函数”，则存在实数对()b a ,，使得()()b x a f x a f =-⋅+，即()b x a=-322时，对R x ∈恒成立 ……2分而322b a x -=最多有两个解，矛盾， 因此()3x x f =不是“Ω函数” (3)（文）若()x x f =是“Ω函数”，则存在实数对()b a ,，使得()()b x a f x a f =-⋅+，即()b x a=-22时，对R x ∈恒成立 ……2分而b a x -=22最多有两个解，矛盾， 因此()x x f =不是“Ω函数” ……3分② 答案不唯一：如取1,0==b a ，恒有12200=-+x x对一切x 都成立， ……5分即存在实数对()1,0，使之成立，所以，()xx f 2=是“Ω函数”．……6分一般地：若()x x f 2=是“Ω函数”，则存在实数对()b a ,，使得b a x a x a ==⋅-+2222 即存在常数对()aa 22,满足()()b x a f x a f =-⋅+，故()xx f 2=是“Ω函数”．（2）解 函数()x x f tan =是一个“Ω函数”设有序实数对()b a ,满足，则()()b x a x a =+⋅-tan tan 恒成立当Zk k a ∈+=,2ππ时，()()x x a x a 2cot tan tan -=+⋅-，不是常数； ……8分 因此Zk k a ∈+≠,2ππ，当Zm m x ∈+≠,2ππ时，则有b x a xa x a x a x a x a =--=-+⨯+-2222tan tan 1tan tan tan tan 1tan tan tan tan 1tan tan ， ……10分即()0)(tan tan 1tan222=-+-b a x a b 恒成立，所以Zk b k a b a b a a b ∈⎪⎩⎪⎨⎧=±=⇒⎩⎨⎧==⇒⎪⎩⎪⎨⎧=-=-⋅1411tan 0tan 01tan 222ππ ……13分当4,,2ππππ±=∈+=k a Z m m x 时，()()()1cot tan tan =-=+⋅-a x a x a满足()x x f tan =是一个“Ω函数”的实数对()Z k k b a ∈⎪⎭⎫⎝⎛±=,1,4,ππ……14分22. 理:（1）【解】由11=a ，()3231+==+n n n n a a a f a 得31,73,53432===a a a ……3分（2）【解】由3231+=+n n n a a a 得 32111=-+n n a a ……8分所以，⎭⎬⎫⎩⎨⎧n a1是首项为1，公差为32的等差数列 ……9分（3）【解】由（2）得()123,31213211+=+=-+=n a n n a n n (10)当2≥n 时 ，⎪⎭⎫⎝⎛+--==-121121291n n a a b n n n ，当1=n 时，上式同样成立， ……12分所以⎪⎭⎫⎝⎛+-=⎪⎭⎫ ⎝⎛++-+⋅⋅⋅+-+-=+⋅⋅⋅++=12112912112151313112921n n n b b b S n n 因为22012-<m S n ，所以22012121129-<⎪⎭⎫ ⎝⎛+-m n 对一切*∈N n 成立， ……14分又⎪⎭⎫ ⎝⎛+-121129n 随n 递增，且291211lim =⎪⎭⎫ ⎝⎛+-∞→n n ，所以2201229-≤m ，所以2021≥m ，2021min =∴m ……16分 文:(1) 【解】. 由y x =2得12=p 所以 准线为41-=y ……3分(2) 【解】. 由y x =2得12=p 所以,焦点坐标为⎪⎭⎫ ⎝⎛41,0 ……4分 由A 作准线41-=y 的垂线,垂足为Q ,当且仅当三点Q A P ,,共线时,AFAP +的最小值，为425416=+, ……7分此时A 点的坐标为()4,2 ……9分 (3)【解1】设点M 的坐标为()y x ,,BC 边所在的方程为1+=kx y (k 显然存在的), ① ……10分又AM 的斜率为x y ,则有1-=⋅k x y ,既y x k -=代入① ……14分 故M 点轨迹为)0(022≠=-+x y x y (注:没写0≠x 扣1分) ……16分【解2】设点M 的坐标为()y x ,,由BC 边所在的方程过定点)1,0(N , ……10分)1,(,),(y x y x --== ……12分0=⋅BC AM 0=⋅∴,所以, 0)1(=-+⋅-y y x x , 既)0(022≠=-+x y x y ……16分 (注:没写0≠x 扣1分)23. 理:(1) 【解】. 由y x =2得12=p 所以,焦点坐标为⎪⎭⎫ ⎝⎛41,0 ……3分(2) 【解1】设点M 的坐标为()y x ,,BC 边所在的方程为b kx y +=(k 显然存在的),与抛物线y x =2交于()()2211,,,y x C y x B 则⎩⎨⎧=+=2x y b kx y 得02=--b kx x ,,21k x x =+b x x -=21 ……5分又点C B ,在抛物线Γ上,故有222211,x y x y ==, 2222121b x x y y ==∴022121=+-=+=⋅∴b b y y x x 1=b 或0=b (舍)1+=∴kx y -------① ……7分又AM 的斜率为x y ,则有1-=⋅k x y ,既y x k -=代入① 故M 点轨迹为)0(022≠=-+x y x y (注:没写0≠x 扣1分) ……9分 另解:由上式①过定点)1,0(P ,)1,(,),(y x y x --== 0=⋅∴,所以, 0)1(=-+⋅-y y x x , 既)0(022≠=-+x y x y 【解2】设点M 的坐标为()y x ,,AB 方程为kx y =,由2π=∠BAC 得AC 方程为x k y 1-=,则⎩⎨⎧==2x y kx y 得()2,k k B , 同理可得⎪⎭⎫ ⎝⎛-21,1k k C∴BC 方程为))(11(222k x k k k k k y -+-=-恒过定点)1,0(P ,)1,(,),(y x y x --== 0=⋅∴,所以, 0)1(=-+⋅-y y x x , 既)0(022≠=-+x y x y (注:没写0≠x 扣1分)（其他解法,可根据【解1】的评分标准给分）(3) 【解1】若存在AB 边所在直线的斜率为2的正三角形ABC ,设),(,),(22q q B p p A , (其中不妨设q p <), 则222=--p q p q ,2=+∴q p ------① ……11分令a AB =,则()()22222a p q p q =-+-,即()()()2222a pq p q p q =-++-将①代入得,()223a p q =-,()q p ap q <=-∴ 3 -----------------② ……13分线段AB 的中点为M ,由①, ②得M 的横坐标为222=+q p ,M 的纵坐标为()()12214222222a p q p q q p +=-++=+ ……15分 又设()2,1= 由⊥得)23(,2,223123a a a a =⎪⎪⎭⎫ ⎝⎛±⋅=⎪⎪⎭⎫ ⎝⎛+±=⎪⎪⎭⎫ ⎝⎛±+⎪⎪⎭⎫ ⎝⎛+=+=∴21212,22222,221221,2222a a a a a a点C 在抛物线y x =2上,则()()2212166121a a a ±=+ ,即01852=±a a , 又因为0>a ,518=∴a ……18分【解2】 设),(,),(22q q B p p A ,),(2r r C ABC ∆的三边所在直线CA BC AB ,,的斜率分别是p r p r p r r q r q r q q p q p q p +=--+=--+=--222222,, ------① ……12分若AB 边所在直线的斜率为2,AB 边所在直线和x 轴的正方向所成角为()0900,<<x α,则2tan =α,所以()()⎪⎩⎪⎨⎧+=+-=+0060tan 60tan ααp r r q ……14分 即536,613260tan tan 160tan tan 613260tan tan 160tan tan 0000=-∴⎪⎪⎩⎪⎪⎨⎧-+=-+=++-=+-=+p q p r r q αααα-----② 又2tan ==+αq p --------------③ ……16分所以, ()()()()[]2222221p q p q p q p q AB ++-=-+-=将②, ③代入上式得边长518=AB ……18分 （其他解法,可根据【解1】的评分标准给分）文:（1）【解】由11=a ，()3231+==+n n n n a a a f a 得31,73,53432===a a a ……3分（2）【解】由3231+=+n n n a a a 得 32111=-+n n a a ……8分 所以，⎭⎬⎫⎩⎨⎧n a 1是首项为1，公差为32的等差数列 ……9分（3）【解】由（2）得()123,31213211+=+=-+=n a n n a n n……11分 当2≥n 时 ，⎪⎭⎫ ⎝⎛+--==-121121291n n a a b n n n ，当1=n 时，上式同样成立， ……13分 所以⎪⎭⎫ ⎝⎛+-=⎪⎭⎫ ⎝⎛++-+⋅⋅⋅+-+-=+⋅⋅⋅++=12112912112151313112921n n n b b b S n n 因为22012-<m S n ，所以22012121129-<⎪⎭⎫ ⎝⎛+-m n 对一切*∈N n 成立， ……16分 又⎪⎭⎫ ⎝⎛+-121129n 随n 递增，且291211lim =⎪⎭⎫ ⎝⎛+-∞→n n ，所以2201129-≤m ，所以2020≥m ， 2020min =∴m ……18分。

