1 . 已知数列
满足①
②
.则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbfc875ca919921e8f63a6fca648561b.png)
______________ ;设
为
的前
项和,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/780019495df34d40fff9d8f31bbf3e74.png)
__________ .(结果用指数幂表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6065aaa8f3f103d1bc960da8318ce35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70b418e89f6a0a1b7f3afd10e700139e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbfc875ca919921e8f63a6fca648561b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/780019495df34d40fff9d8f31bbf3e74.png)
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2 . 如图,这是整齐的正方形道路网,其中小明、小华,小齐分别在道路网臂的
,
,
的三个交汇处,小明和小华分别随机地选择一条沿道路网的最短路径,以相同的速度同时出发,去往
地和
地,小齐保持原地不动,则小明、小华、小齐三人能相遇的概率为 __ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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3 . 海宝塔位于银川市兴庆区,始建于北朝晚期,是一座方形楼阁式砖塔,内有木梯可盘旋登至顶层,极目远眺,巍巍贺兰山,绵绵黄河水,塞上江南景色尽收眼底.如图所示,为了测量海宝塔的高度,某同学(身高173cm)在点
处测得塔顶
的仰角为
,然后沿点
向塔的正前方走了38m到达点
处,此时测得塔顶
的仰角为
,据此可估计海宝塔的高度约为__________ m.(计算结果精确到0.1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e0c2455a9e796bba6861503f0fe31b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea06b78df3f0847f358714357a18d30.png)
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3卷引用:福建省福州市部分学校教学联盟2023-2024学年高一下学期期末模拟考试数学试题
福建省福州市部分学校教学联盟2023-2024学年高一下学期期末模拟考试数学试题宁夏回族自治区银川九中、平罗中学、贺兰二高、西吉中学2024届高三第四次模拟考试联考数学(文)试题(已下线)【高一模块一】难度8 小题强化限时晋级练(较难2)
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解题方法
4 . 已知函数
,则不等式
的解集为_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63c210ade9ec72d8184a8ad001e44281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d0fdf83014454a5ef251bd80cd1653d.png)
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5 .
的展开式中常数项为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2675a7b655dc324be29b3f6be0d06cc9.png)
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6 . 设
是一个随机试验中的两个事件,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/992a45dcac87eeb949b409602a95917a.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c13cf68f47d21115c75d338dd6eb381e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/992a45dcac87eeb949b409602a95917a.png)
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7 . 厦门一中为提升学校食堂的服务水平,组织全校师生对学校食堂满意度进行评分,按照分层抽样方法,抽取200位师生的评分(满分100分)作为样本,在这200个样本中,所有学生评分样本的平均数为
,方差为
,所有教师评分样本的半均数为
,方差为
,总样本的平均数为
,方差为
,若
,抽取的学生样本多于教师样本,则总样本中学生样本的个数至少为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfbe7f95b5d89f9409ec24536da9e826.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a63cadbf6b0d54955a3c3d1b7a62b14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb525270c748eddaaecc4a549cca250e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9289410bd35c9d57326b93cc7f4c4767.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41042207515dd2e8349c805e6aee400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/671f43c79d612c93a6d160335e86e177.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d954d1e6b433661e694eddc231be784.png)
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8 . 已知函数
的图象向左平移
个单位长度得到
的图象,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec27d2122104783eb0e5363724fb7e8d.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/159b8c213a2823d7996bc4f57fd12b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41b6ae6ce67b1e6bacf10a5e163e6eb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec27d2122104783eb0e5363724fb7e8d.png)
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9 . 抛物线
绕其顶点逆时针旋转
之后,得到抛物线
,其准线方程为
,则拋物线
的焦点坐标为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c156c3b344e637b4f86404f2711940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7f86c01dc112967f375c7fb116aa60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856617a253b7e9349516cf591a184b83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
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10 . 已知三棱锥
中,
为等边三角形,
,
,
,
,则三棱锥的外接球的半径为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/822ba132ca9dd0d4a050659aef3c9b26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a15a004f7d47ed595f063e60075223a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/967f74b8993c61634ceed95edca05ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aff008bf9d674fee28e3b4514d0b1c83.png)
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