2024高三·全国·专题练习
解题方法
1 . 设
是两个非空集合,“若
,则必有
”这个命题是假命题,请你举出反例.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f443096be1d8d50ea3e2ab2ac3d49c6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ad78dc8b8aed907b4fe9640c997454.png)
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2 . 对于函数
,若函数
是严格增函数,则称函数
具有性质
.
(1)若
,求
的解析式,并判断
是否具有性质
;
(2)判断命题“严格减函数不具有性质
”是否为真命题,并说明理由;
(3)若函数
具有性质
,求实数
的取值范围,并讨论此时函数
在区间
上零点的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07320a8812534c83460723efe86fa365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d03211706ec9797632dedba4124f398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c388166862b3ccfcc7ca749ebe5949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)判断命题“严格减函数不具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89ef5467076c43c044b5618e6b0a1d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eeed313aa6d81b93f134b56de244214.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3aae9c8988f4a48db69cad3308942c9.png)
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2023·全国·模拟预测
解题方法
3 . 设点
在椭圆
内,直线
.
(1)求
与
的交点个数;
(2)设
为
上的动点,直线
与
相交于
两点.给出下列命题:
①存在点
,使得
成等差数列;
②存在点
,使得
成等差数列;
③存在点
,使得
成等比数列;
请从以上三个命题中选择一个,证明该命题为假命题.
注:若选择多个命题分别作答,则按所做的第一个计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c993e34db40190e64654a10b0c13c672.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d6678a1a5cc14704ecf06a7648ff543.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d4aca03910382accfe738520daf689c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
①存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f23bfdeeaa1efc12f64328e962d395b.png)
②存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8d3db975e7888ac13b4448b874b972d.png)
③存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8d3db975e7888ac13b4448b874b972d.png)
请从以上三个命题中选择一个,证明该命题为假命题.
注:若选择多个命题分别作答,则按所做的第一个计分.
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4 . 设
为实数,定义
生成数列
和其特征数列
如下:
(i)
;
(ii)
,其中
.
(1)直接写出
生成数列的前4项;
(2)判断以下三个命题的真假并说明理由;
①对任意实数
,都有
;
②对任意实数
,都有
;
③存在自然数
和正整数
,对任意自然数
,有
,其中
为常数.
(3)从一个无穷数列中抽出无穷多项,依原来的顺序组成一个新的无穷数列,若新数列是递增数列,则称之为原数列的一个无穷递增子列.求证:对任意正实数
生成数列
存在无穷递增子列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/796bb39a2ab23cfdb6e463ab30a7af2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4758b555ca9b157cc074f1e4a092e34a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f61c0bb2370087736c8e00e108b48c8.png)
(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c051dc675bcca6a8f70a3dbe922354.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3121951a9b059eef49b4a346d3aa2b94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400b893304c51631873ded41027cf48.png)
(1)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4e0c84de10f0f2186313169c3dc997b.png)
(2)判断以下三个命题的真假并说明理由;
①对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fbdf49cd00af1ff87259836ddd9f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/508cd31480a898a71472e2d5d22377c7.png)
②对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fbdf49cd00af1ff87259836ddd9f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c99515d9952f2f7739fd750a31128f.png)
③存在自然数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a178f2c27906fc74afee1b7d7d52746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1563da7b0f046a469476668a3686e8f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f59a60eb4d63ebc879ae5c26413bcdcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)从一个无穷数列中抽出无穷多项,依原来的顺序组成一个新的无穷数列,若新数列是递增数列,则称之为原数列的一个无穷递增子列.求证:对任意正实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da069077c220af26b9e77b02baeee4a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4758b555ca9b157cc074f1e4a092e34a.png)
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名校
5 . 已知命题p:函数
有零点,命题
,
.
(1)若p为真命题,求实数a的取值范围;
(2)若p,q中恰有一个真命题,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/906f6aab4911656e0d9efbaa69883c7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36eba0d6d9950726b146da754fc8637b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d63dde7ac4e9278b4b80f31e059fb8b.png)
(1)若p为真命题,求实数a的取值范围;
(2)若p,q中恰有一个真命题,求实数a的取值范围.
