2018-2019学年福州市高一第二学期期末质量检测数学试题及答案

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1、福州市2018—2019学年第二学期高一期末质量检测高一数学参考答案及评分标准评分说明：1．本解答给出了一种或几种解法供参考，如果考生的解法与本解答不同，可根据试题的主要考查内容比照评分标准制定相应的评分细则。2．对计算题，当考生的解答在某一步出现错误时，如果后继部分的解答未改变该题的内容和难度，可视影响的程度决定后继部分的给分，但不得超过该部分正确解答应给分数的一半；如果后继部分的解答有较严重的错误，就不再给分。3．解答右端所注分数，表示考生正确做到这一步应得的累加分数。4．只给整数分数。选择题

2、和填空题不给中间分。一、选择题：本大题考查基础知识和基本运算．每小题5分，满分60分．1．A2．A3．C4．A5．A6．B7．C8．C9．D10．D11．B12．A二、填空题：本大题考查基础知识和基本运算．每小题5分，满分20分．13．314．15π15．016．①③三、解答题：本大题共6小题，共70分．解答应写出文字说明，证明过程或演算步骤．17．本小题主要考查频率分布直方图、平均数、古典概型等基础知识，考查抽象概括能力、数据处理能力、运算求解能力、应用意识，考查统计与概率思想、分类与整合思想

3、等．满分10分．解：（1）依题意，该厂产品检测的平均值x550.12650.18+750.40+850.22+950.08·······························3分74.6．·····················································································4分（2）设这5件产品分别为a,b,c,1,2，其中1,2为B车间生产的产品，从5人中选出2人，所有的可能的结果有a

4、,b,a,c,a,1,a,2,b,c,b,1,b,2,c,1,c,2,1,2，共10个，·····················································································7分其中含有B车间产品的基本事件有a,1,a,2,b,1,b,2,c,1,c,2,1,2，共7高一数学参考答案及评分细则第1页（共8页）个，···················

5、··········································································8分7所以取出的2件产品中含B车间产品的概率为．·····························10分1018．本小题考查a与S的关系、等差数列的定义及通项公式、数列求和等基础知识，考查nn运算求解能力、推理论证能力，考查函数与方程思想、分类与整合思想等．满分12分．2解：（1）因为22Saa，①nnn2所以当n1时，22aaa

6、，又a0，故a2.··························1分111n12当n2时，22Saa，②n1n1n122①②得，2aaaaa，················································2分nnnn1n1整理得aa1aa0．····················································3分nn1nn1因为aa0，所以aa1，·········

7、·········································4分nn1nn1所以a是以a2为首项，以1为公差的等差数列.·····························5分n1所以a2n11，即an1.····················································6分nn1111（2）由（1）及b得，b，·············8分nnanan1n+1n2n1n2所以Tb

8、bbn12n111111····································10分2334n1n2112n2n．·······································································12分2n219．本小题主要考查同角三角函数关系、三角恒等变换等基础知识，考查运算求解能力、推理论证能力，考查化归与转化思想等．满分1