高一英语月考试题及答案-杭州市西湖高级中学2014-2015学年高一4月月考

浙江省杭州市西湖高级中学2014-2015学年高一10月月考英语试题I. 单项选择（共20小题；每小题1分，满分20分）1. We should not _______ small mistakes, or they might lead to big accidents.A. hurtB. ignoreC. recoverD. dislike2.--- How are you _______ with your study at present?--- very well.A. getting inB. getting overC. getting alongD. getting together3. I am very grateful for your assistance, and hope that one day 1 may be able to do something foryou__________.A. in turnsB. in caseC. in returnD. In use4. Try to _____ the children down. They’re too excited.A. putB. calmC. pullD. push5. As we all know, many Chinese words have come into English, ___ typhoon, tofu and kung fu.A. for exampleB. that isC. such asD. so as to6. ______ students passed the exam although it was a little difficult.A. A great dealB. The number ofC. A large number ofD. A great deal of7. The engine of the ship was out of order and the bad weather ______ the helplessness of the crew at sea.A. added toB. resulted fromC. turned outD. made up8. Since Margot found it difficult to settle in a new place, she felt ______ that the family had to move.A. upsetB. crazyC. happyD. easy9. They became good friends during the war, and since then their lifelong friendship has______ tests of life and death.A. gone throughB. got throughC. stood upD. cleared up10.He is a _______visitor to that country .I mean ,he often goes there .A. gratefulB. looseC. frequentD. native11.In ______1600’s ,Shakespeare made use of _______wider vocabulary than ever before .A. the ;aB./ ;/C. the ;/D./;a12.The open-air celebration has been put off ______the bad weather .A .in case of B. in spite of C. instead of D. because of13.They ________that immediate action be taken to stop the water pollution .A. requestedB. expectedC. wishedD. realized14. ----My sister is very upset today.----It’s your fault. You ________ the bad news to her yesterday.A. should tellB. should have toldC. shouldn’t have toldD. must tell15. Many questions ______ at the meeting, but he answered none.A. came upB. raisedC. were risenD. asked16．________time goes by，Mother’s hair has turned grey and the wrinkles on her face deeper.A．As B．With C．While D．Because17. The Australian boy has a good ______of Chinese and can communicate with others freely.A. requestB. commandC. demandD. usageII. 完形填空（共20小题；每小题1分，满分20分）阅读下面短文，从短文后各题所给的四个选项（A、B、C和D）中，选出最佳选项。

1.1.The poor man’s life was _________ of the king.A.at the mercy ofB. at the callC. at the serviceD. at the experience2.Jumping out of ______ airplane at ten thousand feet is quite _______ exciting experience.A. /; /B. /; anC. an; anD. the; the3.There was a nice little present for everyone , with a suitable poem _________ to it .A. attractedB. attackedC. attachedD. attributed4.He was searching for information on the internet when the computer system ________suddenly.A. broke downB. broke outC. broke 0ffD. broke in5. Would you please keep silent? The weather report ________ and I want to listen.A. is broadcastedB. is being broadcastC. has been broadcastedD. had been broadcast6. I hate _________ when my favorite programs are interrupted by commercial advertisements.A. thatB. itC. thisD. you7. Those who suffer from headache will find they get ___ from this machine.A. reliefB. safetyC. defenseD. shelter8. Once out of the earth’s gravity, the astronaut is ___ by the problem of weightlessness.A. affectedB. effectedC. relatedD. offered9. _______the competition in society is becoming fiercer and fiercer, more and more people turn to ______ drugs to reduce their pressure.A. With; takingB. As; takeC. With; takeD. As; taking10. Great attention must be paid ____ welfare, especially in the poor area.A. developB. to developC. to developingD. developing11. His generosity ___ him the reputation of “The most generous man” in his area.A. madeB. earnedC. achievedD. gave12. You are silly not _____ your door.A. to lockB. to have lockedC. lockingD. having locked13. ----I ____ to a party, but I’ve got nothing to wear.---- Why don’t you have a dress made for the party?A was askedB will askC have askedD have been asked14. ______, the pay isn’t attractive enough, though the job itself is quite inter esting.A. To be honestB. In generalC. On the contraryD. In total15. My teeth are _____________ to cold food; I prefer soup to ice cream.A. sensibleB. sensitiveC. suitableD. acceptable16. ________ your report, what is most important to protect our environment ?A. As a result ofB. Because ofC. With the help ofD. According to17. It was in the garden of his old house ______ he grew up ______ he dug up a pot of gold.A. that; thatB. where; whereC. that; whereD. where; that18. It is Tim, my best friend in my childhood, who tells me he always dreams of ______ for him togo to Shanghai to study and live there.A. there to be a chanceB. there is a chanceC. there being a chanceD. being a chance19. ---Tom stayed up late into night, watching NBA.---______ he felt sleepy in class.A. No doubtB. No wayC. No problemD. No wonder20. --How much do you______ for mending my bike?--Only one dollar, sir.A. payB. offerC. chargeD. applyII. 完型填空（共20小题；每小题1分，满分20分）阅读下面短文，掌握其大意，然后从41-60各题所给的四个选项（A、B、C和D）中，选出最佳选项。

