泾干中学高一数学月考试题

命题：仝昌奇

一.选择题每题4分,共48分

1下列命题正确的是(    )

A.若a∥b，则a与b方向相同            B.若a∥b，则a与b方向相反

C.a＝b，则a与b共线                D.a≠b，则a与b不共线

2.“两向量的模相等”是“两向量相等”的(    )

A.充分但不必要条件                      B.必要但不充分条件

C.充要条件                                      D.不充分也不必要条件

3.化简：〔(2a+8b)-(8a-4b)〕得(    )

A. 2a-b                            B.2b-a                C.b-a                         D.a-b

4.e₁、e₂是两不共线的向量，则a＝e₁+λe₂(λ∈R)，与向量b＝2e₁-e₂共线的充要条件是(    )

A.λ＝0                            B.λ＝-             C.λ＝-1               D.λ＝-2

5.已知向量a＝(1,x)与b＝(x,4)的方向相反，则x的值为(    )

A.2                           B.-2                            C.±2                    D.0

6.已知A(3，2)，B(5，-1)且＝，则C的坐标为(    )

A.(-8，1)             B.(8，-1)                   C.(4，)           D.(-1，-)

7.设e₁、e₂是两个单位向量，它们的夹角为60°，则(2e₁-e₂)·(3e₁+2e₂)等于(    )

A.-8               B.-                   C.                  D.8

8.已知｜a｜＝2,｜b｜＝3，且a⊥b，又(2a+3b)⊥(λa-b)，则λ的值为(    )

A.                   B.-                 C.                  D.-

9.已知点P(cosα，sinα)、Q(cosβ,sinβ)，则｜｜的最大值为(    )

A.4                            B.2                             C.                         D.1

10.按向量a＝(-5,1)把函数y＝3^x的图象F平移到F′，则F′的函数解析式为(    )

A.y＝3^x-5+1                     B.y＝3^x+5+1              C.y＝3^x+5-1               D.y＝3^x-5-1

11.若a＝(1,k),b＝(-2,3)且(a+b)与(a-b)垂直，则k等于(    )

A.k＝2                                           B.k＝-2

C.k＝±2                                            D.k＝

12.已知M(-2，7)、N(10，-2)点P在线段MN上，且＝-2，则点P的坐标为(    )

A.(-14，16)        B.(22，-11)               C.(6，1)                    D.(2，4)

二、填空题每题4分

13.已知a与b的夹角为120°，且｜a｜＝3,｜b｜＝5，则｜a+b｜＝             .

14.已知a＝(1,4),b＝(2,-3),c＝(12,-7)，且a＝mb+nc，则m＝             ,n＝          

15.在△ABC中，A＝2C，且a+c＝2b，角B.为(    )

16.设a、b、c是任意的非零平面向量，且相互不共线，则：

①(a·b)·c-(c·a)·b＝0  ②｜a｜-｜b｜＜｜a-b｜  ③(b·c)·a-(c·a)·b不与c垂直  ④(3a+2b)·(3a-2b)＝9｜a｜²-4｜b｜²中，是真命题的有(    )

三.解答题

17(8分).已知｜a｜＝4,｜b｜＝5,｜a+b｜＝.

求：(1)a·b;(2)(2a-b)·(a+3b).

18．（8分）设、是两个不共线的非零向量，

⑴若=+，=2+8，=3-3，求证A、B、D三点共线；

⑵若k+与+k共线，试确定实数k的值.

19．(8分)在ABC中，sinB=sinAcosC，且ABC的最大边长为12，最小角的正弦等于. ⑴判断ABC的形状；⑵求ABC的面积.

20(8分)、设两向量满足的夹角为60°，若向量2t与向量的夹角为钝角，则实数t的取值范围是          ．

附加题(10分，附加题计入总分，但总分不超过100分)、如图，甲船在A处，乙船在A处的南偏东方向，距A有9n mile,并以20 n mile/h的速度沿南偏西方向行驶，若甲船以28n mile/h的速度行驶，应沿什么方向，用多少h能尽快追上乙船？

