高中家教英语数学试题

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1、句型6as, though, although引导的让步状语从句。注意although位于句首；though位于句首或句中；as位于句中=though=that。它的词序是把句中强调的形容词、副词、动词或名词放在连词前。参考倒装结构 请注意下列句式的变化：例句1. Although/Though Im young, I already know what career I want to follow.Young as/though/that I am, I already know what career I want to follow.我虽然年轻，但我已经明白我应该追随什么样的事业。2.

2、 Although/Though I respect him very much, I cannot agree with his idea.Much as/that/though I respect him, I cannot agree with his idea. 虽然我很尊重他，但是我不同意他的观点。3. Although/Though he is a child, he knows a lot of Chinese characters. Child（省略冠词）as/though/that he is, he knows a lot of Chinese characters. 他虽

3、然还是个孩子，却认识了许多汉字。4. Although he tried, he couldnt solve the problem.Try as he might, he couldnt solve the problem. 尽管他努力了，但是他没有解决问题。5. Although it is raining, Im going out for a walk.Raining as it is, Im going out for a walk. 天虽然在下雨，我还是要出去散步。 6. Strange as it may seem, nobody was injured in the accid

4、ent. 这次意外虽然显得不可思议，却没有人受伤。7. Much as I would like to help, I have a lot to do. 虽然我很想帮助你，但是我有很多事要做。8. Object as you may, I will go. 纵使你反对，我也要去。高考题回放1. Mr. Hall understands that _ math has always been easy for him, it is not easy for the students.（2003北京春季）A. unless B. if C. although D. when 2. Parents

5、 should take seriously their childrens requests for sunglasses _ eye protection is necessary in sunny weather.（2004上海）A. because B. though C. unless D. if 3. _, I have never seen anyone whos as capable as John.（2001上海）A. As long as I have traveled B. Now that I have traveled so muchC. Much as I have

6、 traveled D. As I have traveled so much 4. _, he talks a lot about his favorite singers after class.（2005重庆）A. A quiet student as he may be B. Quiet student as he may beC. Be a quiet student as he may D. Quiet as he may be a student5. _ most of the earths surface is covered by water, fresh water is

7、very rare and precious.（2006上海春季）A. As B. Once C. If D. Although 6. Although the wind has _, the rain remains steady, so you still need a raincoat. A. turned up B. gone back C. died down D. blown out 7. Im certain Davids told you his business troubles. _, its no secret that he owes a lot of money to

8、 the bank.（2006湖北）A. However B. Anyway C. Therefore D. Though 8. Although she did not know Boston well, she made her way _ to the Home Circle Building.（2006湖南）A. easy enough B. enough easy C. easily enough D. enough easily9. Although the causes of cancer _, we do not yet have any practical way to pr

9、event it. A. are being uncovered B. have been uncoveringC. are uncovering D. have uncovered 10. Although medical science _ control over several dangerous disease, what worries us is that some of them are returning.（2006江苏）A. achieved B. has achieved C. will achieve D. had achieved 11. _ he has limit

10、ed technical knowledge, the old worker has a lot of experience. A. Since B. Unless C. As D. Although 句型7 before特殊用法（1）“没来得及就”例句The roof fell before he had time to dash into the room to save his baby.他还没有来得及冲进房间救孩子，房顶就塌了。He ran off before I could stop him. 我还没有来得及阻止，他已经跑了。To my great disappointment,

11、my favorite singer left the concert before I could have a word with her. 让我非常失望的是，我还没有来得及和我最喜欢的歌手打招呼，她就已经离开了。句型8 before特殊用法（2）“过了多久才”或“动作进行到什么程度才”例句They walked about fifty miles to the west before they saw a village.他们西行50英里才看到一个村庄。The workers worked day and night about three days before everything

12、returned to normal.工人们连续工作3天才使一切恢复正常。He almost knocked me down before he knew it.他几乎撞到我了才意识到。We had walked a long way before we found some water. 我们走了很长的路才找到一点水。Five years went by before I knew it. 不知不觉，五年过去了。句型9It was + 时间段+before.“过了多久才（怎么样）”It was not long before.“不久，就”It will (not) be +时间段+befor

13、e.“要过多久（不久）才”(before从句谓语动词要用一般时态)例句It was not long before he sensed the danger of the position.不久他就意识到他处境的危险。It was five days before he came back. 五天后他才回来。It will be half a year before you graduate from the school. 再过半年你才能毕业。It will not be long before they understand each other. 他们大概不久就会互相了解。高考题回放1.