杨浦区2012学年度第一学期高三年级学业质量调研英语试卷2013. 1本试卷分为第I卷（第1-12页）和第II卷（第13页）两部分。

全卷共13页。

满分150分。

考试时间120分钟。

考生注意：1．答第I卷前，考生务必将条形码粘贴在答题纸的指定区域内。

2．第I卷（1-16小题，25---80小题）由机器阅卷，答案必须全部涂写在答题卡上。

考生应将代表正确答案的小方格用铅笔涂黑。

注意试题题号和答题卡编号一一对应，不能错位。

答案需要更改时，必须将原选项用橡皮擦去，重新选择。

答案写在试卷上一律不给分。

第I卷中的第17-24小题,81-84小题和第II卷的试题，其答案用钢笔或水笔写在答题纸的规定区域内，如用铅笔答题，或写在试卷上则无效。

第I卷（共105分）I.Listening Comprehension (30%)Section ADirections: In Section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.1. A. In a post office. B. On the campus.C. In a hotel.D. At the airport.2. A. Doctor and patient. B. Lawyer and client.C. Manager and customer.D. Passer and policeman.3. A. To book a ticket. B. To make complaints.C. To make an appointment.D. To consult a dentist.4. A. She has trouble in getting along with the professor.B. She regrets taking up much of the professor’s time.C. She knows the professor has been busy recently.D. She doesn’t know the professor has run into trouble.5. A. One. B. Two.C. Three.D. Four.6. A. Everyone failed in the exam. B. Everyone passed the exam.C. Sixty students passed the exam.D. All the students got sixty.7. A. It was tiring. B. It cost more money.C. It saved time.D. It was acceptable.8. A. It’s inconvenient to go to work. B. The job was not well paid.C. He didn’t like to have meetings.D. The working hours were not suitable.9. A. $10. B. $13.C. $18.D. $19.10. A. He feels the professor should be merciful.B. He considers the punishment too severe.C. He thinks it right to punish those students.D. He thinks the students deserve sympathy.Section BDirections: In Section B, you will hear two short passages, and you will be asked three questions on each of the passages. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. To charge battery. B. To take in empty bottles.C. To sell subway tickets.D. To exchange money.12. A. To donate it directly. B. To exchange it for a subway ticket.C. To withdraw the cash.D. To charge their credit cards.13. A. At bus stops. B. In schools.C. Outside the bank.D. In residential areas.Questions 14 through 16 are based on the following passage.14. A. 1200. B. 800,000.C. 15,000.D. 120,000.15. A. It is heavy with texts.B. It lacks visual materials.C. It has virtual tours and interactive maps.D. It provides details about price and requirements.16. A. Never trust any third-party website.B. Make contact with the school.C. Apply for a free campus visit.D. Try to be good enough.Section C Longer ConversationsDirections:In Section C, you will hear two longer conversations. The conversations will be read twice. After you hear each conversation, you are required to fill in the numbered blanks with information you have heard. Write your answers on your answer sheet.Blanks 17 through 20 are based on the following conversation.Complete the form. Write ONE WORD for each answer.Adam’s Tailor ShopItem: Cotton dustcoatStyle: The ____17____ designAlternation: 6 buttons in the front/two pockets only on the leftSpecial requirement: Not too _____18___Try-on day: Next ____19____ (Jan. 15th)Charge for tailoring: ____20____ yuanBlanks 21 through 24 are based on the following conversation.Complete the form. Write NO MORE THAN THREE WORDS for each answer.II. Grammar and vocabulary (25%)Section ADirections: Beneath each of the following sentences there are four choices marked A, B, C and D. choose the one answer that best completes the sentence.25.People who had lived _____ the horror and suffering of the war began to rebuild their nation.A. fromB. withC. byD. through26.The gangs were all dealing drugs, but Bob was _____ who got caught.A. someoneB. oneC. the oneD. anyone27. Life is a hospital _____ every patient is possessed by the desire to change his bed.A. thatB. whenC. whereD. whose28. Don’t spend time beating on a wall, _____ to change it into a door.A. hopeB. hopingC. hopedD. to hope29. A man can fail many times, but he isn't a failure _____ he begins to blame somebody else.A. even ifB. untilC. in caseD. once30. The tragedy calls for gun control measures _____ 26 people were killed in the school shootingin Newtown.A. whereB. thatC. whichD. why31. Mere words cannot match the depths of our sorrow, _____ our wounded hearts.A. nor they can healB. so they can healC. nor can they healD. so can they heal32. ______ you look into your heart that your vision will become clear.A. It is only whenB. Only whenC. When it is onlyD. Only when it is33. Don't let the sadness of your past and the fear of your future _____ the happiness of yourpresent.A. ruinB. to ruinC. ruiningD. ruined34. _____ the city's public school system should be open to the children of migrant workers hasbecome the focus of discussion.A. ThatB. WhatC. WhetherD. If35. -- Who _____ be phoning us at this time of night?-- It might be your sister.A. mightB. canC. dareD. must36. Always remember to get every bit of criticism _____ between two thick layers of praise.A. sandwichingB. being sandwichedC. having been sandwichedD. sandwiched37. _____ difficult explorations are, humans have never stopped moving forward.A. WhileB. DespiteC. AsD. However38. To avoid _____ off, you should be prepared to state how your contributions will benefit thecompany.A. layingB. to be laidC. being laidD. having been laid39. -- Do you bring the picture?-- Yes, I _____ it for a whole morning.A. looked forB. have looked forC. have been looking forD. had looked for40. My grandfather, _____ is often the case with old people, is fond of talking about good old days.A. whichB. suchC. asD. whatSection BDirections: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.The most difficult part of a Western-Chinese marriage is the cultural differences. The traditional Chinese culture is established on the Confucian philosophy, while the western culture is based on ancient Greek __41__. Cultural differences exist in almost every aspect and therefore __42__ also on relationships and marriage.From the traditional Chinese point of view, marriage is a relationship __43__ many aspects such as family, friends and relatives, while from the Western point of view, marriage is a contract signed between two people that is based on trust and love. Furthermore, Westerners’marriages __44__ more the independence and __45__ of the couple.That is why Westerners sometimes cannot understand why we Chinese need to support our relatives if we are asked to do so. Chinese need to maintain their “face” and “relations”. Even in a relationship, we are somehow still __46__ to our family and relatives. Our partner has to understand it and at least does not __47__ it.It is not easy to maintain Chinese-Western relationship. Cultural differences may result in __48__. Young Asian ladies are fond of western men because they believe they are more gentlemanly and in addition their appearances are more attractive. Western men may think Chinese ladies are gentler and more feminine.My suggestion for the cross-culture relationship is always trying to put yourself in other’s shoes: accepting rather than changing; always respecting your partner but clarifying your own red lines; showing your interest in his/her different culture and carefully commenting on it and so on.There are more and more cross-culture marriages __49__ recently. I would like to take this chance to sincerely wish them the very best in their love journeys.III. Reading Comprehension (50%)Section ADirections: For each blank in the following passages there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.A new research suggests that animals have a much higher level of brainpower than once thought. If animals do have intelligence, how do scientists measure it? Before defining animals’ intelligence, scientists defined what is not intelligence. Instinct is not intelligence. It is a skill __50__ into an animal’s brain by its genetic heritage（基因遗传）. Tricks can be learned by repetition, but no real thinking is __51__. Cuing, in which animals learn to do or not to do certain things by following outside signals, does not demonstrate intelligence. Scientists believe that insight, the ability to use tools, and communication using human language are all __52__ measures of the mental ability of animals.When judging animal intelligence, scientists look for insight, which they define as a flash of sudden understanding. When a young gorilla（大猩猩）could not reach fruit from a tree, she noticed crates (木板箱) on the lawn near the tree. She __53__ the crates into a pyramid, then climbed on them to reach her __54__. The gorilla’s insight allowed her to solve a new problem without trial and error.The ability to use tools is also an important sign of intelligence. Crows（乌鸦）use sticks to pry （撬开）peanuts out of cracks. The crow __55__ intelligence by showing it has learned what a stick can do. __56__, otters（水獭）use rocks to crack open crab shells in order to get at the meat.Many animals have learned to communicate using human language. One chimp can recognize and correctly use more than 250 __57__ symbols on a keyboard. These symbols __58__ human words. An amazing parrot can __59__ five objects of two different types. He can understand the difference between the number, color, and kind of object. The ability to __60__ is a basic thinking skill. In addition, he seems to use language to express his needs and __61__. When ill and taken to the animal hospital for his fi rst overnight stay, this parrot turned to go. “Come here!” he cried to a scientist who works with him. “I love you. I’m sorry. Wanna go back?”The research on animal intelligence raises important questions. If animals are smarter than __62__ thought, would that change the way humans interact with them? Would animals still be used for food, clothing, or __63__ experimentation? Finding the answer to these tough questions makes a difficult __64__ even for a large-brained, problem-solving species like our own.50. A. developed B. admitted C. programmed D. injected51. A. inherited B. involved C. instructed D. intended52. A. realistic B. unusual C. accurate D. effective53. A. piled B. assembled C. supported D. divided54. A. potential B. reward C. standard D. top55. A. explores B. expands C. explains D. exhibits56. A. Likewise B. Therefore C. However D. Otherwise57. A. magical B. flexible C. abstract D. permanent58. A. substitute for B. stand for C. appeal to D. carry out59. A. foresee B. determine C. combine D. distinguish60. A. classify B. justify C. qualify D. simplify61. A. satisfaction B. emotions C. gratitude D. beliefs62. A. objectively B. professionally C. previously D. scientifically63. A. electrical B. physical C. medical D. logical64. A. decision B. translation C. choice D. puzzleSection BDirections: Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.(A)Brigham Young University students can now receive the unconditional love of dogs without breaking rules prohibiting pets in university housing.Jenna Miller started her company Puppies for Rent this summer in the Provo area as a way for students and others to rent puppies by the hour.The pups have been rented for first dates and surprise parties and by mothers rewarding their children. After signing a contract, customers can rent them for $15 an hour, $25 for two hours and $10 for each additional hour.Miller offers her seven puppies for playtime rentals, with each dog hand delivered straight to the customers’ door. Her lawyer brother helps her with legal contracts and fees. She now has four employees helping look after and deliver the animal.Carl Arky, spokesman for the Humane Society of Utah said his group is against the business. Puppies need consistency and stability in their lives, he said, and renting them to various people might affect the animals' growth and development.Miller said the animals are treated well and she has a 100 percent success rate so far finding them a permanent home. Money paid by renters goes toward adoption fees if they decide to own a puppy.65. Which of the following are not possible renters of the p uppies?A. Young lovers.B. Party organizers.C. Mothers.D. Scientific group members.66. Miller’s brother’s main responsibility is to _____.A. draft contractsB. deliver animalsC. find adoption familiesD. walk dogs67. Why is Carl in disagreement with the service?A. Because playing with pets is harmful to children’s health.B. Because some people will be cruel to the rented animals.C. Because unstable living environment is not good for animal’s growth.D. Because it will prohibit the puppies from finding a permanent home.(B)TENANCY AGREEMENTDEFINITIONSTHE LANDLORD Mrs Gloria Black of 6 Sutton Road, Cambridge CB5 7AQTHE TENANT Marina KahnPROPERTY 24a Wood Road, Cambridge CB2 8BGTOGETHER WITH CONTENTS (fixtures, furniture and equipment) specified in the inventory (attached)TERM from 1 st January 20 ___ to 31 st December 20 ___ (12 months)RENT £500 per calendar month, payable in advance on the first day of each monthDEPOSIT £500, payable on commencement of this AgreementAGREEMENTSA The Landlord may re-enter the Property and terminate this Agreement if the Rent or any part ofit is not paid within fourteen days after it becomes due.B The Landlord may bring the tenancy to an end at any time before the expiry of the Term (butnot earlier than six months from the Commencement Date of this Contract) by giving the Tenant not less than tw o months’ written notice stating that the Landlord requires possession of the Property.C The Landlord shall put the deposit with the Deposit Protection Service, and shall inform theTenant within 14 days of taking the deposit of the contact details of this service and details of how to apply for the release of the deposit from this service.TENANT’S OBLIGATIONS1Pay the Rent into the Landlord’s bank account at the times specified.2Pay for all water, gas and electricity consumed on the Property during the Term; and pay in full for all charges made for the use of the telephone on the Property during the Term.3Keep the interior of the Property during the Term in a good and clean state of repair, condition and decoration.4Permit the Landlord to enter the Property at all reasonable times; to inspect the Property and its contents; and to carry out any works of maintenance or repair to the Property; to show prospective new Tenants around the Property at the end of the tenancy.5Not take in any paying guest without the prior written consent of the Landlord.6Not use the Property other than as a private dwelling; nor carry on any profession, trade or business in the Property.7Not use any musical instrument, wireless or television between midnight and 7 am, nor permit any singing or dancing between these hours.8Not keep in the Property any cat, dog or other pet without the prior written consent of the Landlord.68. What’s the monthly rent of the property?A. £500.B. £575.C. £1000.D.£1500.69. What’s the landlord’s witness?A. A teacher.B. A librarian.C. A house agent.D. A bank clerk.70. Which of the following is allowed in the property?A. Watching TV at any time.B. Holding an all-night dancing party.C. Changing it into a business office.D. Entertaining friends with self-cooked meals.71. Which of the following is the right of the landlord?A. He can show new tenants around the property at any time.B. He can enter the property to inspect its contents.C. He can take back his property whenever he wants.D. He can keep the deposit for himself.(C)Does solving a math problem give you a headache? Do you feel nervous when you sit a math exam? For most students, math can be tough but scientists have proved that math problems can actually trigger physical pain.Scientists came to this conclusion with an in-depth experiment, which was published in the Public Library of Science One journal. They began by finding out how much participants fear math. Those involved were asked a series of questions such as how they feel when they receive a math textbook or when they walk into a math lesson.Based on their answers, participants were divided into groups. One group was made up of people who were particularly afraid of math and participants in the other group were more comfortable with the subject.Both groups were then given either math tasks or word tasks. When a math task was going to come next, a yellow circle would appear but when a word task was soon to come, a blue square would be shown.Using a brain-scan machine, scientists noticed that whenever people from Group One saw a yellow circle, their brain would respond in a way similar to when their body is feeling pain. It was like the pain they would feel, for example, if they burnt their hand on a hot stove. But they reacted less strongly when they knew that they would be faced with a word task.However, scientists saw no strong brain response from people in the second group.Math can be difficult, and for those with high levels of mathematics-anxiety (HMA), math is associated with tension, apprehension and fear. “When you are really thinking about the math problems, your mind is racing and you are worrying about all the things that could go wrong,”explained Ian Lyons from University of Chicago, US, leader of the study. “The higher a person’sanxiety of a maths task, the more he activated brain regions associated with threat detection, and the experience of pain.”More interestingly, the brain activity disappeared when participants actually started dealing with the math tasks. “This means that it’s not that math itself hurts; rather, the anticipation of math is painful,” Lyons said.Based on the study, scientists suggested that things could be done to help students worry less and move past their fear of math, which might mean they perform better in tests.72. In the first stage, scientists ask participants some questions to _____.A. see whether math hurtsB. find out how much they fear mathC. observe how their brain responseD. test their endurance of pain73. The underlined word “the anticipation of math” is closest in meaning to _____.A. the attempt of learning mathB. the motivation to work out math problemC. the effort to understand mathD. the act of thinking about math74. Which is the best title for the passage?A. How to overcome math fear.B. Physical pain affects math performance.C. Math pain in your brain.D. Unknown truth about pain.75. What can be concluded from the experiment?A. The anticipation of math has no relation to students’ confidence in math.B. Moderate mathematic anxiety promotes students’ academic performance.C. Effective solutions have been worked out to lower students’ anxiety of math.D. Physical pain caused by HMA disappears in the process of doing math problem.Section CDirections:Read the following text and choose the most suitable heading from A-F for each paragraph. There is one extra heading which you do not need.Britain may be the most red-headed country in the world. About 1 to 2 percent of the world’s population has red hair, but in the UK the numbers are much higher, with 13 percent of Scots, 10 percent of the Irish, and 6 percent of people in England having red hair, according to the BBC.Scientists have tried to explain why some people have red hair for some time and now they may have found an answer: the dull weather in Britain. The human body needs vitamin D from sunshine, but unfortunately people living in Britain do not have enough of it because of its maritime climate. In fact, Britain gets even more cloud than countries in the far north of Europe. In Sweden, for example, the average daily hours of sunshine is 5.4. In Scotland it is only 3.1 hours.To deal with this, the DNA of people living in these areas has changed slightly; scientists call this a mutation. Originally, the coloring on our body is a mixture of two kinds of melanin – black melanin and red/yellow melanin, but with certain parts of DNA changed, the production of black melanin is suppressed while only red/yellow melanin is made. The result is red hair, light skin color, freckles and a greater sensitivity to sunlight.However, what’s more interesting is that the redhead DNA mutation is recessive, which means it is hidden and can often skip generations without showing. At least 1.6 million Scots carry a red-head gene mutation, and most are unaware that they do. This is why a person who does not have red hair can still produce red-haired children if he or she is a carrier of this special DNA.The research on red hair, like many areas of science, is contradictory. In 2002 researchers showed that redheads are more sensitive to pain, and need more anaesthetic during surgery than people with blonde or dark hair. However, in 2005 scientists found that a MCR1R mutation gives redheads a higher tolerance for pain. Research into these aspects of red hair genetics continues. Redheads should though be more careful about their exposure to sunlight as they are at an increased risk of contracting skin cancer. If you are a redhead, the advice is not to stay out of the sun, but to be careful about how much exposure you get, and to cover yourself with a high factor sunscreen.Section DDirections: Read the passage carefully. Then answer the questions or complete the statements in the fewest possible words.Pizza Hut lovers, you can now smell just like your favorite food. Pizza Hut launches its own perfume that smells like a fresh pizza pie. This is not a joke – although it started as one! While it might seem like an unusual venture for the brand famous for pizza, the company’s perfume is already available as a limited edition product.According to the Globe and Mail, the project started out as a joke by Grip Limited, an advertising firm that works with Pizza Hut in Canada, who asked the chain’s Facebook fans to imagine the pleasant smell of a fresh-delivered pie as a perfume – and to name it. Fans responded tothe idea so enthusiastically that Grip Limited decided to take the joke a step further and make the perfume a reality.A month and a half later, to celebrate that Pizza Hut Canada had gotten 100,000 fans, the chain's community managers announced that the first 100 people to message them would actually get a bottle of Pizza Hut perfume. And sure enough, the bottles were shipped to those 100 lucky fans before Christmas.Grip Limited isn’t the only company to attract attention with odd aromas（芳香）. Four years ago, Burger King offered a $4 meat-scented body spray for men. Before that in 2006, Stilton created a perfume meant to mimic（模拟）the scent of blue cheese.Pizza Hut Canada has not announced any plans to make more of the perfume in the future. But the chain also said in the release that it’s possible the perfume could appear in stores in the future. (Note: Answer the questions or complete the statements in NO MORE THAN TEN WORDS)81. Some people consider the perfume a joke because they think Pizza Hut is a ______________.82. ___________________________ pushed Grip Limited to turn the joke into reality.83. Who are the lucky birds to get the perfume?______________________________________________.84. Why did Pizza Hut follow Burger King’s steps to release a perfume?______________________________________________.第II卷（共45分）I. Translation （20%）Directions: Translate the following sentences into English, using the words given in the brackets.1. 任何人都会犯错，但只有傻瓜坚持他的错误。