杭西高2010 年10 月高一英语试卷命题人：江湘娟，审核人：宋晓红卷I一单项选择：20 分1. If we sit near ______ front of the bus, we 'll have _____ better view.A. /; the B /; a C the; a D the; the2. The trousers cost ______ . What 's more, they are ________ short for me.A. much too; too muchB. too much; much tooC very much; very D. very much; much3. In my opinion, you 'd better eat and sleep more _________ lose any more weight.A. so as toB. in order not toC. to notD. so that not to4. I _______ you would come so early .A. am not expecting B don't expect C. didn 't expect D. not expect5. Oh, I 'm not feeling well in the stomach. I ___ so much fried chicken just now.A. shouldn 'teat B mustn 't have eaten C. shouldn 't have eaten D. mustn 'teat6. This is the first time that I __________ at the meeting.A. had spokenB. have spokenC. amD. was7. -- Mary looks sad. What ________ her ?--- She failed in the maths exam.A. happened toB. happenedC. was happened D were happened8. Lily _______ the League last month and she wants to _______ the activities to helpthe aged in town next week.A. joined in; join in B took part in; attend C. joined in; attend D. joined ; join in9. It was ________ she was injured in the accident _______ she didn 't come to the party yesterday .A.as; whichB. because; that C since; why D. for; how10. -- Mum, have you seen my mobile phone?--- _______ you bought last week? I 'm afraid I haven 't seen _________ .A. The one; it B The one; one C One, it D. One, one11. _________________________________________________________________ With no rain for three months, and the food supplies running out, the present _____________here is getting worse.A. case B condition C state D situation12. The police asked him to _______ the facts just as he remembered them.A. set about B set down C set up D set out13. -- So you missed the meeting.--- _______ . I got there five minutes before it finished.A. Not at all.B. Not exactlyC. Not especially D Not correctly14. Rescuers are ________ for the safety of two men trapped in the mine.A. grateful B concerned C loose D entire15. - Can you ____ all the money that I should pay now?--- Very sorry , madam. Wait a minute, please.A. add upB. add to C add up to D add16. The grass seeds which were sow n in Spring are beg inning to ______A. come outB. come upC. come overD. come in17. The film is ______ a no vel by D.H丄awre nee.A. depe nded onB. based onC. come onD. put on18. Don 'forget to turn to me if youhave any trouble.21 languages there are in the world? There are about 1500, but many of them.En glish is one of the most importa nt la nguages because many people only in En gla nd andAmerica, 24 in other cou ntries of world. About 375000000 their own Ianguage, and another 375000000 use it as 26 Ianguage. It people are lear ning it. 28 boys and girls in schools aretrying to do so.Many En glish childre n study Fren ch. French is also a very importa nt Ianguage.Germa n, Russia n, Japa nese and Chin ese.What is the best 30 to lear n a Ian guage? We know that we all lear ntwe were 32 . If we learn a second Ianguage in the 33 way, it won 'a small child do? It 34 what people say , and it tries to guess what it hears. When it wants something, it has to 35_ it. It is using the Ianguage, 36 ___________________________ in it and talking in it all the time. If people use a secondIanguage 37 , they will learn it 38 .In school, you learn to read, to write, to hear and to speak. It is best to learn all new wordsthrough the 39 .You can read them, spell them and 40 them later .( )21. A. how many B. what nu mber C. a lot of D. so many( )22. A. useful B. necessary C. importa nt D.good( )23. A. like B. use C. lear n D. speak ( )24. A. but B. and C. also D. so ( )25. A. like B. with C. for D. as ( )26. foreig n B. a second C. the sec ond D. a special ( )27. A. easy B. aga in C. difficult D. best( )28. A. Millions of B. Million of Millio ns Several milli on of( )29. A. Some B. Other C. All D. Few( )30. A. time B. way C. thi ng D. place( )31. A. a foreig n B. our mothers ' C. other 's D. our own ( )32. A. born B. childre n C. grow n D. boys( )33. A. same B. differe nt C. useful D. good( )34. A. does B. says C. listens to D. follows( )35. A. ask B. want C. get D. ask for ( )36. speak ing B. writ ing C. thi nki ng D. doing( )37. A. some time B. sometimes C. all the same D. for the timeD. I haven 'A. I don 'B. I won 'C. I can '19. Copy the expressi on __________ , please, without any cha nges.A. as it isB. such as it isC. what it isD. so it is20. Bill _________ his wife that he ________ whe n the fire broke out.A. tells, is sleepi ngB. told, was sleepi ngC. told, sleptD. had told, had slept二、完型填空20分Do you knowaren 'very _2223 it, not people speak it_25 is 27 to say how many29 childre n study 31 Ian guage well whe nt seem so difficult. What does（）38. A. quickly B.soon C. freely D. hardly （）39. A. mouth B.hands C. ears D. mi nd （）40. A. listen to B. use C. love D. write三、阅读理解：阅读下列短文，从每题所给的四个选项，选出最佳选项。

