名校
解题方法
1 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a1a5f2533b8ea54b7022383f875666.png)
(1)讨论函数
的单调性;
(2)当
时,不等式
恒成立,求实数a的取值范围;
(3)令
,若存在
,
且
时,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcadc169efec6fe6d800449bd952fac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a1a5f2533b8ea54b7022383f875666.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d9b08cf69b3ac49d11833e9a47e4e7f.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882ea00f2413de1020f2368786c6dbd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f1a5699410baa270f3fa8153ab346e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5f4aadc17b6d5c9760a75fab7fb760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d136fd3c66c833cc3cf80cbf0b2870b1.png)
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名校
解题方法
2 . 已知
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51474d91e540a475138571e8738de850.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/126054e5ea91877bf9c6c9cdecb33428.png)
A.![]() | B.![]() | C.![]() | D.2 |
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今日更新
|
960次组卷
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4卷引用:四川成华区某校2023-2024学年高一下学期期中考试数学试题
四川成华区某校2023-2024学年高一下学期期中考试数学试题湖北省黄冈市浠水县第一中学2023-2024学年高一下学期期末质量检测数学试题广东省江门市鹤山市第一中学2023-2024学年高一下学期第二阶段考试(5月)数学试题(已下线)【高一模块一】难度3 小题强化限时晋级练(基础3)
名校
解题方法
3 . 已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f27f930806d4ee1a6ac77a0fa6c340.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c9df49c32fa5cfd53197f65e1af42a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f27f930806d4ee1a6ac77a0fa6c340.png)
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名校
4 . 已知复数
满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e0aeeb125cfb42e33094594d4381f5.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a7f045be11d20e85f0fb4881cbfaf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e0aeeb125cfb42e33094594d4381f5.png)
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名校
解题方法
5 . 关于
的不等式
有解,则实数
的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b021b127a6d00ae353a46bf995427923.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
6 . 数列
、
满足:
,
,
,其中
是数列
的前
项和.
(1)求数列
,
的通项公式;
(2)若
,都有
成立,求实数
的取值范围;
(3)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f966272f7781790ff27e40db6b525253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2a49ef11731716bd34cef68a697d13c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ea552c924173b924a160ce75d8f7dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f8365233f341451598eb50525a1557a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2532e928dda51e91a70a26b60e309094.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52c9237cb0b4acc568d4afb12997186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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名校
解题方法
7 . 已知函数
有三个不同的零点
,
,
,且
,则实数a的取值范围是______ ;
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f07ffbfce99b6152ce76eac188afeb2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ded52999771182240a44aaa48cf8fc7a.png)
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解题方法
8 . 函数
在定义域
内可导,记
的导函数为
,
的图象如图所示,则
的单调增区间为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59ae1197b475e3acb4a44bc24f18dad9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851c68ef2e0703706f3b528daa902eb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851c68ef2e0703706f3b528daa902eb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() ![]() |
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名校
解题方法
9 . 如图,在扇形OAB中,半径
,圆心角
,F是扇形弧上的动点,矩形CDEF内接于扇形,设
,则矩形CDEF的面积的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52705567101a48893de582656ef41527.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbc790cfaa59a808c25a7edb95dc29fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60c22f040f353ab28a6e00ddd56913c2.png)
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解题方法
10 . 在
中,角A,B,C的对边分别为a,b,c,其中
,已知S为
的面积且满足
.
(1)若
为锐角三角形,求
的取值范围;
(2)法国著名数学家柯西在数学领域有非常高的造诣.很多数学的定理和公式都以他的名字来命名,如柯西不等式、柯西积分公式.其中柯西不等式在解决不等式证明的有关问题中有着广泛的应用.若P是
内一点,过P作AB,BC,AC垂线,垂足分别为D,E,F,借助于三维分式型柯西不等式:
,
当且仅当
时等号成立.求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3efc64a6c2f8e31c8584cbbd5a2b3cb.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/413323ab92f73c1eabb235731bb5c399.png)
(2)法国著名数学家柯西在数学领域有非常高的造诣.很多数学的定理和公式都以他的名字来命名,如柯西不等式、柯西积分公式.其中柯西不等式在解决不等式证明的有关问题中有着广泛的应用.若P是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fcbd8d6468c909aa229f527bca2581e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48a95e7d22d75a3a7a7c72df362f91fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb5ba135022def1bcc1cddea66496706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a69e37017b56a9d4d100413cf4bc16f4.png)
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