湖南省永州市东安天成实验学校2013-2014学年高二上学期第三次月考数学(文)试题 Word版含答案湘教版

永州市2024年高考第三次模拟考试数 学注意事项：1．本试卷共150分，考试时量120分钟．2．全部答案在答题卡上完成，答在本试题卷上无效．3．考试结束后，只交答题卡．一、选择题：本题共8小题，每小题5分，共40分．在每小题给出的四个选项中，只有一3． 已知非零数列}{n a 满足02221=-++n n n n a a ，则20212024a a=A ．8B ．16C ．32D ．644． 61tan ⎪⎭⎫ ⎝⎛-x x θ的展开式中第四项的系数为540，则θ2cos 的值为A ．3735-B ．3735C ．54-D ．545． 为迎接2024年在永州举行的中国龙舟公开赛，一位热情好客的永州市民准备将9份一样的永州特产分给甲、乙、丙三名幸运观众，若每人至少分得一份，且甲、乙两人分得的份数不相同，则不同的分法总数为7． 已知函数2sin )(+-+-=-x x e e x f x x ，其中e 是自然对数的底数.若4)3()(log 21>+f t f ，则实数t 的取值范围是A ．⎪⎭⎫ ⎝⎛810，B ．18⎛⎫+∞ ⎪⎝⎭，C ．），（80D ．），（∞+88． 已知1F ，2F 分别是双曲线)0,0(12222>>=-b a by a x 的左、右焦点，点O 为坐标原点，过1F 的直线分别交双曲线左、右两支于A ,B 两点，点C 在x 轴上，A F CB 23=，2BF 平分BC F 1∠，其中一条渐近线与线段AB 交于点P ,则=∠2sin POF A ．741B ．742C ．743D ．7112二、多项选择题：本题共3小题，每小题6分，共18分．在每小题给出的选项中，有多项符合题目要求．全部选对的得6分，部分选对的得部分分，有选错的得0分．9． 下列说法正确的是A ．已知随机变量),2(~2σN X ，若(02)0.4P X <<=，则(4)0.1P X >=B ．设0>a ，0>b ，则“3log 3log a b >”成立的充要条件是“1>>b a ”C ．已知21)|(=A B P ，83)(=AB P ，则163)(=A P D ．若()61=AB P ，31)(=A P ，41)(=B P ，则事件A 与B 相互独立10．已知抛物线y x C 2:2=的焦点为F ，过点F 且倾斜角为锐角的直线l 与抛物线C 相交于A ，B 两点（点A 在第一象限），过点A 作抛物线C 的准线的垂线，垂足为M ，直线l 与抛物线C 的准线相交于点N ，则A ．BF AF +的最小值为2 B ．当直线l 的斜率为3时，8=AB C ．设直线BM ，MF 的斜率分别为1k ，2k ，则2121=k k D ．过点B 作直线AM 的垂线，垂足为Q ，BQ 交直线MF 于点P ，则PQ BP =11．在平面四边形ABCD 中，2==AB ,AD AB ⊥,BCD ∆为等边三角形，将ABD∆沿BD 折起，得到三棱锥BCD A -1，设二面角C BD A --1的大小为α．则下列说法正确的是A ．当︒=150α时，M ，N 分别为线段BD ，C A 1上的动点，则MN 的最小值为1421B ．当︒=120α时，三棱锥BCD A -1外接球的直径为313C ．当︒=90α时，以C A 1为直径的球面与底面BCD 的交线长为π33D ．当︒=60α时，AD 绕D 点旋转至D A 1所形成的曲面面积为π32三、填空题：本题共3小题，每小题5分，共15分．12．已知复数i )65(221+--=m m m z ，i )3(1022m m z --=，若21z z <（z 为z 的共轭复数），则实数m 的取值范围为 ．13．已知在ABC ∆中，角A ，B ，C 所对的边分别为a ，b ，c ，且C c A b B a cos 2cos cos -=+，87)62sin(=+πA ，则=-)cos(B A ．14．已知函数)(x f 的定义域为R ，1)1()(=-+x f x f ，)7(2)(xf x f =，且对于1021≤≤≤x x ，恒有)()(21x f x f ≤，则=)20241(f ．四、解答题：本题共5小题，共77分．解答应写出文字说明、证明过程或演算步骤．15．（本题满分13分）绿化祖国要扩绿、兴绿、护绿并举．某校植树节分别在甲，乙两块不同的土地上栽种某品种树苗各500株．甲地土质含有M 元素，乙地土质不含有M 元素，其它土质情况均相同，一段时间后，为了弄清楚该品种树苗的成活情况与M 元素含量是否有关联，分别在甲，乙两块土地上随机抽取树苗各50株作为样本进行统计分析．经统计，甲地成活45株，乙地成活40株．（1）根据所给数据，完成下面的2⨯2列联表（单位：株），并判断依据小概率值α=0.10的独立性检验，能否认为该品种树苗成活与M 元素含量有关联？（2）若将频率视为概率，从样本中不成活的树苗中随机抽取3株，其中取自甲地的株数为X ，求X 的分布列及方差．参考公式：()()()()()22,n ad bc n a b c da b c d a c b d χ-==+++++++参考数据：16．（本题满分15分）如图，在多面体ABCDEF 中，底面ABCD 为直角梯形，CD AB //，BC AB ⊥，ABCD EC 平面⊥，442===AB BC CD ．（1）证明：AE BD ⊥；（2）若BF EC 2=，EC BF //，且多面体ABCDEF 的体积为311，求直线AC 与平面AEF 所成角的正弦值．2⨯2列联表类别树苗成活情况合计成活不成活含M 元素不含M 元素合计17．（本题满分15分）已知函数x b x x f ln 33|13|---=）（.（1）当1=b 时，求)(x f 在），（∞+31的单调区间及极值.（2）若0)(≥x f 恒成立，求b 的取值范围.18．（本题满分17分）已知数列}{n a 为等比数列，}{n b 为等差数列，且211==b a ,588a a =,84b a =．（1）求}{n a ，}{n b 的通项公式；（2）数列⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧⋅-⎥⎦⎤⎢⎣⎡+-21)42sin(2211n n b ππ）（的前n 项和为n S ，集合⎭⎬⎫⎩⎨⎧∈≥⋅⋅=*++N n t a n b S n A n n n ,224共有5个元素，求实数t 的取值范围；（3）若数列}{n c 中，11=c ，)2(1log 2412≥-=n b a c nnn ，求证：112123c c c c c c +⋅+⋅⋅+⋅⋅⋅1232n c c c c +⋅⋅⋅⋅⋅⋅⋅⋅<．19．（本题满分17分）已知O 为坐标原点，动点M 在椭圆12:22=+y x C 上，动点N满足ON =N 的轨迹为E ．（1）求轨迹E 的方程；（2）在轨迹E 上是否存在点T ，使得过点T 作椭圆C 的两条切线互相垂直？若存在，求点T 的坐标；若不存在，请说明理由；（3）过点M 的直线)0(≠+=m m kx y 交轨迹E 于A ，B 两点，射线OM 交轨迹E 于点P ，射线MO 交椭圆C 于点Q ，求四边形APBQ 面积的最大值．永州市2024年高考第三次模拟考试数学参考答案及评分标准一、单项选择题题号12345678答案ADDCCA CB二、多项选择题题号91011答案ADBCDACD三、填空题12．}3{13．8714．1617.解析：0cos 11cos 21cos )(≥+=-+⋅≥-++='--x x e e x e e x f x x x x ．)(x f ∴在R 上单调递增．令2)()(g -=x f x ，)(x g 为奇函数，)(g x ∴在R 上单调递增，2)()(+=x g x f ．则4)3()(log 21>+f t f 化为42)3(2)(log 21>+++g t g ．3log )3()(log )3()(log 212121->⇔->⇔->t g t g g t g ．解得80<<t ．)8,0(∈∴t ．8.解析：如图A F CB 23= ，BC F AF F 121~∆∆∴,c F F 2||21=，c CF 4||2=设t AF =||1，则t BF 3||1=，t AB 2||=2BF 平分BC F 1∠,2||||||||2121==∴F F C F BF BC ,t BF BC 6||2||1==，t BC AF 2||31||2==,由双曲线定义可知a t AF AF 2||||12==-，a BF BF 2||||21=-,a AB AF BF 4||22===∴，B CAO2F 1F0260=∠ABF ,在21BF F ∆中，由余弦定理知aa c a a B F B F F F B F B F BF F 462)2()4()6(||||2||||||cos 22221221222121⋅⋅-+=⋅-+=∠化简得a c 7=，由222c b a =+得742=c b ，abPOF =∠2tan ，742sin 2==∠∴c b POF .11.解析：当M 为BD 中点且C A MN 1⊥时，MN 长度最短，由等面积法求得最小值为1421．故A 对．半径为313．故B 错．如图，过1A 作BD E A ⊥1，连接EC ，过球心O 作EC OO ⊥1则1O 为EC 的中点，且211=OO ，又球半径为1，球与BCD ∆的一交点为H ，则23=OH ，又过1O 作BC F O ⊥1，431=F O ，球与底面BCD ∆的交线如图，交线长为ππ333332=⋅，故C 对．转过的曲面为圆锥的一部分侧面积，该圆锥母线长为2，底面圆半径为1，故面积为πππ32312=⋅⋅．故D 对．EODO 1A 1F HC B060DBO 1C FH14.解析：)7(2)71(21)1(1)(x f x f x f x f =--=--=，217()71(=+-∴x f x f 21)71()0(=+f f ，1)1()0(=+f f ，2171()1(=-∴f f ，71(2)71(21)1(f f f =+=21)71(=f ，∴当)21,71(∈x 时，21)(=x f ，而），（21712024343∈161)2024343(81)202449(4120247(21)20241(====∴f f f f .四、解答题15．（本题满分13分）解：（1）依题意可得2⨯2列联表如下：…………………2分零假设为0H :该品种树苗成活与M 元素含量无关联．…………………3分根据列联表中的数据，10.022706.2961.15110015855050)5401045(100x =<≈=⨯⨯⨯⨯-⨯⨯=χ．…………………5分根据小概率值10.0=α的独立性检验，没有充分证据推断0H 不成立，因此可以认为0H 成立，即认为该品种树苗成活与M 元素含量无关联．…………………6分（2）由题意知，不成活的树苗共有15株，甲地不成活的树苗有5株，X 的可能取值为0，1，2，3…………………7分故9124)0(31531005===C C C X P ，9145)1(31521015===C C C X P ，类别树苗成活情况合计成活不成活含M 元素45550不含M 元素401050合计85151009120)2(31511025===C C C X P ，912)3(31501035===C C C X P ．故X 的分布列为…………………11分（一个概率1分）期望19123912029145191240)(=⨯+⨯+⨯+⨯=X E （另解：易知X 服从超几何分布，则11553)(=⨯=X E ）…………………12分方差74)13(912)12(9120)11(9145)10(9124)(2222=-⨯+-⨯+-⨯+-⨯=X D ．…………………13分16.（本题满分15分）解：（1）在BCD Rt ∆中，21tan ==∠CD BC BDC ，…………………1分在ABC Rt ∆中，21tan ==∠BC AB ACB ，ACB BDC ∠=∠∴，…………………2分︒=∠+∠=∠+∠∴90ACD ACB ACD BDC ，…………………3分∴BD AC ⊥，…………………4分又⊥EC 平面ABCD ，⊂BD 平面ABCD ，∴BD EC ⊥，又C EC AC = ，AC ⊂平面AEC ，EC ⊂平面AEC ，…………………5分⊥∴BD 平面AEC ，…………………6分又AE ⊂平面AEC ，AE BD ⊥∴．……………7分（其他方法酌情给分）（2）设多面体ABCDEF 的体积为V ，x BF EC 22==．X0123P912491459120912则311423131313131=⋅⋅+⋅⋅=⋅⋅+⋅⋅=+=∆--x x S EC S AB V V V ACD BCEF ACD E BCEF A 四边形求得1=x ．…………………9分如图，以C 为坐标原点，CD ，CB ，CE 所在直线分别为x ，y ，z 轴建立空间直角坐标系，…………10分则)0,2,1(A ，)2,0,0(E ，)1,2,0(F ，)0,0,0(C )1,2,0(-=EF ，)1,0,1(-=AF ，)0,2,1(--=AC …………11分设平面AEF 的法向量),,(z y x n =，则有0AF n EF n ⎧⋅=⎪⎨⋅=⎪⎩，即⎩⎨⎧=-=+-020z y z x ，令2=z ，则2=x ，1=y ，即)2,1,2(=n …………………12分设直线AC 与平面AEF 所成角为θ，那么1554354|,cos |sin =⋅==><=n AC θ．…………………15分17．