2014-2015学年浙江省杭州市西湖中学高二(下)4月月考数学试卷(文科)一、选择题(共15小题,每小题5分,满分75分)1.椭圆的焦点坐标为( )A.(0,5)和(0,﹣5)B.(,0)和(﹣,0)C.(0,)和(0,﹣)D.(5,0)和(﹣5,0)2.已知动点M(x、y)到点F(4,0)的距离比到直线x＋5＝0的距离小1,则点M的轨迹方程为( )A.x＋4＝0B.x﹣4＝0C.y2＝8xD.y2＝16x3.已知曲线C的方程为x2＋2x＋y﹣1＝0,则下列各点中在曲线C上的点是( )A.(0,1)B.(﹣1,3)C.(1,1)D.(﹣1,1)4.设x是实数,则“x＞0”是“|x|＞0”的( )A.充分不必要条件B.必要不充分条件C.充要条件D.既不充分也不必要条件5.双曲线的渐近线方程是( )A. B. C. D.6.命题“若a＞b,则a＋c＞b＋c”的逆否命题为( )A.若a＜b,则a＋c＜b＋cB.若a≤b,则a＋c≤b＋cC.若a＋c＜b＋c,则a＜bD.若a＋c≤b＋c,则a≤b7.已知椭圆G的中心在坐标原点,长轴在x轴上,离心率为,且椭圆G上一点到其两个焦点的距离之和为12,则椭圆G的方程为( )A.＋＝1B.＋＝1C.＋＝1D.＋＝18.F1,F2是椭圆的两个焦点,A为椭圆上一点,且∠AF1F2＝45°,则三角形AF1F2的面积为( )A.7B.C.D.9.抛物线y＝ax2的准线方程是y＝2,则a的值为( )A. B. C.8 D.﹣810.点P在双曲线﹣＝1(a＞0,b＞0)上,F1、F2是这条双曲线的两个焦点,∠F1PF2＝90°,且△F1PF2的三条边长成等差数列,则此双曲线的离心率是( )A. B. C.2 D.511.已知抛物线y2＝2px(p＞0)的焦点为F,点P1(x1,y1),P2(x2,y2),P3(x3,y3)在抛物线上,且2x2＝x1＋x3,则有( )A.|FP1|＋|FP2|＝|FP3|B.|FP1|2＋|FP2|2＝|FP3|2C.2|FP2|＝|FP1|＋|FP3|D.|FP2|2＝|FP1|•|FP3|12.过抛物线y2＝2px(p＞0)的焦点F且倾斜角为60°的直线l与抛物线在第一、四象限分别交于A、B两点,则的值等于( )A.5B.4C.3D.213.若点A的坐标为(3,2),F为抛物线y2＝2x的焦点,点P是抛物线上的一动点,则|PA|＋|PF|取得最小值时点P的坐标是( )A.(0,0)B.(1,1)C.(2,2)D.14.已知点M(,0),椭圆＋y2＝1与直线y＝k(x＋)交于点A、B,则△ABM的周长为( )A.4B.8C.12D.1615.过双曲线M：x2﹣＝1的左顶点A作斜率为1的直线l,若l与双曲线M的两条渐近线分别相交于点B,C,且|AB|＝|BC|,则双曲线M的离心率是( )A. B. C. D.二.填空题：本大题共5小题,每小题5分,共25分.16.抛物线的焦点坐标是.17.短轴长为2,离心率e＝的椭圆的两焦点为F1、F2,过F1作直线交椭圆于A、B两点,则△ABF2周长为.18.平面上有三点A(﹣2,y),B(0,),C(x,y),若,则动点C的轨迹方程为.19.如果椭圆的弦被点(4,2)平分,则这条弦所在的直线方程是.20.已知P是椭圆＋上的一个动点,F1,F2分别是左右焦点,则cos∠F1PF2的最小值为.试卷Ⅱ一.选择题(每题4分,共12分)21.已知点P(3,﹣4)是双曲线﹣＝1(a＞0,b＞0)渐近线上的一点,E,F是左、右两个焦点,若•＝0,则双曲线方程为( )A.﹣＝1B.﹣＝1C.﹣＝1D.﹣＝122.设O为坐标原点,F1,F2是椭圆＋＝1(a＞b＞0)的左、右焦点,若在椭圆上存在点P 满足∠F1PF2＝,且|OP|＝a,则该椭圆的离心率为( )A. B. C. D.23.已知椭圆C：(a＞b＞0)的离心率为,过右焦点F且斜率为k(k＞0)的直线于C相交于A、B两点,若.则k＝( )A.1B.C.D.2二.解答题(共28分,其中24题8分,25,26题10分)24.已知p：方程表示双曲线,q：过点M(2,1)的直线与椭圆恒有公共点,若p∧q为真命题,求k的取值范围.25.如图,在四棱锥P﹣ABCD中,已知侧面PAD为等腰直角三角形,底面ABCD为直角梯形, AB∥CD,∠ABC＝∠APD＝90°,侧面PAD⊥底面ABCD,且AB＝4,AP＝PD＝BC＝CD＝2.(1)求证：PA⊥BD;(2)若E为侧棱PB的中点,求直线AE与底面ABCD所成角的正弦值.26.已知定点F(0,1)和直线l1：y＝﹣1,过定点F与直线l1相切的动圆圆心为点C.(1)求动点C的轨迹方程;(2)过点F的直线l2交动点C的轨迹于两点P、Q,交直线l1于点R,求•的最小值;(3)过点F且与l2垂直的直线l3交动点C的轨迹于两点R、T,问四边形PRQT的面积是否存在最小值？若存在,求出这个最小值;若不存在,请说明理由.2014-2015学年浙江省杭州市西湖中学高二(下)4月月考数学试卷(文科)参考答案与试题解析一、选择题(共15小题,每小题5分,满分75分)1.椭圆的焦点坐标为( )A.(0,5)和(0,﹣5)B.(,0)和(﹣,0)C.(0,)和(0,﹣)D.(5,0)和(﹣5,0) 【考点】椭圆的标准方程.【专题】计算题;圆锥曲线的定义、性质与方程.【分析】直接利用椭圆方程求出长轴、短轴的长,然后求解焦距即可.【解答】解：由题意得,a2＝16,b2＝9,∴c2＝a2﹣b2＝16﹣9＝7,∴c＝,∴椭圆的焦点为(,0)和(﹣,0).故选：B.【点评】本题考查椭圆的标准方程,考查学生的计算能力,属于基础题.2.已知动点M(x、y)到点F(4,0)的距离比到直线x＋5＝0的距离小1,则点M的轨迹方程为( )A.x＋4＝0B.x﹣4＝0C.y2＝8xD.y2＝16x【考点】抛物线的定义.【专题】计算题.【分析】由题意得,点M(x、y)到点F(4,0)的距离和到直线x＋4＝0的距离相等,点M的轨迹是以点F为焦点,直线x＋4＝0为准线的抛物线,方程为 y2＝2Px,＝4.【解答】解：∵动点M(x、y)到点F(4,0)的距离比到直线x＋5＝0的距离小1,∴点M(x、y)到点F(4,0)的距离和到直线x＋4＝0的距离相等,点M的轨迹是以点F为焦点,直线x＋4＝0为准线的抛物线.∴＝4,∴P＝8,故抛物线方程为y2＝16x,故选 D.【点评】本题考查用定义法求点的轨迹方程,抛物线的定义和性质的应用.3.