山东省曲阜师范大学附属中学2017-2018学年高一下学期期中考试数学试题

曲师大附中2017级高一下学期期中教学质量检测

数学试题

2018.5考试时间：120分钟

满分：150分

命题、审题：高一数学备课组本试卷分第Ⅰ卷和第Ⅱ卷两部分，共4页。注意事项：1.答题前，考生务必用0.5毫米黑色签字笔将自已的姓名、准考证号、县区和科类填写在答填写在答题卡和试卷规定的位置上。2.第Ⅰ卷每小题选出答案后，用2B铅笔把答题卡上对应题目上的答案符号涂黑;如需改动，用像皮擦干净后，再选涂其他答案标号，答案不能答在试卷上。3.第II卷必须用0.5毫米黑色签字笔作答，答案必须写在答题卡各题目指定区域内相应的位置，不能写在试卷上；如需改动，先划掉原来的答案，然后再写上新的答案；不能使用涂改液、胶带纸、修正带。不按以上要求作答的答案无效。4.填空题请直接填写答案，解答题应写出文字说明、证明过程或演算步骤。第I卷(共60分)一、选择题（本大题共12小题，每小题5分，共60分）1.若SKIPIF1<0，则角SKIPIF1<0的终边在A.第一、二象限 B.第一、三象限 C.第一、四象限D.第二、四象限2.若SKIPIF1<0,且SKIPIF1<0为第四象限角,则SKIPIF1<0的值等于A.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<03.已知SKIPIF1<0,SKIPIF1<0，若SKIPIF1<0，则SKIPIF1<0A．8B．SKIPIF1<0C．2D．SKIPIF1<024.下列函数中，在区间SKIPIF1<0上为增函数且以SKIPIF1<0为周期的函数是A.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<05.在SKIPIF1<0中，角SKIPIF1<0，那么角SKIPIF1<0A．SKIPIF1<0B．SKIPIF1<0 C．SKIPIF1<0D．SKIPIF1<0或SKIPIF1<06.将函数SKIPIF1<0的图象向右平移SKIPIF1<0个单位后，其图象的一条对称轴方程为A.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<07.平面向量SKIPIF1<0与SKIPIF1<0的夹角为SKIPIF1<0，SKIPIF1<0则SKIPIF1<0A.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.48.已知扇形的弧长是SKIPIF1<0,面积是SKIPIF1<0,则扇形的圆心角的弧度数是A.1B.2C.4D.1或49.在SKIPIF1<0中，已知SKIPIF1<0是SKIPIF1<0边上的一点，若SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0A.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<010.函数SKIPIF1<0的图象如图所示,为了得到SKIPIF1<0的图象,只需把SKIPIF1<0的图象上所有点A.向右平移SKIPIF1<0个单位长度B.向右平移SKIPIF1<0的单位长度C.向左平移SKIPIF1<0个单位长度D.向左平移SKIPIF1<0的单位长度11.记SKIPIF1<0,那么SKIPIF1<0A.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<012.函数SKIPIF1<0的图象在SKIPIF1<0内有且仅有一条对称轴，则实数SKIPIF1<0的取值范围是A.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<0第II卷(共90分)填空题（本大题共4小题，每小题5分，共20分）13.已知向量SKIPIF1<0，则SKIPIF1<0在SKIPIF1<0方向上的投影等于▲;14.已知SKIPIF1<0，则SKIPIF1<0▲;15.化简:SKIPIF1<0▲；16.已知函数SKIPIF1<0,其中SKIPIF1<0.若对满足SKIPIF1<0的SKIPIF1<0,有SKIPIF1<0,则不等式SKIPIF1<0的解集为▲．三、解答题（本大题共6小题，共70分，请将每小题答案写在相应位置，并写出详细的解答过程）17.（本题满分10分）在△ABC中，角SKIPIF1<0所对的边分别为SKIPIF1<0，且SKIPIF1<0．(Ⅰ)求角SKIPIF1<0的大小；(Ⅱ)若SKIPIF1<0，判断△ABC的形状.（本题满分12分）已知SKIPIF1<0是同一平面内的三个向量,其中SKIPIF1<0.(Ⅰ)若SKIPIF1<0,且SKIPIF1<0,求SKIPIF1<0的坐标;(Ⅱ)若SKIPIF1<0,且SKIPIF1<0与SKIPIF1<0垂直,求SKIPIF1<0与SKIPIF1<0的夹角SKIPIF1<0.（本题满分12分）已知向量SKIPIF1<0,函数SKIPIF1<0.(Ⅰ)求SKIPIF1<0的解析式;(Ⅱ)求SKIPIF1<0在SKIPIF1<0上的单调递减区间.（本题满分12分）如图，在平面直角坐标系SKIPIF1<0中，点SKIPIF1<0，点SKIPIF1<0在单位圆上，SKIPIF1<0.xAyBo(Ⅰ)若点SKIPIF1<0，求SKIPIF1<0的值；xAyBo(Ⅱ)若SKIPIF1<0，求SKIPIF1<0.（本题满分12分）已知SKIPIF1<0的坐标分别为SKIPIF1<0.(Ⅰ)若SKIPIF1<0三点共线,求角SKIPIF1<0的值;(Ⅱ)若SKIPIF1<0,且四边形SKIPIF1<0为平行四边形,求SKIPIF1<0的取值范围.22.（本题满分12分）已知函数SKIPIF1<0的图象相邻对称轴之间的距离为SKIPIF1<0.(Ⅰ)求SKIPIF1<0的值;(Ⅱ)当SKIPIF1<0时,求SKIPIF1<0最大值与最小值及相应的SKIPIF1<0的值;(Ⅲ)是否存在锐角SKIPIF1<0,使SKIPIF1<0同时成立?若存在,求出角SKIPIF1<0的值;若不存在,请说明理由.曲师大附中2017级高一下学期期中教学质量检测