14、 It was evening _ we reached the little town of Winchester.（2004天津）A. that B. until C. since D. before 2. Scientists say it may be five or six years _ it is possible to test this medicine on human patients.（2004福建） A. since B. after C. before D. when 3. Someone called me up in the middle of the nigh

15、t, but they hung up _ I could answer the phone.（NMET2000）A. as B. since C. until D. before 4. He made a mistake, but then he corrected the situation _ it got worse. A. until B. when C. before D. as 5. It was some time _ we realized the truth.（2005山东）A. when B. until C. since D. before 6. The America

16、n Civil War lasted four years _ the North won in the end.（2005广东）A. after B. before C. when D. then 7. Why didnt you tell him about the meeting?He rushed out of the room _ I could say a word.（2006四川）A. before B. until C. when D. after 8. How long do you think it will be_ China sends a manned spacesh

17、ip to the moon?Perhaps two or three years.（2006福建）A. when B. until C. that D. before句型10in case of(+n.) “以防；万一”；in case that“以防，万一”（谓语动词用一般现在时态或should+动词原形）例句In case of fire, what should we do?Please remind me about it in case I forget/should forget. 万一我忘了，请提醒我。In case (that) John comes/should come,

18、 please tell him to wait.Please take your umbrella in case (that it rains/should rain).带上雨伞，以防下雨。高考题回放1. The sign reads “In case of _ fire, break the glass and push _ red button.” (NMET2003)A. 不填；a B. 不填；the C. the; the D. a; a 2. I dont think I will need any money, but Ill bring some _.（NMET2003）A.

19、 at last B. in case C. once again D. in time 3. I always take something to read when I go to the doctors _ I have to wait.（全国II）A. in case B. so that C. in order D. as if 4. Youd better take something to read when you go to the doctor _ you have to wait. A. even if B. as if C. in case D. in order th

20、at 5. He got to the station early, _ missing his train.（2004江苏）A. in case of B. instead of C. for fear of D. in search of 6. We always keep _ spare paper, in case we run out.（2006浙江高考题）A. too much B. a number of C. plenty of D. a good many1. look _ : 调查; ( into ) 2. belong _: 属于; ( to )3. _search of

21、 : 寻找 ; 搜寻 ; (in ) 4. _return : 作为报答 ; ( in )5. _ war : 处于交战状态 ; ( at ) 6. take _ : 拆开 ; ( apart )7. think highly _ : 给与高度评价; 赞扬 ; ( of ) 8. _with : 对付 ; 处理 ; (deal )9. add _ : 增加 ; 增添 ; ( to ) 10. care _ : 关心 ; 在乎 ; ( about )11. agree _ : 同意 (某人的观点) ; ( with )12. rather _ : 而不是 ; 与其 ; ( than )13. p

22、ay attention _ : 注意 ; ( to ) 14. look _ : 照顾 ; 照料 ; ( after )15. serve _ : 担任 ; 公职 ; ( as )单元 2 : 根据词意完成短语并造句 :1. take part _ : 参与 ; 参加 ; ( in ) 2. a set _ : 一组 ; 一套 ; ( of )3. as well _ : 也 ; 又 ; ( as ) 4. every _years : 每四年 ; ( four )5. one _ another : 陆续地 ; 一个接一个地 ; ( after ) 6. change ones _ : 改