已知曲线C的方程为x2＋2x＋y﹣1＝0,则下列各点中在曲线C上的点是( )A.(0,1)B.(﹣1,3)C.(1,1)D.(﹣1,1)【考点】曲线与方程.【专题】计算题;圆锥曲线的定义、性质与方程.【分析】将选项代入验证,即可得出结论.【解答】解：将选项代入验证,可得(0,1)满足x2＋2x＋y﹣1＝0,故选：A.【点评】本题考查曲线与方程,考查学生的计算能力,比较基础.4.设x是实数,则“x＞0”是“|x|＞0”的( )A.充分不必要条件B.必要不充分条件C.充要条件D.既不充分也不必要条件【考点】充要条件.【专题】计算题.【分析】化简不等式,判断出两个命题对应的两个集合的包含关系;得到前者是后者的什么条件.【解答】解：|x|＞0⇔x＞0或x＜0∵{x|x＞0}⊊{x|x＞0或x＜0}∴“x＞0”是“|x|＞0”的充分不必要条件故选A【点评】本题考查解决充要条件问题常先化简各个命题、考查将判断条件问题转化为判断集合的包含关系问题.5.双曲线的渐近线方程是( )A. B. C. D.【考点】双曲线的简单性质.【专题】计算题;圆锥曲线的定义、性质与方程.【分析】求出双曲线的a,b,再由渐近线方程,即可得到.【解答】解：双曲线的a＝3,b＝2,则双曲线的渐近线方程为：y＝x,即为y＝x.故选B.【点评】本题考查双曲线的方程和性质：渐近线方程,考查运算能力,属于基础题.6.命题“若a＞b,则a＋c＞b＋c”的逆否命题为( )A.若a＜b,则a＋c＜b＋cB.若a≤b,则a＋c≤b＋cC.若a＋c＜b＋c,则a＜bD.若a＋c≤b＋c,则a≤b【考点】四种命题间的逆否关系.【专题】阅读型.【分析】把所给的命题看做一个原命题,写出这个命题的逆否命题是题设和结论否定并且要交换位置,得到结果.【解答】解：把“若a＞b,则a＋c＞b＋c”看做原命题,它的逆否命题是题设和结论否定并且要交换位置,∴它的逆否命题是：“若a＋c≤b＋c,则a≤b”,故选D.【点评】本题考查求一个命题的逆否命题,实际上把一个命题看做原命题是根据需要来确定的,所有的命题都可以看做原命题,写出它的其他三个命题.属基础题.7.已知椭圆G的中心在坐标原点,长轴在x轴上,离心率为,且椭圆G上一点到其两个焦点的距离之和为12,则椭圆G的方程为( )A.＋＝1B.＋＝1C.＋＝1D.＋＝1【考点】椭圆的标准方程.【专题】计算题;圆锥曲线的定义、性质与方程.【分析】设椭圆G的方程为＋＝1(a＞b＞0),根据椭圆的定义得2a＝12,算出a＝6.再由离心率的公式建立关于a、b的等式,化简为关于b的方程解出b2＝9,即可得出椭圆G的方程.【解答】解：设椭圆G的方程为＋＝1(a＞b＞0),∵椭圆上一点到其两个焦点的距离之和为12,∴根据椭圆的定义得2a＝12,可得a＝6.又∵椭圆的离心率为,∴e＝＝,即＝,解之得b2＝9,由此可得椭圆G的方程为＝1.故选：C【点评】本题给出椭圆G满足的条件,求椭圆G的标准方程.着重考查了椭圆的定义与标准方程、简单几何性质等知识,属于基础题.8.F1,F2是椭圆的两个焦点,A为椭圆上一点,且∠AF1F2＝45°,则三角形AF1F2的面积为( )A.7B.C.D.【考点】椭圆的简单性质.【专题】计算题.【分析】求出F1F2的长度,由椭圆的定义可得AF2＝6﹣AF1,由余弦定理求得AF1＝,从而求得三角形AF1F2的面积.【解答】解：由题意可得 a＝3,b＝,c＝,故,AF 1＋AF2＝6,AF2＝6﹣AF1, ∵AF22＝AF12＋F1F22﹣2AF1•F1F2cos45°＝AF12﹣4AF1＋8,∴(6﹣AF1)2＝AF12﹣4AF1＋8,AF1＝,故三角形AF1F2的面积S＝×××＝.【点评】本题考查椭圆的定义、标准方程,简单性质,以及余弦定理的应用,求出 AF1的值,是解题的关键.9.抛物线y＝ax2的准线方程是y＝2,则a的值为( )A. B. C.8 D.﹣8【考点】抛物线的定义.【分析】首先把抛物线方程转化为标准方程x2＝my的形式,再根据其准线方程为y＝﹣即可求之.【解答】解：抛物线y＝ax2的标准方程是x2＝y,则其准线方程为y＝﹣＝2,所以a＝﹣.故选B.【点评】本题考查抛物线在标准方程下的准线方程形式.10.点P在双曲线﹣＝1(a＞0,b＞0)上,F1、F2是这条双曲线的两个焦点,∠F1PF2＝90°,且△F1PF2的三条边长成等差数列,则此双曲线的离心率是( )A. B. C.2 D.5【考点】双曲线的简单性质.【专题】计算题;等差数列与等比数列;圆锥曲线的定义、性质与方程.【分析】设|PF2|,|PF1|,|F1F2|成等差数列,且分别设为m﹣d,m,m＋d,则由双曲线定义和勾股定理求出m＝4d＝8a,c＝d,a＝d,由离心率公式计算即可得到.【解答】解：设|PF2|,|PF1|,|F1F2|成等差数列,且分别设为m﹣d,m,m＋d,则由双曲线定义和勾股定理可知：m﹣(m﹣d)＝2a,m＋d＝2c,(m﹣d)2＋m2＝(m＋d)2,解得m＝4d＝8a,c＝d,a＝d,故离心率e＝＝5.故选D.【点评】本题主要考查等差数列的定义和性质,以及双曲线的简单性质的应用,属于中档题.11.已知抛物线y2＝2px(p＞0)的焦点为F,点P1(x1,y1),P2(x2,y2),P3(x3,y3)在抛物线上,且2x2＝x1＋x3,则有( )A.|FP1|＋|FP2|＝|FP3|B.|FP1|2＋|FP2|2＝|FP3|2C.2|FP2|＝|FP1|＋|FP3|D.|FP2|2＝|FP1|•|FP3|【考点】抛物线的简单性质.【专题】计算题;压轴题.【分析】把2x2＝x1＋x3等式两边同时加p整理成进而根据抛物线的定义可得2|FP2|＝|FP1|＋|FP3|.【解答】解：∵2x2＝x1＋x3,∴,∴由抛物线定义可得2|FP2|＝|FP1|＋|FP3|故选C.【点评】本题主要考查了抛物线的简单性质.属基础题.12.过抛物线y2＝2px(p＞0)的焦点F且倾斜角为60°的直线l与抛物线在第一、四象限分别交于A、B两点,则的值等于( )A.5B.4C.3D.2【考点】直线的倾斜角;抛物线的简单性质.【专题】计算题;综合题;压轴题.【分析】设出A、B坐标,利用焦半径公式求出|AB|,结合,求出A、B的坐标,然后求其比值.【解答】解：设A(x1,y1),B(x2,y2),,,又,可得,则,故选C.【点评】本题考查直线的倾斜角,抛物线的简单性质,考查学生分析问题解决问题的能力,是基础题.13.