山東省曲阜師范大學(xué)附屬中學(xué)2017-2018學(xué)年高一下學(xué)期期中考試數(shù)學(xué)試題

曲師大附中2017級高一下學(xué)期期中教學(xué)質(zhì)量檢測

數(shù)學(xué)試題

2018.5考試時間：120分鐘

滿分：150分

命題、審題：高一數(shù)學(xué)備課組本試卷分第Ⅰ卷和第Ⅱ卷兩部分，共4頁。注意事項：1.答題前，考生務(wù)必用0.5毫米黑色簽字筆將自已的姓名、準考證號、縣區(qū)和科類填寫在答填寫在答題卡和試卷規(guī)定的位置上。2.第Ⅰ卷每小題選出答案后，用2B鉛筆把答題卡上對應(yīng)題目上的答案符號涂黑;如需改動，用像皮擦干凈后，再選涂其他答案標號，答案不能答在試卷上。3.第II卷必須用0.5毫米黑色簽字筆作答，答案必須寫在答題卡各題目指定區(qū)域內(nèi)相應(yīng)的位置，不能寫在試卷上；如需改動，先劃掉原來的答案，然后再寫上新的答案；不能使用涂改液、膠帶紙、修正帶。不按以上要求作答的答案無效。4.填空題請直接填寫答案，解答題應(yīng)寫出文字說明、證明過程或演算步驟。第I卷(共60分)一、選擇題（本大題共12小題，每小題5分，共60分）1.若SKIPIF1<0，則角SKIPIF1<0的終邊在A.第一、二象限 B.第一、三象限 C.第一、四象限D(zhuǎn).第二、四象限2.若SKIPIF1<0,且SKIPIF1<0為第四象限角,則SKIPIF1<0的值等于A.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<03.已知SKIPIF1<0,SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0A．8B．SKIPIF1<0C．2D．SKIPIF1<024.下列函數(shù)中，在區(qū)間SKIPIF1<0上為增函數(shù)且以SKIPIF1<0為周期的函數(shù)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.將函數(shù)SKIPIF1<0的圖象向右平移SKIPIF1<0個單位后，其圖象的一條對稱軸方程為A.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<07.平面向量SKIPIF1<0與SKIPIF1<0的夾角為SKIPIF1<0，SKIPIF1<0則SKIPIF1<0A.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.48.已知扇形的弧長是SKIPIF1<0,面積是SKIPIF1<0,則扇形的圓心角的弧度數(shù)是A.1B.2C.4D.1或49.在SKIPIF1<0中，已知SKIPIF1<0是SKIPIF1<0邊上的一點，若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0A.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<010.函數(shù)SKIPIF1<0的圖象如圖所示,為了得到SKIPIF1<0的圖象,只需把SKIPIF1<0的圖象上所有點A.向右平移SKIPIF1<0個單位長度B.向右平移SKIPIF1<0的單位長度C.向左平移SKIPIF1<0個單位長度D.向左平移SKIPIF1<0的單位長度11.記SKIPIF1<0,那么SKIPIF1<0A.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<012.函數(shù)SKIPIF1<0的圖象在SKIPIF1<0內(nèi)有且僅有一條對稱軸，則實數(shù)SKIPIF1<0的取值范圍是A.SKIPIF1<0B.SKIPIF1<0C.SKIPIF1<0D.SKIPIF1<0第II卷(共90分)填空題（本大題共4小題，每小題5分，共20分）13.已知向量SKIPIF1<0，則SKIPIF1<0在SKIPIF1<0方向上的投影等于▲;14.已知SKIPIF1<0，則SKIPIF1<0▲;15.化簡:SKIPIF1<0▲；16.已知函數(shù)SKIPIF1<0,其中SKIPIF1<0.若對滿足SKIPIF1<0的SKIPIF1<0,有SKIPIF1<0,則不等式SKIPIF1<0的解集為▲．三、解答題（本大題共6小題，共70分，請將每小題答案寫在相應(yīng)位置，并寫出詳細的解答過程）17.（本題滿分10分）在△ABC中，角SKIPIF1<0所對的邊分別為SKIPIF1<0，且SKIPIF1<0．(Ⅰ)求角SKIPIF1<0的大小；(Ⅱ)若SKIPIF1<0，判斷△ABC的形狀.（本題滿分12分）已知SKIPIF1<0是同一平面內(nèi)的三個向量,其中SKIPIF1<0.(Ⅰ)若SKIPIF1<0,且SKIPIF1<0,求SKIPIF1<0的坐標;(Ⅱ)若SKIPIF1<0,且SKIPIF1<0與SKIPIF1<0垂直,求SKIPIF1<0與SKIPIF1<0的夾角SKIPIF1<0.（本題滿分12分）已知向量SKIPIF1<0,函數(shù)SKIPIF1<0.(Ⅰ)求SKIPIF1<0的解析式;(Ⅱ)求SKIPIF1<0在SKIPIF1<0上的單調(diào)遞減區(qū)間.（本題滿分12分）如圖，在平面直角坐標系SKIPIF1<0中，點SKIPIF1<0，點SKIPIF1<0在單位圓上，SKIPIF1<0.xAyBo(Ⅰ)若點SKIPIF1<0，求SKIPIF1<0的值；xAyBo(Ⅱ)若SKIPIF1<0，求SKIPIF1<0.（本題滿分12分）已知SKIPIF1<0的坐標分別為SKIPIF1<0.(Ⅰ)若SKIPIF1<0三點共線,求角SKIPIF1<0的值;(Ⅱ)若SKIPIF1<0,且四邊形SKIPIF1<0為平行四邊形,求SKIPIF1<0的取值范圍.22.（本題滿分12分）已知函數(shù)SKIPIF1<0的圖象相鄰對稱軸之間的距離為SKIPIF1<0.(Ⅰ)求SKIPIF1<0的值;(Ⅱ)當SKIPIF1<0時,求SKIPIF1<0最大值與最小值及相應(yīng)的SKIPIF1<0的值;(Ⅲ)是否存在銳角SKIPIF1<0,使SKIPIF1<0同時成立?若存在,求出角SKIPIF1<0的值;若不存在,請說明理由.曲師大附中2017級高一下學(xué)期期中教學(xué)質(zhì)量檢測