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2022-10-15更新
|
718次组卷
|
4卷引用:山东省枣庄市滕州市滕州市第一中学2022-2023学年高三上学期10月月考数学试题
6 . 数列
对任意
,且
,均存在正整数
,满足
.
(1)求
可能值;
(2)命题p:若
成等差数列,则
,证明p为真,同时写出p逆命题q,并判断命题q是真是假,说明理由:
(3)若
成立,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c703ace0d2c22dd947a19d8afc74eac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d9f79b02c30f810f7d9c661fa7e44c7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
(2)命题p:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26b39cb7d4efd2dd15a1f39ac6ef72c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b30bfc8674948c31b09f824402ebada.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3557b9d9ef8529d963d2cd5962add5e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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21-22高一·湖南·课后作业
7 . 判断下列命题的真假:
(1)
,
;
(2)
,
;
(3)线段的垂直平分线上的点到这条线段两个端点的距离相等;
(4)平面上任意两条直线必有交点.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ee09b14494ad377b52cd9ed8e2b6f40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdbf50b34d559607dc5a75c90a72e558.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ccd7af9298cd5ff19d8866fedb42ec4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdbf50b34d559607dc5a75c90a72e558.png)
(3)线段的垂直平分线上的点到这条线段两个端点的距离相等;
(4)平面上任意两条直线必有交点.
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2022-02-23更新
|
629次组卷
|
9卷引用:第02讲 常用逻辑用语 (精讲+精练)-2
(已下线)第02讲 常用逻辑用语 (精讲+精练)-2(已下线)1.2.3 全称量词和存在量词(已下线)第06讲 全称量词命题与存在量词命题-【暑假自学课】2022年新高一数学暑假精品课(苏教版2019必修第一册)(已下线)突破1.5全称量词与存在量词(课时训练)(已下线)2.3 全称量词命题与存在量词命题(1)(已下线)2.3 全称量词命题与存在量词命题(2)(已下线)1.5.1全称量词与存在量词(分层作业)-【上好课】湘教版(2019)必修第一册课本习题1.2.3全称量词和存在量词(已下线)第07讲 全称量词与存在量词6种常见题型 -【同步题型讲义】(人教A版2019必修第一册)
8 . 已知p3+q3=2,求证:p+q≤2.
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9 . 设
:实数
满足
,
:实数
满足
.
(Ⅰ)当
时,若
为真,求实数
的取值范围;
(Ⅱ)当
时,若
是
的必要条件,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e214ee67f5ab6252520118d1c718b3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1495e524e9341750e16d3a7033829da0.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f675824e539f50cec53120959d32e554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(Ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e26b38e357c7d985656ba7bb3c794a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2018-07-17更新
|
1986次组卷
|
8卷引用:安徽省江南片2019届高三上学期开学摸底联考理科数学试题
安徽省江南片2019届高三上学期开学摸底联考理科数学试题(已下线)专题1.2 命题及其关系、逻辑联结词、充分条件与必要条件-《2020年高考一轮复习讲练测》(浙江版)(已下线)专题1.2 全称量词与存在量词、充要条件(讲)-2021年新高考数学一轮复习讲练测(已下线)专题1.2 全称量词与存在量词、充要条件(讲)- 2022年高考数学一轮复习讲练测(新教材新高考)【全国校级联考】福建省龙岩市一级达标校2017-2018学年高二下期期末考试文科数学试题【市级联考】河北省廊坊市2018-2019学年高二第二学期期中联合调研考试文科数学试题河北省廊坊市2018-2019学年高二第二学期期中联合调研考试文科数学试题四川省凉山州2019-2020学年高二上学期期末考试数学(理科)试题
10 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b13667d65f8d6e6911d0103bfc4a1e9.png)
(1)求函数f(x)的最小值;
(2)已知m∈R,p:关于x的不等式f(x)≥m2+2m-2对任意x∈R恒成立,q:函数y=(m2-1)x是增函数,若p正确,q错误,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b13667d65f8d6e6911d0103bfc4a1e9.png)
(1)求函数f(x)的最小值;
(2)已知m∈R,p:关于x的不等式f(x)≥m2+2m-2对任意x∈R恒成立,q:函数y=(m2-1)x是增函数,若p正确,q错误,求实数m的取值范围.
您最近一年使用:0次