23、变注意 ; ( mind )7. _over the world : 遍及全世界 ; ( all ) 8. compete _ : 与比赛 / 为比赛 ( against / for ) ;9. as _matter of fact : 事实上 ; ( a )10. play an important role _:在中起重要作用 ; ( in )11. work _ : 计算出 ; 制定出 ; ( out ) 12. pick _: 拾起; 接收; 开车去接 ; ( up )13. be married _: 与结婚 ; (to ) 14. promise _ : 承诺做 ; ( to do

24、 )15. carry _: 开展; 执行 ; ( out )单元 3 : 根据词意完成短语并造句 :1. have _common : 共有; 公用; ( in ) 2. _ones opinion : 依.看;据认为 ; ( in )3. so _. : 如此以致于 ; (that )4. deal _ : 处理; 安排; 对付 ; (with)5. _ a way : 在某种程度上; ( in ) 6. make _ : 弥补; 补足 ; 整理 ; ( up )7. after _: 毕竟 ; ( all ) 8. watch _ : 看守 ; 监视 ; ( over )9. _ int

25、elligence : 人工智能 ; ( artificial ) 10. _oneself : 单独; 独自 ; ( by )11. share _. : 与分享 ; ( with )12. as _ : 好像 / 似乎 ; ( if / though )13. go _ : 走过 ; 顺道拜访 ; ( by )14. bring _ : 带入 ; 使进入 ; ( into )15. take _ : 轮流; 依次 ; ( turns )单元 4 : 根据词意完成短语并造句 :1. _a result : 结果 ; ( as ) 2. die _ : 灭亡 ; 逐渐消失 ; ( out )3

26、. _peace : 和平地; 安详地 ; 和睦地 ; ( in ) 4. _danger : 在危险中 ; 垂危 ; ( in )5. protect _ : 保护不受 (危险) ; ( from )6. pay attention _ : 注意 ; ( to ) 7. come _being : 形成 ; 产生 ; ( into )8. be concerned _ : 担心; 烦恼 ; 忧虑 ; ( about )9. _dressed : 穿上衣服 ; 穿戴起来 ; ( get )10. have an effect _ : 对又影响 ; ( on ) 11. set _: 开办 ;

27、创立 ; ( up )12. even _ : 即使 ; ( if / though ) 13. apply _ : 适用于 ; 适合于 ; ( to )单元 5 : 根据词意完成短语并造句 :1. dream _ : 梦见; 梦想; 设想 ; ( of )2. be honest _ : 对说老实话 ; ( with )3. play jokes _ :戏弄 ; ( on )4. _ so : 大约; ( or )5. break _ : 打碎 ; 分裂 ; 解体 ; ( up ) 6. _ chance : 偶然; 意外地 ; ( by )7. sort _ : (v.) : 分类 ; (

28、 out ) 8. stick _ : 坚持 ; ( to )9. _ all : 最重要的是 ; 首要的是 ; ( above )10. base _ : 以基础 ; ( on )11. come _ : 实现 ; ( true )12. come _with : 提出 ; 赶上 ; ( up )13. as well _ : 和一样好 ; ( as )2012年普通高等学校招生全国统一考试（江西卷）一选择题：本大题共10小题，每小题5分，共50分1若集合A=-1，1，B=0，2，则集合zz=x+y,xA,yB中的元素的个数为A5 B.4 C.3 D.22.下列函数中，与函数y=定义域相同的

29、函数为Ay= B.y= C.y=xex D. 3.若函数f(x)= ，则f(f(10)=A.lg101 B.b C.1 D.04.若tan+ =4,则sin2=A B. C. D. 5.下列命题中，假命题为A.存在四边相等的四边形不是正方形Bz1,z2c,z1+z2为实数的充分必要条件是z1,z2互为工复数C.若x,yCR，且x+y2，则x,y至少有一个大于1D对于任意nN,C+C1.+C。都是偶数6观察下列各式：a+b=1.a+b2=3，a3+b3=4 ，a4+b4=7,a5+b5=11,，则a10+b10=A.28 B.76 C.123 D.1997.在直角三角形ABC中，点D是斜边AB的