若点A的坐标为(3,2),F为抛物线y2＝2x的焦点,点P是抛物线上的一动点,则|PA|＋|PF|取得最小值时点P的坐标是( )A.(0,0)B.(1,1)C.(2,2)D.【考点】抛物线的简单性质.【专题】计算题.【分析】利用抛物线的定义,将点P到其焦点的距离转化为它到其准线的距离即可.【解答】解：根据题意,作图如下,设点P在其准线x＝﹣上的射影为M,有抛物线的定义得：|PF|＝|PM|,∴欲使|PA|＋|PF|取得最小值,就是使|PA|＋|PM|最小,∵|PA|＋|PM|≥|AM|(当且仅当M,P,A三点共线时取“＝”),∴|PA|＋|PF|取得最小值时(M,P,A三点共线时)点P的纵坐标y0＝2,设其横坐标为x0,∵P(x0,2)为抛物线y2＝2x上的点,∴x0＝2,∴点P的坐标为P(2,2).故选C.【点评】本题考查抛物线的简单性质,将点P到其焦点的距离转化为它到其准线的距离是关键,考查转化思想的灵活应用,属于中档题.14.已知点M(,0),椭圆＋y2＝1与直线y＝k(x＋)交于点A、B,则△ABM的周长为( )A.4B.8C.12D.16【考点】直线与圆锥曲线的关系.【专题】圆锥曲线的定义、性质与方程.【分析】直线过定点,由椭圆定义可得 AN＋AM＝2a＝4,BM ＋BN＝2a＝4,由△ABM的周长为AB＋BM＋AM＝(AN＋AM)＋(BN＋BM),求出结果.【解答】解：直线过定点,由题设知M、N是椭圆的焦点,由椭圆定义知：AN＋AM＝2a＝4,BM＋BN＝2a＝4.△ABM的周长为AB＋BM＋AM＝(AN＋BN)＋BM＋AM＝(AN＋AM)＋(BN＋BM)＝8,故选：B.【点评】本题考查椭圆的定义,直线经过定点问题,直线和圆锥曲线的关系,利用椭圆的定义是解题的关键,属于中档题.15.过双曲线M：x2﹣＝1的左顶点A作斜率为1的直线l,若l与双曲线M的两条渐近线分别相交于点B,C,且|AB|＝|BC|,则双曲线M的离心率是( )A. B. C. D.【考点】双曲线的简单性质.【专题】计算题;压轴题.【分析】过双曲线的左顶点A(﹣1,0)作斜率为1的直线l：y＝x＋1,若l 与双曲线M的两条渐近线,分别相交于点B(x1,y1),C(x2,y2),联立方程组代入消元得(b2﹣1)x2＋2x﹣1＝0,然后由根与系数的关系求出x1和x2的值,进而求出双曲线M的离心率.【解答】解：过双曲线的左顶点A(﹣1,0)作斜率为1的直线l：y＝x＋1, 若l与双曲线M的两条渐近线分别相交于点B(x1,y1),C(x2,y2),联立方程组代入消元得(b2﹣1)x2﹣2x﹣1＝0,∴,∴x1＋x2＝﹣2x1x2,又|AB|＝|BC|,则B为AC中点,2x1＝﹣1＋x2,代入解得,∴b2＝9,双曲线M的离心率e＝,故选A.【点评】本题考题双曲线性质的综合运用,解题过程中要注意根与系数的关系的运用.二.填空题：本大题共5小题,每小题5分,共25分.16.抛物线的焦点坐标是(0,1) .【考点】抛物线的简单性质.【专题】计算题.【分析】抛物线方程即 x2＝4y,从而可得 p＝2,＝1,由此求得抛物线焦点坐标.【解答】解：抛物线即 x2＝4y,∴p＝2,＝1,故焦点坐标是(0,1),故答案为 (0,1).【点评】本题主要考查抛物线的标准方程,以及简单性质的应用,属于基础题.17.短轴长为2,离心率e＝的椭圆的两焦点为F1、F2,过F1作直线交椭圆于A、B两点,则△ABF2周长为12 .【考点】椭圆的简单性质.【专题】圆锥曲线的定义、性质与方程.【分析】不妨设椭圆的标准方程为(a＞b＞0).由于短轴长为2,离心率e＝.可得b＝,,a2＝b2＋c2.利用椭圆的定义即可得出.【解答】解：不妨设椭圆的标准方程为(a＞b＞0).∵短轴长为2,离心率e＝.∴b＝,,a2＝b2＋c2.解得a＝3.∴△ABF2周长＝|AF1|＋|AB|＋|BF1|＝4a＝12.故答案为：12.【点评】本题考查了椭圆的定义、标准方程及其性质,属于基础题.18.平面上有三点A(﹣2,y),B(0,),C(x,y),若,则动点C的轨迹方程为y2＝8x(x≠0) .【考点】数量积判断两个平面向量的垂直关系;轨迹方程.【专题】平面向量及应用.【分析】利用⇔＝0即可得出.【解答】解：∵＝,,,∴＝＝0,化为y2＝8x.因此动点C的轨迹方程为y2＝8x(x≠0).故答案为：y2＝8x(x≠0).【点评】熟练掌握⇔＝0是解题的关键.19.如果椭圆的弦被点(4,2)平分,则这条弦所在的直线方程是x＋2y﹣8＝0 .【考点】直线与圆锥曲线的综合问题.【专题】计算题.【分析】若设弦的端点为A(x1,y1)、B(x2,y2),代入椭圆方程得9x12＋36y12＝36×9①,9x22＋36y22＝36×9②;作差①﹣②,并由中点坐标公式,可得直线斜率k,从而求出弦所在的直线方程.【解答】解：设弦的端点为A(x1,y1)、B(x2,y2),代入椭圆方程,得9x12＋36y12＝36×9①,9x22＋36y22＝36×9②;①﹣②得9(x1＋x2)(x1﹣x2)＋36(y1＋y2)(y1﹣y2)＝0;由中点坐标＝4,＝2,代入上式,得36(x1﹣x2)＋72(y1﹣y2)＝0,∴直线斜率为k＝＝﹣,所求弦的直线方程为：y﹣2＝﹣(x﹣4),即x＋2y﹣8＝0.故答案为：x＋2y﹣8＝0.【点评】本题考查了圆锥曲线中由中点坐标公式,通过作差的方法,求得直线斜率k的应用模型,属于基础题目.20.已知P是椭圆＋上的一个动点,F1,F2分别是左右焦点,则cos∠F1PF2的最小值为.【考点】椭圆的简单性质.【专题】计算题;圆锥曲线的定义、性质与方程.【分析】当点P是椭圆的短轴的端点时,∠F1PF2取得最大值,此时cos∠F1PF2可取得最小值.【解答】解：∵椭圆＋＝1,∴a＝3,b＝2,c＝.当点P是椭圆的短轴的端点时,∠F1PF2取得最大值,∴sin(∠F1PF2)＝,∴os∠F1PF2的最小值＝1﹣2sin2(∠F1PF2)＝.故答案为：.【点评】正确理解当点P是椭圆的短轴的端点时,∠F1PF2取得最大值,此时cos∠F1PF2可取得最小值是解题的关键.试卷Ⅱ一.选择题(每题4分,共12分)21.已知点P(3,﹣4)是双曲线﹣＝1(a＞0,b＞0)渐近线上的一点,E,F是左、右两个焦点,若•＝0,则双曲线方程为( )A.﹣＝1B.﹣＝1C.﹣＝1D.﹣＝1【考点】双曲线的标准方程.【专题】计算题.