高三数学试题第1页（共13页）泉州市2025届高中毕业班适应性练习卷参考答案2025.04高三数学一、选择题：选择题：本题共8小题，每小题5分，共40分。在每小题给出的四个选项中，只有一项是符合题目要求的。1~8：CDCABBDC二、选择题：本题共3小题，每小题6分，共18分。在每小题给出的选项中，有多项符合题目要求。全部选对的得6分，有选错的得0分，部分选对的得部分分。9．AB10．BCD11．ACD三、填空题：本题共3小题，每小题5分，共15分。12．0.7（710也可）13．42914．2π．四、解答题：本题共5小题，共77分。解答应写出文字说明，证明过程或演算步骤。15.（13分）某旅行社推出“文化古城游”旅游路线后，为了解游客的满意度，对该路线的游客进行随机抽样调查，得到如下满意度评分的频率分布直方图．（1）估计“文化古城游”路线游客满意度评分的众数和第80百分位数；（同一组中的数据用该区间的中点值为代表）（2）现从参与“文化古城游”的游客中随机抽取3人，设这3人中满意度评分不低于90分的人数为X，求X的分布列和数学期望．（以样本数据中游客的满意度评分位于各区间的频率作为游客的满意度评分位于该区间的概率）【命题意图】本题主要考查频率分步直方图、样本的数字特征、二项分布等基础知识；考查数据处理能力、运算求解能力等；考查数形结合思想、化归与转化思想、或然与必然思想等；体现基础性与应用性，导向对发展数学运算、数据分析、数学建模等核心素养的关注．【试题解析】（1）估计“文化古迹游”路线游客满意度评分的众数为909592.52，···································1分保密★使用前高三数学试题第2页（共13页）满意度评分在70,95内的频率为0.0080.0120.0200.0400.07050.750.8（），故第80百分位数位于[95,100]，·····················································································2分所以第80百分位数为0.80.75955960.25．（列式1分，计算1分，只写答案扣1分）·········4分（2）解法一：由表可知，“文化古迹游”线路游客满意度评分不低于90分的概率为30.0700.05050.65（），5分依题意，X的可能取值为0,1,2,3，·················································································6分则3380(1)5125PX，·························································································7分12333361(1)55125PXC，······················································································8分22333542(155125PXC）（），·················································································9分332735125PX（），······························································································10分所以X的分布列为：X0123P8125361255412527125·······························································································································11分所以5028365427913125125125125EX．（列式1分，计算1分）·························13...