2012学年度第一学期初三期中质量调研化学（满分100分，考试时间90分钟） 2012.11考生注意：1.本试卷共三个大题。

2.答题时考生务必按答题要求在答题纸规定的位置上作答，在草稿纸、试卷上答题一律无效。

可能用到的相对原子质量：H—1 C—12 N—14 O—16 S—32 K—39 Cr—52一、选择题（共25分，每题均只有一个正确选项）1.下列选项中不属于化学研究范畴的是A. 研发低成本制取清洁能源B. 用石油生产多种化工产品C. 用植物秸杆合成可降解塑料D. 培育农作物新品种，增加农作物产量2.千姿百态的物质世界存在着多种相互作用，也不断发生变化．下列变化属于化学变化的是 A．食物腐烂B．玻璃破碎C．车胎爆炸D．冰雪融化3.空气的成分中，约占空气总体积78%的气体是A. 氧气B. 氮气C. 稀有气体D. 二氧化碳4. 水是生命之源，以下生活中的“水”属于纯净物的是A．蒸馏水 B．泉水C．雨水D．矿泉水5.下列仪器不宜用作化学反应容器的有A．试管 B．烧杯C．燃烧匙D．量筒6.地壳中含量最多的非金属元素和含量最多的金属元素组成化合物的化学式为A．SiO2 B．Al2O3 C．Fe2O3 D．CaO7.下列物质在氧气中充分燃烧，生成黑色固体的是A.白磷B.木炭C.硫D.铁丝8.正确的实验操作对实验结果、人身安全都非常重要。

