2021钦州高一下学期期末考试数学试题扫描版含答案

这是一份2021钦州高一下学期期末考试数学试题扫描版含答案，共8页。

钦州市2021年春季学期教学质量监测参考答案高一 数 学一、选择题答案：（每小题5分，共60分）题号123456789101112答案ACCBBDCADBDC二、填空题答案：（每小题5分，共20分）13.    ；14．   ；15．  ；6．三、解答题：本大题共6题，共70分．解答应写出文字说明、证明过程或演算步骤．17．解：（1）由题意，当时，不等式,即   ··································2分,解得.不等式的解集为      ···············································5分（2），恒成立，解得；实数的取值范围为   ··············································10分18. 解：（1），,的中点的坐标为，    ···············································2分又设边的垂直平分线所在的直线的斜率为则，可得的方程为，即．边的垂直平分线所在的直线的方程    ···································6分（2）边所在的直线成为设边上的高为即点到直线的距离为且     ··························································10分解得 解得点的坐标为   ···················································12分19.解：（1）由题意，得 成等比数列.，   ···································2分化得又因为，又∵，代入解得∴数列的通项公式为．  ············································· 6分（2）由（1）得，， ···················································9分∴．···························································12分20.解：（1）在中，，，，   ···························································2分为等腰三角形，，、两点的距离      ·················································4分（2）在中，，，，由正弦定理可得，，   ···························································7分在中，，，，由余弦定理可得，∴又∴此海洋蓝洞的口径是超过100 m.     ···································12分21.解：（1）∵底面     ∴    ······································3分     又∵点是底面的半圆弧上的点     ∴     ∴平面   ···································6分（2）证明：连，，，∵为矩形，∴为中点，连接，为中点，∴，   ··························································9分∵平面，平面，∴平面．  ······················································12分22 解：（1）由题意知，圆的圆心也在直线上，联立解得，∴半径为，圆的标准方程为   ·················································3分又∵，而，圆与圆相外切.     ·················································5分（2）∵直线的方程为，设直线上是存在点满足题意，设，由可知，，即，所以，即，   ··························································8分整理得，解得，，或，.当时，点B为圆与圆的公切点，此时， ，B重合，不符合题意.∵存在点，满足  ·················································12分