2020高三上·全国·专题练习
1 . 下列说法中,正确说法的序号为___________ .(写出所有正确说法的序号)
①正切函数
的图象关于点
对称;
②若
,则
成等比数列;
③函数
和函数
具有相同的单调区间;
④若函数
的图象恒在x轴上方,则
的取值范围是
.
①正切函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fffa8ddcbbe89ab0f250f56673e2d36c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef183993d9ca7294a680d8797ce79647.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1c8379fe535e68721fd84be969d257f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eecf783b0385c573f96e497f7399d038.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6d534d9ff88292d2801ef0b0da5deb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c653ed9cff365dfe6648dfd195be416.png)
④若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec4fbc9e47ae6b6abea9d0ffafeaab9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23cd4b3d8c4419209e8560e60fb322c.png)
您最近一年使用:0次
2020高三上·全国·专题练习
解题方法
2 . 下列说法中,正确说法的序号为___________ .(写出所有正确说法的序号)
①正切函数
的图象关于点
对称;
②若
,则
成等比数列;
③函数
和函数
具有相同的单调区间;
④若函数
在
上为增函数,则
的取值范围是
.
①正切函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fffa8ddcbbe89ab0f250f56673e2d36c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef183993d9ca7294a680d8797ce79647.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1c8379fe535e68721fd84be969d257f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eecf783b0385c573f96e497f7399d038.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6d534d9ff88292d2801ef0b0da5deb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c653ed9cff365dfe6648dfd195be416.png)
④若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec4fbc9e47ae6b6abea9d0ffafeaab9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60cce332317884d04b38b1ebe8a50d18.png)
您最近一年使用:0次
名校
3 . 已知函数
,
有以下结论:
①
的图象关于直线
轴对称②
在区间
上单调递减
③
的一个对称中心是
④
的最大值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
则上述说法正确的序号为__________ (请填上所有正确序号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac0da99e273bf774b7a5987067f454a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e083a1a8485c3f5ed1e0ec7518096c1.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f63f827cdf0e83612e5ade389c297b0.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47c1fad7af7df8e93160cf83788bec5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
则上述说法正确的序号为
您最近一年使用:0次
2019-07-29更新
|
5714次组卷
|
15卷引用:海南省海口市第一中学2019-2020学年高三上学期10月月考数学试题
海南省海口市第一中学2019-2020学年高三上学期10月月考数学试题河北省石家庄市辛集市中学2019-2020学年高三第三次月考数学(文)试题2020届福建省莆田第二十五中学高三上学期期末数学(文)试题2020届海南省儋州市第一中学高三上学期第二次月考数学试题(已下线)专题03 三角(第二篇)-备战2020高考数学黄金30题系列之压轴题(新课标版)黑龙江省哈尔滨市第六中学校2020-2021学年高三9月月考数学(文)试题黑龙江省哈尔滨市第六中学2020-2021学年度高三上学期九月月考文科数学试题(已下线)河南省三门峡市2020-2021学年度高三第一次大练习数学(理科)试题黑龙江省双鸭山市第一中学2022-2023学年高三上学期开学考试数学试题辽宁省凌源二中2018-2019学年高一下学期期末数学试题山东省菏泽市2018-2019学年高一下学期期末数学试题山东省菏泽市东明县第一中学2018-2019学年高一下学期期末数学试题山西省山西大学附属中学2019-2020学年高一下学期5月模块诊断数学试题(已下线)5.6 函数y=Asin(ωx+φ) -2021-2022学年高一数学同步辅导讲义与检测(人教A版2019必修第一册)上海市奉贤区致远高级中学2021-2022学年高一下学期期中在线教学评估数学试题
4 . 在数列
中,若
(
,
,
为常数),则
称为“等方差数列”.下列对“等方差数列”的判断:
①若
是等方差数列,则
是等差数列;
②
是等方差数列;
③若
是等方差数列,则
(
,
为常数)也是等方差数列.其中正确命题序号为
__________ (写出所有正确命题的序号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44818d415cf4e4af51151193e204bdd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362832fa3d3c13c1eafd565349d66dce.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ef891fc99921b6093392c1e3c5347d1.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a561552fc52b697f1a7f1c81c2f637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b6d151d3f864bae873987f6db9327a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2018-05-02更新
|
739次组卷
|
2卷引用:【全国市级联考】四川省南充市2018届高三第三次联合诊断考试数学文科试题
5 . 在数列
中,若
为常数
,则
为“等方差数列”,下列是对“等方差数列”的判断;
①
是等方差数列,则
是等差数列;
②
是等方差数列;
③ 若
是等方差数列,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bed8c521ba833022d7f57a4d44b2824f.png)
为常数
也是等方差数列;
④ 若
既是等方差数列,又是等差数列,则该数列为常数列.
