23. It’s said that more than 100 _________ will attend this meeting in Shanghai.
A. man teachers B. woman teachers
C. men teachers D. womans teachers
22. -Would you please carry the heavy box for me?
-______.
A. With pleasure B. It’s a pleasure C. Have a good time D. Not at all
第一节:单项选择。(共15小题;每小题1分,满分15分)
从各题所给的A、B、C、D四个选项中选出可以填入相应空白处的最佳选项,并标在答题卡上的相应位置。
21. France is ______ European country, India is _______ Asian country.
A. a; the B. the; an C. a; an D. an; an
第四节:(共5小题;每小题1分,满分5分)
听短文,选择正确答案。短文读两遍。
( ) 16. Where are Jim and Kate now?
A. In America. B. In England. C. In Australia.
( ) 17. How long have they been in that country?
A. For one year. B. For two years. C. For three years.
( ) 18. How many languages can Jim and Kate speak?
A. Three. B. Four. C. Five.
( ) 19. Which country are the Greens going to return to?
A. England. B. Japan. C. America.
( ) 20. Why are Jim and Kate very happy?
A. Because they won’t have to move any more.
B. Because they will go to another new country.
C. Because they can see their friends all over the world.
第三节:(共5小题;每小题1分,满分5分)
听对话,选择正确的答案。对话和问题读两遍。
( ) 11. A. In a hospital. B. In a shop. C. In a library.
( ) 12. A. English. B. Chinese. C. Science.
( ) 13. A. Next Sunday. B. Next Saturday. C. Next Thursday.
( ) 14. A. 100 yuan. B. 2000 yuan. C. 1000 yuan.
( ) 15. A. Because there was something wrong with her.
B. Because there was something wrong with me.
C. Because there was something wrong with her car.
第二节:(共5小题;每小题1分,满分5分)
听句子,从题中所给的A、B、C三个选项中选出最佳答语。每个句子读两遍。
( ) 6. A. Thank you. B. You are welcome. C. Forget it.
( ) 7. A. Very interesting. B. Sure I did. C. Yes, I like it.
( ) 8. A. Thanks a lot. B. Here you are. C. I’d like to.
( ) 9. A. I’m sorry I’m late.
B. Don’t be late next time.
C. My taxi broke down halfway.
( ) 10. A. Neither have I. B. No, I didn’t see it. C. No, I haven’t seen it.
(磁带只放一遍,开始和结束以音乐为标志。做题时,先将答案划在试题上。录音内容结束后,你将有两分钟的时间将试卷上的答案转涂到答题卡上。)
第一节:(共5小题;每小题1分,满分5分)
听句子,选出与所听句子内容一致的图片。每个句子念一遍。
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22.(14分)已知函数f(x)=Asin(ωx+φ)+B(A>0,0<ω<2,|φ|<)的一系列对应值如下表:
x |
- |
|
|
|
|
|
|
y |
-1 |
1 |
3 |
1 |
-1 |
1 |
3 |
(1)根据表格提供的数据求函数y=f(x)的解析式;
(2)若对任意的实数a,函数y=f(kx)(k>0),x∈
(a,a+]的图象与直线y=1有且仅有两个不同的交点,又当x∈[0,]时,方程f(kx)=m恰有两个不同的解,求实数m的取值范围.
解:(1)依题意,T==2[-(-)],∴ω=1.
又,解得
f()=2sin(+φ)+1=3,|φ|<,解得φ=-
图3
∴f(x)=2sin(x-)+1为所求.
(2)由已知条件可知,函数y=f(kx)=2sin(kx-)+1的周期为,又k>0,∴k=3
令t=3x-,∵x∈[0,],
∴t=3x-∈[-,]
而y=sint在[-,]上单调递增,在[,]上单调递减,且sin=sin=(如图3),
∴sint=s在[-,]上有两个不同的解的充要条件是s∈[,1),
方程f(x)=m恰有两个不同的解的充要条件是m∈
[+1,3).
21.(12分)(2009·江西九校联考)已知函数f(x)=m·n,其中m=(sinωx+cosωx,cosωx),n=(cosωx-sinωx,2sinωx),其中ω>0,若f(x)相邻两对称轴间的距离不小于.
(1)求ω的取值范围;
(2)在△ABC中,a,b,c分别是角A,B,C的对边,a=,b+c=3,当ω最大时,f(A)=1,求△ABC的面积.
解:(1)f(x)=cos2ωx-sin2ωx+2sinωxcosωx=cos2ωx+sin2ωx=2sin(2ωx+).
∵ω>0,∴函数f(x)的周期T==,
由题意可知≥,即T≥π,
解得0<ω≤1,即ω的取值范围是{ω|0<ω≤1}.
(2)由(1)可知ω的最大值为1,
∴f(x)=2sin(2x+),
∵f(A)=1,∴sin(2A+)=.
而<2A+<π,
∴2A+=π,∴A=.
由余弦定理知cosA=,
∴b2+c2-bc=3,又b+c=3,
联立解得或,
∴S△ABC=bcsinA=.
20.(12分)(2009·江苏南京模拟)已知函数f(x)=2cos2x+
2sinxcosx.
(1)求函数f(x)在[-,]上的值域;
(2)在△ABC中,若f(C)=2,2sinB=cos(A-C)-cos(A+C),求tanA的值.
解:(1)f(x)=2cos2x+2sinxcosx=1+cos2x+sin2x
=2sin(2x+)+1,
∵-≤x≤,
∴-≤2x+≤,-≤sin(2x+)≤1.
∴0≤2sin(2x+)+1≤3.
∴f(x)在区间[-,]上的值域为[0,3].
(2)f(C)=2sin(2C+)+1=2,sin(2C+)=,
∵0<C<π,∴<2C+<2π+.
∴2C+=,即C=.
∵2sinB=cos(A-C)-cos(A+C)=2sinAsinC,
∴sin(A+C)=sinAsinC,sinAcosC+cosAsinC=sinAsinC,
tanA===.
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