30、中点，点P为线段CD的中点，则A.2 B.4 C.5 D.108.某农户计划种植黄瓜和韭菜，种植面积不超过50亩，投入资金不超过54万元，假设种植黄瓜和韭菜的产量、成本和售价如下表年产量/亩年种植成本/亩每吨售价黄瓜4吨1.2万元0.55万元韭菜6吨0.9万元0.3万元为使一年的种植总利润（总利润=总销售收入-总种植成本）最大，那么黄瓜和韭菜的种植面积（单位：亩）分别为A.50,0 B.30.0 C.20,30 D.0,509.样本（x1,x2，xn）的平均数为x，样本（y1，y2，yn）的平均数为。若样本（x1,x2，xn，y1，y2，yn）的平均数，其中0，则n，m的大小关系为A.nm B

31、.nm C.n=m D.不能确定10.如图，已知正四棱锥S-ABCD所有棱长都为1，点E是侧棱SC上一动点，过点E垂直于SC的截面将正四棱锥分成上、下两部分。记SE=x（0x1），截面下面部分的体积为V（x），则函数y=V（x）的图像大致为11.计算定积分_。12.设数列an,bn都是等差数列，若a1+b1=7，a3+b3=21，则a5+b5=_。13椭圆（ab0）的左、右顶点分别是A,B,左、右焦点分别是F1，F2。若|AF1|，|F1F2|，|F1B|成等比数列，则此椭圆的离心率为_.14下图为某算法的程序框图，则程序运行后输出的结果是_.三、选做题：请在下列两题中任选一题作答。若两题都做

32、，则按第一题评阅计分。本题共5分。15.（1）（坐标系与参数方程选做题）曲线C的直角坐标方程为x2y2-2x=0，以原点为极点，x轴的正半轴为极轴建立积坐标系，则曲线C的极坐标方程为_。15.（2）（不等式选做题）在实数范围内，不等式|2x-1|+|2x+1|6的解集为_。四解答题：本大题共6小题，共75分。解答应写出文字说明、证明过程或演算步骤。16.（本小题满分12分）已知数列an的前n项和,且Sn的最大值为8.（1）确定常数k，求an；（2）求数列的前n项和Tn。17.（本小题满分12分）在ABC中，角A,B,C的对边分别为a，b，c。已知，。（1）求证：（2）若，求ABC的面积。18.

33、（本题满分12分）如图，从A1（1,0,0），A2（2,0,0），B1（0，2，0），B2（0,2,0），C1（0,0,1），C2（0,0,2）这6个点中随机选取3个点，将这3个点及原点O两两相连构成一个“立体”，记该“立体”的体积为随机变量V（如果选取的3个点与原点在同一个平面内，此时“立体”的体积V=0）。（1）求V=0的概率；(2)求V的分布列及数学期望。19.（本题满分12分）在三棱柱ABC-A1B1C1中，已知AB=AC=AA1=，BC=4，在A1在底面ABC的投影是线段BC的中点O。（1）证明在侧棱AA1上存在一点E，使得OE平面BB1C1C，并求出AE的长；（2）求平面A1B1C

34、与平面BB1C1C夹角的余弦值。20. （本题满分13分）已知三点O（0,0），A（-2,1），B（2,1），曲线C上任意一点M（x，y）满足.（1） 求曲线C的方程；（2）动点Q（x0，y0）（-2x02）在曲线C上，曲线C在点Q处的切线为l向：是否存在定点P（0，t）（t0），使得l与PA，PB都不相交，交点分别为D,E，且QAB与PDE的面积之比是常数？若存在，求t的值。若不存在，说明理由。21. （本小题满分14分）若函数h(x)满足（1）h(0)=1，h(1)=0；（2）对任意，有h(h(a)=a；（3）在（0,1）上单调递减。则称h(x)为补函数。已知函数（1）判函数h(x)是否为补函数，并证明你的结论；（2）若存在，使得h(m)=m，若m是函数h(x)的中介元，记时h(x)的中介元为xn，且，若对任意的，都有Sn ,求的取值范围；（3）当=0，时，函数y= h(x)的图像总在直线y=1-x的上方，求P的取值范围。