其中正确命题序号为__________ .(将所有正确的命题序号填在横线上)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ca1c0c66577dd728e61895ebc96b3ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c806dc9bf2cad0cb20220d23bd252a2f.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ef891fc99921b6093392c1e3c5347d1.png)
③ 若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bed8c521ba833022d7f57a4d44b2824f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b6a244eab64b41c3f98222feb04855.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
④ 若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
其中正确命题序号为
您最近一年使用:0次
解题方法
6 . 为提升学生用数学知识解决现实生活或其他学科领域中的问题的能力,发展学生数学建模素养,某市面向全市高中学生开展数学建模论文征文活动.对于参加征文活动的每篇论文,由两位评委独立评分,取两位评委评分的平均数作为该篇论文的初评得分.从评委甲和评委乙负责评审的论文中随机抽取10篇,这10篇论文的评分情况如下表所示.
(1)从这
篇论文中随机抽取1篇,求甲、乙两位评委的评分之差的绝对值不超过
的概率;
(2)从这
篇论文中随机抽取3篇,甲、乙两位评委对同一篇论文的评分之差的绝对值不超过
的篇数记为
,求
的分布列及数学期望;
(3)对于序号为
的论文,设评委甲的评分为
,评委乙的评分为
,分别记甲、乙两位评委对这10篇论文评分的平均数为
,
,标准差为
,
,以
作为序号为
的论文的标准化得分.对这10篇论文按照初评得分与标准化得分分别从高到低进行排名,判断序号为2的论文的两种排名结果是否相同?(结论不要求证明)
序号 | 评委甲评分 | 评委乙评分 | 初评得分 |
1 | 67 | 82 | 74.5 |
2 | 80 | 86 | 83 |
3 | 61 | 76 | 68.5 |
4 | 78 | 84 | 81 |
5 | 70 | 85 | 77.5 |
6 | 81 | 83 | 82 |
7 | 84 | 86 | 85 |
8 | 68 | 74 | 71 |
9 | 66 | 77 | 71.5 |
10 | 64 | 82 | 73 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
(2)从这
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(3)对于序号为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2968ea9d16fcf1181908c9790c423336.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f95e54a9b7c66c97dc6ee6161a25c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc00379c7af113543302417b685c7d6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80746e5e22851a0f1075374a3c3280ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab7a1a659607d4d81c81f4f6545df241.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b02526771dc5a6d66fb9029bff5eac3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4bf6d5a546594c4176867be0ec896b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356a0eecfd01ef9b7fec91cf600603ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
您最近一年使用:0次
7 . 定义
是
的导函数
的导函数,若方程
有实数解
,则称点
,
为函数
的“拐点”.可以证明,任意三次函数
都有“拐点”和对称中心,且“拐点”就是其对称中心,请你根据这一结论判断下列命题:
①存在有两个及两个以上对称中心的三次函数;
②函数
的对称中心也是函数
的一个对称中心;
③存在三次函数
,方程
有实数解
,且点
为函数
的对称中心;
④若函数
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac322fc4206da717226ad89530effdd5.png)
.
其中正确命题的序号为_______ (把所有正确命题的序号都填上).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac282e92da3691942a6ba8511de2303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d0c99ddd028f0bc3b1d64924ff0f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1fa6ca9eb7cea9131dad36db6a0ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b589732202941f828016f982c92996b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f60a6d986c80039124c8a869b0e481af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012429b7101ba0f84e7b45598ed12db9.png)
①存在有两个及两个以上对称中心的三次函数;
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06c087948f0abff7f6b3218860c973f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6efc139f70df469a51f530e03c98abaa.png)
③存在三次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a42dfca9f27abe558892fc0b7db96df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb0c68f6e69ab9da3ea2c8c2f48f683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed0aa12ed308e80e35f1bb6101d36d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
④若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b8df99b8a0839cba0eb04427c0a1b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac322fc4206da717226ad89530effdd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb688d1f5aa60c67b53486b84f0aa432.png)
其中正确命题的序号为
您最近一年使用:0次
2012·四川自贡·三模
8 . 对于三次函数
,定义
是
的导函数
的导函数,若方程
有实数解
,则称点
为函数
的“拐点”,可以证明,任何三次函数都有“拐点”,任何三次函数都有对称中心,且“拐点”就是对称中心,请你根据这一结论判断下列命题:
①任意三次函数都关于点
对称:
②存在三次函数
有实数解
,点
为函数
的对称中心;
③存在三次函数有两个及两个以上的对称中心;
④若函数
,则: ![](https://img.xkw.com/dksih/QBM/2013/6/7/1571240628027392/1571240633196544/STEM/cbdd6b14556e4870b23f8c1dcfe4e3ad.png?resizew=373)
其中正确命题的序号为_____ (把所有正确命题的序号都填上).
