台州市2023学年高二第二学期期末质量评估数学试题及答案

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【语篇导读】本文是夹叙夹议文,告诉我们“远兼如近邻”的道理。5.A【解析】细节理解题。根据第一段 Much morerobably it is a close female friend calling to tell you thatshe has split up with her boyfriend again or perhaps'simply that a good movie has just started on TV,可知最有可能来自一个朋友,故选A。6C【解析】细节理解题。根据第三段 TV shows likethis tell us that our romantic relationships may not lastbut we need to keep in touch with out close friends, ifwant to survive可知 TV shows like Friend告诉我们亲密的朋友帮助我们面对生活中的困难。故选C。7D【解析】推理判断题。根据最后一段 This is trueof Erika and Jane's friendship. With Erikas family 200miles away, it is Jane who keeps a spare set of keys toErika's apartment and waters her plants whenever she isaway.可知Enka和Jane在日常生活中互相信任和支持。故选D。8A【解析】推理判断题。纵观全文,特别是最后一E My friends have more to do with my life than my par-ents and, therefore, 1. don t have to spend a lot of timeexplaining things to them. Friends are more up to datewith what is happening.可知远亲不如近邻。故选A。

17.(1)证明:因为acosB=bosA+c,所以sinAcosB=sinBcosa+sinC.…2分又sinC=sin(A+B),………………………………………3分所以2sinbcosa=0.……标4分因为sinB>0,所以COSA=0…………………5分则A=,故△ABC是直角三角形…………6分(2)解:因为cos∠BDCBD+CD-BC2BDXCD8分所以cs∠BDA=-cs∠BDC·“+“““9分又A=5,所以AD=BDos∠BDA=10分因为c∠BDA=,所以sn∠BDA=4………………………………11分故△ABD的面积为AD×BAsin∠BDA………12分

+25A依题意,可得解得故C的方程是x+y=1b21