江苏省徐州市2018届高三上学期期中抽测数学试题（图片版）

徐州市2017-2018学年度高三年级摸底考试 数学I参考答案 一、填空题 1． 2． 3．6 4． 5． 6． 7．4 8． 9．88 10． 11． 12． 13． 14． 二、解答题 15．（1）因为，由正弦定理，得．················2分 因为，所以． 即， 所以． ····························································································4分 因为，所以．················································································6分 又因为，所以．···············································································7分 （2）由余弦定理及得，， 即． ··································································································10分 又因为，所以，····················································································12分 所以．·································································14分 16. （1）因为平面，平面， 平面平面，所以．·························································3分 因为平面，平面， 所以平面． ···························································································6分 （2）因为为的中点，，所以为的中点． 又因为，所以， ············································································8分 又，，所以． ···························································10分 又平面，， 所以平面． ···························································································12分 因为平面，所以平面平面．············································14分 17．（1）由题意，，，且为等边三角形， 所以，，·····································································2分 ，．····················································6分 （2）要符合园林局的要求，只要最小， 由（1）知，， 令，即， 解得或（舍去），·························································10分 令，， 当时，是单调减函数； 当时，是单调增函数， 所以当时，取得最小值. 答：符合园林局要求的的余弦值为. ··············· ... ...