【分析】根据题意,设E、F的坐标为E(﹣c,0),F(c,0),又由•＝0,结合数量积的坐标运算,可得c的值,进而由P坐标与双曲线的定义2a＝||PE|﹣|PF||,可得a的值,根据则b ＝,可得b的值,将a、b的值代入可得双曲线的方程.【解答】解：设E(﹣c,0),F(c,0),于是有＝(3＋c,﹣4)•(3﹣c,﹣4)＝9﹣c2＋16＝0.于是c2＝25,则E(﹣5,0),F(5,0),由双曲线的定义,可得2a＝||PE|﹣|PF||＝6,则a＝3;则b＝＝4;故双曲线方程为﹣＝1;故选C.【点评】本题考查双曲线的标准方程,解题时结合双曲线的定义,并注意区分双曲线与椭圆定义的区别.22.设O为坐标原点,F1,F2是椭圆＋＝1(a＞b＞0)的左、右焦点,若在椭圆上存在点P 满足∠F1PF2＝,且|OP|＝a,则该椭圆的离心率为( )A. B. C. D.【考点】椭圆的简单性质.【专题】计算题;圆锥曲线的定义、性质与方程.【分析】要求椭圆的离心率,即要求a,c的关系,首先由定义和余弦定理得到一个关系,再由中线长公式得到一个关系,联立可得.【解答】解：设|PF1|＝x,|PF2|＝y,则x＋y＝2a;①由余弦定理cos∠F1PF2＝＝,∴x2＋y2﹣xy＝4c2;②∵中线长公式OP2＝(PF12＋PF22＋2)∴＝(x2＋y2＋2xycos∠F1PF2),∴x2＋y2＝3a2﹣xy;③∴①②③联立代换掉x,y得：a2＝4c2;∴e＝＝.故选：A.【点评】本题主要考查椭圆的定义,余弦定理及中线长公式,考查学生的计算能力,属于中档题.23.已知椭圆C：(a＞b＞0)的离心率为,过右焦点F且斜率为k(k＞0)的直线于C相交于A、B两点,若.则k＝( )A.1B.C.D.2【考点】直线与圆锥曲线的综合问题.【专题】计算题;压轴题.【分析】设A(x1,y1),B(x2,y2),根据求得y1和y2关系根据离心率设,b＝t,代入椭圆方程与直线方程联立,消去x,根据韦达定理表示出y1＋y2和y1y2,进而根据y1和y2关系求得k.【解答】解：A(x1,y1),B(x2,y2),∵,∴y1＝﹣3y2,∵,设,b＝t,∴x2＋4y2﹣4t2＝0①,设直线AB方程为,代入①中消去x,可得, ∴,,解得,故选B【点评】本题主要考查了直线与圆锥曲线的综合问题.此类题问题综合性强,要求考生有较高地转化数学思想的运用能力,能将已知条件转化到基本知识的运用.二.解答题(共28分,其中24题8分,25,26题10分)24.已知p：方程表示双曲线,q：过点M(2,1)的直线与椭圆恒有公共点,若p∧q为真命题,求k的取值范围.【考点】直线与圆锥曲线的关系;复合命题的真假;双曲线的标准方程.【专题】综合题.【分析】分别求出p,q为真时,k的取值范围,再利用p∧q为真命题,即可求k的取值范围.【解答】解：p：方程表示双曲线,则(k﹣4)(k﹣6)＜0,∴4＜k＜6,(2分) q：过点M(2,1)的直线与椭圆恒有公共点,则,∴k＞5. (4分)又p∧q为真命题,则5＜k＜6,所以k的取值范围是(5,6). (6分)【点评】本题考查复合命题的真假研究,解题的关键是求出p,q为真时,k的取值范围.25.如图,在四棱锥P﹣ABCD中,已知侧面PAD为等腰直角三角形,底面ABCD为直角梯形,AB∥CD,∠ABC＝∠APD＝90°,侧面PAD⊥底面ABCD,且AB＝4,AP＝PD＝BC＝CD＝2.(1)求证：PA⊥BD;(2)若E为侧棱PB的中点,求直线AE与底面ABCD所成角的正弦值.【考点】直线与平面所成的角;直线与平面垂直的性质.【专题】综合题;空间位置关系与距离;空间角.【分析】(1)利用平面ADP⊥平面ABCD,证明BD⊥平面ADP,即可证明PA⊥BD;(2)证明∠EAH即为直线AE与平面ABCD的所成角,再求出直线AE与底面ABCD所成角的正弦值.【解答】(1)证明：由已知条件易得：,则BD⊥AD,又平面ADP⊥平面ABCD,平面ADP∩平面ABCD＝AD,BD⊂平面ABCD,故BD⊥平面ADP,又AP⊂平面ADP,从而有AP⊥BD…(6分)(2)解：如图,取AD中点O,连接PO,OB,并取OB中点H,连接AH,EH,∵PA＝PD,∴PO⊥AD,又平面PAD⊥平面ABCD,平面PAD∩平面ABCD＝AD,PO⊂平面PAD,∴PO⊥平面ABCD,又EH∥PO,∴EH⊥平面ABCD则∠EAH即为直线AE与平面ABCD的所成角由(1)AP⊥BD,又AP⊥PD,PD∩BD＝D∴AP⊥平面PBD∴AP⊥PB,∴∴∴,直线AE与平面ABCD的所成角的正弦值为.…(14分)【点评】本题考查直线AE与底面ABCD所成角的正弦值,考查平面与平面垂直的性质,考查学生分析解决问题的能力,属于中档题.26.已知定点F(0,1)和直线l1：y＝﹣1,过定点F与直线l1相切的动圆圆心为点C.(1)求动点C的轨迹方程;(2)过点F的直线l2交动点C的轨迹于两点P、Q,交直线l1于点R,求•的最小值;(3)过点F且与l2垂直的直线l3交动点C的轨迹于两点R、T,问四边形PRQT的面积是否存在最小值？若存在,求出这个最小值;若不存在,请说明理由.【考点】直线与圆锥曲线的综合问题.【专题】圆锥曲线中的最值与范围问题.【分析】(1)由已知条件推导出点C的轨迹是以F为焦点,l1为准线的抛物线,由此能求出动点C的轨迹方程.(2)设l2：y＝kx＋1,由,得x2﹣4kx﹣4＝0,设P(x1,y1),Q(x2,y2),则,由直线PQ的斜率k≠0,得R(﹣,﹣1),由此能求出•的最小值.(3)由,得y2﹣(4k2＋2)y＋1＝0,所以PQ＝,同理可得：RT＝,由此能求出四边形PRQT的面积存在最小值32.【解答】解：(1)∵定点F(0,1)和直线l1：y＝﹣1,过定点F与直线l1相切的动圆圆心为点C,∴点C的轨迹是以F为焦点,l1为准线的抛物线,∴动点C的轨迹方程为x2＝4y.(2)设l2：y＝kx＋1,由,得x2﹣4kx﹣4＝0,设P(x1,y1),Q(x2,y2),则,由直线PQ的斜率k≠0,得R(﹣,﹣1),∴＝()•(x2＋,y2＋1)＝＝＝﹣＝,∵,当且仅法k2＝1取等号.∴•≥8＋8＝16.∴•的最小值是16.(3)由,得y2﹣(4k2＋2)y＋1＝0,∴PQ＝,设,代入x2＝4y,同理可得：RT＝,∴S PRQT＝＝8()≥32.当且仅当k2＝1时取等号,∴四边形PRQT的面积存在最小值32.【点评】本题考查点的轨迹方程的求法,考查向量的数量积的最小值的求法,考查四边形面积是否有最小值的判断与求法,解题时要认真审题,注意均值定理的合理运用.。

