福建省漳州三中2025-2026学年高三上学期第二次月考数学试卷（含答案）

漳州三中2025-2026学年高三毕业班第二次月考数学参考答案及建议评分标准 （时间：120分钟，满分：150分） 1 2 3 4 5 6 7 8 9 10 11 B D C B A D A B BCD AB ACD 12.（1,1） 13.-160 14. 15．【解】（1）因为，所以， 化简，得，所以，所以等比数列的公比.·······························3分 因为，所以；·················································6分 （2）由（1）知，所以.·················9分 .································································13分 16．【解】（1）甲、乙、丙答对题目分别记为事件，三人中恰有两人答对题目记为事件，，·······················3分 ，·········································5分 所以．···························································7分 （2）由题意可知，的所有可能取值为，0，3，6，·······································8分 则，，， ．··································································12分 所以的分布列为 0 3 6 故．················································15分 17．【解】（1）四边形是正方形，， ，，平面， 平面，·······································································1分 平面，，····························································2分 四边形是正方形，， ，，平面. 平面，·······································································3分 平面，，····························································4分 ，平面， 平面，······································································5分 四棱锥是一个“阳马”；··························································6分 （2）由（1）得平面，， ， 以点为原点，，，所在的直线分别为轴，轴，轴，建立如图所示的空间直角坐标系， 由题意可得，，，，，··································7分 所以， ，， 设是平面的一个法向量，则， ，令，则，，·········································9分 设是平面的一个法向量，则， ，令，则，，·····································11分 ，或（舍去）.·······················13分 ，， 平面，直线与底面所成角的正切值为.···············15分 18．【详解】（1）因为，所以由正弦定理可得，············1分 所以， 所以，又因为，所以， 所以，又因为，所 ... ...