解题方法
1 . 已知
是平面内两两不共线的向量,且
则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e12e95f703ad30ab9a3d38376830989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e7d52487370db340020d55d7fd0793e.png)
A.![]() | B.![]() |
C.![]() | D.当![]() ![]() ![]() |
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解题方法
2 . 对于分别定义在
上的函数
以及实数
若存在
使得
则称函数
与
具有关系![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9902e568d7b1f5229f6ebf5c43e18ab.png)
(1)若
判断
与
是否具有关系
并说明理由;
(2)若
与
具有关系
求实数
的取值范围;
(3)已知
为定义在
上的奇函数,且满足:
①在
上,当且仅当
时,
取得最大值1;
②对任意
有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a67cba3a83a7d7f44570a197db5c9111.png)
判断是否存在实数
使得
与
具有关系
若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee5f7f88d327670ad628ace52f5b792f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fd1e808e015f4cb43d2e3a0529ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e924e716802ea0e503812d4168de1ae0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb097db757dcce8d1e114eaa35cfb5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2c9050bc59bcfe21e528bf1e336996.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9902e568d7b1f5229f6ebf5c43e18ab.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4efcf59a67eda20aff6a74fd1b5102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c217be22ee74ee758755bc18917e3eae.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67240f24d5be6db366b4f218003d8896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a17a7dd0a9319f92eec1ac43eb93106d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ea020f6ee69455b961fa9fed5e82dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0446794d4e31bb0bd3907b1dd27dbd6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
①在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57a78355986534b6e50bd7cabc9290a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede97915bccd6a7b22d7400c30f8adea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
②对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bbce12f6911dacf78262ba950c0be55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a67cba3a83a7d7f44570a197db5c9111.png)
判断是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ed0e00c9b96bf8b70b3ea1de85852ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65353833b295abc6a7ddd390046f69c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b4942cf1c67cc84090c77e373809d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d869a4478e36efba14ec203efbd00342.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
3 . 已知函数
,函数
,且
,定义运算
设函数
,则下列命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afbecf96f4a56400b24bc3dc6c5b547e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/116b80ed2eedbb36fa1898b7fcd681c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a4eaa80b44625890339d6a0065c241.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c29c4327642af92a63376313e3498d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bf97f28c31f9dbd8823694f666610e.png)
A.![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() |
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7卷引用:广西钦州市2024届高三年级第三次教学质量监测 数学
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4 . 平面几何中有一定理如下:三角形任意一个顶点到其垂心(三角形三条高所在直线的交点)的距离等于外心(外接圆圆心)到该顶点对边距离的2倍.已知
的垂心为D,外心为E,D和E关于原点O对称,
.
(1)若
,点B在第二象限,直线
轴,求点B的坐标;
(2)若A,D,E三点共线,椭圆T:
与
内切,证明:D,E为椭圆T的两个焦点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24e12c97516329a6776fe48c450d93b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c8ef6f3640bd70e40f3b591c8bcc14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b45db8dd8768994af51206565379fd.png)
(2)若A,D,E三点共线,椭圆T:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2024-05-08更新
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5 . 已知函数
在区间
上恰有3个零点,则ω的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d08c44e202934be9d8c98b8566c5e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71163f419555f2ed76075c8ff659fbfc.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-01-27更新
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4卷引用:广西壮族自治区钦州市浦北县浦北中学2023-2024学年高一下学期3月月考数学试题
广西壮族自治区钦州市浦北县浦北中学2023-2024学年高一下学期3月月考数学试题四川省宜宾市2023-2024学年高一上学期期末学业质量监测数学试卷湖南省长沙市麓山国际实验学校2023-2024学年高一下学期第一次学情检测数学试题(已下线)高一数学期末模拟试卷02-《期末真题分类汇编》(北师大版(2019))
名校
解题方法
6 . 根据社会人口学研究发现,一个家庭有
个孩子的概率模型为:
(其中
)
每个孩子的性别是男孩还是女孩的概率均为
,且相互独立,事件
表示一个家庭有
个孩子
,事件B表示一个家庭的男孩比女孩多(若一个家庭恰有一个男孩,则该家庭男孩多).
(1)若
,求
,并根据全概率公式
求
;
(2)是否存在
值,使得
,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![]() | 1 | 2 | 3 | 0 |
![]() | ![]() | ![]() | ![]() | ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e362ab25e6f8719efd1b515094b69561.png)
每个孩子的性别是男孩还是女孩的概率均为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a2e2ff5453e97b261328dc9569d1468.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f970f380a12c843bb4a74ff34a15b2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f587a573abdf89724c89c97e53a5bdab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/108ab49f370919e730e3567070deee65.png)
(2)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667df0f959f5626681d6d9aecaf05be1.png)
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解题方法
7 . 如图,在长方体
中,点
在平面
的射影为
.
(1)证明:
为
的垂心.
(2)若
,且点
在平面
的射影为点
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0a582c36d62d83c16425b2f54b4354.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/7/37e61b98-1318-418f-b939-6e590a30b023.png?resizew=217)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de60f6ffd5ab327d4cfe32d26d95da70.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ab5a353686725ea697ea410a8ad9c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0a582c36d62d83c16425b2f54b4354.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/577b7032795d3900dbce9cbe60ab2a1d.png)
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8 . 已知函数
.
(1)判断
的单调性,并说明理由;
(2)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a9367e6c6f1e35aab53cf807440a91b.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad28a33734627fda91369bf12381c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ca13a93b5f401c0d39ba52b0cffcb0.png)
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9 . 已知定义域为
的函数
的导函数为
,且
,则下列不等式恒成立的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9470e429c8833930e9294e2638648784.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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5卷引用:广西壮族自治区钦州市2022-2023学年高二下学期期末教学质量监测数学试题
广西壮族自治区钦州市2022-2023学年高二下学期期末教学质量监测数学试题湖北省十堰市2022-2023学年高二下学期6月期末数学试题江西省龙南中学2022-2023学年高二下学期6月期末考试数学试题江西省南昌市部分学校2022-2023学年高二下学期6月期末数学试题(已下线)第三章 利用导数比较大小 专题四 利用导数比较大小综合训练综合训练
解题方法
10 . 已知函数
,
的定义域均为
,且
,
.若
的图象关于直线
对称,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb53d24d71dd22aa5973522385cc0241.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/487c8ddb9e96d3b6cd2aaeb8cb5569aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f6aa6fe6d80f0a42eb19313406aff44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/762fee662775c2b27c4b3ef8910ef157.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb53d24d71dd22aa5973522385cc0241.png)
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