下列实验操作正确的是9. 下图是用向下排空气法收集气体，正确的操作是10. 焊接金属时，为了隔绝空气，常需要在高温条件下化学性质稳定的气体作保护气。

下列各组气体中都能作为保护气的一组是A．N2 O2B．N2 Ar C．CO2 CO D．N2 H211.由于涉嫌铬超标，国家食品药品监督管理局4月16日发出紧急通知，要求对13个药用空心胶囊产品暂停销售和使用。

下列有关铬（Cr）的化合物的叙述错误的是A．在Cr(OH)3中铬、氧、氢三种元素的原子个数比1﹕3﹕3B．K2Cr2O7由三种元素组成C．在K2Cr2O7中铬元素的化合价为+6价D．在K2Cr2O7中铬元素的含量最高12.元素R在化合物中只有一种化合价，下列化学式有错的是A、RNO3B、RCl3C、R2O3D、R2(SO4)313.水族馆中，表演者常常携带氧气瓶在水中与鱼“共舞”。

杨浦区2011学年度第一学期高三学科测试历史试卷参考答案一、选择题选不得分；30题选B给3分、选A给1分选C、D为0分；31题选D给3分、选C给1分，选A、B为0分；32题选C给3分、选B给1分选、AD为0分；33题选D给3分、选C给1分选、AB为0分）二、非选择题：34、（8分）（1）特点：岛屿众多，海岸线曲折（2分）影响：有利于商业贸易和航海殖民；（1分）对雅典城邦政治和多元文化产生等都有一定的影响。

（1分）（2）雅典（2分）；以民主政治而著称。

（2分）35、（12分）（1）孔子以“仁”作为最高的道德准则，有利于建立和谐的人际关系（2分）以“礼”规范人们的言行，有利于实现社会秩序的安定。

（2分）（2）汉武帝时期的董仲舒提出“天人感应”之说，（1分）政治上认为王者受命于天，倡导“君权神授”（1分）伦理上强调“三纲五常”，（1分）顺从了汉武帝加强中央集权的需要提出了“大一统”的主张（2分）从而使儒家的学说扩展到中央集权的官僚政治中去。

（1分）（3）汉代以来，儒家思想逐渐成为历代封建王朝的统治思想。

（2分）36、（10分）（1）英法资产阶级通过武装斗争或自下而上的革命手段，推翻本国封建专制统治，同时为资本主义发展扫除障碍。

（2分）在革命期间或革命后采用法律的形式，保证公民的民主权利，以巩固革命成果。

（2分）例如英国议会颁布《权利法案》限制王权，保证了议会的最高权力，为英国的君主立宪制度奠定了基础；（2分）法国革命中发表《人权宣言》和《拿破仑法典》等法律文件，为限制王权专制，保证公民的民主权利提供了法律保证。

（2分）（2）以民主代替专制（1分）以法治代替人治（1分）37、（12分）（1）特点：采用国家大规模干预经济的手段；（2分）实质：在一定程度上调整资本主义生产关系。

（2分）（2）不同意。

（1分）首先新政的实施主要是依赖于美国雄厚的经济实力。

例如政府出资成立联邦储蓄保险公司对小额存款提供信用保障；以工代赈、建立养老金制度等措施都依赖于政府的资金支持；（2分）其次主张国家干预经济的凯恩斯主义也为新政提供了理论依据；（2分）新政的措施中除了经济调控外，还加大了社会保障力度，实行失业救济等措施，在一定程度上起到了缓和阶级矛盾化解危机的作用。

杨浦区2011学年度高三学科测试化学试卷 2011.12本试卷分为第I 卷(第1—4页)和第Ⅱ卷(第5—8页)两部分。

全卷共8页。

满分l50分，考试时间l20分钟。

第I 卷 (共66分)考生注意：1．答第I 卷前，考生务必在答题卡上用钢笔或圆珠笔清楚填写学校、姓名、准考证号，并用2B 铅笔正确涂写准考证号。

2．第I 卷(1-22小题)，由机器阅卷，答案必须全部涂写在答题卡上。

考生应将代表正确答案的小方格用2B 铅笔涂黑。

注意试题题号和答题纸编号一一对应，不能错位。

答案需要更改时，必须将原选项用橡皮擦去，重新选择。

答案不能涂写在试卷上，涂写在试卷上一律不给分。

相对原子质量：H-1 C-12 N-14 O-16 F-19 S-32 Cl-35.5 Fe-56一、选择题(本题共10分，每小题2分，只有一个正确选项。

)1．卢瑟福的α粒子散射实验证明原子中存在A ．α粒子B ．电子C ．中子D ．原子核2．我国是世界最大的耗煤国家。

下列对煤综合利用的叙述错误的是A ．煤的气化是化学变化B ．煤的干馏是物理变化C ．煤的液化是化学变化D ．煤焦油分馏出苯的同系物是物理变化3．已知：C(金刚石，固)C(石墨，固) +1.9kJ ，则下列判断正确的是A ．金刚石转变为石墨可用右图表示B ．等质量的石墨比金刚石能量高C ．石墨比金刚石稳定D ．金刚石转化为石墨没有化学键的断裂与生成4．下列对化学用语的理解正确的是A 12C ，也可以表示13CB ．比例模型：表示二氧化碳分子，也可以表示水分子C ．电子式 ：表示羟基，也可以表示氢氧根离子D ．结构简式(CH 3)2CHOH ：表示2–丙醇，也可以表示1–丙醇5．下列物质发生变化时，所克服的粒子间相互作用属于同种类型的是A ．液溴和己烷分别受热变为气体B ．干冰和氯化铵分别受热变为气体C ．硅和铁分别受热熔化D ．氯化氢和蔗糖分别溶解于水二、选择题(本题共36分，每小题3分，只有一个正确选项。

