廣東省廣州市七區(qū)2022-2023學(xué)年高一上學(xué)期期末數(shù)學(xué)試題（原卷版）

高一上學(xué)期期末數(shù)學(xué)試題本試卷共4頁，22小題，滿分150分．考試用時(shí)120分鐘．一、選擇題：本題共8小題，每小題5分，共40分，在每小題給出的四個(gè)選項(xiàng)中，只有一項(xiàng)是符合題目要求的．1.設(shè)集合SKIPIF1<0，SKIPIF1<0，SKIPIF1<0()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<02.下列函數(shù)為增函數(shù)的是()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<03.設(shè)a，SKIPIF1<0，則“SKIPIF1<0”是SKIPIF1<0()A.充分不必要條件 B.必要不充分條件C.充要條件 D.既不充分也不必要條件4.已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<05.已知SKIPIF1<0是第四象限角，且SKIPIF1<0，則SKIPIF1<0()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.76.已知SKIPIF1<0，則SKIPIF1<0的最小值為()A.SKIPIF1<0 B.4C.SKIPIF1<0 D.SKIPIF1<07.已知SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的值為()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<08.已知函數(shù)SKIPIF1<0，若方程SKIPIF1<0有四個(gè)不同的根SKIPIF1<0，則SKIPIF1<0的取值范圍為()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<0二、選擇題：本題共4小題，每小題5分，共20分．在每小題給出的選項(xiàng)中，有多項(xiàng)符合題目要求．全部選對(duì)的得5分，部分選對(duì)的得2分，有選錯(cuò)的得0分．9.下列函數(shù)為奇函數(shù)的是()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<010.下列命題為真命題的是()A.任意兩個(gè)等邊三角形都相似 B.所有的素?cái)?shù)都是奇數(shù)C.SKIPIF1<0，SKIPIF1<0 D.SKIPIF1<0，SKIPIF1<011.記函數(shù)SKIPIF1<0，SKIPIF1<0，其中SKIPIF1<0．若SKIPIF1<0，則()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0為奇函數(shù) D.SKIPIF1<0為奇函數(shù)12.已知正實(shí)數(shù)x，y，z滿足SKIPIF1<0，則()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<0三、填空題：本題共4小題，每小題5分，共20分．13.若函數(shù)SKIPIF1<0只有一個(gè)零點(diǎn)，則實(shí)數(shù)a值為_____________．14.計(jì)算SKIPIF1<0_____________．15.已知函數(shù)SKIPIF1<0，SKIPIF1<0分別由下表給出，x012SKIPIF1<0121x012SKIPIF1<0210則SKIPIF1<0_____________；滿足SKIPIF1<0的x的值是_____________．16.已知SKIPIF1<0，SKIPIF1<0(SKIPIF1<0且SKIPIF1<0)，若對(duì)任意的SKIPIF1<0，都存在SKIPIF1<0，使得SKIPIF1<0成立，則實(shí)數(shù)a的取值范圍是_____________．四、解答題：本題共6小題，共70分．解答應(yīng)寫出文字說明、證明過程或演算步驟．17.已知角SKIPIF1<0的始邊與x軸的非負(fù)半軸重合，終邊過點(diǎn)SKIPIF1<0．(1)求SKIPIF1<0的值；(2)求SKIPIF1<0的值．18已知函數(shù)SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0．(1)求函數(shù)SKIPIF1<0的解析式；(2)根據(jù)定義證明函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增．19.已知函數(shù)SKIPIF1<0．(1)求函數(shù)SKIPIF1<0的最小正周期；(2)在SKIPIF1<0中，若SKIPIF1<0，求SKIPIF1<0的最大值．20.某小區(qū)要在一塊扇形區(qū)域中修建一個(gè)矩形的游泳池．如圖，在扇形OPQ中，半徑SKIPIF1<0，圓心角SKIPIF1<0，C是扇形弧上的動(dòng)點(diǎn)，矩形ABCD內(nèi)接于扇形．記SKIPIF1<0，矩形ABCD的面積為SKIPIF1<0．(1)將面積S表示為角SKIPIF1<0的函數(shù)；(2)當(dāng)角SKIPIF1<0取何值時(shí)，S最大？并求出這個(gè)最大值．21.已知函數(shù)SKIPIF1<0最大值為SKIPIF1<0．(1)求a值：(2)當(dāng)SKIPIF1<0時(shí)，求函數(shù)SKIPIF1<0