北京清華附中上地學(xué)校C21級(jí)數(shù)學(xué)基礎(chǔ)練習(xí)四及答案

基礎(chǔ)專題練習(xí)（四）一、選擇題（共16分，每題2分）第1-8題均有四個(gè)選項(xiàng)，符合題意的選項(xiàng)只有一個(gè).1.2023航空航天大興論壇于月17數(shù)字民航”“電動(dòng)航空”“商業(yè)航天”“通航維修”四場(chǎng)專題論壇.若某位航空科研工作者隨機(jī)選擇一個(gè)專題論壇參與活動(dòng)，則他選中電動(dòng)航空的概率是121418A.1B.C.D.2.下列圖形中，是中心對(duì)稱圖形而不是軸對(duì)稱圖形的為A.B.C.D.3.關(guān)于一元二次方程x2?3x?1=0的根的情況，下列說(shuō)法正確的是A．有兩個(gè)不相等的實(shí)數(shù)根C．沒(méi)有實(shí)數(shù)根B．有兩個(gè)相等的實(shí)數(shù)根D．無(wú)法判斷4．拋物線A．=-2y=?(x?2)2+1的對(duì)稱軸為．x．=-1Dx=15．在平面直角坐標(biāo)系xOy中，將拋物線y=3x2先向右平移4個(gè)單位長(zhǎng)度，再向上平移1個(gè)單位長(zhǎng)度，得到的拋物線是A.y=3(x+4)2?1B.y=3(x+4)2+1C.y=3(x?4)2?1D.y=3(x?4)+126.若圓的半徑為1的圓心角所對(duì)的弧長(zhǎng)為πππA．B．πC．D．2637.如圖，菱形OABCA，，C⊙O上，過(guò)點(diǎn)B⊙O的切線交OA的延長(zhǎng)線于點(diǎn)D．若⊙O的半徑為2BD的長(zhǎng)為A2．22．23D．48.如圖,點(diǎn)A,B⊙O上且點(diǎn)A,O,B不在同一條直線上,點(diǎn)P是⊙O上一個(gè)動(dòng)點(diǎn)(點(diǎn)P不與點(diǎn)A,B重合),在點(diǎn)P運(yùn)動(dòng)的過(guò)程中有如下四個(gè)結(jié)論:①恰好存在一點(diǎn)P,使得∠=90°;②若直線垂直于AB,=∠OBP;③∠的大小始終不變.上述結(jié)論中,所有正確結(jié)論的序號(hào)是．．A.①②B.①③C.D.①②③二、填空題（共分，每題2分）(?)a3x23x?4=0是關(guān)于的一元二次方程，則的取值范圍是?xa9.若.10.若關(guān)于x的一元二次方程x2?3x+m=0有一個(gè)根為則m的值為?上,.=(?)24在平面直角坐標(biāo)系中,若點(diǎn)(2,y),(4,y在拋物線y2x312則y1y2填“>”,“=”或“<”).12.如圖，四邊形ABCD內(nèi)接于⊙O，點(diǎn)E在的延長(zhǎng)線上，。若∠CDE=80°，則∠ABC的度數(shù)是．13.的內(nèi)切圓⊙O與ABBC分別相切于點(diǎn)D=BC=6,則△ABC的周長(zhǎng)為1401x>0y隨x的增大而增大的二次函數(shù)的解析式15.杭州亞運(yùn)會(huì)的吉祥物琮琮”“宸宸”“蓮蓮”組合名為“江南憶”，出自唐朝詩(shī)人白居易的名句“江南憶，最憶..是杭州”，它融合了杭州的歷史人文、自然生態(tài)和創(chuàng)新基因．吉祥物一開(kāi)售，就深受大家的喜愛(ài)．經(jīng)統(tǒng)計(jì)，某商店吉祥物江南憶”6月份的銷售量為1200件，8月份的銷售量為1452件，設(shè)吉祥物江南憶”6月份到8月份銷售量的月平均增長(zhǎng)率為x，則可列方程為_(kāi)____________________.16如圖,在平面直角坐標(biāo)系中,二次函數(shù)(2,1).給出下面三個(gè)結(jié)論:①2a-b=0;y=ax+bx+c(a0)的圖象經(jīng)過(guò)點(diǎn)(0,1),2②a++c>1;③關(guān)于x的一元二次方程ax2++cm=m<1)有兩個(gè)異號(hào)實(shí)數(shù)根.上述結(jié)論中,所有正確結(jié)論的序號(hào)是_____________________.17-21題每題5題623題524-26題每題6題每題7分）解答應(yīng)寫出文字說(shuō)明、演算步驟或證明的過(guò)程.17.解方程：x+8x=9.218.a是方程x2?2x?1=0的一個(gè)根，求代數(shù)式(a?2+a(a?的值.19．已知關(guān)于x的一元二次方程(1)求m的取值范圍;x2?x+2m?2=0有兩個(gè)實(shí)數(shù)根.(2)當(dāng)m取最大整數(shù)值時(shí)求方程的根.20.已知拋物線yx2bxc經(jīng)過(guò)點(diǎn)(1,0),(0,-3).(1)求拋物線的解析式;(2)求該拋物線的頂點(diǎn)坐標(biāo).21.如圖在△ABC,C=45°,=2,O為△的外接圓求⊙O的半徑.22.2023年9月23月819賽（測(cè)試滿分為100分，得分x均為不小于80名學(xué)生的測(cè)試成績(jī)，；．xA80x85B85x90C90x95；D．xa.八年級(jí)名學(xué)生的成績(jī)是：80，，，，，，8687899090，94，，，，96，，100．b.九年級(jí)名學(xué)生的成績(jī)?cè)贑組中的數(shù)據(jù)是：，，，，，，94．c.八、九年級(jí)抽取的學(xué)生競(jìng)賽成績(jī)的平均數(shù)、中位數(shù)、眾數(shù)如下：年級(jí)平均數(shù)中位數(shù)眾數(shù)八年級(jí)九年級(jí)909090mn100d.