杨浦区2012学年度第一学期高三年级学业质量调研数学试卷（文、理科） 2013.1.考生注意： 1．答卷前，考生务必在答题纸写上姓名、考号, 并将核对后的条形码贴在指定位置上．2．本试卷共有23道题，满分150分，考试时间120分钟．一．填空题（本大题满分56分）本大题共有14题，考生应在答题纸相应编号的空格内直接填写结果，每个空格填对得4分，否则一律得零分． 1. 若函数()x x f 3=的反函数为()x f 1-，则()=-11f．2．若复数ii z -=1 (i 为虚数单位) ，则=z .3．抛物线x y 42=的焦点到准线的距离为 . 4. 若线性方程组的增广矩阵为⎪⎪⎭⎫⎝⎛211321，则该线性方程组的解是 ． 5．若直线l :012=--x y ，则该直线l 的倾斜角是 . 6. 若7)(a x +的二项展开式中，5x 的系数为7，则实数=a ． 7. 若圆椎的母线cm 10=l ,母线与旋转轴的夹角030=α,则该圆椎的侧面积为 2cm .8. 设数列}{n a (n ∈*N )是等差数列.若2a 和2012a 是方程03842=+-x x 的两根，则数列}{n a 的前2013 项的和=2013S ______________．9. （理）下列函数：① xx f 3)(=, ②3)(x x f =, ③xx f 1ln)(= ， ④2cos)(xx f π=⑤1)(2+-=x x f 中,既是偶函数，又是在区间()∞+,0上单调递减函数为 （写出符合要求的所有函数的序号）.（文）若直线l 过点()1,1-，且与圆221x y +=相切，则直线l 的方程为 ．10.将一颗质地均匀的骰子连续投掷两次，朝上的点数依次为b 和c ， (文) 则2≤b 且3≥c 的概率是____ ___ .(理) 则函数c bx x x f ++=2)(2图像与x 轴无公共点的概率是____ ___ . 11.若函数1)23(log )(+-=x a x f (1,0≠>a a )的图像过定点P ,点Q 在曲线 022=--y x 上运动,则线段PQ 中点M 轨迹方程是 ． 12．如图，已知边长为8米的正方形钢板有一个角锈蚀，其中4AE =米，6C D =米. 为了合理利用这块钢板,将在五边 形A B C D E 内截取一个矩形块B N P M ，使点P 在边D E 上. 则矩形BNPM 面积的最大值为____ 平方米 .13．(文)设ABC ∆的内角C B A 、、的对边长分别为c b a 、、，且c A b B a 53cos cos =- ，则B A cot tan 的值是___________．(理)在ABC ∆中，若4π=∠A ，7)tan(=+B A ，23=AC ，则ABC ∆的面积为___________．14．(文) 已知函数()()⎩⎨⎧≤-->+=.0,2,0,1log 22x x x x x x f 若函数()()m x f x g -=有3个零点， 则实数m 的取值范围是___________． (理)在平面直角坐标系xOy 中，直线mx y 23+=与圆222n yx =+相切，其中、m n ∈*N ，10≤-<n m ．若函数()n m x f x -=+1的零点()1,0+∈k k x ，Z k ∈, 则=k ________．二、选择题（本大题满分20分）本大题共有4题，每题有且只有一个正确答案，考生应在答题纸的相应编号上，填上正确的答案，选对得5分，否则一律得零分.15． “3=a ”是“函数22)(2+-=ax x x f 在区间[)+∞,3内单调递增”的………（ ）)(A 充分非必要条件． )(B 必要非充分条件． )(C 充要条件． )(D 既非充分又非必要条件．16．若无穷等比数列{}n a 的前n 项和为n S ，首项为1，公比为23-a ，且a S n n =∞→lim ，A MEPDCBNF(n ∈*N )，则复数ia z +=1在复平面上对应的点位于 ………（ ）)(A 第一象限． )(B 第二象限． )(C 第三象限． )(D 第四象限．)(A． )(B)(C． )(D ．18. 已知数列{}n a 是各项均为正数且公比不等于1的等比数列（n ∈*N ）. 对于函数()y f x =，若数列{}ln ()n f a 为等差数列，则称函数()f x 为“保比差数列函数”. 现有定义在(0,)+∞上的如下函数：①1()f x x=， ②2()fx x =， ③()e x f x =， ④()f x =，则为“保比差数列函数”的所有序号为 ………（ ）)(A ①②． )(B ③④． )(C ①②④． )(D ②③④ ．三、解答题（本大题满分74分）本大题共5题，解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤 .19．（本题满分12分）本题共有2个小题，第1小题满分5分，第2小题满分7分 ． 如图，在三棱锥ABC P -中，⊥PA 平面ABC ，AB AC ⊥，4==BC AP ，︒=∠30ABC ,E D 、分别是AP BC 、的中点， （1）求三棱锥ABC P -的体积；（2）若异面直线AB 与ED 所成角的大小为θ，求θtan 的值.20．（本题满分14分）本题共有2个小题，第1小题满分7分，第2小题满分7分 ．PABCDE(文) 已知函数π()cos()4f x x =-，（1）若()10f α=，求sin 2α的值；（2）设()()2g x f x f x π⎛⎫=⋅+⎪⎝⎭，求()g x 在区间ππ,63⎡⎤-⎢⎥⎣⎦上的最大值和最小值. （理）已知 x x x f 2sin 22sin 3)(-= ，（1）求)(x f 的最小正周期和单调递减区间；（2）若⎥⎦⎤⎢⎣⎡-∈3,6ππx ，求)(x f 的最大值及取得最大值时对应的x 的取值．21．（本题满分14分）本题共有2个小题，第1小题满分6分，第2小题满分8分 ． （文）已知椭圆:C 22221(0)x y a b ab+=>>的两个焦点分别是()0,11-F 、()0,12F ，且焦距是椭圆C 上一点P 到两焦点21F F 、距离的等差中项. （1）求椭圆C 的方程；（2）设经过点2F 的直线交椭圆C 于N M 、两点，线段M N 的垂直平分线交y 轴于点),0(0y Q ，求0y 的取值范围.已知函数)0(121)(>-=x x x x f 的值域为集合A ，（1）若全集R U =，求A C U ； （2）对任意⎥⎦⎤⎝⎛∈21,0x ，不等式()0≥+a x f 恒成立，求实数a 的范围； （3）设P 是函数()x f 的图像上任意一点，过点P 分别向直线x y =和y 轴作垂线，垂足分别为A 、B ，求PB PA ⋅的值．23．（本题满分18分）本题共有3个小题，第1小题满分4分，第2小题满分6分，第3小题满分8分.(文) 设数列{}n x 满足0>n x 且1≠n x （n ∈*N ）,前n 项和为n S ．已知点),(111S x P , ),(222S x P ,()n n n S x P ,,⋅⋅⋅都在直线b kx y +=上(其中常数k b 、且0≠k ,1≠k ， 0≠b ),又n n x y 21log=．（1）求证：数列{}n x 是等比数列； （2）若n y n 318-=，求实数k ，b 的值；（3）如果存在t 、∈s *N ，t s ≠使得点()s y t ,和点()t y s ,都在直线12+=x y 上．问是否存在正整数M ，当M n >时，1>n x 恒成立？若存在，求出M 的最小值，若不存在，请说明理由．（理）对于实数x ，将满足“10<≤y 且y x -为整数”的实数y 称为实数x 的小数部分，用记号x 表示，对于实数a ，无穷数列{}n a 满足如下条件：⎪⎩⎪⎨⎧=≠==+.0,0,0,1,11n n nn a a a a a a 其中⋅⋅⋅=,3,2,1n .（1）若2=a ，求数列{}n a ；（2）当41>a 时，对任意的n ∈*N ，都有a a n =，求符合要求的实数a 构成的集合A ．（3）若a 是有理数，设qp a = （p 是整数，q 是正整数，p 、q 互质），问对于大于q 的任意正整数n ，是否都有0=n a 成立，并证明你的结论．。

考场班级______ 座位号_______ 班级__________ 姓名___________ 学号____________……………………………………………………………密………………封………………线……………………………………………………………2012学年度第一学期七年级数学期中考试卷（满分100分，考试时间 90分钟） 2012.11一、填空题(每空2分，共42分) 1、用代数式表示“比x 的523倍还少4”为 _____ 2、当32=x 时，代数式12-x 的值是 _____3、当3=a ，23-=b 时，代数式ab a -2的值是 _____4、若代数式12-+x x 的值为3，则代数式2313131x x +-的值是 _____5、将多项式y x y x xy y x 423264357+-+-按字母x 降幂排列 __________6、若一个长方形的长是y x 52+，宽是y x 34-，则这个长方形的周长是 _____ ，面积是 _____7、计算（直接写出结果）①)23(5--a a = ___________________ ②2265231xy xy xy+-= _________________③ )2()3(33m m -⋅-= _______________ ④ 3242)3(54a a a -+⋅= ________________ ⑤ 454)125.0(42-⨯⨯= ______________ ⑥ )3)(23(b a b a -+= __________________ ⑦ )52)(52(x x +-= _________________ ⑧ 2)21(-y = ____________________⑨ )4)(2)(2(2-+-m m m = ____________________ ⑩)1)(1()3(2x x x -+-+-= ____________________8、已知关于x 的代数式4)1(2+--x a x 是完全平方式，则a = ___ 9、因式分解：① ()()=---y a y a y 5_______________ ② =-164m _________________10、已知2<a ，如果一个正方形的面积是22)44(cm a a +-，则这个正方形的周长是____ ______ cm .二、选择题（每小题2分，共8分）11、单价为每千克a 元的甲种糖果m 千克与单价为每千克b 元的乙种糖果n 千克，混合后的平均价格是 ( ) A ．nm b a ++ B.ba n m ++ C.nm bn am ++ D.ba bn am ++12、下列说法正确的是 ( )A ．3y x +与yx 1+都是多项式 B. 52z xy -的系数与次数分别是-5与4C ．31与4是同类项 D.31+x 是单项式13、下列运算正确的是 ( )A. 844743x x x =+B. 6321243a a a =⋅C. 1099222=+D. n n n b a b a +=+)(14、下列各式可以用完全平方公式因式分解的是 ( )A. 2242y xy x +-B. 222b ab a --C. 4142+-m m D. 269x x +-三、计算（每题4分，共20分）15、)]3(32[222x y xy xy y x --- 16、657312---a a17、22)32()5643(ab ab b a -⋅-18、)2)(3(2)7)(2(x x x x +--+-19、)32)(32(8)2(2--+---+b a b a ab b a四、因式分解（每题4分，共16分）20、))((2)(82n m n m n m -+-+ 21、22)(4)(9y x y x --+22、81)6(18)6(222++++a a a a 23、4224168y y x x +-五、解答题（第24、25题各5分，第26题4分，共14分）24、化简求值：)33(3)()3(3223222ab b a b a ab b ab a ab -+--+-其中43-=a ，32=b25、已知：正方形ABCD 与正方形AEFG ，点E 、G 分别在边AB 、AD 上，正方形ABCD 的边长为a ，正方形AEFG 的边长为b ，且b a >。

杨浦区2012学年第一学期六年级期中质量调研数学试卷(考试时间90分钟，满分100分)题号一二三四五总分得分一、填空题：（本大题共14题，每题2分，满分28分）1.6和18的最大公因数是________2.把48分解素因数：48=________________3.15的所有因数的和是________4.在数5、7、9、15、17、21、23、27、33、37、57、97中，素数有______个5.将除法57÷的商表示成分数：57=÷_______6.如果的总体表示1，那么用最简分数表示为_________7.在括号内填入适当的数：() 25=4088.用最简分数表示：2小时35分=________小时9.比较大小：56_____78（填“>”、“<”、或“=”）10.计算：73128-=________11.计算：32343⨯=_______12.在人民广场，地铁1号线每3分钟发车，地铁8号线每5分钟发车，如果地铁1号线和地铁8号线早上6点同时发车，那么至少再经过__________分钟它们又同时发车。

13.某校某班（总人数超过10人但少于30人）参加秋游，如果每4人分为一组，则余2人，如果每5人分为一组，则余1人，这个班级共有________人。

14.写出一个大于23且小于34的最简分数：_________二、选择题：（本大题共4题，每题2分，满分8分）15.下列各数中，能同时被2、3、5整除的数是………………………………（）（A）20 （B）25 （C）30 （D）3516.下列说法中错误的是……………………………………………………（）（A）最小的素数是2 （B）1既不是素数也不是合数（C）两个素数一定互素（D）互素的两个数一定都是素数17.分数234介于两个相邻整数之间，这两个整数是………………………（）（A）4与5 （B）5与6 （C）6与7 （D）7与818.下列说法中：①互为倒数的两个数之积为1；②任何数都有倒数；③互为倒数的两个数一定不相等；④互为倒数的两个数之和为0；⑤互为倒数的两数可能相等，其中错误说法的序号是……………………………………（）（A）①②③（B）②③④（C）②④⑤（D）③④⑤三、简答题：（本大题共6题，每题6分，满分36分）19.用短除法求45与27的最大公因数和最小公倍数。

