26. China is famous _________ the Great Wall and also ________ one of the largest countries with the largest population.
A. as, for B. for, for C. as, as D. for, as
25. —What ________ when the gang broke in?
— I ________ the TV and was going to bed.
A.were you doing; was turning off B.did you do; has turned off
C.had you done; was turning off D.were you doing; had turned off
24. Both my patents are ________ now. They are both ________teachers.
A. retiring; retired B. retired; retired C. retired; retiring D. retiring; retiring
23. He made up his mind to _________ a new record in the 100-meter race.
A. put down B. set down C. put up D. set up
22. She ______ Japanese when she was in Japan. Now she can speak it freely. A. picked out B. made out C. made up D. picked up
第二部分 英语知识运用
第一节 单项填空(共15小题;每小题1分, 满分15分)
从A、B、C、D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。
21. ______, they were not afraid to face the flood.
A. Although surprised B. Because surprised C. If surprising D.As long as surprising
22.(本小题满分12分)设角A,B,C是△ABC的三个内角,已知向量m=(sinA+sinC,sinB-sinA),n=(sinA-sinC,sinB),且m⊥n.
(1)求角C的大小;
(2)若向量s=(0,-1),t=(cosA,2cos2),求|s+t|的取值范围.
解:(1)由题意得m·n=(sin2A-sin2C)+(sin2B-sinAsinB)=0,
即sin2C=sin2A+sin2B-sinAsinB,设a,b,c为内角A,B,C所对的边长,由正弦定理得c2=a2+b2-ab,
再由余弦定理得cosC==,∵0<C<π,
∴C=.
(2)∵s+t=(cosA,2cos2-1)=(cosA,cosB),
∴|s+t|2=cos2A+cos2B
=cos2A+cos2(-A)
=+
=cos2A-sin2A+1
=-sin(2A-)+1,
∵0<A<,∴-<2A-<,
∴-<sin(2A-)≤1,
∴≤|s+t|2<,∴≤|s+t|<.
21.(本小题满分12分)[2014·长沙一模]风景秀美的凤凰湖畔有四棵高大的银杏树,记作A、B、P、Q,欲测量P、Q两棵树和A、P两棵树之间的距离,但湖岸部分地方围有铁丝网不能靠近,现可测得A、B两点间的距离为100 m,如图,同时也能测量出∠PAB=75°,∠QAB=45°,∠PBA=60°,∠QBA=90°,则P、Q两棵树和A、P两棵树之间的距离各为多少?
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解:在△PAB中,∠APB=180°-(75°+60°)=45°,
由正弦定理得=,解得AP=50.
在△QAB中,∠ABQ=90°,∴AQ=100.
又∠PAQ=75°-45°=30°,
由余弦定理得PQ2=AP2+AQ2-2AP·AQ·cos∠PAQ=(50)2+(100)2-2×50×100×cos30°=5000,
∴PQ==50.
∴P、Q两棵树之间的距离为50 m,A、P两棵树之间的距离为50 m.
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