七彩联盟高一期末考试数学答案2025.06.25单选12345678ACCBBDAB多选91011BCDACDAC填空12.【答案】10013.【答案】3213.【答案】22215.【答案】（1）1,12ab；（2）4,3ab【详解】（1）解法一：由已知有，方程210azbz的两根为1i，··························2分由根与系数的关系得1121112biiaiia····························································5分1,12ab··································································································6分解法二：由已知有21110aibi，····························································2分120babi由复数的相等得1020bab，···················································5分1,12ab··································································································6分（2）设,zabiabR，················································································7分22379abiabi，由复数的相等有223739aabb，································9分解得4,3ab.······························································································13分（注：54a是增根，未舍去的扣2分）16.【答案】（1）证明见解析；（2）225【详解】（1）证明：在ABC中， 222ABACBC，∴ACAB，·························2分在直三棱柱111ABCABC中，1AA平面ABC，∴1AAAC， 1AA,AB是平面11AABB内两条相交直线，∴AC平面11AABB，∴1ACAB.····································································5分又知四边形11AABB是正方形，∴11ABAB. AC,1AB是平面1ABC内两条相交直线，∴1AB平面1ABC.得证.·····························8分（2）在直三棱柱111ABCABC中，11//BCBC，∴11BC与平面1ABC所成的角等于BC平面1ABC所成的角，设大小为，·······················10分设11ABABO，连接OC.由（1）知，BO平面1ABC，∴BC平面1ABC所成的角为BCO，·····························13分在RtABC中，22sinsin5BOBCOBC.·························································15分17.【答案】（1）0.012a；（2）93；（3）792【详解】（1）解法一：设成绩在90,150的频率为p，则成绩在30,90的频率为1p，根据题目165x，2115x，平均成绩97x，有11516597pp，解得0.64p；····························································2分则根据频率分布直方图有0.0140.006200.64a，解得0.012a.························································...