福建省2022-2023學(xué)年高二上學(xué)期11月期中數(shù)學(xué)試題（原卷版）

2022年秋季高二年期中質(zhì)量監(jiān)測(cè)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.已知直線SKIPIF1<0：SKIPIF1<0，SKIPIF1<0：SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0()A.0 B.1 C.2 D.SKIPIF1<03.如圖所示，在平行六面體SKIPIF1<0中，SKIPIF1<0為SKIPIF1<0與SKIPIF1<0交點(diǎn)，若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0()A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<04.若點(diǎn)SKIPIF1<0在圓SKIPIF1<0外部，則實(shí)數(shù)SKIPIF1<0的取值范圍是()A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<05.在長方體SKIPIF1<0中，SKIPIF1<0，SKIPIF1<0，則異面直線SKIPIF1<0與SKIPIF1<0所成角余弦值為A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<06.在日常生活中，可以看見很多有關(guān)直線與橢圓的位置關(guān)系的形象，如圖，某公園的一個(gè)窗戶就是長軸長為4米，短軸長為2米的橢圓形狀，其中三條豎直窗欞將長軸分為相等的四段，則該窗戶的最短的豎直窗欞的長度為()A.SKIPIF1<0 B.SKIPIF1<0 C.2 D.37.設(shè)點(diǎn)SKIPIF1<0為直線SKIPIF1<0：SKIPIF1<0上的動(dòng)點(diǎn)，點(diǎn)SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的最小值為A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<08.設(shè)橢圓SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，點(diǎn)SKIPIF1<0，SKIPIF1<0在SKIPIF1<0上(SKIPIF1<0位于第一象限)，且點(diǎn)SKIPIF1<0，SKIPIF1<0關(guān)于原點(diǎn)SKIPIF1<0對(duì)稱，若SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的離心率為()A.SKIPIF1<0 B.SKIPIF1<0 C.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.對(duì)于直線SKIPIF1<0，下列說法正確的有()A.直線l過點(diǎn)SKIPIF1<0 B.直線l與直線SKIPIF1<0垂直C.直線l的一個(gè)方向向量為SKIPIF1<0 D.直線l的傾斜角為45°10.下列方程能夠表示圓的是()ASKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<011.橢圓SKIPIF1<0的左、右焦點(diǎn)分別為SKIPIF1<0，SKIPIF1<0，O為坐標(biāo)原點(diǎn)，以下說法正確的是()A.橢圓C的離心率為SKIPIF1<0B.橢圓C上存在點(diǎn)P，使得SKIPIF1<0C.過點(diǎn)SKIPIF1<0的直線與橢圓C交于A，B兩點(diǎn)，則SKIPIF1<0的周長為8D.若P為橢圓SKIPIF1<0上一點(diǎn)，Q為圓SKIPIF1<0上一點(diǎn)，則點(diǎn)P，Q的最大距離為212.在平面直角坐標(biāo)系中，三點(diǎn)A(－1，0)，B(1，0)，C(0，7)，動(dòng)點(diǎn)P滿足PA=SKIPIF1<0PB，則以下結(jié)論正確的是()A.點(diǎn)P的軌跡方程為(x－3)2+y2=8 B.△PAB面積最大時(shí)，PA=2SKIPIF1<0C.∠PAB最大時(shí)，PA=SKIPIF1<0 D.P到直線AC距離最小值為SKIPIF1<0三、填空題：本題共4小題，每小題5分，共20分.13.直線SKIPIF1<0與SKIPIF1<0平行，則它們的距離是_____14.已知點(diǎn)SKIPIF1<0在直線SKIPIF1<0上，則SKIPIF1<0最小值為________．15.如圖所示，若正方形SKIPIF1<0的邊長為SKIPIF1<0，SKIPIF1<0平面SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0分別為SKIPIF1<0的中點(diǎn)，則點(diǎn)SKIPIF1<0到平面SKIPIF1<0的距離為________.16.如圖，橢圓的中心在坐標(biāo)原點(diǎn)，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0分別為橢圓的左、右、下、上頂點(diǎn)，SKIPIF1<0為其右焦點(diǎn)，直線SKIPIF1<0與SKIPIF1<0交于點(diǎn)P，若SKIPIF1<0為鈍角，則該橢圓的離心率的取值范圍為______．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.SKIPIF1<0的三個(gè)頂點(diǎn)SKIPIF1<0、SKIPIF1<0、SKIPIF1<0，D為BC中點(diǎn)，求：(1)BC邊上的高所在直線的方程；(2)中線AD所在直線的方程．18.已知圓SKIPIF1<0的圓心在SKIPIF1<0軸上，且經(jīng)過點(diǎn)SKIPIF1<0.(1)求圓SKIPIF1<0的標(biāo)準(zhǔn)方程；(2)過點(diǎn)SKIPIF1<0的直線SKIPIF1<0與圓SKIPIF1<0相交于SKIPIF1<0兩點(diǎn)，且SKIPIF1<0，求直線SKIPIF1<0的方程.19.如圖，已知SKIPIF1<0平面ABCD，底面ABCD為正方形，PA＝AD＝AB＝2，M，N分別為AB，PC的中點(diǎn)．(1)求證：SKIPIF1<0平面PCD；(2)求PD與平面PMC所成角的正弦值．20.如圖所示，已知橢圓的兩焦點(diǎn)為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0為橢圓上一點(diǎn)，且SKIPIF1<0SKIPIF1<0(1)求橢圓的標(biāo)準(zhǔn)方程；(2)若點(diǎn)SKIPIF1<0在第二象限，SKIPIF1<0，求SKIPIF1<0的面積．21.如圖，在三棱錐SKIPIF1<0中，SKIPIF1<0，O為AC的中點(diǎn)．(1)證明：SKIPIF1<0⊥平面ABC；(2)若點(diǎn)M在棱BC上，且二面角SKIPIF1<0為SKIPIF1<0，求SKIPIF1<0的值．22.已知橢圓SKIPIF1<0經(jīng)過點(diǎn)SKIPIF1<0，離心率為SKIPIF1<0(1)求橢圓SKIPIF1<0的方程；(2)設(shè)直線SKIPIF1<0