西湖中学高一英语考试卷及答案Document number：PBGCG-0857-BTDO-0089-PTT1998考试时间90分钟满分100分）第Ⅰ卷 (共75分)第一部分：听力（共两节，满分15分）第一节：听下面5段对话。

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听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1.What ice cream does the woman recommendA. The banana.B. The strawberry.C. The cheesecake.2.What is important among friends in the woman’s opinionA. Humour.B. Honesty.C. Unselfishness.3.When was the train due to arriveA. At 9:14.B. At 9:20 .C. At 9:40.4.What do we know about the manA.He won’t attend the opening ceremony.B.He is disappointed with the woman.C.He is in a great hurry.5.Where is the man nowA. On Hornby.B. On Nelson Street.C. On West Hastings Street.第二节：听下面5段对话。

每段对话后有2-3个小题，从题中所给的A B C三个选项中选出最佳选项，并标在试卷的相应位置。

听完每段对话后，你都有5秒钟的时间来回答有关小题。

每段对话读两遍。

听下面一段对话，回答第6-7题。

6.What is wrong with the manA. He’s got a toothache.B. He’s got a backache.C. He’s got a headache.7.What is the purpose of using a towelA.To make the onion work more effectively.B.To keep the onion halves where they are.C.To keep the skin clean and dry.听下面一段对话，回答第8-9题。

浙江省杭州市西湖职业中学高一英语月考试题含解析一、选择题1. —Tom, may I remind you that we will go to see the movie Com ing Home directed by Zhang Yimou tomorrow morning?—Oh, that’s right. I __ about it.A. forgot B .forget C. had forgotten D have forgotten参考答案：A句意：--汤姆，我可以提醒你明天早上我们要看张艺谋执导的电影Coming Home吗？--哦，是的，我忘记了。

这里因为在第一个人提醒之前这个人忘记了，现在又想起来了，所以忘记是过去的事情，用一般过去时。

选A。

【考点】时态【举一反三】--Our English teacher is back home from Britain now.--Yes, she _____there for just three months.A. has beenB. had beenC. isD. wasD考查时态：句意：--我们的英语老师现在从英国回来了。

--是，她在那里呆了三个月。

可知现在回来了，在英国的三个月是过去的时间。

用一般过去时，选D。

25. －Which do you prefer, tea or coffee?－______. I’m not particular about drinks.A. BothB. NoneC. EitherD. Neither参考答案：C略3. John is the boy legs were badly hurt in the accident.A. whoseB. thatC. who参考答案：A略4. I _____ “Harry Potter” for some time. So far, I have read sixteen chapters.A. have been readingB. have readC. had readD. was reading参考答案：A略5. Although it was the first time for them to meet, it was ______they had known each other for years.A. even thoughB. as thoughC. as soon asD. as long as参考答案：B6. The book was boring. It wasn’t ___________ to me.A. benefitB. benefitedC. of little benefitD. of much benefit参考答案：D7. Have you seen Jack recently？I wonder________with his classmates.A．how is he getting along B．that he is getting along wellC．what he is getting along D．if he is getting along well参考答案：D略8. .---Thank you very much for giving me a hand.---____.A. With pleasureB. It’s my pleasureC. Cheer upD. That’s right参考答案：B9. The magazine ______ once a month.A. publishesB. comes outC. comes overD. comes back参考答案：B10. A middle-aged woman came ________ to the bus stop only ________ the bus had gone.A. run; to findB. running; to findC. and ran; foundD. running; finding参考答案：B解析： running是现在分词作方式状语；不定式作结果状语时，表示结果出乎主语的意料之外，尤其是和only连用时。

