2025届高三年级5月份联合考试数学试卷(pdf版,含详解)

点石联考 5月高三联考 数学 2025 届高三年级 5月份联合考试 数学 说明： 一、本解答给出的解法仅供参考，如果考生的解法与本解答不同，可根据试题的主要考查内 容比照评分标准制订相应的评分细则. 二、对解答题，当考生的解答在某一步出现错误时，如果后继部分的解答未改变该题的内容 和难度，可视影响的程度决定后继部分的给分；如果后继部分的解答有较严重的错误， 就不再给分. 三、解答右端所注分数，表示考生正确做到这一步应得的累加分数. 四、只给整数分数，选择题和填空题不给中间分. 一、单选题（本大题共 8 小题，每小题 5 分，共 40 分。在每小题所给的四个选项中，有且只有一项是符合 题目要求的） 1 2 3 4 5 6 7 8 D B C D C B B B 二、多选题（本大题共 3 小题，每小题 6 分，共 18 分。在每小题所给的四个选项中，有多项符合题目要求。 全部选对的得 6 分，部分选对的得部分分，有选错的得 0 分） 9 10 11 AD BCD ABD 三、填空题（本大题共 3 小题，每小题 5 分，共 15 分，第 14 题第 1个空 2 分，第 2 个空 3 分） 12． 4 13． 2, 14．294 ，12 四、解答题（本大题共 5 小题，共 77 分。解答时应写出必要的文字说明、证明过程或演算步骤） 15．（13分）解： （1）由 3b 2csin B及正弦定理，得 3 sin B 2sinC sin B．················································· 3分 而0 B π，所以 sin B 0,sinC 3 ．··············································································4分 2 π 又VABC π 为锐角三角形，所以 0 C ，所以C .······························································5分 2 3 a b c 2 3 4 （2）由正弦定理 sin A sin B sinC 3 ，································································· 7分 2 得 a 4sin A,b 4sin B．··································································································8分 因为 sin Asin B 5 ，所以 ab 10．··················································································· 10分 8 由余弦定理得 c2 a2 b2 2ab cosC ，·················································································· 11分 12 a2 b2 2 10 1即 ，······························································································ 12分 2 — 1— 点石联考 5月高三联考 数学 所以 a2 b2 22 .··········································································································· 13分 16．（15分）解： （1）证明：由已知可得 ⊥ , 即 ⊥ , ⊥ , 又 AE∩PE=E， 故 ⊥ 平面 , ············································ ... ...