（本题满分15分）解：（1）当1=b ，31>x 时，4ln 33ln 3313)(--=---=x x x x x f …………………1分xx x x f )1(333)(-=-='…………………2分令0)(>'x f ，解得1>x ，令0)(<'x f ，解得131<<x ，…………………4分)(x f ∴的单调递减区间为)1,31(，单调递增区间为),1(+∞)(x f ∴在1=x 处取得极小值1)1(-=f ，无极大值．…………………7分（2）依题意x b x x f ln 3313)(---=，对任意),0(+∞∈x ，0)(≥x f 恒成立，即x x b ln 3133--≤，…………………8分令x x x g ln 313)(--=，yxzEDF CBA当]31,0(∈x 时，x x x g ln 331)(--=，)(x g 单调递减．…………………9分当）+∞∈,31(x 时，x x x g ln 313)(--=，x x x x g 3333)(-=-='，…………………10分令0)(>'x g ，解得1>x ，令0)(<'x g ，解得131<<x ，…………………11分综上所述，)(x g 在)1,0(上单调递减，在),1(+∞上单调递增…………………13分因此2)1()(min ==g x g ，23≤∴b ，即32≤b 故b 的取值范围为]32，（∞-．…………………15分18．（本题满分17分）解：（1）设数列}{n a 公比的为q ，数列}{n b 公差的为d则由588a a =,283=∴=q q ，n n n q a a 211==∴-，…………………2分1684==b a ，即216728=∴=+=d d b ，n n b n 22)1(2=-+=∴．………………4分（2）设21)42sin(2211nn n b d ⋅-=⎥⎦⎤⎣⎡+-ππ）（则48128234224214243424144-=--+=+++------n b b b b d d d d n n n n n n n n ………………6分2)8048128()(414243443214+-=++++⋅⋅⋅++++=∴---n n d d d d d d d d S n n n n n ）（(6416)n n =+…………………7分nn n n n n n n n a n b S 2)2)(832(22216642224++=+⋅+=⋅⋅∴+++）（）（…………………8分令nn n n f 2)2)(832()(++=，则112)42)(832(2)3)(4032()()1(++++-++=-+n n n n n n n f n f nn n n n n 2)114(4288832212+--=+--=+，可得)()4()3()2()1(n f f f f f >⋅⋅⋅>>><，故当2=n 时，)(n f 最大.…………………11分60)1(=f 且，4147)5(=f ，25)6(=f ，∴414725≤<t ，即t 的取值范围为]414725，（．…………………12分（3）由11=c ，)2()1)(1(12≥-+=-=n n n nn n c n ，则当2≥n 时，)1(543)1)(1(423312121+⨯⨯⋅⋅⋅⨯⨯⨯=+-⨯⋅⋅⋅⨯⋅⨯⋅⨯=⋅⋅⋅n n n n n n c c c n 2111122(1)!(1)!!(1)!n n n n n n ⎡⎤⎡⎤+-===-⎢⎥⎢⎥+++⎣⎦⎣⎦…………………14分当1=n 时，11=c 也满足上式）（*∈⎥⎦⎤⎢⎣⎡+-=⋅⋅⋅∴N n n n c c c n )!1(1!1221…………………15分nc c c c c c c c c c ⋅⋅⋅⋅⋅+⋅⋅⋅+⋅⋅+⋅+∴3213212112)!1(22)!1(1!131212112<+-=⎦⎤⎢⎣⎡+-+⋅⋅⋅+-+-=n n n ！！！故原不等式成立.…………………17分19．（本题满分17分）解：（1）设),(00y x M ，）（y x N ,，则(,)ON x y =,00(,)OM x y =．由ON得00(,),)x y x y =，即30x x =，30y y =，…………………2分又),(00y x M 在椭圆C 上，所以122020=+y x .代入化简得22163x y +=所以点N 的轨迹E 的方程为22163x y +=．…………………4分（2）当两条切线的斜率存在时，设过00(,)T x y 点的切线为()00y y k x x -=-联立()002212y y k x x x y ⎧-=-⎪⎨+=⎪⎩，消去y 得()()()2220000124220k x k y kx x y kx ++-+--=则由判别式()22008120k y kx ⎡⎤∆+--=⎣⎦=…………………6分得()22200002210x k x y k y --+-=，设两条切线的斜率分别为1k ，2k ，依题意得201220112y k k x -⋅==--，即22003x y +=，…………………7分又点T 在轨迹E 上，2002163x y ∴+=解得000x y ==，T ∴或…………………8分当两条切线的斜率有一条不存在时，结合图像得不合题意．…………………9分综上，存在满足条件的点T ，且点T的坐标为或．…………10分（3）设()()1122,,,A x y B x y 将y kx m =+代入轨迹E 的方程，可得()222124260k x kmx m +++-=由222222164(12)(26)8(63)0k m k m k m ∆=-+-=+->，可得2236m k <+①且2121222426,1212km m x x x x k k -+=-=++…………………12分所以12212x x k -=+…………………13分因为直线y kx m =+与y 轴交点的坐标为()0,m所以OAB ∆的面积01212S m x x =⋅-==…………………14分将y kx m =+代入椭圆C 的方程可得()222124220k x kmx m +++-=由228(12)0k m ∆=+-≥，可得2212m k ≤+②令2212m t k=+,由①②可知01t <≤…………………15分因此0S ,故02S ≤当且仅当1t =，即2212m k =+时，0S 取得最大值2…………………16分由题知,OP =ABP ∴∆的面积101)S S =,又易知ABQ ∆面积202S S =从而四边形APBQ 的面积120=+=1S S S S ），所以四边形APBQ 面积的最大值为2）．…………………17分。

东安县天成实验学校2014年上期月考英语试题（总分：150分时量：120分钟命题人：蒋柏荣）Listening Comprehension(30 marks)Section A (22.5 marks)Directions: In this section, you will hear six conversations between two speakers. For each conversation, there are several questions and each question is followed by three choices marked A, B and C. Listen carefully and then choose the best answer for each question.You will hear each conversation TWICE.Conversation 11. When will the meeting be?A. On Friday morning.B. Around noon on Friday.C. After lunch on Friday.2. How will the woman reply to the man?A. By calling him back.B. By telling him in person.C. By leaving a message on his table. Conversation 23.What does the man mainly use the Internet for?A. Playing games.B. Reading the news.C. Making friends.4. What does the woman think of online computer games?A. Interesting.B. Boring.C. So-so.Conversation 35. Why did the woman’s parents go to Walt-Mart?A. To pick up Bill.B. To buy a birthday present.C. To buy some decorations.C. She was riding a bike.6. Who is the party for?A. Bill.B. Maria.C. Mike.Conversation 47. What do we know about the restaurant downtown?A. It’s quite expensive.B. They serve the best vegetables.C. There’re al ways many customers there.8. What does the woman think of raw fish?A. It tastes good.B. It sounds disgusting.C. She really wants to try it.9. What will the woman have?A. Raw fish.B. Cooked fish.C. Crabs.Conversation 510. Where does the woman want to put her picture?A. On LinkedInB. On Facebook.C. On her blog.11.What does the man suggest the woman do?A. Up load her picture.B. Use a cartoon picture.C. post her resume.12. According to the man, what can a picture show?A. How smart someone is.B. What someone is thinking.C. How someone looks on a certain day. Conversation 613. When is the concert?A. This Saturday.B. Next Friday.C. Next Saturday.14. How many years ago did the woman go to a U2 concert?A. Seven.B. Nine.C. Ten.15. What does the woman think about meeting Bono?A. She is very excited.B. She doesn’t really care.C. She’d rather meet someone else. Section B (7.5 marks)Directions: In this section, you will hear a short passage. Listen carefully and then fill in the numbered blanks with the information you have heard. Fill in each blank with NO MORE THAN THREE WORDS.You will hear the short passage TWICE.Part Ⅱ Language Knowledge(45 marks）Section A (15 marks)Directions：for each of the following unfinished sentences there are four choices marked A,B,C and D. Choose the one that best completes the sentence.21. The man was seriously wounded, so a doctor must be ________at once.A. looked forB. called forC. sent forD. asked for22. —Where is Peter? I can’t find him anywhere.—He ________TV in his bedroom.A. must have watchedB. might have watchedC. must watchD. must be watching23. —Is there anything important in his speech?