浙江省杭州市西湖高级中学2014-2015学年高一11月月考英语试题I. 单项选择（共20小题；每小题1分，满分20分）1. You’d better ____ your scores and see if you have passed the exam.A. add upB. add up toC. add toD. add to up2. The cyclists hoped to ______ money to help tens of thousands of children in the earthquake-hit area.A. riseB. roseC. raiseD. take3. ----I’m going to the United States.---- How long ____you ____in the States ？A. are; stayedB. are; stayingC. have; stayedD. did; stay4. “N ot all of the dinosaurs (恐龙) were dangerous”. This sentence means _______.A. none of the dinosaurs were dangerous.B. no dinosaurs were dangerousC. few of the dinosaurs were dangerous.D. all of the dinosaurs were not dangerous.5. As soon as he heard the ________ news of his death, she _______ tears.A. shocked; burst outB. shocking; burst intoC. shocked; burst intoD. shocking; burst out6. The place ___ interested me most was the Children's Palace.A. whichB. whereC. whatD. in which7. ---When are you leaving？---My plane ______ at 11：05．A. took offB. takes offC. is about to take offD. will take off8. ---The police came to your office this morning?---Yes. This is the second time I ______ about this in the past six days.A. have been askedB. was askedC. will be askedD. have been asking9. Don’t lose heart _______ you fail. Just keep up your courage.A. untilB. unlessC. even ifD. as though10._______ have known the results of the exam.A. It seemed as if heB. It seemed to him toC. He seemed that heD. He seemed to11. Dinosaur(恐龙) has disappeared; ______________ can be found any more.A. such no animalB. such an animalC. no such animalD. no such an animal12. It is ___ to see a monkey ____the bicycle.A. fun; ridingB. a fun; ridingC. fun; be ridingD. funny;rode13. To their disappointment, they found the lecture given by the professor difficult ________________________________.A. to be understoodB. to understandC. understandingD. understood14. You can never be ___________________ when you camp ________a high altitude, where the air is hard to breathe.A. enough careful; atB. too careful; onC. careful enough; onD. too careful; at15. I have never dreamed of ___________such a beautiful place.A. there isB. there to beC. there beingD. having16. If you have a good ____ of English, you will have no difficulty working as avolunteer for the Olympic Games.A. commandB. requirementC. requestD. series17. Mary __ with her grandma for thirteen years, but now she is living with her mother.A. livedB. has livedC. had livedD. is living18. Having failed the exam, the little boy _______ go home and face his father.A. dared notB. dare not toC. dared not toD. didn’t dared to19. I could never see any movie more than once,_____ good it is.A. whicheverB. wheneverC. whateverD. however20. A lot of questions___________________at the meeting yesterday.A. came toB. came aroundC. came upD. came up withII. 完形填空（共20小题；每小题1分，满分20分）阅读下面短文，从短文后各题所给的四个选项（A、B、C和D）中，选出最佳选项。

浙江省杭州市西湖高级中学2014-2015学年高一12月月考英语试题Ⅰ.听力理解（每小题1分, 共20分）第一节听下面5段对话，每段对话仅读一遍。

1.What’s the weather like today?A.Cloudy.B. Rainy.C. Sunny.2.What did the woman buy last Wednesday?A. A hat.B. A skirt.C. A shirt.3.Where are the speakers?A.On a planeB. On a bus.C. In a car.4.What are the two speakers talking about in general?A. A pool.B. A book.C. A holiday.5.What do we know about the man?A.He can’t find his seat.B. He has taken a booked seat.C.He has changed seats with the woman.第二节听下面5段对话，每段对话读两遍。

听第6段材料，回答第6、7题。

6.Where can visitors see lions?A.In Yellowcave Park.B. In Eastern Park.C. In Safari Park.7.How much is a family ticket for the Eastern Park?A.$5.B. $8.C. $16.听第7段材料，回答第8、9题。

8.What kind of room does the man want?A. A top-floor one.B. A quiet one.C. A fully equipped one.9.How does the hotel welcome the guests?A.By offering them fresh flowers.B.By giving them a new suitcase.C.By washing clothes for them.听第8段材料，回答第10-12题。

杭西高2018年4月高一英语试卷第一部分：听力（共两节，满分 30 分）第一节（共 5 小题；每小题 1.5 分，满分 7.5 分）听下面 5 段对话。

每段对话后有一个小题，请从题中所给的 A、B、C 三个选项中选出最佳选项，并标在答题卷的相应位置。

听完每段对话后，你都有 10 秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1.What are the speakers doing ?A. Seeing a doctor.B. Enjoying a concertC. Buying some tickets2.What will the man do next Thursday ?A. Start his new jobB. Have an interviewC. Meet Professor Green.3. What is the woman’s first lesson this morning ?A. ScienceB. GeographyC. Maths.4. What day is it probably today ?A.MondayB. WednesdayC. Friday5. What kind of music does the woman like best ?A. Country musicB. Rock musicC. Pop music第二节（共 15 小题；每小题 1.5 分，满分 22.5 分）听下面 5 段对话。

每段对话后有几个小题，从题中所给的 A、B、C 三个选项中选出最佳选项，并标在试卷的相应位置。

听每段对话前，你将有时间阅读各个小题，每小题 5 秒钟；听完后，各小题将给出 5 秒钟的作答时间。

每段对话读两遍。

听下面一段对话，回答第 6 和第 7 两个小题。

6 .How old is the woman now ?A.Eight years oldB. Ten years oldC. Eighteen years old7.Where does the woman plan to go next year ?A.To CanadaB. To AmericaC. To France听下面一段对话，回答第 8 和第 9 两个小题。