1 . 如图1,在等腰直角三角形
中,
,
,
为
的中点,连接
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/79abde39-6de4-4659-8cfd-d59a45ac0888.png?resizew=350)
(1)若
,求
的长度;
(2)若将图1中
绕点
顺时针旋转任意角度
到
,如图2所示,连接
,
为
上的中点,连接
、
,请探究
与
的位置关系和数量关系,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8e9ec412ea0355e4e5cd06c60e5fee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f215a42c4b7078d8d65923eb9980e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/79abde39-6de4-4659-8cfd-d59a45ac0888.png?resizew=350)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d79e7020414add95907e061df505ef0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
(2)若将图1中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59af0a498a28005947c87a7ece352094.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6b87e8fbd45bdbfc480508057c0298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
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2 . 已知
,函数
.
(1)当
时,求函数展开式中含
的一次项系数之和;
(2)当
时,
①求函数
展开式中的常数项;
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2e59b4e5bf92bf17a136bb555422ff.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ccb9e8d67d838579455ad9f17560a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8d850abc2f58230047cc3f95b846f9.png)
①求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9e70ec8d04593ad6285cd42505e4444.png)
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解题方法
3 . 请用二项式定理解决下列问题:
(1)求
除以100的余数?
(2)已知
,请比较
与
的大小,并证明你的结论.
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32bce704393f7b0081a14c656e54dd95.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ddcb15eb419ed659536e1385b09af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceef1abeeef220b4fe5f7d96feedd90.png)
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解题方法
4 . 设二次函数
,其图像过点
,且与直线
有交点.
(1)求证:
;
(2)若直线
与函数
的图像从左到右依次交于 A,B,C,D四点,若线段
能构成钝角三角形,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/225705de8bb0a3e08619e73c7f0c49be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2af31a8d791f28399fc13be3250136dc.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1508daa783a4587860a1578e0bb332b.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2af31a8d791f28399fc13be3250136dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fd713a9809d5df1de33c6f11b81eca7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b467455ea6b8b7f5e6dd53110bc22060.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6ce02259a85ea191541f4a708738f1.png)
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5 . 设二次函数
.
(1)若
,
且二次函数的最大值为正数,求
的取值范围.
(2)若
的解集是
,求
的解集.
(3)设二次函数
的两个零点分别为
,
,满足
,证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8352b2e643a7ce605334f1b0e572bfb0.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239ea0e903fbb4c8ce04133b9969578c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/566bfdd14f1aa396f620e0ca6895a21c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8f3d2d9f66307b7af2398efdb893bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa220ab7c91ffa40202bcc544aa2bb2.png)
(3)设二次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd69aebdafb31468eb13ce3b28a36e47.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/57cfda1c04b6eaeb5e78018539c2880e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e37902f139fee3d5a5ac74b21b0a0e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1ad9f639b70bf98fe33ca163a8922f.png)
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6 . 如图,圆O是△ABC的外接圆,D是圆外一点,BD与圆O相切于点B,
,证明:A,O,C三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dc5270c3aa0965eee31bd3dd779e00b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/cb838256-b5a9-487d-a834-85940d85fd56.png?resizew=150)
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7 . (1)用反证法证明命题“存在实数x,使得sinx=x”时,“假设”的内容是:___________ .
(2)已知命题p:∀x≥1,使得
,则
p为___________ .
(2)已知命题p:∀x≥1,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bff1a588a67b0b29fbd65b78dd68543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a45a62af2453837041c28e79295415.png)
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8 . 如图,
是
的中线,
是线段
上一点
不与点
重合)
交
于点
,连结
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/d373104c-f5f8-40c6-8fd2-865a29c641fa.png?resizew=494)
(1)如图1,当点
与
重合时,求证:四边形
是平行四边形;
(2)如图2,当点
不与
重合时,(1)中的结论还成立吗?请说明理由.
(3)如图3,延长
交
于点
,若
,且
.
①求
的度数;
②当
时,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebe7eaf967808dad0a184eeedfa27721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63096579c886a305cd737dff3f4133ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/d373104c-f5f8-40c6-8fd2-865a29c641fa.png?resizew=494)
(1)如图1,当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
(2)如图2,当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)如图3,延长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24ad0a87392245e4bf5bafe26089803b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c52a15fb25eaec30869d0f264ada3326.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bab53e0cb6e6ec13764e326b98f26b6.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8865a72c77a0dd80ff3be1c6e746a0d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e4fa04825ac7d071968056322d88be.png)
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解题方法
9 . 已知定义在
上的奇函数
满足:“对于区间
上的任意
、
,都有
成立”.
(1)求
的值,并指出
在区间
上的单调性;
(2)用增函数的定义证明:函数
是
上的增函数;
(3)判断
是否为
上的增函数,如果是,请给出证明;如果不是,请举出反例.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/623d70bfdaa5da8cf288fa1a3ca26f0a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e38fffbc7ab9882480f4faa72390e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
(2)用增函数的定义证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75e8e1c23498053dece274fc224982d8.png)
(3)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
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名校
解题方法
10 . 设A是集合P={1,2,3…
}的一个
元子集(即由
个元素组成的集合),且A的任何两个子集的元素之和不相等;而集合P的包含集合A的任意
+1元子集B,则存在B的两个子集,使这两个子集的元素之和相等.
(1)当n=6时,试写出一个三元子集A.
(2)当n=16时,求证:k≤5;
(3)在(2)的前提下,求集合A的元素之和S的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)当n=6时,试写出一个三元子集A.
(2)当n=16时,求证:k≤5;
(3)在(2)的前提下,求集合A的元素之和S的最大值.
您最近一年使用:0次
2021-07-31更新
|
715次组卷
|
10卷引用:上海市宝山区行知中学2020-2021学年高一上学期10月月考数学试题
上海市宝山区行知中学2020-2021学年高一上学期10月月考数学试题(已下线)第一章 集合与常用逻辑用语(选拔卷)-【单元测试】2021-2022学年高一数学尖子生选拔卷(人教A版2019必修第一册)(已下线)第一章 集合与常用逻辑用语单元检测(能力挑战卷)-【一堂好课】2021-2022学年高一数学上学期同步精品课堂(人教A版2019必修第一册)第1章 集合(章末测试提高卷)-2021-2022学年高一数学同步单元测试定心卷(苏教版2019必修第一册)第1章 集合与逻辑单元测试-【A+课堂】2021-2022学年高一数学同步精讲精练(沪教版2020必修第一册)(已下线)期中综合检测 (综合培优) B卷-2021-2022学年高一数学同步单元AB卷(人教A版2019必修第一册)(已下线)专题01 集合与常用逻辑用语常考基础题型-2021-2022学年高一《新题速递·数学》(人教A版2019)(已下线)1.1集合之间的关系(第3课时)(已下线)第1章 集合与逻辑(基础、典型、新文化、压轴)分类专项训练-2022-2023学年高一数学考试满分全攻略(沪教版2020必修第一册)(已下线)高一上学期第一次月考解答题压轴题50题专练-举一反三系列