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解题方法
1 . 已知
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7dbc702617c765a573961953cc0901.png)
A.![]() | B.![]() |
C.![]() | D.![]() ![]() |
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2卷引用:河北省保定市唐县第一中学2023-2024学年高二下学期5月期中考试数学试题
名校
解题方法
2 . 已知
且
,若函数
在
上单调递减,则实数a的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7326ea56be82bd616fec7e6aa3c884c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6027c04510bd896d5106eab149f31b09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c12b378e1f4d6f437c73a15c3f9f0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3卷引用:广东省惠州市实验中学2023-2024学年高二下学期5月期中考试数学试题
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3 . 已知集合
,那么
的真子集有______ 个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17fa273c7e3cfac49fb4b966c4734248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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4 . 已知集合
,
,
,则集合
的真子集个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d362fcd96379ade0ab47ee49df4bf274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843cef8fb1cfb59f17e461e78d8d1809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffc00530f6f306d83e3e197b6df5d1c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.2 | B.3 | C.4 | D.8 |
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5 . 将正整数12分解成两个正整数的乘积有
三种,又
是这三种分解中两数的差最小的,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
,下列有关函数
的说法,正确的是:______ (把正确的答案题号都填上).
①
;②
;③
;④若
是一个质数,则
;⑤若
是一个完全平方数,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446ca8039ed3cc70424063ffbb54e2b6.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/92929613550308d597d738dc4963a2f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066de86a46332d480269aa125a47c714.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b842f73e28cf0a875fc9de9b93dea2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066de86a46332d480269aa125a47c714.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/153d72dfa6aa662b1091bc8305e59b60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4ffe89e7474ffe38f5e156ed559876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af3160a1358406bc85a7fbc4e6dadd8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60173658c5bffc8bf1efc74e19986901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c494f86e8b3286215fb254a0549653c.png)
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6 . 已知数列
的各项均为正整数,设集合
,
,记
的元素个数为
.
(1)若数列A:1,3,5,7,求集合
,并写出
的值;
(2)若
是递减数列,求证:“
”的充要条件是“
为等差数列”;
(3)已知数列
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7f885247785940c5c849210fb6f8abc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4884c506476f191d7919cd266c8c0212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47a0c2bb484bf523189b093485eca999.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1ff5cb5a9d88ed7db2c06683c3e355.png)
(1)若数列A:1,3,5,7,求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1ff5cb5a9d88ed7db2c06683c3e355.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3197c615558fee3993d2a8deb9091f0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d509697c5391a7c24d9bbc2c82422b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff241fc46c23ac975c5b39e87a9e46a.png)
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7 . 对任意
,记
,并称
为集合
的对称差.例如:若
,则
.下列命题中,为真命题的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ac95a142fdad28e7878ab9115fda4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef32fab366056915807eb0d495b7e90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68f70b226287d4a61f2a96afca02183f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b6158c2d0501cf187f4832fca3a132c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de89b0ee6e6bb5bfcf6d26f7e745e7f2.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.存在![]() ![]() |
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8 . 对于
,
满足
,且对于
,恒有
.则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3769c374cc6143e24838b06ccf17d1b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efd460cd48d5bb73990cbfc99d44a3f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ee7abd882ba99660bca68ebf544cd6.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024·全国·模拟预测
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解题方法
9 . 函数
的大致图象是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0dd22725974329df321206b0f2771c0.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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10 . 已知集合
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/530f2ac7c8635c3ac8e49ee62d2574e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b9b470218359a4a47be9244980489e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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