名校
1 . 已知
,函数
,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e6404cd8d3bb839cccf6e4176c8fb9a.png)
A.![]() |
B.若![]() ![]() ![]() ![]() |
C.若函数![]() ![]() ![]() |
D.若![]() ![]() ![]() |
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3卷引用:河南省南阳市西峡县第一高级中学2023-2024学年高二下学期第一次月考数学试卷
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2 . 某学校附近有条长500米,宽6米的道路(如图1所示的矩形ABCD),路的一侧划有100个长5米,宽2.5米的停车位(如矩形AEFG),由于停车位不足,放学时段道路拥堵,学校安保处李老师提出一个改造方案,在不改变停车位形状大小、不改变汽车通道宽度的条件下,可通过压缩道路旁边绿化带及改变停车位方向来增加停车位,记绿化带被压缩的宽度
(米),停车位相对道路倾斜的角度度
,其中
.
,求
和
的长;
(2)求d关于
的函数表达式
;
(3)若
,按照李老师的方案,该路段改造后的停车位比改造前增加多少个?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990a3680645f22737907fc1b5b10d99a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eb60187001a6a7bbf887d2a233e5e26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09463dc187d5b2574170f1566ac4c382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9088e31e00eaa4e95c1e6717b0c82cdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827be85b8f921007a5cf9edb64bd3491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c495fd86e62c3090caba0702bbcffd7.png)
(2)求d关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3f74946c4e57365e0de85d277ba8d2a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f2572192cc7ca046e9a3155ef3e56a.png)
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解题方法
3 . 若非空集合A与B,存在对应关系f,使A中的每一个元素a,B中总有唯一的元素b与它对应,则称这种对应为从A到B的映射,记作f:A→B.
设集合
,
(
,
),且
.设有序四元数集合
且
,
.对于给定的集合B,定义映射f:P→Q,记为
,按映射f,若
(
),则
;若
(
),则
.记
.
(1)若
,
,写出Y,并求
;
(2)若
,
,求所有
的总和;
(3)对于给定的
,记
,求所有
的总和(用含m的式子表示).
设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f471707062efa20856b51c22e6f84dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21baa8bc435ec6b2c9b67877171a3173.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/361386446d504a14471b9fd89130f1c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78e2cf3c6d97e637b06bc3f173e2294b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf22d7d1a965bda25168a233fb6290c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2cab9bca9269b6a450c4b52f0557ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32cb04516f1b2735ce3f3b4650dd44d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab9dd64d5d8d3e0da1bd6a1821735620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/804359bfe1c504ea7c4fef24f816c1ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64a050b856ea45102abeca042f7fa51c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e951e5ed59afb9cbca7ba7b3f57d637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/454dd532a75670c2c5fe340e7cf6394e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66803407d09e203ad26667f83d13cb73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e951e5ed59afb9cbca7ba7b3f57d637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65882cdf1d004742addf809d8b9085cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e3e85ec77053cebbd8b2f6f6300ac66.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/024b3cc2f0b74a8e3b34bae24fa44707.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab44704e5aa4ff926a58cebdcc4dad99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1eb6e559b36bbfab633520897b7c9d8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3334356ffb98a848fe7a027437e8fbcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab44704e5aa4ff926a58cebdcc4dad99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1eb6e559b36bbfab633520897b7c9d8.png)
(3)对于给定的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f278ad5460e4a89bea4068beabb8df15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a31ccd147dd0dd022bd2e605d2b0f7fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1eb6e559b36bbfab633520897b7c9d8.png)
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2卷引用:重庆市乌江新高考协作体2023-2024学年高一下学期第二阶段性学业质量联合调研抽测(5月)数学试题
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解题方法
4 . 已知
是定义域为
的奇函数,函数
,且当
时恒成立,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c19b5e7ec97fb0dc579c3f0c47f2727.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/967d2a64967055bf7847d26f5eb7bb08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f66193ff4404822ce1410b60d251569.png)
A.![]() | B.不等式![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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5 . 已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/727088002886910f1b8bff4492c8f453.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0fa0035770a41d223aadf0a1c5e186b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/727088002886910f1b8bff4492c8f453.png)
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解题方法
6 . 已知函数
满足对任意
,都有
,且当
时,
,函数
是定义域为
的偶函数,满足
,且当
时,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fd7af568e3d9f444beb0ff41426477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74325e5da185c3f6c5f20d91027a4589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd26cf4ba8fe98bc4dbc37103b805dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71bb7883ea87e6275472dbe14ee62357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1275f567f4313471df4daad443743f43.png)
A.![]() | B.![]() |
C.![]() ![]() | D.![]() |
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7 . 已知函数
(
,且
)是定义在R上的奇函数.
(1)求a的值;
(2)若关于t方程
在
有且仅有一个根,求实数k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/571ce51eb32810277fb2fb9bd55a57bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d32d1a5a0732c7e4af737555e44ff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)求a的值;
(2)若关于t方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aade7468c98884534ab383a655a5f58c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9099a75c433e97bbe05052a00110571.png)
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23-24高一下·四川成都·开学考试
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解题方法
8 . 已知定义在
上的奇函数
满足
,且当
时,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86d78dec1c1e00ec02d7bdaf76ef8901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdcdce390913ba35a3c3d13af6ac335f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d401c3df7c96e6ce125a3ad3f1c1cf5c.png)
A.![]() | B.![]() ![]() |
C.![]() | D.函数![]() |
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9 . 函数
满足:当
时,
,
是奇函数.记关于
的方程
的根为
,若
,则
的值可以为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1092d77e2570be5584ebc0cdcdca2ea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b08d939cee48042d0a565a53dbeadf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57d500a74b865ade2b576720c04becd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ed0b01191624fcc0469ecad0287a0b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fdb4c1ad5fce7cf952767c03b8eb6ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
A.![]() | B.![]() | C.![]() | D.1 |
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|
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解题方法
10 . 设函数
,
,
,若
,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ef8b24e48758bbed0d8b8942f020049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ab586aefae2e8c69d0b165f7a1a8ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24aa16b780156e18f12baa2b8ee0f9a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff20e95162d66c00f30b4b35d0d4f20d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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|
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