—Not really. Although we don’t have much good news, ________he said so is wrong, I think.A. whichB. thatC. whatD. when24. As he would soon go to an ________ country, he had to take an evening course of language.A. speaking EnglishB. spoken EnglishC. English-spokenD. English-speaking25. ________leaves the office last ought to close the windows.A. Those whoB. WhoeverC. WhoD. Anyone26. To ________ the truth, I am ________ a telegram from him.A. say, waitingB. speak, hopingC. talk, wishingD. tell, expecting27. She tried to stop her daughter ________ in bed but the girl would not listen.A. readingB. to readC. readD. to be reading28. Our manager ________ to be back before 8, so you won’t have to wait long.A. expectsB. is expectedC. expectedD. was expected29. I t’s reasonable, ________it’s not true.A. soB. thereforeC. and butD. and yet30. The poster of the new show will ________ and you can have a look yourself.A. put upB. put onC. be put upD. be put on31. —Why, you are wet all over! —I _____ just now and I rushed all the way here.A. was caught in the rainB. was caught by the rainC. caught the rainD. caught a rain32. —Do you mind my taking this seat? —_____.A. Yes, pleaseB. Never mindC. No, you mustn’tD. Sorry, but my wife has taken it33. His TV set is only________.A. half size of yoursB. half the size of yoursC. one-third size of yoursD. two-third the size of yours34. I have five foreign friends, two ________ and three ________.A. Frenehmans, GermansB. Frenchmen, GermenC. Frenchmans, GermenD. Frenchmen, Germans35. We must always remember to do ________ the Party tells us to.A. likeB. asC. forD. becauseSection B (18 marks)Directions：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 words or phrases that best fits the context.I lived in Dallas，Texas nearly all my life with my mom，dad and older sister．We were raised to respectothers，value __36__，and get all that we could out of life．“You can be anything you want to be，” my parents always say．“Work hard and the world is yours” is often quoted in my house．My parents are never without a helpful word of advice or a bit of encouragement when life gets __37__．I always knew that going to college was __38__ of me．After all，both of my parents are college graduates with multiple degrees．Even after I decided at 16 years old that I’d rather get married to a man who was so __39__ wrong for me than go to college，they never __40__ telling me that they loved me and that I could do anything I wanted to do．Thankfully，they talked some sense into me．I graduated from high school and currently __41__ the University of Oklahoma．I am Pre-Med with a minor in Spanish．I want to make the world a better place．And I know that my parents are the __42__ for this．Every time I call home to tell them about a __43__ I received in Chemistry Lab or Zoology or whichever class it is that I’m working hardest for at the moment，they tell me how _44__ of me they are．I know there are college kids out there that hav e no one to call home to when they get an “A” on a project and I feel extremely __40__ to have my parents．I __46__ everything I am to my parents．Without their constant love and encouragement，I wouldn’t believe that I can change the world．My parents taught me never to __47__ and to always fight for what I believe in．And so I’m working toward something really great and can only hope that I continue to make them proud．36．A．freedom B．education C．reformation D．creation37．A．unusual B．boring C．difficult D．different38．A．hoped B．required C．expected D．dreamed39．A．gradually B．mentally C．clearly D．partly40．A．continued B．remembered C．avoided D．stopped41．A．attend B．escape C．admit D．admire42．A．example B．pressure C．preparation D．reason43．A．failure B．grade C．reward D．praise44．A．nervous B．proud C．reliable D．grateful45．A．confirmed B．confused C．blessed D．balanced46．A．contribute B．owe C．offer D．devote47．A．settle B．blame C．complain D．performSection C (12marks)Directions: Complete the following passage by filling in each black with one word that best fits the context.Some day,48．________ you are lucky，you may see a bongo(大羚羊)．But the only way most people will see it is in a zoo．They are found in Africa,49．________ they live deep in forests．Even in Africa，very few people ever get to see a bongo．The bongo does not come out of the forest very often．It is an animal 50．________ keepsto itself．The bongo has beautiful coloring．Its hair is bright brown mixed 51．________ orange and red．Down its back and across its sides the bongo has yellow-white strips(条纹)．Animals that look 52．________ food at night usually have big eyes．This helps them see 53．________ at night．The forests in which bongos live are very dark．The eyes of bongos are very big．So，they have 54．________ trouble living in the darkness．Bongos in zoos do not like to go outside in bright days．They only go outside in those days 55．________ it is dark or very cloudy．Part Ⅲ Reading Comprehension (30marks)Directions: Read the following 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.Passage AWhen we see well, we do not think about our eyes very often. It is only when we cannot see perfectly that we realize how important our eyes are.People who are near-sighted can only see things that are very close to their eyes, Everything else seems blurry(=unclear). Many people who do a lot of work, such as writing, reading and sewing become near—sighted. ThenPeople who are far-sighted suffer from just the opposite problem. They can see things that are far away, but they have difficulty in reading a book unless they hold it at arm’s length. If they want to do much readi ng ,they must get glasses, too.Other people do not see clearly because their eyes are not exactly the right shape. They have what is called astigmatism (散光). This, too, can be corrected by glasses. Some people’s eyes become cloudy because of cataracts (白内障). Long ago these people often became blind. Now, however, it is possible to operate on the cataracts and remove them.Having two good eyes is important for judging distances. Each eye sees things from a slightly different angle (角度). To prove this to yourself, look at an object our of one eye; then look at the same object out of your other eye. You