2012-2013学年上海市杨浦区九年级(上)期中数学试卷2012-2013学年上海市杨浦区九年级（上）期中数学试卷2012-2013学年上海市杨浦区九年级（上）期中数学试卷一、选择题1．（3分）下列各组线段中，成比例线段的一组是（）A．1，2，3，4 B．2，3，4，6 C．1，3，5，7 D．2，4，6，82．（3分）（2010•嘉定区一模）如图，已知AB ∥CD∥EF，BD：DF=2：5，那么下列结论正确的是（）A．A C：AE=2：5B．A B：CD=2：5C．C D：EF=2：5D．C E：EA=5：7 3．（3分）在△ABC中，∠C=90°，cosA=，那么sinA的值等于（）A．B．C．D．4．（3分）下列命题中，假命题的是（）A．两个等边三角形一定相似B．有一个锐角相等的两个直角三角形一定相似C．两个全等三角形一定相似D．有一个锐角相等的两个等腰三角形一定相似5．（3分）下列各组条件中一定能推得△ABC与△DEF相似的是（）A．B．，且∠A=∠EC．，且∠A=∠D D．，且∠A=∠D6．（3分）如图，在△ABC中，D、E在AB边上，且AD=DE=EB，DF∥BC交AC于点F，设，，下列式子中正确的是（）A．B．C．D．二、填空题：7．（3分）若，且a+b+c=15，则a=_________．8．（3分）线段3和6的比例中项是_________．9．（3分）等边三角形的中位线与高之比为_________．10．（3分）点P是线段AB的黄金分割点（AP＞BP），则= _________．11．（3分）如果，那么用、表示为：=_________．12．（3分）（2010•徐汇区一模）如图：在△ABC中，∠C=90°，AC=12，BC=9．则它的重心G到C点的距离是_________．13．（3分）在△ABC中，∠A与∠B是锐角，sinA=，cotB=，那么∠C=_________度．14．（3分）（2010•徐汇区一模）如图，直线l1∥l2∥l3，已知AG=0.6cm，BG=1.2cm，CD=1.5cm，CH=_________cm．15．（3分）（2010•徐汇区一模）如图，△ABC中，AB＞AC，AD是BC边上的高，F是BC的中点，EF⊥BC交AB于E，若BD：DC=3：2，则BE：AB=_________．16．（3分）（2012•南宁模拟）如图，将一副直角三角板（含45°角的直角三角板ABC及含30°角的直角三角板DCB）按图示方式叠放，斜边交点为O，则△AOB与△COD的面积之比等于_________．17．（3分）（2010•嘉定区一模）如图：在△ABC中，点D 在边AB上，且∠ACD=∠B，过点A作AE∥CB交CD的延长线于点E，那么图中相似三角形共有_________对．18．（3分）（2012•安徽）如图，P是矩形ABCD内的任意一点，连接PA、PB、PC、PD，得到△PAB、△PBC、△PCD、△PDA，设它们的面积分别是S1、S2、S3、S4，给出如下结论：①S1+S2=S3+S4；②S2+S4=S1+S3；③若S3=2S1，则S4=2S2；④若S1=S2，则P点在矩形的对角线上．其中正确的结论的序号是_________（把所有正确结论的序号都填在横线上）．三、解答题19．（6分）计算：cos60°+sin45°•tan30°．20．（6分）如图，在平行四边形ABCD中，点F在AD边上，BA的延长线交CF的延长线于点E，EC交BD于点M，求证：CM2=EM•FM．21．（6分）已知非零向量，，（1）求作：；（2）求作向量分别在，方向上的分向量．注：不写作法，但须说明结论．22．（6分）如图，梯形ABCD中，AD∥BC，AD=2，BC=6，DC=5，梯形ABCD的面积S ABCD=16，求∠B的余切值．23．（6分）如图，点P是等腰△ABC的底边BC上的点，以AP为腰在AP的两侧分别作等腰△AFP和等腰△AEP，且∠APF=∠APE=∠B，PF交AB于点M，PE交AC于点N，连接MN．求证：MN∥BC．24．（8分）在△ABC中，AC=2，AB=3，BC=4，点D在BC边上，且CD=1（1）求AD的长；（2）点E是AB边上的动点（不与A、B重合）连接ED，作射线DF交AC边于点F，使∠EDF=∠BDA．请补全图形，说明线段BE与AF的比值是否为定值？请证明你的结论．25．（8分）如图，tan∠MAB=2，AB=6，点P为线段AB上一动点（不与点A、B重合）．过点P作AB的垂线交射线AM于点C，连接BC，作射线AD交射线CP于点D，且使得∠BAD=∠BCA，设AP=x（1）写出符合题意的x的取值范围；（2）点N在射线AB上，且△ADN∽△ABC，当x=2时，求PN的长；（3）试用x的代数式表示PD的长．2012-2013学年上海市杨浦区九年级（上）期中数学试卷参考答案与试题解析一、选择题1．（3分）下列各组线段中，成比例线段的一组是（）A．1，2，3，4 B．2，3，4，6 C．1，3，5，7 D．2，4，6，8考点：比例线段．分析：如果其中两条线段的乘积等于另外两条线段的乘积，则四条线段叫成比例线段．对选项一一分析，排除错误答案．解答：解：A、1×4≠2×3，故本选项错误；B、2×6=3×4，故本选项正确；C、1×7≠3×5，故本选项错误；D、2×8≠4×6，故本选项错误．故选B．点评：本题考查了比例线段，熟记成比例线段的定义是解题的关键．注意在线段两两相乘的时候，要让最小的和最大的相乘，另外两条相乘，看它们的积是否相等进行判断．2．（3分）（2010•嘉定区一模）如图，已知AB∥CD∥EF，BD：DF=2：5，那么下列结论正确的是（）A．A C：AE=2：5B．A B：CD=2：5C．C D：EF=2：5D ．C E：EA=5：7考点：平行线分线段成比例．分析：由AB∥CD∥EF ，BD ：DF=2：5，根据平行线分线段成比例定理，即可求得=，又由AE=AC+CE，即可求得答案．解答：解：∵AB∥CD∥EF，BD：DF=2：5，∴=，∵AE=AC+CE，∴CE：EA=5：7．故选D．点评：此题考查了平行线分线段成比例定理．此题比较简单，解题的关键是注意对应线段．3．（3分）在△ABC中，∠C=90°，cosA=，那么sinA的值等于（）A．B．C．D．考点：同角三角函数的关系．分析：根据公式cos2A+sin2A=1解答．解答：解：∵cos2A+sin2A=1，cosA=，∴sin2A=1﹣=，∴sinA=．故选B．点评：本题考查公式cos2A+sin2A=1的利用．4．（3分）下列命题中，假命题的是（）A．两个等边三角形一定相似B．有一个锐角相等的两个直角三角形一定相似C．两个全等三角形一定相似D．有一个锐角相等的两个等腰三角形一定相似考点：命题与定理；相似三角形的判定．分析：本题需先根据真命题和假命题的定义判断出各题的真假，最后得出结果即可．解答：解：两个等边三角形，三角相等，一定相似，A是真命题；有一个锐角相等的两个直角三角形，三角相等，一定相似，B是真命题；全等三角形是特殊的相似三角形，C 是真命题；有一个锐角相等的两个等腰三角形，其它两角不一定相等，不能判定这两个三角形相似．故选：D ．点评：本题主要考查了命题与定理，正确的命题叫真命题，错误的命题叫做假命题．判断命题的真假关键是要熟悉课本中的性质定理．5．（3分）下列各组条件中一定能推得△ABC与△DEF相似的是（）A．B．，且∠A=∠EC．，且∠A=∠D D．，且∠A=∠D考点：相似三角形的判定．分析：根据三角形相似的判定方法（①两角法：有两组角对应相等的两个三角形相似可以判断出A、B的正误；②两边及其夹角法：两组对应边的比相等且夹角对应相等的两个三角形相似）进行判断．解答：解：A、△ABC与△DEF的三组边不是对应成比例，所以不能判定△ABC与△DEF相似．故本选项错误；B、∠A与∠E不是△ABC与△DEF的对应成比例的两边的夹角，所以不能判定△ABC与△DEF相似．故本选项错误；C、△ABC与△DEF的两组对应边的比相等且夹角对应相等，所以能判定△ABC与△DEF相似．故本选项正确；D、，不是△ABC与△DEF的对应边成比例，所以不能判定△ABC与△DEF相似．故本选项错误；故选C．点评：此题主要考查了相似三角形的判定，关键是掌握三角形相似的判定方法：（1）平行线法：平行于三角形的一边的直线与其他两边相交，所构成的三角形与原三角形相似；（2）三边法：三组对应边的比相等的两个三角形相似；（3）两边及其夹角法：两组对应边的比相等且夹角对应相等的两个三角形相似；（4）两角法：有两组角对应相等的两个三角形相似．6．（3分）如图，在△ABC中，D、E在AB边上，且AD=DE=EB，DF∥BC交AC于点F，设，，下列式子中正确的是（）A．B．C．D．考点：*平面向量．分析：先根据相似三角形对应边成比例列出比例式，求出BC=3DF，再根据向量的三角形法则求出，然后选择答案即可．解答：解：∵AD=DE=EB ，DF ∥BC，∴AB=3AD，△ADF∽△ABC ，∴==，∴BC=3DF，∴=﹣，即3=﹣，∴=﹣+．故选C．点评：本题考查了平面向量，主要利用了相似三角形的判定与性质，向量的三角形法则．二、填空题：7．（3分）若，且a+b+c=15，则a=3．考点：比例的性质．分设比值为k，然后用k表示出a、b、c，代入等式求出k析：值，再计算即可求出a．解答：解：设===k，则a=2k，b=3k，c=5k，∵a+b+c=15，∴2k+3k+5k=15，解得k=，∴a=2k=2×=3．故答案为：3．点评：本题考查了比例的性质，利用“设k法”表示出a、b、c可以使运算更加简便．8．（3分）线段3和6的比例中项是3．考点：比例线段．分析：根据线段比例中项的概念，可得线段3和6的比例中项的平方=3×6=18，依此即可求解．解答：解：∵3×6=18，（±3）2=18，又∵线段是正数，∴线段3和6的比例中项为3．故答案为：3．点评：考查了比例中项的概念．注意线段不能是负数．9．（3分）等边三角形的中位线与高之比为1：．考点：三角形中位线定理；等边三角形的性质．分析：可设等边三角形的边长为2a，根据三角形的中位线定理和等边三角形的性质以及勾股定理可分别求出中位线的长和高的长度即可求出其比值．解答：解：设等边三角形的边长为2a，则中位线长为a，高线的长为=a，所以等边三角形的中位线与高之比为a：a=1：，故答案为：1：．点评：本题考查了等边三角形的性质和三角形的中位线定理，中位线是三角形中的一条重要线段，由于它的性质与线段的中点及平行线紧密相连，因此，它在几何图形的计算及证明中有着广泛的应用．10．（3分）点P是线段AB的黄金分割点（AP＞BP），则=．考点：黄金分割．分把一条线段分成两部分，使其中较长的线段为全线段与析：较短线段的比例中项，这样的线段分割叫做黄金分割，他们的比值叫做黄金比．解答：解：∵点P是线段AB 的黄金分割点（AP＞BP），∴==．故答案为．点评：本题考查了黄金分割的定义，牢记黄金分割比是解题的关键．11．（3分）如果，那么用、表示为：=．考点：*平面向量．分析：根据向量方程的求解方法，可以先移项，再系数化一，即可求得答案．解答：解：∵，∴2=﹣3，∴=．故答案为：﹣+．点评：此题考查了平面向量的知识．解此题的关键是掌握向量方程的求解方法．12．（3分）（2010•徐汇区一模）如图：在△ABC中，∠C=90°，AC=12，BC=9．则它的重心G到C点的距离是5．考点：三角形的重心；直角三角形斜边上的中线；勾股定理．专题：计算题．分析：根据勾股定理求出AB的长，然后再利用三角形重心的性质，即可求出重心G到C点的距离．解答：解：∵∠C=90°，AC=12，BC=9，∴AB===15，设△ABC斜边上的中线为x，则x=AB=×15=7.5，又∵G是△ABC的重心，∴CG==×7.5=5．故答案为：5．点评：此题主要考查学生对直角三角形斜边上的中线等于斜边的一半，三角形重心和勾股定理的理解和掌握，难度不大，属于基础题．13．（3分）在△ABC中，∠A与∠B是锐角，sinA=，cotB=，那么∠C=75度．