答案

1C 2B  3  B 4  B  5  B   6  C  7C   8C   9D  10B  11C   12D

13. 14  m=2, n=5  15, arccos 16  2,4

17.解(1)︱a+b︱16+25+2a.b=21

即  a.b=-10---------------------------4

(2).(2a-b).(a+3b)=2a48+5(-10)-75=-77------------8

18解：⑴∵+=(2+8)+(3-3)=5(+)=5，-----2

又=+，∴=5，-----------------------------3

故A、B、D三点共线.--------------------------------------4

⑵由k+与+k共线知，存在实数使k+=(+k)，

即k+=+k，-----------------------------------6

∴，----------------------------------------------7

消去得，k²=1，∴k=1. --------------------------------8

19解：⑴由sinB=sinAcosC得：b=a·，---------------1

即，∴ABC是直角三角形.-----------------------3

⑵设最小角为，则sin=，∴cos=，--------------5

由题设和⑴知，a=12，∴------------------------6

=·a cos·a sin=a² sin·cos=16. ------------8

20、:①设－t=m[－(+)](m∈R)  化简得=

4分

∵与不共线 ∴------------------------6分

∴t=时，、t、(+)终点在一直线上   ②|－t|²=（－t）²=||²+t²||－2t

|| ||cos 60°=（1+t²－t）||², ∴t=时，|－t|有最小值

------------8分

附加题、解：设用t h,甲船追上乙船，且在C处相遇，那么在△ABC中，AC=28t,BC=20t,AB=9, ∠ABC=180°-15°-45°=120°,由余弦定理得：

（28t）²=81+(20t)²-2×9×20t×(),128t²-60t-27=0,t=,(t=舍去)

AC=21（n mile），BC=15（n mile），根据正弦定理，得sinBAC=

又∠ABC=120°，∴∠BAC为锐角，∠BAC=，而

甲船沿南偏东的方向用小时可以追上乙船

第二篇：124中学高一上第一次月考试题

辽宁省124中学高一第一次月考

第一部分：英语知识运用

第一节：单项选择

1 I am ______captain of our class team at school and also _____ member of the senior high team

A the ; a B a; a C 不填；the D 不填； a 2 Mr.Brown knows little Japanese, so he can’t understand the______ on the bottle of the pills

A explanations B instructions C descriptions D introductions 3 No dictionaries can ____ all the English idioms

A tell B show C say D cover 4 They were very______ then they heard the _____news that he would come back in two days

A surprising; surprised B surprising;surprising

C surprised; surprising D surprised; surprised

5 The coffee produced in Brazil is more famous than ______in Mexico

A one B that C those D it 6 They look forward _____a chance to receive further education

A of getting B in getting C to get D to getting 7 Hurry up!Look at the timetable. Flight 156 flying to Beijing ___at 12:20

A takes off B take off C has taken off D took off 8 The office is ______ that one ,so we can have our meeting there

A six times bigger as B six times as big as

C six times big as D six times as bigger as

9 ----Your father has just returned from his hometown

------__________, and _________

A So he does, so have I B So does he, so I have

C So have I , so does he D So I have , so does he

10 ----Excuse me,could you tell me the time,please?

-----Sorry, I don’t have a watch with me

-----_______

A Thanks a lot B what a pity

C I’m sorry to hear that D Thank you all the same

第二节：完形填空

阅读下面短文，从短文后各题所给的四个选项中，选出可以填入空白处的最佳选项，并在答题卡上将该项涂黑。

The lecture on smoking was over at last.As we boys were rushing towards the playground,Jim slipped by the table.The watch,which Mrs Smith had__11___ on the table as she started her lecture,disappeared.

We were ___12__ to go back for class again when the headmaster called us __13___ and said,"I have got a little __14___ for you boys.Mrs Smith has just lost her watch on the playground.This kind of thing has happened___15___ , she says—it just___16__ off her wrist.So look around for it,will you? ___17___ if you are clever enough to find it.Let's ___18___it clear the boy who does ___19___ will get a useful reward."

At once we started looking for the watch.Everybody wished to be the

___20___one.Suddenly,Jim stopped and bent down as if to ___21___ something.And __22__ he was in front of Mrs Smith,all smiles, __23__ the watch to her.

Mrs Smith,however,didn't seem at all looked___24___ .In fact,she looked angry,She took the watch without ___25___ a "Thank you".

Jim got __ 26____ a large piece of paper from the headmaster,who___27__ him to write a composition __28____ the dangers of smoking.What could __29___ Jim write about?He hadn't listened to the lecture and had nothing to say on the ____30___

11. A seen B dropped C found D laid

12. A about B able C sorry D sure

13. A forward B together C straight D out

14. A fun B trick C job D prize

15. A before B now C here D there

16. A goes B throws C slips D falls

17. A Say B see C Guess D Check

18. A get B put C make D keep

19. A this B such C that D so

20. Lucky B quick C early D worthy

21. A put down B give away C find out D pick up

22. A the following moment B the next moment

C for a moment D just a moment

23. A handing out B turning in C giving up D Heeding back

24. A pleased B hurt C interested D worried

25. A just B ever C even D almost

26. A her punishment B her prize C his job D his reward

27. A had B made C told D helped

28. A of B on C in D at

29. A poor B nervous C quick D good

30. A lecture B point C matter D subject

第二部分 阅读理解

阅读下列短文，然后从所给的四个选项中选出最佳选项，并在答题卡上将该项涂黑。

A

Mr. Harris used to work in Dover, but then he changed his work, and he and his wife moved to another town. They did not have many friends there, but they soon met a lot of interesting people, and after a few weeks, they often went to dinner or to parties at other people's houses.