will find the object’s relation to the background and other things around it has changed. The difference between these two different eye views helps us to judge how far away an object is. People who have only one eye cannot judge distance as people with two eyes.56. We should take good care of our eyes .A. only when we can see wellB. only when we cannot see perfectlyC. even if we can see wellD. only when we realize how important our eyes are57. When things far away seem indistinct(模糊不清) , one is probably .A. near-sightedB. far-sightedC. astigmaticD. suffering from cataracts58. The underlined word suffer in the third paragraph probably means .A. experienceB. imagineC. feel painD. are affected with59. Having two eyes instead of one is particularly useful for .A. seeing at nightB. seeing objects far awayC. looking over a wide areaD. judging distances60. People who suffer from astigmatism have .A. one eye bigger than the otherB. eyes that are not exactly the right shapeC. a difficulty that can be corrected by an operationD. an eye difficulty that cannot be corrected by glassesPassage BGrandma was a wonderful story-teller, and she had a set of priceless, individually (独特地) tailored stories with which American grandparents of her day brought up children. There was the story of the little boys who had been taught complete, quick obedience (服从). One day when they were out on the grassy plain, their father shouted. “Fall down on your faces!” They did, and the terrible prairie(草原) fire swept over them and they wer en’t hurt. There was also the story of three boys at school, each of whom received a cake sent from home. One saved his, and the mice ate it; one ate all of his , and he got sick; and who do you think had the best time? —Why, of course, the one who shared his cake with his friends.61. What is the main idea of this passage?A. Children should obey their parents quickly.B. Children should share with others.C. The author remembers many of her grandma’s wonderful stories.D. The grandma’s stories helped teach the children morals and good manners.62. Which of the following details supports the main idea of the passage?A. The children were saved from the fire because they followed directions.B. Grandma told a story of three boys at school.C. Each of the three boys got a cake sent from home.D. The big prairie fire soon spread over to the village.63. Which of the following statements is true?A. The author was saved from the fire.B. The author was brought up from his grandmother.C. Grandma was good at telling children stories.D. Grandma told stories to children just for fun.64. All of the following were not praised by the author except ___________.A. the boy who shared his cake with othersB. the boy who ate up all his cake by himselfC. the boy who kept the cake for the futureD. the boys who didn’t obey their parents65. According to this passage, the underlined word tailored probably means __________.A. measuredB. specially preparedC. cutD. inventedPassage CPete Rose，the famous baseball player，whom I have never met，taught me something so valuable that it changed my life．Pete was being interviewed in spring training the year he was about to break Ty Cobb’s all­time hits record．One reporter asked, “Pete，you only need 78 hits to break the record．How many at-bats (轮到击球) do you think you’ll need to get the 78 hits？” Without hesitation，Pete said，“78．” The reporter yelled back，“Ah，come on Pete．You don’t exp ect to get 78 hits in 78 at-bats，do you？”Mr．Rose calmly shared his rule in life with all the reporters who were anxiously awaiting his reply．“Every time I step up to the plate，I expect to get a hit! If I don’t expect to get a hit，I have no right to step i n the batter’s box in the first place! If I go up hoping to get a hit，then I probably don’t have a prayer of getting a hit．It is the positive expectation that has gotten me all of the hits in the first place．”When I thought about Pete Rose’s rule and how it was applied to everyday life，I felt a little embarrassed．As a business person，I was hoping to make my sales meet the quotas (定额)．As a father，I was hoping to be a good dad．As a married man，I was hoping to be a good husband．The truth was that I_was_an_adequate_salesperson，I was not so bad as a father，and I was an okay husband．I immediately decided that being okay was not enough! I wanted to be a great salesperson，a great father and a great husband．I changed my attitude to one of positive expectation，and the results were amazing．I was fortunate enough to win a few sales trips，I won Coach of the Year in my son’s baseball league，and I share a loving relationship with my wife! Thanks，Mr．Rose!66．Which of the following sayings can most appropriately be used to describe Mr．Rose’s rule?A．He who doesn’t want to be a general can’t be a good soldier．B．Before everything else，getting ready is the secret of success．C．If you work hard enough，your dreams will come true．D．Rome was not built in one day．67．What can be inferred about Pete Rose from the passage?A．He was generous to share all his rules with everyone．B．He got all the hits he wanted because of good luck．C．He set himself a goal of being the best．D．He liked to dream of something impossible．68．By saying “I was an adequate salesperson” (in Para．3) the writer probably means “________”．A．he could make adequate money as a salespersonB．he didn’t do an excellent job as a salespersonC．he was good enough to be a salespersonD．he knew how to sell goods in a proper way69．Which of the following is NOT a role of the writer?A．A teammate of Rose．B．A salesman．C．A father．D．A baseball coach．70．Why does the writer thank Mr．Rose at the end of the passage?A．Because Mr．Rose showed him how to be a successful salesperson．B．Because Mr．Rose taught him to face life with positive expectation．C．Because Mr．Rose trained him to win Coach of the Year for his son．D．Because Mr．