廣東省廣州市2022-2023學(xué)年高二上學(xué)期期末數(shù)學(xué)試題（原卷版）

廣東省廣州市2023學(xué)年高二上學(xué)期期末數(shù)學(xué)試題一、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.直線SKIPIF1<0的傾斜角為()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<02.已知圓SKIPIF1<0的方程為SKIPIF1<0，則圓心SKIPIF1<0的坐標(biāo)為()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<03.已知雙曲線SKIPIF1<0，則該雙曲線的離心率為()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<04.等差數(shù)列SKIPIF1<0中，已知SKIPIF1<0，SKIPIF1<0，則公差SKIPIF1<0等于A.3 B.-6 C.4 D.-35.已知點(diǎn)SKIPIF1<0到直線SKIPIF1<0的距離為1，則SKIPIF1<0的值為()A.5或15 B.5或15C.5或15 D.5或156.已知等比數(shù)列SKIPIF1<0的各項(xiàng)均為正數(shù)，公比SKIPIF1<0，且滿足SKIPIF1<0，則SKIPIF1<0()A.8 B.4 C.2 D.17.如圖所示，在平行六面體SKIPIF1<0中，E，F(xiàn)，H分別為SKIPIF1<0，SKIPIF1<0，DE的中點(diǎn)．若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則向量SKIPIF1<0可用SKIPIF1<0表示為()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<08.已知橢圓SKIPIF1<0右焦點(diǎn)SKIPIF1<0與拋物線SKIPIF1<0的焦點(diǎn)重合，過(guò)點(diǎn)SKIPIF1<0的直線交SKIPIF1<0于SKIPIF1<0兩點(diǎn)，若SKIPIF1<0的中點(diǎn)坐標(biāo)為SKIPIF1<0，則橢圓SKIPIF1<0方程為()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.已知非零空間向量SKIPIF1<0，則下列說(shuō)法正確的是()A.若SKIPIF1<0，則SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.若SKIPIF1<0，則SKIPIF1<0不共面10.已知點(diǎn)SKIPIF1<0在圓SKIPIF1<0：SKIPIF1<0上，直線SKIPIF1<0SKIPIF1<0，則()A直線SKIPIF1<0與圓SKIPIF1<0相交 B.直線SKIPIF1<0與圓SKIPIF1<0相離C.點(diǎn)SKIPIF1<0到直線SKIPIF1<0距離最大值為SKIPIF1<0 D.點(diǎn)SKIPIF1<0到直線SKIPIF1<0距離最小值為SKIPIF1<011.設(shè)SKIPIF1<0為等比數(shù)列SKIPIF1<0的前n項(xiàng)和，已知SKIPIF1<0，SKIPIF1<0，則下列結(jié)論正確的是()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<012.已知橢圓SKIPIF1<0的中心為坐標(biāo)原點(diǎn)，焦點(diǎn)SKIPIF1<0在SKIPIF1<0軸上，短軸長(zhǎng)等于2，離心率為SKIPIF1<0，過(guò)焦SKIPIF1<0作SKIPIF1<0軸的垂線交橢圓SKIPIF1<0于SKIPIF1<0兩點(diǎn)，則下列說(shuō)法正確的是()A.橢圓SKIPIF1<0的方程為SKIPIF1<0 B.橢圓SKIPIF1<0的方程為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.已知SKIPIF1<0，SKIPIF1<0，則向量SKIPIF1<0坐標(biāo)為______.14.古希臘著名科學(xué)家畢達(dá)哥拉斯把1，3，6，10，15，21，…這些數(shù)量的(石子)，排成一個(gè)個(gè)如圖一樣的等邊三角形，從第二行起每一行都比前一行多1個(gè)石子，像這樣的數(shù)稱為三角形數(shù).那么把三角形數(shù)從小到大排列，第11個(gè)三角形數(shù)是______.15.已知拋物線SKIPIF1<0，直線SKIPIF1<0過(guò)拋物線的焦點(diǎn)，直線SKIPIF1<0與拋物線交于SKIPIF1<0兩點(diǎn)，弦SKIPIF1<0長(zhǎng)為12，則直線SKIPIF1<0的方程為______.16.數(shù)學(xué)著作《圓錐曲線論》中給出了圓的一種定義：平面內(nèi)，到兩個(gè)定點(diǎn)A，B距離之比是常數(shù)SKIPIF1<0(SKIPIF1<0，SKIPIF1<0)的點(diǎn)M的軌跡是圓.若兩定點(diǎn)SKIPIF1<0，SKIPIF1<0，動(dòng)點(diǎn)M滿足SKIPIF1<0，點(diǎn)M的軌跡圍成區(qū)域的面積為______，△ABM面積的最大值為______.四、解答題：本題共6小題，共70分.解答應(yīng)寫出文字說(shuō)明、證明過(guò)程或演算步驟.17.已知圓SKIPIF1<0的圓心為SKIPIF1<0，且經(jīng)過(guò)點(diǎn)SKIPIF1<0.(1)求圓SKIPIF1<0的標(biāo)準(zhǔn)方程；(2)已知直線SKIPIF1<0與圓SKIPIF1<0相交于SKIPIF1<0兩點(diǎn)，求SKIPIF1<0.18.已知數(shù)列SKIPIF1<0前n項(xiàng)和為SKIPIF1<0,且SKIPIF1<0(1)求SKIPIF1<0的通項(xiàng)公式(2)求證數(shù)列SKIPIF1<0是等差數(shù)列19.如圖，在棱長(zhǎng)為2的正方體SKIPIF1<0中，SKIPIF1<0分別為SKIPIF1<0的中點(diǎn).(1)求證：SKIPIF1<0；(2)求點(diǎn)SKIPIF1<0到平面SKIPIF1<0的距離.20.已知SKIPIF1<0，且SKIPIF1<0在直線SKIPIF1<0上，其中SKIPIF1<0是數(shù)列SKIPIF1<0中的第SKIPIF1<0項(xiàng).(1)求數(shù)列SKIPIF1<0的通項(xiàng)公式；(2)設(shè)SKIPIF1<0，求數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和SKIPIF1<0.21.如圖，SKIPIF1<0底面SKIPIF1<0，SKIPIF1<0底面SKIPIF1<0，四邊形SKIPIF1<0是正方形，SKIPIF1<0.(1)證明：SKIPIF1<0平面SKIPIF1<0；(2)求直線SKIPIF1<0與平面SKIPIF1<0所成角的正切值.22.已知橢圓SKIPIF1<0：SKIPIF1<0(SKIPIF1<0)的離心率為SKIPIF1<0，其左?右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0為橢圓SKIPIF1<0上任意一點(diǎn)，SKIPIF1<0面積的最大值為1.(1)求橢圓SKIPIF1<0的標(biāo)準(zhǔn)方程；(2)已知SKIPIF1<0，過(guò)點(diǎn)SKIPIF1<0