![](https://img.xkw.com/dksih/QBM/2013/6/7/1571240628027392/1571240633196544/STEM/21ac331a5b0e4b30b00b0bfc8770a14a.png?resizew=213)
![](https://img.xkw.com/dksih/QBM/2013/6/7/1571240628027392/1571240633196544/STEM/60cd76baa3484586a3fab13c0e7d75f7.png?resizew=41)
![](https://img.xkw.com/dksih/QBM/2013/6/7/1571240628027392/1571240633196544/STEM/ca5c67acb37e4344aca4776bfadbb516.png?resizew=61)
![](https://img.xkw.com/dksih/QBM/2013/6/7/1571240628027392/1571240633196544/STEM/9b22cb4ef676428f863b199d569eff7a.png?resizew=65)
![](https://img.xkw.com/dksih/QBM/2013/6/7/1571240628027392/1571240633196544/STEM/4aeca168313f4352a09e9371cf7fe4f8.png?resizew=67)
![](https://img.xkw.com/dksih/QBM/2013/6/7/1571240628027392/1571240633196544/STEM/bed6f27974b441c4901f45d1999f3071.png?resizew=19)
![](https://img.xkw.com/dksih/QBM/2013/6/7/1571240628027392/1571240633196544/STEM/4a1972c93ff74273a10d6e3a25e47433.png?resizew=75)
![](https://img.xkw.com/dksih/QBM/2013/6/7/1571240628027392/1571240633196544/STEM/ca5c67acb37e4344aca4776bfadbb516.png?resizew=61)
①任意三次函数都关于点
![](https://img.xkw.com/dksih/QBM/2013/6/7/1571240628027392/1571240633196544/STEM/86f6c82c145b4959a4570a0ff352e9e1.png?resizew=104)
②存在三次函数
![](https://img.xkw.com/dksih/QBM/2013/6/7/1571240628027392/1571240633196544/STEM/9263178288534479a8555ceebddfcf6e.png?resizew=64)
![](https://img.xkw.com/dksih/QBM/2013/6/7/1571240628027392/1571240633196544/STEM/bed6f27974b441c4901f45d1999f3071.png?resizew=19)
![](https://img.xkw.com/dksih/QBM/2013/6/7/1571240628027392/1571240633196544/STEM/4a1972c93ff74273a10d6e3a25e47433.png?resizew=75)
![](https://img.xkw.com/dksih/QBM/2013/6/7/1571240628027392/1571240633196544/STEM/ca5c67acb37e4344aca4776bfadbb516.png?resizew=61)
③存在三次函数有两个及两个以上的对称中心;
④若函数
![](https://img.xkw.com/dksih/QBM/2013/6/7/1571240628027392/1571240633196544/STEM/6f90ab20b1234a0b8c61bb78c5026c69.png?resizew=155)
![](https://img.xkw.com/dksih/QBM/2013/6/7/1571240628027392/1571240633196544/STEM/cbdd6b14556e4870b23f8c1dcfe4e3ad.png?resizew=373)
其中正确命题的序号为
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2011·广东广州·高考模拟
名校
9 . 将正整数12分解成两个正整数的乘积有
,
,
三种,其中
是这三种分解中,两数差的绝对值最小的,我们称
为12的最佳分解.当
是正整数
的最佳分解时,我们规定函数
,例如
.关于函数
有下列叙述:①
,②
,③
,④
.其中正确的序号为_____ (填入所有正确的序号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/505ce232f5f27e5de6d336b327df64d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1c2ffd50c810f3925d51e69c1df588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/085a73c2b8fb60fa810642040b599a5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/085a73c2b8fb60fa810642040b599a5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/085a73c2b8fb60fa810642040b599a5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb59495f2858ab4c9ca2954e9c57c33b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e973e1e296455562a84e8e76ff685a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3780fb8822d2de7e270d450d4facad60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914c08afa3b18ce6ee1480d71d59d4af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65d292cdb1d66ea7f96e96047ca9a44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/591f87fb0bcbb996e93a1b99141f4d8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77fc0c95d2531e01e4470034b571892c.png)
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10 . 某种产品的广告支出费用x(单位:万元)与销售量y(单位:万件)之间的对应数据如表所示:
根据表中的数据可得回归直线方程
2.27x
,R2≈0.96,则
①第三个样本点对应的残差
1
②在该回归模型对应的残差图中,残差点比较均匀地分布在倾斜 的带状区域中
③销售量的多少有96%是由广告支出费用引起的
上述结论判断中有一个是错误 的,其序号为 _____________
广告支出费用x | 2.2 | 2.6 | 4.0 | 5.3 | 5.9 |
销售量y | 3.8 | 5.4 | 7.0 | 11.6 | 12.2 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4327541f8ccd5171555d20d74fd1b8cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c746256cb4248b41dd7a61b83dbd03.png)
①第三个样本点对应的残差
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82168f587f74eb68e682b1535e955410.png)
②在该回归模型对应的残差图中,残差点比较均匀地分布在
③销售量的多少有96%是由广告支出费用引起的
上述结论判断中有一个是
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