Then Mrs. Harris said to her husband, "We've been to a lot of other people's houses, and now we must invite them to our house, mustn't we?"

"Yes, certainly," answered her husband, "A big party will be the easiest thing, won't it? Then we can start to invite people to dinner in small numbers next month."

So Mrs. Harris said, "Yes, I'll invite all our friends here to a big party on 5th December." "How many will that be?" Mr. Harris asked. "Don't invite too many."

Mrs. Harris was beginning to write the invitations when her husband saw that she was writing, "Party: 6:30 to 8:30 p.m."

"That isn't very nice, is it?" he said. "You're telling our guests that they must go at 8:30." So Mrs. Harris just wrote "Party: 6:30 p.m."

A lot of guests came, and they all had a good time, so they did not go home at 8:30. In fact they were still there at mid-night when the door bell rang and a policeman arrived. He said, "You must stop making a noise, because someone has complained(抱怨)."

Mr. Harris said he did not want to quarrel with the policeman, so everyone went home. They were sorry to have to go.

When Mr. and Mrs. Harris were alone again, she said to him. "That was a surprise, wasn't it? Who complained about the noise?"

"I did," Mr Harris answered in a tired voice.

31. Why did Mr. Harris and his wife move to another town?

A. They wanted to make some new friends.

B. Mr. Harris changed his work.

C. They wanted to meet a lot of interesting people.

D. They enjoyed going to parties and visiting other people's houses.

32. What made Mr. and Mrs. Harris hold a party at their house?

A. It was easy to hold a big party at home.

B. They could ask people to dinner in small numbers.

C. They had gone to other people's parties many times.

D. They liked making friends with others.

33. How long would Mrs. Harris like the party to last?

A. From the morning till night. B. About fourteen hours.

C. About two hours. D. Till midnight

34. When did the party end that evening?

A. At about 8:30.

B. When the policeman talked with Mr. Harris on the phone.

C. About twelve o'clock..

D. When someone telephoned the police station.

35. Why did Mr. Harris telephoned the policeman about the noise?

A. Because someone rang his door bell many times at mid-night.

B. He did not want his friends to stay late that night.

C. His friends had a good time that night and also feel tired.

D. Because he hated the noise.

B

A famous doctor once received a little child who was badly ill. Thanks to his skill and care, his young patient got well and was soon able to get up and run about again.

The child’s mother was very much obliged to the doctor, and she called on him to thank him for what he had done for her child. “Doctor,” she said, “you have saved my little son. I don’t know how to thank you enough. I feel that money alone cannot repay you, so I have made this little purse with my own hands, as a sign of my gratitude. I hope you will accept it.” The doctor stood up and said coldly, “Madam, a little present like that is very nice between friends, but a doctor needs to be paid properly for what he has done.” The lady was so surprised and hurt so much that she could not reply for a moment. Then she said quietly, “Perhaps you will tell me how much your fee is?”

“Fifty pounds”, he answered.

The lady opened the little purse and took out four fifty-pound bank notes. She handed one of them to the doctor, and put the other three back into the purse. She put the purse into her handbag and, saying good bye to the doctor, went out of the room.

36. The lady was thankful to the doctor because ________.

A. he had saved her life B. he had saved her son’s life

C. he had lent her some money D. he often called on her

37. The doctor refused the lady’s purse because he thought ______.

A. the purse should be given between friends

B. the purse was too small

C. the lady was not kind to him

D. the lady just gave him that purse and wouldn’t give him the medical fee

38. What the doctor said ______ the lady.

A. worried B. interested C. frightened D. hurt

39. The money in the purse _______.

A. was only 150 pounds B. was less than 200 pounds

C. was much more than the medical fee D. was not enough for the medical fee

40. How do you think the doctor would feel in the end?

A. Sorry and worried B. Regret and proud

C. Excited and proud D. Sorry and regret

第四部分 短文改错

41. He is looking forward to visit my hometown

42. He is an interested person

43. Tom is one of my friend

44. If they come,please let me know

45. This was my first visit to a English family

46. Peter was the best cook in the world but could make the most delicious dishes

47. Finding information on the Internet is easily

48. Where do you do the Greens come from?

49. I will send you the photos we take together last week

50. She is a friend of me