九年級(jí)抽取的學(xué)生競(jìng)賽成績(jī)扇形統(tǒng)計(jì)圖如下：根據(jù)以上信息，解答下列問(wèn)題：(1)寫出表中m,n的值及九年級(jí)抽取的學(xué)生競(jìng)賽成績(jī)?cè)贒組的人數(shù);(2)若該校九年級(jí)共400人參加了此次知識(shí)競(jìng)賽活動(dòng),估計(jì)九年級(jí)競(jìng)賽成績(jī)不低于分的人數(shù)是____________________；(3)績(jī)?cè)贒.D組的兩名學(xué)生，用畫樹(shù)狀圖或列表的方法，求甲、乙兩人同時(shí)被選上的概率.xOyy=bk0+()的圖象經(jīng)過(guò)點(diǎn)A（）和B（，23.在平面直角坐標(biāo)系中，函數(shù)(1)求該函數(shù)的解析式；1y=x+n的值小于函數(shù)ybk0的值且大于=+()(2)當(dāng)x2x52寫出n的值．基礎(chǔ)練習(xí)專題四答案一、選擇題（共分，每題2分）題號(hào)答案12345678CAABDDCA二、填空題（共分，每題2分）題號(hào)9101213141516答案不唯一，如：答案a32=8016012=1452+②③y=x2+1三、解答題（共68分，第17-21題每題5分，第22題6分，第23題5分，第24-26題每題6分，第27-28題，每題7分）解答應(yīng)寫出文字說(shuō)明、演算步驟或證明的過(guò)程.17.解：2+8=9.2+8x+16=9+16.··································································1分(+4)2=25.………………2分±5.············································································3分解得x=1，x·······························································5分1218.解：(a?2+a(a?=a2?2a+1+a2?2a····························································2分=2a2?4a+1·······································································3分∵a是方程x?2x?1=0的一個(gè)根，2∴a2?2a?1=0，∴a2?2a=1．······································································4分=a-+12∴原式=21+1·············································································5分19.解：（1）∵方程有兩個(gè)實(shí)數(shù)根，0················································································1分∵＝－1)2－4×1×(2m－2)=1?8m+8=9?8m9?8m09m···············································································2分89（2），m為最大整數(shù)，8m=1.··············································································3分∴2﹣＝0.解得：x=0，x=1.·······························································5分1220.解：y=x2+c經(jīng)過(guò)點(diǎn)（1，0，0，，（1）∵拋物線b+c=0∴c=3.··········································································2分b=2解得c=.∴y=x2+2x．·····································································3分（2）y=x2+2x.=(+)2x1∴頂點(diǎn)坐標(biāo)為（-1，-4）.··························································5分21.解：連接OA，OB，············································1分∵∠C＝45°,∴∠AOB＝2∠C=90°.··········································2分在Rt△AOB中，∵OA2OB2AB2,AB=2，OAOB，∴2OA2=4.························································4分∴OA2=2.∴OA=2（舍負(fù)）.∴⊙O2.···········································5分22.解：（1）D43分（2）240.····················································································4分（3）設(shè)D組的另外兩名同學(xué)為丙，丁.宣講員甲乙丙丁主持人乙丙丁甲丙丁甲乙丁甲乙丙12甲和乙同時(shí)被選上的結(jié)果有2種，21所以P（甲乙同時(shí)被選上）==．·······························································6分12623.解：（1）把A（-1,2）和B（1,4）代入y=kx+b(k≠0)中，?k+b=2,k