解题方法
1 . 已知函数
,其中m为常数,且
.
(1)求m的值;
(2)用定义法证明
在R上是减函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8315722b05049fde7ab3d90412d6c77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70dfd3b70aab0849a459a241d904aa73.png)
(1)求m的值;
(2)用定义法证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8315722b05049fde7ab3d90412d6c77.png)
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2022-03-22更新
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5卷引用:新疆吐鲁番市2021-2022学年高一上学期期末考试数学试题
新疆吐鲁番市2021-2022学年高一上学期期末考试数学试题(已下线)第02讲 函数的单调性与最大(小)值(讲+练)-2023年高考数学一轮复习讲练测(新教材新高考)(已下线)专题19 函数的基本性质 (1)河北省石家庄市元氏县第四中学2022-2023学年高一上学期入学摸底数学(A)试题(已下线)第二章 函数的概念与性质 第二节 函数的单调性与最值(讲)
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解题方法
2 . 已知椭圆
过点
,且
.
(1)求椭圆
的方程;
(2)设
为原点,过点
的直线
与椭圆
交于
,
两点,且直线
与
轴不重合,直线
,
分别与
轴交于
,
两点.求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/079ca2b1f25fb6475d1eb9f125b06286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd99c5000629d7f49499d666e68f40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b104867a12d24a353d94858c2fa17c8f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37df9dad3961893b22d6639c4311e267.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2562727c414103b1d3f71f5205ab0b96.png)
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2021-01-20更新
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5卷引用:新疆吐鲁番市高昌区第二中学2021-2022学年高二上学期期末考试数学(理)试题
新疆吐鲁番市高昌区第二中学2021-2022学年高二上学期期末考试数学(理)试题 北京市丰台区2020-2021学年高二上学期期末练习数学试题(已下线)专练35 综合拔高练-2021-2022学年高二数学上册同步课后专练(人版A版选择性必修第一册)江苏省连云港市2022-2023学年高三上学期期中复习数学试题北京市西城区北京师范大学第二附属中学2023-2024学年高二下学期期中考试数学试题
3 . 期末考试结束,高二(1)班班主任张老师从班里的40名学生中,随机抽取10名同学的语文和数学成绩进行抽样分析,研究学生偏科现象.将10名学生编号为1,2,3
10,再将他们的两科成绩(单位:分)绘成折线图如下:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/08222c03-51d1-4e6e-b862-293f1e3e5217.png?resizew=399)
(1)从这10名学生中随机抽取一名学生,求抽取的这名学生两科成绩相差大于10分的概率;
(2)从两科成绩均超过70分的学生中随机抽取2人进行访谈,求这2人中恰有一个是语文成绩高于数学成绩的概率;
(3)设该班语文和数学两科成绩的平均值分别为
,方差分别为
,根据折线图,试推断
和
,
和
的大小关系(直接写出结论,不需证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/08222c03-51d1-4e6e-b862-293f1e3e5217.png?resizew=399)
(1)从这10名学生中随机抽取一名学生,求抽取的这名学生两科成绩相差大于10分的概率;
(2)从两科成绩均超过70分的学生中随机抽取2人进行访谈,求这2人中恰有一个是语文成绩高于数学成绩的概率;
(3)设该班语文和数学两科成绩的平均值分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6867a7873e4818c12074206da32f0ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee5f7f88d327670ad628ace52f5b792f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096b1ece1dcd29c59a46a4b3e02cb548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5031a3a951c4a1d1c5e9f80a5e26513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c296e45b84cf67a98939aa7334e7d478.png)
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2021-01-28更新
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2卷引用:新疆吐鲁番市高昌区第二中学2021-2022学年高二上学期期末考试数学(理)试题
4 . 已知:空间四边形ABCD,E、F分别是AB、AD的中点,求证:EF∥平面BCD
![](https://img.xkw.com/dksih/QBM/2020/7/1/2496513356775424/2497011713425409/STEM/4987e051254543f1bee8f1ba7dcea7f6.png?resizew=105)
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解题方法
5 . 已知
.
(1)求不等式
的解集;
(2)设
、
、
均为正实数,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e98cce8754766bd990672e08124a859.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4b781b577380833bf91d2b2f1169c50.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fed96d3652b1785f5346ba98d3d9723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754a0b7002c7adda391ae9c297a64f33.png)
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解题方法
6 . 如图,在四棱锥
中,底面是正方形
平面
且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/edda625f-31d4-4195-bc32-51848e8a5bb3.png?resizew=156)
(1)求证:
;
(2)求异面直线
与
所成角的大小;
(3)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba4c15fb8fc3239d45bd4e7d8971f58e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/edda625f-31d4-4195-bc32-51848e8a5bb3.png?resizew=156)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccbd1316b9d1f0c1e71fd078deec61f6.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33b7213d99a817bff19bcf740a0697c.png)
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7 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a83589711b32860e89c01175028a1919.png)
(1)求
的定义域;
(2)用单调性定义证明函数
单调性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a83589711b32860e89c01175028a1919.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)用单调性定义证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a83589711b32860e89c01175028a1919.png)
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解题方法
8 . 函数
对于任意的
,都有
,若
时,
,求证:
是
上的单调递减函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd29ef32d9bc2e32ef2b8639b57dc9a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd522b593f298eefe8bcdee91eaa16f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
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