考点：特殊角的三角函数值．专题：探究型．分析：先根据，∠A与∠B是锐角，sinA=，cotB=求出∠A 及∠B的度数，再根据三角形内角和定理进行解答即可．解答：解：∵∠A与∠B是锐角，sinA=，cotB=，∴∠A=45°，∠B=60°，∴∠C=180°﹣∠A﹣∠B=180°﹣45°﹣60°=75°．故答案为：75°．点评：本题考查的是特殊角的三角函数值及三角形内角和定理，熟记各特殊角度的三角函数值是解答此题的关键．14．（3分）（2010•徐汇区一模）如图，直线l1∥l2∥l3，已知AG=0.6cm，BG=1.2cm，CD=1.5cm，CH=0.5cm．考平行线分线段成比例．分析：由直线l1∥l2∥l3，即可得到，又由设CH=xcm，则DH=1.5﹣x（cm），代入数值解方程即可求得CH的长．解答：解：∵l1∥l2∥l3，∴，∵AG=0.6cm，BG=1.2cm，CD=1.5cm，设CH=xcm，则DH=1.5﹣x（cm），∴，解得：x=0.5．即CH=0.5cm．故答案为：0.5．点评：本题考查平行线分线段成比例定理．注意解题时要找准对应关系．15．（3分）（2010•徐汇区一模）如图，△ABC中，AB＞AC，AD是BC边上的高，F是BC的中点，EF⊥BC交AB于E，若BD：DC=3：2，则BE：AB=5：6．考点：平行线分线段成比例．专数形结合．分析：结合图形，已知F是BC的中点，且BD ：DC=3：2，即可推知BD：BC=3：5．再根据平行线分线段成比例定理，即可得出BE和AB之间的比例关系．解答：解：F是BC的中点，所以FB=BC，因为BD：DC=3：2，所以BD=，所以FD=BD﹣FB=BC﹣BC=BC，所以BF：FD=：=5：1因为EF⊥BC，AD⊥BC，所以AD∥EF，所以根据平行线等分线段定理，得BE：EA=BF：FD=5：1即BE：AB=5：6．故答案为5：6．点评：本题主要考查了平行线分线段成比例定理的应用，要求学生能够把握题目的要求，认真分析所给条件，属于基础性题目．16．（3分）（2012•南宁模拟）如图，将一副直角三角板（含45°角的直角三角板ABC及含30°角的直角三角板DCB）按图示方式叠放，斜边交点为O，则△AOB与△COD的面积之比等于1：3．考点：相似三角形的判定与性质；解直角三角形．专题：计算题．分析：结合图形可推出△AOB∽△COD，只要求出AB与CD 的比就可知道它们的面积比，我们可以设BC为a，则AB=a，根据直角三角函数，可知DC=a，即可得△AOB 与△COD的面积之比解答：解：∵直角三角板（含45°角的直角三角板ABC及含30°角的直角三角板DCB）按图示方式叠放∴∠D=30°，∠A=45°，AB∥CD∴∠A=∠OCD，∠D=∠OBA∴△AOB∽△COD设BC=a∴CD= a∴S△AOB：S△COD=1：3故答案为1：3点评：本题主要考查相似三角形的判定及性质、直角三角形的性质等，本题关键在于找到相关的相似三角形17．（3分）（2010•嘉定区一模）如图：在△ABC中，点D 在边AB上，且∠ACD=∠B，过点A作AE∥CB交CD的延长线于点E，那么图中相似三角形共有4对．考点：相似三角形的判定．分析：由AE∥CB可得∠EAD=∠B，则∠EAD=∠ACD=∠B，结合公共角判断相似三角形．解答：解：依题意得∠EAD=∠ACD=∠B，∵AE∥CB，∴△AED∽△BCD，∵∠CAD=∠BAC，∴△ACD∽△ABC，∵∠AED=∠CEA，∴△AED∽△CEA，由相似三角形的传递性，得△BCD∽△CEA．故有4对相似三角形．故答案为：4．点评：本题考查了相似三角形的判定方法．关键是利用平行线找相等角，利用公共角判断三角形相似．18．（3分）（2012•安徽）如图，P是矩形ABCD内的任意一点，连接PA、PB 、PC、PD，得到△PAB、△PBC、△PCD、△PDA，设它们的面积分别是S1、S2、S3、S4，给出如下结论：①S1+S2=S3+S4；②S2+S4=S1+S3；③若S3=2S1，则S4=2S 2；④若S1=S2，则P点在矩形的对角线上．其中正确的结论的序号是②和④（把所有正确结论的序号都填在横线上）．考点：矩形的性质．专题：压轴题．分析：根据三角形面积求法以及矩形性质得出S1+S3=矩形ABCD面积，以及=，=，即可得出P点一定在AC 上．解答：解：如右图，过点P分别作PF⊥AD于点F，PE⊥AB于点E，∵△APD以AD为底边，△PBC以BC为底边，∴此时两三角形的高的和为AB，即可得出S1+S3=矩形ABCD面积；同理可得出S2+S4=矩形ABCD面积；∴②S2+S4=S1+S3正确，则①S1+S2=S3+S4错误，③若S3=2S1，只能得出△APD 与△PBC高度之比，S 4不一定等于2S2；故此选项错误；④若S1=S2，×PF×AD=PE×AB，∴△APD与△PBA高度之比为：=，∵∠DAE=∠PEA=∠PFA=90°，∴四边形AEPF是矩形，∴此时矩形AEPF与矩形ABCD位似，∴=，∴P点在矩形的对角线上．故④选项正确，故答案为：②和④．点评：此题主要考查了矩形的性质以及三角形面积求法，根据已知得出=是解题关键．三、解答题19．（6分）计算：cos60°+sin45°•tan30°．考特殊角的三角函数值．点：专题：探究型．分析：先根据把各角的三角函数值代入，再根据实数的运算法则进行计算即可．解答：解：原式=﹣×+•，=2﹣+，=+．故答案为：+．点评：本题考查的是特殊角的三角函数值、二次根式的化简、实数的运算，熟记特殊角的三角函数值是解答此题的关键．20．（6分）如图，在平行四边形ABCD中，点F在AD边上，BA的延长线交CF的延长线于点E，EC交BD于点M，求证：CM2=EM•FM．考点：相似三角形的判定与性质；平行四边形的性质．专题：证明题．分析：首先利用AB∥CD，AD∥BC，得出△BEM∽△CDM，△BMC∽△DMF，进而利用相似三角形的性质得出比例式之间关系，求出即可．解答：证明：∵在平行四边形ABCD 中，AB ∥CD ，AD∥BC，∴△BEM∽△CDM，△BMC ∽△DMF，∴=，=，∴=，∴CM2=EM•FM．点评：此题主要考查了相似三角形的判定与性质，利用平行得出△BEM∽△CDM，△BMC∽△DMF是解题关键．21．（6分）已知非零向量，，（1）求作：；（2）求作向量分别在，方向上的分向量．注：不写作法，但须说明结论．考点：*平面向量．分析：（1）将平移到如图所示的位置，可求出：=；（2）将平移到如图所示的位置，然后分别过向量b方向及向量a向量方向上的垂线，则可得出向量分别在，方向上的分向量．解答：解：（1）作图如下：就是所作的；（2）作图如下：向量分别在，方向上的分向量分别为：、．点评：本题考查了向量的知识，注意在作图的时候先平移，使进行计算的两个向量有公共点，这样就方便求解了．22．（6分）如图，梯形ABCD中，AD∥BC，AD=2，BC=6，DC=5，梯形ABCD的面积S ABCD=16，求∠B的余切值．考点：梯形；勾股定理；锐角三角函数的定义．分析：过A，D分别作AE⊥BC，DF⊥BC交BC于E，F点，根据已知梯形面积和梯形的面积公式求出AE的长，由勾股定理求出CF的长，进而求出BE，利用余切的定义即可求出∠B的余切值．解答：解：过A，D分别作AE⊥BC，DF⊥BC交BC于E，F 点，∵AD∥BC，∴四边形AEFD是矩形，∴AE=DF，AD=EF，∵梯形ABCD的面积S ABCD=16，∴16=，∵AD=2，BC=6，∴AE=4，∴DF=AE=4，在Rt△DEC中，DC=5，由勾股定理得CF=3，∴BE=BC﹣EF﹣CF=6﹣3﹣2=1，∴∠B的余切值=．点评：本题主要考查对梯形、矩形．勾股定理等知识点的理解和掌握，把梯形转化成矩形和直角三角形是解此题的关键．题型较好．23．（6分）如图，点P是等腰△ABC的底边BC上的点，以AP为腰在AP的两侧分别作等腰△AFP和等腰△AEP，且∠APF=∠APE=∠B，PF交AB于点M，PE交AC于点N，连接MN．求证：MN∥BC．考等腰三角形的性质；全等三角形的判定与性质．点：专题：证明题．分析：由已知条件可以得出AF=AP，∠F=∠APN，∠FAM=∠PAN，可以得出△AFM≌△APN，得到AM=AN，从而得出结论．解答：证明：∵△ABC、△AFP和△AEP是等腰三角形，∴AF=AP，∠F=∠APN，∠FAM=∠PAN，在△AFM和△APN中，∵∴△AFM≌△APN（ASA），∴AM=AN．∴∠AMN=∠B，∴MN∥BC．点评：本题考查了等腰三角形的性质，全等三角形的判定与性质的运用．24．（8分）在△ABC中，AC=2，AB=3，BC=4，点D在BC边上，且CD=1（1）求AD的长；（2）点E是AB边上的动点（不与A、B重合）连接ED，作射线DF交AC边于点F，使∠EDF=∠BDA．请补全图形，说明线段BE与AF的比值是否为定值？请证明你的结论．考点：相似三角形的判定与性质；勾股定理．分析：（1）利用两边对应成比例且夹角相等得出△ADC∽△BAC，即可求出AD的长；（2）利用已知得出∠BDE=∠ADF以及∠B=∠DAF，即可求出△BDE∽△ADF，进而利用对应边关系得出BE 与AF的比值．解答：（1）解：在△ADC和△BAC中，∵∠C=∠C，==，∴△ADC∽△BAC，∴=，∵AB=3，∴AD=1.5；（2）如图所示：线段BE与AF的比值为定值2，证明：∵∠EDF=∠BDA，∴∠BDE=∠ADF，∵△ADC∽△BAC，∴∠B=∠DAF，∴△BDE∽△ADF，∴=，∵BC=4，CD=1，AD=1.5，∴===2．∴线段BE与AF的比值为定值2．点评：此题主要考查了相似三角形的判定与性质，熟练应用相似三角形的判定与性质得出是解题关键．25．（8分）如图，tan∠MAB=2，AB=6，点P为线段AB上一动点（不与点A、B重合）．过点P作AB的垂线交射线AM于点C，连接BC，作射线AD交射线CP于点D，且使得∠BAD=∠BCA，设AP=x（1）写出符合题意的x的取值范围；（2）点N在射线AB上，且△ADN∽△ABC，当x=2时，求PN的长；（3）试用x的代数式表示PD的长．考点：相似形综合题．分析：（1）由于点P为线段AB上一动点（不点A、B重合），则有0＜x＜6；（2）由于△ADN∽△ABC，根据相似的性质得∠AND=∠ACB，而∠BAD=∠BCA，则∠AND=∠NAD，又DP⊥AN，可判断△DAN为等腰三角形，根据其性质有PN=PA=2；（3）如左图过B点作BE⊥AC于点E ，在Rt△ABE中，利用三角函数的定义tan∠EAB==2，得到BE=2AE，再利用勾股定理可计算出AE=，则BE=，在Rt△APC 中运用同样的方法得到CP=2AP=2x，AC=x，则CE=AC﹣AE=x﹣，再利用∠BAD=∠BCA 可证得Rt △APD ∽Rt △CEB，根据相似的性质得到=，即=，即可求出AD．解解：（1）x的取值范围为：1.2＜x＜6；答：（2）如右图，∵△ADN∽△ABC，∴∠AND=∠ACB，∵∠BAD=∠BCA，∴∠AND=∠NAD，∵DP⊥AN，∴△DAN为等腰三角形，∴PN=PA，当x=2时，PN=2；（3）如左图，过B点作BE⊥AC于点E，在Rt△ABE中，AB=6，∵tan∠EAB==2，∴BE=2AE，∵AE2+BE2=AB2，∴AE2+4AE2=36，解得AE=，∴BE=，在Rt△APC中，AP=x，∵tan∠CAP==2，∴CP=2AP=2x，∴AC==x，∴CE=AC﹣AE=x﹣，∵∠BAD=∠BCA，∴Rt △APD∽Rt△CEB，∴=，即=，∴PD=．点评：本题考查了相似形综合题：运用相似比和勾股定理进行几何计算是常用的方法；理解三角函数值的定义和等腰三角形的判定与性质．参与本试卷答题和审题的老师有：CJX；gsls；HJJ；zcx；wdxwwzy；yangwy；dbz1018；zjy011；ZHAOJJ；fxx；sd2011；gbl210；星期八；zhangCF；caicl（排名不分先后）菁优网2013年10月11日。

