江蘇省徐州市2022-2023學(xué)年高二上學(xué)期期末數(shù)學(xué)試題（原卷版）

2022~2023學(xué)年度第一學(xué)期期末抽測(cè)高二年級(jí)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.拋物線SKIPIF1<0的準(zhǔn)線方程是()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<02.雙曲線SKIPIF1<0的漸近線方程是()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<03.在SKIPIF1<0軸上截距為SKIPIF1<0，傾斜角為SKIPIF1<0的直線方程為()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<04.中國(guó)古代數(shù)學(xué)著作《張丘建算經(jīng)》中記載：“今有馬行轉(zhuǎn)遲，次日減半，疾七日，行七百里”.意思是說(shuō)有一匹馬行走的速度逐漸減慢，每天行走的里數(shù)是前一天的一半，七天一共行走了700里路，則該馬第七天走的里數(shù)為()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<05.設(shè)SKIPIF1<0，SKIPIF1<0為實(shí)數(shù)，若直線SKIPIF1<0與圓SKIPIF1<0相交，則點(diǎn)SKIPIF1<0與圓的位置關(guān)系是()A.在圓上 B.在圓外 C.在圓內(nèi) D.不能確定6.已知集合SKIPIF1<0和SKIPIF1<0分別是由數(shù)列SKIPIF1<0和SKIPIF1<0的前100項(xiàng)組成，則SKIPIF1<0中元素的和為()A.270 B.273 C.363 D.68317.設(shè)SKIPIF1<0分別是橢圓SKIPIF1<0和雙曲線SKIPIF1<0的公共焦點(diǎn)，P是它們的一個(gè)公共點(diǎn)，且SKIPIF1<0，線段SKIPIF1<0的垂直平分線經(jīng)過(guò)點(diǎn)SKIPIF1<0，若SKIPIF1<0和SKIPIF1<0的離心率分別為SKIPIF1<0，則SKIPIF1<0的值為()．A.3 B.2 C.SKIPIF1<0 D.SKIPIF1<08.已知SKIPIF1<0，則()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<0二?多選題：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.已知曲線SKIPIF1<0，則下列說(shuō)法正確的是()A.若SKIPIF1<0是橢圓，則其長(zhǎng)軸長(zhǎng)為SKIPIF1<0B.若SKIPIF1<0，則SKIPIF1<0是雙曲線C.C不可能表示一個(gè)圓D.若SKIPIF1<0，則SKIPIF1<0上點(diǎn)到焦點(diǎn)的最短距離為SKIPIF1<010.已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，則()A.SKIPIF1<0B.SKIPIF1<0的前10項(xiàng)和為SKIPIF1<0C.SKIPIF1<0的前11項(xiàng)和為SKIPIF1<0D.SKIPIF1<0的前16項(xiàng)和為SKIPIF1<011.連續(xù)曲線上凹弧與凸弧的分界點(diǎn)稱為曲線的拐點(diǎn),拐點(diǎn)在統(tǒng)計(jì)學(xué)?物理學(xué)?經(jīng)濟(jì)學(xué)等領(lǐng)域都有重要應(yīng)用.若SKIPIF1<0的圖象是一條連續(xù)不斷的曲線,SKIPIF1<0的導(dǎo)函數(shù)SKIPIF1<0都存在,且SKIPIF1<0的導(dǎo)函數(shù)SKIPIF1<0也都存在.若SKIPIF1<0,使得SKIPIF1<0,且在SKIPIF1<0的左?右附近,SKIPIF1<0異號(hào),則稱點(diǎn)SKIPIF1<0為曲線SKIPIF1<0的拐點(diǎn).則以下函數(shù)具有唯一拐點(diǎn)的是()ASKIPIF1<0 B.SKIPIF1<0CSKIPIF1<0 D.SKIPIF1<012.設(shè)有一組圓SKIPIF1<0，下列命題正確是()A.不論SKIPIF1<0如何變化，圓心SKIPIF1<0始終在一條直線上B.存在圓SKIPIF1<0經(jīng)過(guò)點(diǎn)SKIPIF1<0C.