Rose gave him advice on managing a happy family．Part Ⅳ Writing （45 marks）Section A（10 mark）Directions: Read the following passage. Fill in the numbered blanks by using the information from the passage.Write NO MORE THAN THREE WORDS for each answer.Do you think that daydreaming is a waste of time？Probably so．“On the contrary，”says L．Giambra，an expert of psychology，“Daydreaming is quite necessary．Without it，the mind couldn’t get done all the thinking it has to do during a normal day．．．You can’t possibly do all your thinking with consciousness．Instead，your unconscious mind is working out problems all the time．Daydreaming then may be one way that the unconscious and conscious states of mind have silent dialogues．”Early psychology experts paid no attention to the importance of daydreams or even considered them harmful．At one time daydreaming was thought to be a cause of some mental illnesses．They did not have a better understanding of daydreams until the late 1980’s．Eric Klinger，a professor of psychology，is the writer of the book DAYDREAMING．Klinger says，“We know now that daydreaming is one of the main ways that we organize our lives，learn from our experiences，and plan for our futures．．．Daydreams really are a window on the things we fear and the things we long for in life．”Daydreams are usually very simple and direct，quite unlike sleep dreams，which may be hard to understand．It’s easier to gain a deep understanding of your life by paying close attention to your daydreams than by trying to examine your sleep dreams carefully．Daydreams help you recognize the difficult situations in our life and find out a possible way of dealing with them．Daydreams cannot be predicted．They move off in unexpected directions which may be creative and full of ideas．For many famous artists and scientists，daydreams were and are a main source of creative energy．Sect ion B(10 marks)Directions: Read the following passage. Answer the questions according to the information given in the passage.The Intel Science Talent Search is the oldest American science contest for students in their last year of high school．The competition was created in 1942．It can interest high school students in science and engineering positions．The Westinghouse Company worked with the Society for Science and the Public to hold the first of these contests．Since then，the Science Talent Search has provided 4 million dollars for college education to almost 3,000 young people．The organizers say that some c ontestants later won more than 100 of the world’s top science honors，including the Nobel Prize and the National Medal of Science．Every year，more than 1,500 American high school students enter the Intel Science Talent Search．Judges select 300 semi-finalists(参加半决赛者)，and then reduce that number to 40 finalists(参加决赛者)．Each finalist receives 5,000 dollars，a new laptop computer and a trip to Washington D．C．．During the trip，finalists meet with government officials before meeting separately with the judges from the Science Talent Search．The judges question the young people about their projects and on their general scientific knowledge．10 winners are chosen from the group of 40 finalists and the 10 winners receive money to pay for their college education．The most recent students to reach this stage studied subjects such as colon cancer，mathematics and insect environments．At the last stage，one tops out．This year，the third place winner received 50,000 dollars．The second place winner received 75,000 dollars while the top prize was 100,000 dollars forcollege．This year，the first place prize went to Shivani Sud，who developed a method to improve the health of those people at risk of colon cancer．Her method can tell which of these patients have a higher than normal chance that the cancer will return．Shivani Sud also studied the best medicines to treat these cancers．She says that she plans to become a doctor and continue to engage in medical research．81．Who can the Intel Science Talent Search interest？(no more than 8 words)82．How many stages does the first place winner have to go through before he of she beats the other contestants？(no more than 2 words)83．According to the organizers，what is the purpose of the Intel Science Talent Search？(no more than 8 words)84．What does the Intel Science Talent Search mainly examine？(no more than 6 words)Section C (25 marks)Directions: write on English composition according to the i nstructions given below in Chinese.下表是你平时了解到的中国高三学生选择高考志愿的信息。

东安县天成实验学校2013年上期高一期中考试英语试题（总分：150分时量：120分钟命题人：蒋柏荣）Listening Comprehension(30 marks)Section A (22.5 marks)Directions: In this section, you will hear six conversations between two speakers. For each conversation, there are several questions and each question is followed by three choices marked A, B and C. Listen carefully and then choose the best answer for each question.You will hear each conversation TWICE.Conversation 11. Why can‟t the woman sleep well?A. She studies math too hard.B. She spends much time on TV.C. She has too much time for dinner.2. What does the doctor tell her to do?A. Go to bed early.B. Eat more fruit.C. Relax herself.Conversation 23. Where does the conversation take place?A. In a bank.B. In a post office.C. In a shop.4. What is the man going to do next?A. Go to the bank.B. Change his clothes.C. Buy something in the shop. Conversation 35. What should the woman do at the second crossing?A. Turn right.B. Turn left.C. Go straight ahead.6. How will the woman probably go there?A. By bus.B. By bike.C. On foot.Conversation 47. What time is it now?A. 8:00.B. 8:10.C. 9:00.8. How are the speakers going to the wedding?A. By bus.B. By car.C. By train.9. In which month does this conversation take place?A. April.B. May.C. June.Conversation 510. When will the man get up in the morning?A. At 6:00.B. At 7:00.C. At 8:00.11. On which floor is the dining room?A. The first floor.B. The second floor.C. The third floor.12. How often is the laundry collected?A. Once a day.B. Twice a day.C. Every day. Conversation 613. Why is the woman‟s uncle disabled?A. Because of a disease.B. Because of a car accident.C. Because of a war.14. When did he become disabled?A. Five years ago.B. Four years ago.C. Three years ago.15. What is the woman‟s uncle now?A. A professor.B. A publisher.C. A doctor.Section B (7.5 marks)Directions: In this section, you will hear a short passage. Listen carefully and then fill in the numbered blanks with the information you have heard. Fill in each blank with NO MORE THAN THREE WORDS.You will hear the short passage TWICE.A Speech on Culture DifferenceI. In North America●The gift-giving rules are simple.