名校
解题方法
1 . 已知
的内角
的对边分别为
,且
,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b414b71d5a872e2e775088cbdf4dd003.png)
A.![]() |
B.若 ![]() ![]() |
C.当![]() ![]() |
D.若 ![]() ![]() ![]() |
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2卷引用:浙江省名校新高考研究联盟(Z20名校联盟)2024届高三第三次联考(三模)数学试题
名校
2 . 水平相当的甲、乙、丙三人进行乒乓球擂台赛,每轮比赛都采用3局2胜制(即先贏2局者胜),首轮由甲乙两人开始,丙轮空;第二轮由首轮的胜者与丙之间进行,首轮的负者轮空,依照这样的规则无限地继续下去.
(1)求甲在第三轮获胜的条件下,第二轮也获胜的概率;
(2)求第
轮比赛甲轮空的概率;
(3)按照以上规则,求前六轮比赛中甲获胜局数的期望.
(1)求甲在第三轮获胜的条件下,第二轮也获胜的概率;
(2)求第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)按照以上规则,求前六轮比赛中甲获胜局数的期望.
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3卷引用:浙江省北斗星盟2023-2024学年高二下学期5月阶段性联考数学试题
浙江省北斗星盟2023-2024学年高二下学期5月阶段性联考数学试题(已下线)专题06 离散型随机变量与正态分布--高二期末考点大串讲(苏教版2019选择性必修第二册)辽宁省大连市部分学校2024届高三下学期联合模拟考试数学试题
3 . 已知函数
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdfe48038034eb671b3852e261c24f3.png)
A.![]() ![]() | B.![]() ![]() |
C.方程![]() | D.导函数![]() ![]() |
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4 . 已知无穷数列
,构造新数列
满足
,
满足
,
,
满足
,若
为常数数列,则称
为
阶等差数列;同理令
,
,
,
,若
为常数数列,则称
为
阶等比数列.
(1)已知
为二阶等差数列,且
,
,
,求
的通项公式;
(2)若
为
阶等差数列,
为一阶等比数列,证明:
为
阶等比数列;
(3)已知
,令
的前
项和为
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22e75bf99dcb0fe32f66fa90a74f9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc06ff2f65c456efb6a114e67b62cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d16e3ca4fb65342b0e9a0594d661ba3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaf623a6dd661f87cf64ea150072fd78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcbdf91bb5a49f293f9b52ac8dcfa35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc2b6b23da3e065820c15cf6c675e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1ca0ac3789432a3d1ce975a9a6f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ab5abd104649f9a3c231df9a55813a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1ca0ac3789432a3d1ce975a9a6f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69c653f3a05dd25f6affdba7baeab38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f0606df3b6fbc6fcf863f9c59e0e54f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc2b6b23da3e065820c15cf6c675e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab214e5f34d976717284bed52c645e10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020e796a0144ff9b3329c7064a01c5c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d8e8f821111de8075e5c3dfb22a5d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56a4b318fa151fab14b3857942ed3cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07418f1fa0f6569b50944b5a13ffa021.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b00f4eb7f1bd2ccefbabf0c1dfa8f69.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7778648d93a10ed66ddd99672d3ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a77316e06c00a9086be642f7f590684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2a5a414f3f5d724058a2e887f3d1c0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c3fec47d2dd2b8099d86c87b6e57de8.png)
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名校
解题方法
5 . 已知函数
,则函数在区间
内零点的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ef4dbd03c3f454f804890076d9ab79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad14579830d0293b1390911cb603eb02.png)
A.1 | B.2 | C.3 | D.5 |
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名校
6 . 下列说法错误的个数为( )
①已知
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b08ca29db8f436e0eb09d367943a1502.png)
②已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5561372d2b22000e1bd1b275f7152d1.png)
③投掷一枚均匀的硬币5次,已知正面向上不少于3次,则出现5次正面向上的概率为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b8d1ca7682da10dc7f36e858593d51f.png)
①已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ae41b4e83c79f13cb4d410ec6c642da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2b1b910246ef656d8270529cf68e1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b08ca29db8f436e0eb09d367943a1502.png)
②已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58f36e1cabd0972a7677f852793ef5e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5561372d2b22000e1bd1b275f7152d1.png)
③投掷一枚均匀的硬币5次,已知正面向上不少于3次,则出现5次正面向上的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b8d1ca7682da10dc7f36e858593d51f.png)
A.0 | B.1 | C.2 | D.3 |
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2卷引用:浙江省金华市卓越联盟2023-2024学年高二下学期5月阶段联考数学试题
解题方法
7 . 若
展开式的二项式系数之和为128,则展开式中
的系数为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47b12af9f76f37024f3756e644de0315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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名校
解题方法
8 . 已知函数
是定义在
上的奇函数.
(1)求实数
的值;
(2)判断
在定义域上的单调性,并用单调性定义证明;
(3)
,使得
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13cbc2ed4bad6431037602fc427e6756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5667bc1ea875422f618529aa5f254f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e9b1365d76a10c212db1c91c5f91f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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名校
解题方法
9 . 如图,点
是棱长为2的正方体
的表面上一个动点,
是线段
的中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
A.存在点![]() ![]() |
B.若点![]() ![]() ![]() ![]() |
C.若点![]() ![]() ![]() ![]() |
D.当点![]() ![]() ![]() ![]() |
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3卷引用:浙江省重点中学四校2023-2024学年高一下学期5月联考数学试题
解题方法
10 . 我国历史悠久,各地出土文物众多.甲图为湖北五龙宫遗址出土的道家篆书法印.图乙是此印章中抽象出的几何图形的示意图.如图乙所示,在边长为2的正八边形ABCDEFGH中,P是正八边形边上任意一点,则
的最大值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab7aaa871ceb78e5b80b531a7cf4f1c9.png)
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