解题方法
1 . 绿色已成为当今世界主题,绿色动力已成为时代的驱动力,绿色能源是未来新能源行业的主导.某汽车公司顺应时代潮流,最新研发了一款新能源汽车,并在出厂前对该批次汽车随机抽取100辆进行了单次最大续航里程(理论上是指新能源汽车所装载的燃料或电池所能够提供给车行驶的最远里程)的测试.现对测试数据进行分析,得到如图所示的频率分布
(同一组中的数据用该组区间的中点值代表);
(2)若单次最大续航里程在
到
的汽车为“
类汽车”,以抽样检测的频率作为实际情况的概率,从该汽车公司最新研发的新能源汽车中随机抽取10辆,设这10辆汽车中为“
类汽车”的数量为
,求
.
(3)某汽车销售公司为推广此款新能源汽车,现面向意向客户推出“玩游戏,送大奖”活动,客户可根据拋掷硬币的结果,操控微型遥控车在方格图上行进,若遥控车最终停在“胜利大本营”,则可获得购车优惠券.已知硬币出现正、反面的概率都是
,方格图上标有第0格、第1格、第2格、
、第30格.遥控车开始在第0格,客户每掷一次硬币,遥控车向前移动一次,若掷出正面,遥控车向前移动一格(从
到
),若掷出反面,遥控车向前移动两格(从
到
),直到遥控车移到第29格(胜利大本营)或第30格(失败大本营)时,游戏结束.已知遥控车在第0格的概率为
,设遥控车移到第
格的概率为
,试证明:数列
是等比数列,并解释此方案能否成功吸引顾客购买该款新能源汽车?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c85481cd7e94130ef3aa05b4a39e79cd.png)
(2)若单次最大续航里程在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3bcb74e7cb4235102c7b8eda1f504f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad9a2c58a224e801450544406635596.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b0bd6753e573bfbe6742d08ef6dfe83.png)
(3)某汽车销售公司为推广此款新能源汽车,现面向意向客户推出“玩游戏,送大奖”活动,客户可根据拋掷硬币的结果,操控微型遥控车在方格图上行进,若遥控车最终停在“胜利大本营”,则可获得购车优惠券.已知硬币出现正、反面的概率都是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b00f4eb7f1bd2ccefbabf0c1dfa8f69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4792fd59c4ca11ff03dc32e367c3983f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cceb0153024c9beaf92e76b633d239b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a923a83a659f0a544954f73a29241e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45c53fb3df93e2c2bb9f3140b07c92fb.png)
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2卷引用:云南省三校2025届高三高考备考实用性联考卷(一)数学试卷
2 . 已知集合
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15710549c90383a60660149fdd3bfbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d86adf750d687339059bee99ce60754a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
3 . 已知全集
,集合
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19e5aaed2d3a621b49bee420cdb1aa71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73eb01a0f462951dcb55ebd5cf378180.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bc733e1d8cb8d0215d209d0d7aceeaf.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 已知集合
,
,则满足条件
的集合
的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a22f8d9188279429b395c30b2898ac1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baacdd9773a97d82cdb6a79ab7eae20d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd089af2b898c37371cee5ebbc07be7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.1 | B.2 | C.3 | D.4 |
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5 . 已知集合
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/902b012fa6535bbf6d225ad9485aa113.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ef23d1608222047ebb47d938e32a9d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1336d38741aab2255a35c26612bbd7cc.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2卷引用:云南师范大学附属中学2023-2024学年高三下学期5月月考数学试题
解题方法
6 . 在长方体
中,已知
,
,
,点
为底面
内一点,若
和底面
所成角与二面角
的大小相等,点
在底面
的投影为点
,则三棱锥
体积的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b59ab6bf6111dda4a3d428454768b77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ad3a1ea6790177130e16c2124984087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adebae2f9d7543915eb5a36427f9b6d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e07010ccdf2d83b7d3a6944034d3c95.png)
A.![]() | B.2 | C.![]() | D.![]() |
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解题方法
7 . 在平面直角坐标系
中,已知动点
到定点
的距离和它到定直线
的距离之比为
,记
的轨迹为曲线
.
(1)求
的方程;
(2)已知点
,不过
的直线
与
交于
,
两点,直线
,
,
的斜率依次成等比数列,求
到
距离的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ce47fde921058026708a4321a0e213.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e9efa96b6ec20a6ce18c7f458e4379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839c7616cd0d90265f4b2c9c021254fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383f12cb70ca55eba4ff012771dbfa9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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解题方法
8 . 已知集合
,
,任取
,则
为偶函数的概率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64fec0517a959cc0e672d9f8608f41e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b897f7391c3892214c271f79734c25a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0940c99f26a7f7dee1d67624cd75cab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d7af0e3a995decd0f500d2232247b2.png)
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9 . 已知集合
,且
,则实数
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b455ee5305faa2a2b14239a7ee02fb64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff109d3fadee141f93b199a5a72bc161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3卷引用:河南省郑州市中复教育2023-2024学年高三下学期5月月考数学试卷
河南省郑州市中复教育2023-2024学年高三下学期5月月考数学试卷广西南宁市第三十六中学2024届高三下学期适应性训练数学试题(已下线)高二数学期末模拟试卷01【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北师大版2019选择性必修第二册)
解题方法
10 . 设集合
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb97fda6a451f50538f83ef6c6e73f50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02982556df5d0d04fe83f3a1c30009b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e5e1e33c1259195f7bb0198a3e6f65a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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