数学试题

参考答案及评分标准

2018.5第I卷(共60分)一、选择题（本大题共12小题，每小题5分，共60分）题号123456789101112答案BDADBCBCDAAC第II卷(共90分)填空题（本大题共4小题，每小题5分，共20分）13.SKIPIF1<0；14.SKIPIF1<0;15.SKIPIF1<0;16.SKIPIF1<0.三、解答题（本大题共6小题，共70分，请将每小题答案写在相应位置，并写出详细的解答过程）17.（本题满分10分）解：(Ⅰ)由余弦定理，得SKIPIF1<0SKIPIF1<0………5分(Ⅱ)SKIPIF1<0，SKIPIF1<0SKIPIF1<0SKIPIF1<0为等边三角形.………10分（本题满分12分）解:(Ⅰ)由SKIPIF1<0可设SKIPIF1<0SKIPIF1<0SKIPIF1<0或SKIPIF1<0.………4分(Ⅱ)SKIPIF1<0与SKIPIF1<0垂直,SKIPIF1<0即SKIPIF1<0SKIPIF1<0………8分SKIPIF1<0SKIPIF1<0………12分（本题满分12分）解:(Ⅰ)SKIPIF1<0.………2分SKIPIF1<0………6分(Ⅱ)由SKIPIF1<0得SKIPIF1<0………10分SKIPIF1<0在SKIPIF1<0上的单调递减区间为SKIPIF1<0.………12分（本题满分12分）解:(Ⅰ)由三角函数定义,得SKIPIF1<0………3分SKIPIF1<0………6分(Ⅱ)SKIPIF1<0SKIPIF1<0,即SKIPIF1<0SKIPIF1<0………8分SKIPIF1<0………10分SKIPIF1<0………12分（本题满分12分）解:(Ⅰ)SKIPIF1<0三点共线,SKIPIF1<0………2分又SKIPIF1<0SKIPIF1<0又SKIPIF1<0,SKIPIF1<0………4分(Ⅱ)SKIPIF1<0四边形SKIPIF1<0为平行四边形,SKIPIF1<0,………5分而SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0………7分设SKIPIF1<0………9分则SKIPIF1<0SKIPIF1<0SKIPIF1<0它是一条开口向下,对称轴为SKIPIF1<0的抛物线,SKIPIF1<0………12分22.（本题满分12分）解:(Ⅰ)SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0