存在定直線始終與圓SKIPIF1<0相切D.若圓SKIPIF1<0上總存在兩點(diǎn)到原點(diǎn)的距離為SKIPIF1<0，則SKIPIF1<0三?填空題：本題共4小題，每小題5分，共20分.13.已知直線SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0的值為______.14.已知等差數(shù)列SKIPIF1<0的公差SKIPIF1<0，若SKIPIF1<0成等比數(shù)列，則SKIPIF1<0的值為______.15.已知函數(shù)SKIPIF1<0,若SKIPIF1<0恒成立,則實(shí)數(shù)SKIPIF1<0的取值范圍為______.16.已知拋物線SKIPIF1<0的焦點(diǎn)為SKIPIF1<0為SKIPIF1<0上一點(diǎn)，以線段SKIPIF1<0為直徑的圓SKIPIF1<0與SKIPIF1<0交于另外一點(diǎn)SKIPIF1<0為圓心，SKIPIF1<0為坐標(biāo)原點(diǎn).當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0的長(zhǎng)為______，點(diǎn)SKIPIF1<0到SKIPIF1<0軸的距離為______.四?解答題：本題6小題，共70分.解答應(yīng)寫出件字說(shuō)明?證明過(guò)程或演算步驟.17.在①SKIPIF1<0,②SKIPIF1<0,③SKIPIF1<0這三個(gè)條件中選擇兩個(gè),補(bǔ)充在下面問(wèn)題中,并進(jìn)行解答.已知等差數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和為SKIPIF1<0,______,______.(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.注:如果選擇多組條件分別解答,按第一個(gè)解答計(jì)分.18.已知圓SKIPIF1<0，圓SKIPIF1<0.(1)判斷SKIPIF1<0與SKIPIF1<0的位置關(guān)系；(2)若過(guò)點(diǎn)SKIPIF1<0的直線SKIPIF1<0被SKIPIF1<0、SKIPIF1<0截得的弦長(zhǎng)之比為SKIPIF1<0，求直線SKIPIF1<0的方程.19.某新建小區(qū)規(guī)劃利用一塊空地進(jìn)行配套綠化.如圖，已知空地的一邊是直路SKIPIF1<0，余下的外圍是拋物線的一段，SKIPIF1<0的中垂線恰是該拋物線的對(duì)稱軸，SKIPIF1<0是SKIPIF1<0的中點(diǎn).擬在這塊地上劃出一個(gè)等腰梯形SKIPIF1<0區(qū)域種植草坪，其中SKIPIF1<0均在該拋物線上.經(jīng)測(cè)量，直路SKIPIF1<0段長(zhǎng)為60米，拋物線的頂點(diǎn)SKIPIF1<0到直路SKIPIF1<0的距離為40米.以SKIPIF1<0為坐標(biāo)原點(diǎn)，SKIPIF1<0所在直線為SKIPIF1<0軸建立平面直角坐標(biāo)系SKIPIF1<0.(1)求該段拋物線方程；(2)當(dāng)SKIPIF1<0長(zhǎng)為多少米時(shí)，等腰梯形草坪SKIPIF1<0的面積最大？20.已知曲線SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線與SKIPIF1<0軸的交點(diǎn)為SKIPIF1<0，且SKIPIF1<0.(1)求數(shù)列SKIPIF1<0的通項(xiàng)公式；(2)設(shè)SKIPIF1<0為數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和，求使得SKIPIF1<0成立的正整數(shù)SKIPIF1<0的最小值.21.已知雙曲線SKIPIF1<0的左?右焦點(diǎn)分別為SKIPIF1<0，且SKIPIF1<0，過(guò)SKIPIF1<0的直線SKIPIF1<0與SKIPIF1<0的左支交于SKIPIF1<0兩點(diǎn)，當(dāng)直線SKIPIF1<0垂直于SKIPIF1<0軸時(shí)，SKIPIF1<0.(1)求SKIPIF1<0的標(biāo)準(zhǔn)方程；(2)設(shè)SKIPIF1<0為坐標(biāo)原點(diǎn)，線段SKIPIF1<0的中點(diǎn)為SKIPIF1<0，射線SKIPIF1<0交直線SKIPIF1<0于點(diǎn)SKIPIF1<0，點(diǎn)SKIPIF1<