[九年级数学]上海市杨浦区2012-2013学年度九年级第一学期期中质量抽测数学试题（无答案）杨浦区2012年学年度第一学期期中质量抽测(满分:100分完卷时间:90分钟)一、选择题1、下列各组线段中，成比例线段的一组是( )1,2,3,42,3,4,61,3,5,72,4,6,8A. B. C. D.2、如图，已知ABCDEF////，BDDF:2:5,，那么下列结论正确的是( )A.ACAE:2:5,B. ABCD:2:5,C. CDEF:2:5,D. CEEA:5:7,3?ABCtanB3、在中，，，那么的值等于( ) cosA,，,C9053434 B. C. D. A.55434、下列命题中，假命题的是( )A. 两个等边三角形一定相似B. 有一个锐角相等的两个直角三角形一定相似C. 两个全等三角形一定相似D. 有一个锐角相等的两个等腰三角形一定相似?DEF?ABC5、下列各组条件中一定能推得与相似的是( ) ABACEFABDE，,，AE A. B.，且 ,,,DFDEBCBCDFABACABDE，,，AD，,，ADC. ，且 D. ，且 ,,DFDEDFACEABADDEEB,,DF?ABCDFBC//AC6、如图，在中，、在边上，且，交于点，设，，下列式子中正确的是( ) EBa,ECb,1111 A. B. DFab,，DFab,,33331111C. D. DFab,,，DFab,,,3333AABDFDCEEFBC(第2题)(第3题)二、填空题:abca,abc，，,157、若,,，且，则 235368、线段和的比例中项是9、等边三角形的中位线与高之比为BPPABAPBP>10、点是线段的黄金分割点()，则 ,AP11、如果，那么用、表示为: 32axb，,xabx,?ABCAC,12BC,9GC12、在中，，，，则它的重心到点的距离是，,C9023，A，BsinA,cotB,，,C?ABC13、在中，与是锐角，，，那么 23CH,AG,0.6cmBG,1.2cmCD,1.5cm14、如图，直线，已知，，， lll////123 ADABF?ABCABAC>BCBCEFBC,15、如图，中，，是边上的高，是的中点，交于E，BEAB:,BDDC:3:2,若，则DAAECAOHGCBBCDDBF(第15题)(第14题)(第16题) 16、将一副直角三角板(含角的直角三角板ABC 及含角的直角三角板DCB)按图示4530方式叠放，斜边O?AOB?COD交点为，则与的面积之比等于ABAD?ABC，,，ACDBAECB//CD17、如图，在中，点在边上，且，过点作交的延E长线于点那么图中相似三角形共有对PPD?PABPAPBABCDPC?PBC18、如图，是矩形内的任意一点，连接、、、，得到、、?PCD?PDA，设它们的面积分别是、、、，给出如下结论: SSSS1234P? ? ?若，则 ? 若，则点在SSSS++,SSSS++,SS,2SS,2SS,12342413314212矩形的对角线上其中正确的结论的序号是 (把所有正确结论的序号都填在横线上)DEACDPBCAB(第17题)(第18题)三、解答题19、计算: 123cos60sin45tan30,，ADEFBA20、如图，在平行四边形ABCD中，点在边上，的延长线交CF的延长线于点，BDEC交于点2M，求证: CMEMFM,EFADMBC21、已知非零向量，， abc1(1)求作:; ab，2(2)求作向量分别在，方向上的分向量. cab注:不写作法，但须说明结论。