●Bring 16 or a small gift from your country when you‟re invited to one‟s home fordinner.●Family and 17 don‟t give gifts to each other except on someone‟s birthday andChristmas.II. 18●People give gifts quite often.●There‟re many rules for everything from the color to the 19 of giving the gift.III. In Europe●Europeans don‟t generally give business gifts.●They may bring flowers when visiting homes, but the color of flowers can carry 20 .Part Ⅱ Language Knowledge(45 marks）Section A (15 marks)Directions：for each of the following unfinished sentences there are four choices marked A,B,C and D. Choose the one that best completes the sentence.21. ____he always serves the people very well is known.A. WhatB. ThatC. WhichD. Who22.____has passed the test will get a prize .A. WhoeverB. No matter whoC. WhomeverD. Who23.Is____ true that the famous scientist will give us a lecture next week?A thatB itC hisD he24.It has not been decided ___ they will leave for New York.A. when B why C that D what25. Obviously___ we do morning exercises every day ___ us good.A. that doB. if; do C what; does D. that; dose26 It is said____ ____ was all ___ he said.A that; that; thatB what; what; whatC that; which; whatD that; that; which27___ gets home first is to cook the supper.A. Who B Whom C. Those who D. Whoever28___ moved us most was___ he looked after the old man for more than twenty years.A. That; thatB. What; that C What; what D. That; what29.___ you did it is not known to all.A. WhoB. WhatC. HowD. Which30.___ you do should be well done.A How B. That C. Whatever D Why31. The Smiths ____China since the summer of 1993.A. has been toB. have been toC. has been inD. have been in32. Not only the parents but also Mary ____ London .They will come back in five days.A. has been toB. have been toC. has gone toD. have gone to33. In our country, the old ___taken good care of and the young___ well educated.A. isB. areC. hasD. have34. Each man and each woman____ bring some water here.A. HasB. haveC. has toD. have to35. Everyone except Tom and John_____ there then.A. isB. wasC. areD. wereSection B (18 marks)Directions：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 words or phrases that best fits the context.I am an eleven-year-old primary school boy and all of my teachers complained about my unreadable handwriting．So I started taking my laptop to school and using it instead of paper，books and __36__．At first I thought I was in heaven．Writing essays had become so easy．Copying notes took seconds．I don‟t have to worry about spelling mistakes and whether I have __37__ to carry my textbooks．I was always organized，as I could not leave my books at home anymore as they were saved in my machine，so you would think that it was __38__ as a learning tool．Unfortunately，soon I completely__39__all my ability to write，which is very limiting when still at school．My spelling became worse as I no longer had to think about it due to the computer‟s auto corrector．However，this wasn‟t what __40__ me the most．It was the fact that I was no longer learning what I used to in class．The simple act of writing something down was a way of learning for me，and a laptop could never __41__that．Exams started to become harder as I no longer knew all the words and phrases，because I __42__wasn‟t learning it just by typing it down．Also each lesson was at least five minutes shorter because of the time needed to __43__ at the beginning of the class and pack away at the end of lessons．Finding and learning notes in your computer is also less __44__．Furthermore，a computer does not have the same __45__ of use as paper，as paper doesn‟t have to be fully charged．Fin ally I couldn‟t focus on my class knowing I had the whole Internet at my fingertips．So during lessons I would often search the Internet and have __46__．As you can see，the __47__ are far more than the benefits．Therefore I stopped taking my computer to lessons．Now I perform better at school．36．A．bags B．articles C．dictionaries D．pens37．A．decided B．forgotten C．dreamed D．learned38．A．particular B．decisive C．beneficial D．exact39．A．enjoyed B．dropped C．ignored D．lost40．A．bothered B．puzzled C．shocked D．interested 41．A．mix B．change C．replace D．avoid42．A．simply B．carelessly C．finally D．slowly43．A．get across B．start up C．give out D．round up 44．A．useful B．valuable C．effective D．careful45．A．importance B．convenience C．difference D．guidance 46．A．fun B．luck C．success D．advantage 47．A．excitements B．negatives C．dangers D．termsSection C (12marks)Directions: Complete the following passage by filling in each black with one word that best fits the context.In North America people are always in 48．________ hurry．Children have special lessons or sports activities after school．Parents often wo rk late and don‟t get home until 7 or 8 o‟clock 49．________ night．Most North American families don‟t have time to prepare a meal．That is 50．________ fast food is so popular in North America．People spend about 40% of their dollars 51．________ fast food．People usually buy fast food from restaurant chains such as Pizza Hut，McDonald‟s，or KFC，52．________ they can enjoy pizza，sandwiches，fried chicken and so on．