数学参考答案及评分建议第1页（共7页）学科网（北京）股份有限公司普通高中教学检测数学参考答案及评分建议一、选择题（每小题5分，共40分）二、选择题（每小题6分，共18分。在每小题给出的选项中有三个正确，选对一个给2分；有二个选项正确，选对一个给3分。出现错误选项，该小题0分）三、填空题（每小题5分，共15分）12．13．14．或(分，答案不完整不给分）；（3分）四、解答题15.解：（1）由已知，切点坐标为.····························································1分又，······························································3分则切线斜率，所以切线方程为；···································································5分（2）由（1）知，则，·······6分因为，，····················································7分313224211)1,0(122cos2)('−+=axxxf1)0('==fk1+=xy122cos2)('−+=axxxfaxxf22sin4)("+−=]3,6[−x]32,3[2−x12345678DCCBBABD91011BCABDACD数学参考答案及评分建议第2页（共7页）学科网（北京）股份有限公司所以3sin212x−≤≤，······································································8分因为在上具有单调性，则()0fx≥或()0fx≤恒成立，··························································9分即时，有24sin2ax≥，或24sin2ax≤，即24a≥，或223a−≤，有a≥2，或3a−≤.所以的取值范围是.·············································13分16．解：(1)零假设:喜欢户外运动与性别无关.··················································1分由列联表可知··················5分由于4.0403.841＞，···········································································6分故零假设不成立，所以喜欢户外运动与性别有关.··································7分（2）不喜欢户外运动的员工按分层抽样抽取9人，其中女员工人.··············8分可能的取值为.····································································9分，，)('xf]3,6[−]3,6[−xa),2[]3,(+−−0H040.4)80100()120100()80120()100100()12010080100(40022++++−=0H4X3210，，，425)0(393504===CCCXP4220)1(392514===CCCXP数学参考答案及评分建议第3页（共7页）学科网（北京）股份有限公司，.·····································································13分的分布列为的期望为.·······························15分17．解：（1）由已知，············································································1分因为△的周长为，··································································2分即，，···························································...