數(shù)學(xué)試題

參考答案及評分標準

2018.5第I卷(共60分)一、選擇題（本大題共12小題，每小題5分，共60分）題號123456789101112答案BDADBCBCDAAC第II卷(共90分)填空題（本大題共4小題，每小題5分，共20分）13.SKIPIF1<0；14.SKIPIF1<0;15.SKIPIF1<0;16.SKIPIF1<0.三、解答題（本大題共6小題，共70分，請將每小題答案寫在相應(yīng)位置，并寫出詳細的解答過程）17.（本題滿分10分）解：(Ⅰ)由余弦定理，得SKIPIF1<0SKIPIF1<0………5分(Ⅱ)SKIPIF1<0，SKIPIF1<0SKIPIF1<0SKIPIF1<0為等邊三角形.………10分（本題滿分12分）解:(Ⅰ)由SKIPIF1<0可設(shè)SKIPIF1<0SKIPIF1<0SKIPIF1<0或SKIPIF1<0.………4分(Ⅱ)SKIPIF1<0與SKIPIF1<0垂直,SKIPIF1<0即SKIPIF1<0SKIPIF1<0………8分SKIPIF1<0SKIPIF1<0………12分（本題滿分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上的單調(diào)遞減區(qū)間為SKIPIF1<0.………12分（本題滿分12分）解:(Ⅰ)由三角函數(shù)定義,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（本題滿分12分）解:(Ⅰ)SKIPIF1<0三點共線,SKIPIF1<0………2分又SKIPIF1<0SKIPIF1<0又SKIPIF1<0,SKIPIF1<0………4分(Ⅱ)SKIPIF1<0四邊形SKIPIF1<0為平行四邊形,SKIPIF1<0,………5分而SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0………7分設(shè)SKIPIF1<0………9分則SKIPIF1<0SKIPIF1<0SKIPIF1<0它是一條開口向下,對稱軸為SKIPIF1<0的拋物線,SKIPIF1<0………12分22.（本題滿分12分）解:(Ⅰ)SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0