Fast food saves work and time，53．________ it is not nutritious．Fast food is popular in many countries．American fast-food companies now have restaurants all over the world．But not 54．________ is happy about the spread(扩展) of North American fast food．A group of people in Italy want to fight 55．________ the spread of American fast food．They don‟t like the ide a of more fast food chains opening restaurants in their country．Part Ⅲ Reading Comprehension (30marks)Directions: Read the following 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.Passage AA man is going to the house of a rich man. He sees a box of good apples by the road. He says, “I don‟t want those apples, because the rich man will give me a lot of good food.” Then he takes the apples and throws them away into the dust.He comes to a river. The water in the river is very deep and he can‟t go over. He waits for some time and then says, “I can‟t go to the rich man‟s house, because I can‟t cross the river.” So he begins to go home.He has nothing to eat that day. He is very hungry, so he comes to the apples. He is glad to take them out of the dust.Don‟t throw good things away, for you may be glad to have them sometimes.56. The man finds a box of apples _________.A. by the riverB. in the middle of the riverC. at the rich man‟s doorD. on his way to the rich man‟s house57. He throws the apples away because __________.A. he doesn‟t like the apples any moreB. he thinks he can eat good things soonC. he can‟t carry themD. the apples are too small58. He can‟t cross the river because_________.A. the rich man doesn‟t give him a boatB. there‟s some water in the riverC. something is wrong with the boatD. the water in the river is very deep59. He is hungry because ___________.A. he eats nothing at allB. he wants to cross the riverC. the rich man doesn‟t give him anything to eatD. he doesn‟t have breakfast60. The story tells us ________.A. Take up everything on the roadB. To be brave to cross the riverC. Don‟t throw good things awayD. Don‟t throw anything awayPassage BOne of Mike‟s friends loved money very much and never gave anything to anybody. Soon he became rich. One day he was walking along the river with his friends. He was talking and laughing and suddenly he fell into the river. His friends tried to help him. One of them held out his hand and said, “Give me your hand , and I‟ll pull you out!” The rich man‟s head went under the water and then came out again, but he did not give his hand to his friend. Again another of his friend cried , but again the same thing happened.Then Mike said, “Take my hand and I‟ll pull you out!” The rich man took his hand immediately, and Mike pulled him out of the water.“You don‟t know our friend very well,” he said to the others. “When you say …Give‟ to him, he does nothing but when you say …Take‟, he takes!”61. Mike‟s friend liked ________ very much.A. MikeB. to walkC. moneyD. the river62. One day, he _________.A. was walking with MikeB. was talking with MikeC. was walking with his friendsD. was talking with his friends63. The rich man ______.A. gave his hand to MikeB. gave his hand to his friendsC. took out his hand to his friendsD. took out his hand to Mike64. Mike _________.A. knew the rich manB. liked the rich manC. couldn‟t understand his friendD. liked to be with the rich man65. The rich man was _________.A. a kind manB. a helpful manC. too selflessD. too selfishPassage CO. Henry was a pen name used by an American writer of short stories. His real name was William Sydney Porter. He was born in North Carolina in 1862. As a young boy he lived an exciting life. He did not go to school for very long, but he managed to teach himself everything he needed to know. When he was about 20 years old, O. Henry went to Texas, where he tried different jobs. He first worked on a newspaper, and then had a job in a bank, when some money went missing from the bank O. Henry was believed to have stolen it. Because of that, he was sent to prison. During the three years in prison, he learned to write short stories. After he got out of prison, he went to New York and continued writing. He wrote mostly about New York and the life of the poor there. People liked his stories, because simple as the tales were, they would finish with a sudden change at the end, to the reader‟s surprise.66. In which order did O. Henry do the following things?a. Lived in New York.b. Worked in a bank.c. Travelled to Texas.d. Was put in prison.e. Had a newspaper Job.f. Learned to write stories.A. e. c. f. b. d. aB. c. e. b. d. f. aC. e. b. d. c. a. f.D. c. b. e. d. a f.67. People enjoyed reading O. Henry‟s stories becauseA. they had surprise endingsB. they were easy to understandC. they showed his love for the poorD. they were about New York City68. O. Henry went to prison because .A. people thought he had stolen money from the newspaperB. he broke the law by not using his own nameC. he wanted to write stories about prisonersD. people thought he had taken money that was not his69. What do we know about O. Henry before he began writing?A. He was well-educated.B. He was not serious about his work.C. He was devoted to the poor.D. He was very good at learning.70. Where did O. Henry get most material for his short stories?A. His life inside the prison.B. The newspaper articles he wrote.C. The city and people of New York.D. His exciting early life as a boy.Part ⅣWriting （45 marks）Section A（10 mark）Directions: Read the following passage. Fill in the numbered blanks by using the information from the passage.Write NO MORE THAN THREE WORDS for each answer.The Chinese are very generous when it comes to educating their children．Some parents send their children to the best schools or even abroad to England，the US or Australia，regardless of how much this costs．Many also want their children to take extra-curriculum activities where they either learn a musical instrument or ballet，or other classes that will give them a head start in life．The Chinese believe that the more expensive an education is，the better it is，so parents often spend unreasonable amounts of money on education．Even poor couples buy a computer for their sons or daughters．However，what most parents fail to see is that the best education they can give their children is usually very cheap．Parents can see that their children‟s skills vary；they will usually be skilled in some areas while poor in others．What most parents fail to realise though，is that today‟s children lack self-respect and self- confidence．The problem is that parents are only educating their children on how to take multiple-choice tests and how to study effectively．They are not teaching them the most important skills they need to be confident，happy and clever．Parents can help achieve this by teaching their children practical skills like cooking，sewing and other housework．Teaching a child to cook will improve many of the skills that he will need later in life．Cooking demands patience and time．It is an enjoyable but difficult experience．A good cook always tries to improve his cooking，so he will learn to work hard and gradually finish his job successfully．The result，a well-cooked dinner，will give a child a lot of satisfaction and confidence．An old machine，such as a broken radio or TV set that you give your child as a toy may make him curiousand arouse his interest．If he will spend hours looking at it，and try to mend it—your child might become an engineer when he grows up．Such activities do more than teaching a child to read a book；but rather than teaching them to think，and to use their minds．This is much more important than learning by reading a book．educate their children properly．Sect ion B(10 marks)Directions: Read the following passage. Answer the questions according to the information given in the passage.(IOC President‟s Speech at the Closing Ceremony of the Games of the XXIX Olympiad)Dear Chinese Friends，Tonight，we come to the end of 16 glorious days which we will cherish(缅怀) forever．Thank you to the people of China，all the wonderful volunteers and BOCOG！Through these Games，the world learned more about China，and China learned more about the world．Athletes from 204 National OlympicCommittees came to these dazzling venues and awed us with their talent．New stars were born．Stars from past Games amazed us again．We shared their joys and their tears，and we marveled at (were surprised at) their ability．We will long remember the achievements we witnessed here．As we celebrate the success of these Games，let us together wish the best for the talented athletes who will soon participate in the Paralympic Games(残奥会)．They also inspire us．To the athletes tonight：You were true role models．You have shown us the unifying power of sport．The Olympic spirit lives in the warm embrace of competitive rivals(competitors) from nations in conflict(competition)．Keep that spirit alive when you return home．These were truly exceptional Games!And now，in accordance with(依照) tradition，I declare the Games of the XXIX Olympiad closed，and I call upon the youth of the world to assemble (gather) four years from now in London to celebrate the Games of the XXX Olympiad．Thank you!81．What did China get from the XXIX Olympiad according to the speech？(no more than 6 words)82．What would take place in Beijing after the XXIX Olympiad closed？(no more than 8 words)83．Why did IOC President say the athletes were true role models？(no more than 13 words)84．When will London hold the XXX Olympiad？(no more than 4 words)Section C (25 marks)Directions: write on English composition according to the i nstructions given below in Chinese.9月22日你所在的城市和另外107个城市开展了"无车日"活动，倡议人们选用公共汽车、自行车或步行等绿色交通方式来代替开私家车。

考场座位号 班级 _姓名 考号 ◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆装◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆订◆◆◆◆◆◆◆◆◆◆◆◆◆线◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆东安天成实验学校2013年12月月考高一年级数学试卷满分150分；考试用时120分钟。

一、选择题(本大题共8小题，每小题5分，共40分)1、已知集合{1,2,3,4,5,6},{134}U A ==，，，，则U C A =（ ）（A ）{5,6} （B ）{1,2,3,4} （C ）{2,5,6} （D ）{2,3,4,5,6} 2．下列命题中，错误的是（ ）A ．平行于同一个平面的两个平面平行B ．平行于同一条直线的两个平面平行C ．一个平面与两个平行平面相交，交线平行D ．一条直线与两个平行平面中的一个相交，则必与另一个相交3. 正方体1111D C B A ABCD -的对角线1AC 的长为3cm ，则它的体积为（ ）A ．34cm B ． 38cm C .372112cm D ．333cm 4. 如图，将一个长方体沿相邻三个面的对角线截出一个棱锥， 则棱锥的体积与原长方体的体积之比为 （ ）A. 1﹕3B. 1﹕4C. 1﹕5D. 1﹕6 5、把函数1y x=的图象向左平移1个单位，再向上平移2个单位后，所得函数的解析式应为（ ） （A ）321x y x -=- （B ）211x y x -=- （C ）211x y x +=-+ （D ）231x y x +=+6、函数()212log 45y x x =--的递减区间为（ ）（A ）()-∞，2 （B ）()2+∞，（C ）()--1∞， （D ）()5+∞，7、函数2223()(1)m m f x m m x --=-- 是幂函数，且在(0,)x ∈+∞ 是减函数，则实数m =（ ）（A ）2（B ）3 （C ）1 （D ）-18．设γβα,,为两两不重合的平面，n m l ,,为两两不重合的直线，给出下列四个命题： ①若γα⊥，γβ⊥，则//αβ；②若α⊂m ，α⊂n ，//m β，//n β，则//αβ；③若//αβ，α⊂l ，则//l β； ④若l =βα ，m =γβ ，n =αγ ，//l γ，则//m n ．其中真命题的个数是（ ）A ．1B ．2C ．3D ．4 二、填空题：（本大题共7小题，每小题5分，共35分）9、函数()f x =的定义域为______. 10、若一次函数()f x x b =+有一个零点2，那么函数2()+g x bx x =的零点是 . 11. 用一平面去截球所得截面的面积为π2cm 2，已知球心到该截面的距离为1 cm ，则该球的体积是 cm 3.12、已知0<a<1,则方程log x a a x =的解的个数为 个 .13、定义集合运算{|,,}{12},{02}A B z z xy x A y B A B *==∈∈==，设，，， 则集合A B *的所有元素之和为 .14．一个正方体纸盒展开后如图，在原正方体纸盒中有下列结论：①AB ⊥EF ；②AB 与CM 成60°；③EF 与MN 是异面直线；④MN ∥CD ． 其中正确结论的序号是________．15、已知()(2)(3)f x m x m x m =-++，()22x g x =-，若同时满足条件：①,x R ∈任意的有()0f x <或()0g x < ； ②存在(,4)x ∈-∞- ,使得()()0f x g x < .则()0g x <的解集是 ， m 的取值范围是_______.三、解答题：（本大题共6小题，共75分） 16、（满分12分）计算下列各式的值.（1） ()()1223021329.63 1.548--⎛⎫⎛⎫ ⎪⎪⎝⎭⎝⎭---+（2） 2lg5lg 20(lg 2)⋅+17、（满分12分）已知()f x 是定义在(0，+∞)上的增函数，且满足条件以下条件：()()()f xy f x f y =+,(2)1f =.（1）求证：(8)3f =.(2)求不等式()3(2)f x f x >+-的解集.18．(本小题满分12分)如图为一个几何体的三视图，求这个几何体的表面积和体积．19. (本小题满分13分)如图，正方体1111D C B A ABCD -中， E 是1DD 的中点． （1）求证：1BD ∥平面AEC ； （2）求1BC 与平面11A ACC 所成的角.B A CBA20、（本小题满分13分）如图，在矩形ABCD 中，AB=33，BC=3，沿对角线BD 将BCD折起，使点C 移到点C ˊ，且C ˊ在平面ABD 的射影O 恰好在AB 上 （1）求证：BC ˊ⊥面ADC ˊ； （2）求二面角A —BC ˊ—D 的正弦值。