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解题方法
1 . 某厂为估计其产品某项指标的平均数,从生产的产品中随机抽取10件作为样本,得到各件产品该项指标数据如下:9.8 10.3 10.0 10.2 9.8 10.0 10.1 10.2 9.7 9.9,将该项指标的样本平均数记为
,样本标准差记为s,总体平均数记为
;
(1)求
与s(s精确到三位小数,参考数据:
)
(2)记样本量为n,查阅资料可知:关于
的不等式
的解集是总体平均数
的一个较好的估计范围;
①根据以上资料,求出该产品的总体平均数
的估计范围;
②在①的估计结果下,将指标不在总体平均数
的估计范围内的产品称作“超标产品”.现从这10件样品中不放回随机抽取2件,将事件“抽到的2件产品都是超标产品”记为A,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfbe7f95b5d89f9409ec24536da9e826.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80746e5e22851a0f1075374a3c3280ad.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfbe7f95b5d89f9409ec24536da9e826.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de88c36df6f5638445482f8e08e7ab3.png)
(2)记样本量为n,查阅资料可知:关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80746e5e22851a0f1075374a3c3280ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31a56c2a447e24658d3cfd462b35c78b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80746e5e22851a0f1075374a3c3280ad.png)
①根据以上资料,求出该产品的总体平均数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80746e5e22851a0f1075374a3c3280ad.png)
②在①的估计结果下,将指标不在总体平均数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80746e5e22851a0f1075374a3c3280ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27b6f8cb2faaad82b53b2a66ee817a37.png)
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2 . 对于实数
,
的不同取值,求关于
的方程
的解集.
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a951f2a78ac3870b285128055f091e99.png)
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3 . 已知圆C:
.
(1)当
,
,
时,过点
且斜率为k的直线l与圆C有两个不同的交点,求k的取范围;
(2)当圆C以坐标原点O为圆心,且与直线
相切时,圆与x轴交于A,B两点,圆内的动点P使
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d7c223faadd624d524399fc0f7f39e.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcdb7a488910743dc5c63afb394b87e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7551011cfb75b26f35b07d6617c6a18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25e326fdf9e5456f48e8a99a069f379.png)
(2)当圆C以坐标原点O为圆心,且与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bb2c3c88ffd31fe98cb36b03566cca8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc495b7c04ff1d3c2bd7098bf96c5649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59880e470359d8e9faf6ae5ce155cf2a.png)
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4 . 已知双曲线
的右焦点为
,过右焦点
作斜率为正的直线
,直线
交双曲线的右支于
,
两点,分别交两条渐近线于
两点,点
在第一象限,
为原点.
(1)求直线
斜率的取值范围;
(2)设
,
,
的面积分别是
,
,
,求
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbadddf8d6d2a0f0f16c10100795d867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/cf639890f27a42e1383cc6cfa14117a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bbf417026dc57a5e9ce85359188beec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532d9de08698f61d7c010805c61a4ec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c8561afa0f1454ea382a625d000a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d678455f156f5de3f6c0cc78adbe6d2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60b99d522f019832ececfb82fd2bcb87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30654ba32a8ac50a05dc7e34bba72dcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4635ef9bf093c4f65a1dda2d37033e40.png)
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2022-10-16更新
|
959次组卷
|
6卷引用:重庆市南开中学2023届高三上学期第二次质量检测数学试题
5 . 某社区要建一个矩形活动场所(如图),其中
为矩形,
为正方形,若场所周长为360米,设
米,场所面积为
平方米,
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/8/b01cdf78-9232-477a-8b56-f527ee228068.png?resizew=164)
(1)写出
关于
的函数关系式,并指出
的取值范围.
(2)求
的最大值及
取得最大值时
的取值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6240d4cf0fb44aa1e6bdaf2a4bdfb37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7a3d679b4dae63575903387a76ce45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/8/b01cdf78-9232-477a-8b56-f527ee228068.png?resizew=164)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
名校
6 . 已知二次函数y=ax2+bx+3的自变量x的部分取值和对应函数值y如下表:
(1)求二次函数y=ax2+bx+3的表达式;
(2)将二次函数y=ax2+bx+3的图象向右平移k(k>0)个单位,得到二次函数y=mx2+nx+q的图象,使得当-1<x<3时,y随x增大而增大;当4<x<5时,y随x增大而减小,求实数k的取值范围;
(3)A、B、C是二次函数y=ax2+bx+3的图象上互不重合的三点.已知点A、B的横坐标分别是m、m+1,点C与点A关于该函数图象的对称轴对称,求出∠ACB的度数.
x | … | -1 | 0 | 1 | 2 | 3 | … |
y | … | 4 | 3 | 0 | -5 | -12 | … |
(2)将二次函数y=ax2+bx+3的图象向右平移k(k>0)个单位,得到二次函数y=mx2+nx+q的图象,使得当-1<x<3时,y随x增大而增大;当4<x<5时,y随x增大而减小,求实数k的取值范围;
(3)A、B、C是二次函数y=ax2+bx+3的图象上互不重合的三点.已知点A、B的横坐标分别是m、m+1,点C与点A关于该函数图象的对称轴对称,求出∠ACB的度数.
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名校
解题方法
7 . 《绿色通道》作业88面第12题:已知双曲线
左右两个焦点分别为
,过
的直线交双曲线的右支于点
,且满足:
,
的周长等于焦距的3倍,若
,则双曲线离心率的取值范围是______.
我校高二某班的小楚同学在处理这个题目时提出了自己的见解,他认为这个曲线的离心率在已知比例和周长的条件下应该是个确定的值而不是某个范围,所以条件
可能是个多余的“伪条件”.你是否认同小楚同学的观点?若认同,请你求出此曲线的离心率,若不认同,请你说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a01e0c43c8c52d04824420717eb52969.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3a7681c38f74e21181bb9de077b0c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c07ebcbfacda073208d483c58e8a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291d1caba33704c0a5ddaf328e0f6037.png)
我校高二某班的小楚同学在处理这个题目时提出了自己的见解,他认为这个曲线的离心率在已知比例和周长的条件下应该是个确定的值而不是某个范围,所以条件
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291d1caba33704c0a5ddaf328e0f6037.png)
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8 . 已知关于x的函数
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/936719ca6ef48b7baa054ebe4561e5a7.png)
(1)若
,求x取值的集合;
(2)若对
,关于x的不等式
恒成立,求实数a的取值范围;
(3)若
,试讨论x取值的集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b927dfb4506976cbf2ab941442be8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecd4af7c872fb479131df3d2a01db5e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/936719ca6ef48b7baa054ebe4561e5a7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12021b74e36a4394c9786d2de00cbbf5.png)
(2)若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4242185064b5c5a4f34ecd9d10af6c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c37c6ff48f613a54d47f226bcf60a43.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1cec04a1887313401ec574d0b46ea6d.png)
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解题方法
9 . 求范围和图象:
(1)
的函数图象先向左平移
个单位, 然后横坐标变为原来的
,得到
的图象,求
在
上的取值范围.
(2)如图所示, 请用“五点法”列表,并画出函数
一个周期的图象.
![](https://img.xkw.com/dksih/QBM/2022/3/14/2927732832747520/2937564027559936/STEM/69418aa885c148baad8dd40f0ed7084e.png?resizew=297)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3162d2c7b650bba3e401ffbb1e13bb45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f457df0f9d14437a7f0443bb297e6ee8.png)
(2)如图所示, 请用“五点法”列表,并画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c3d302e263382a01339fa43fece182.png)
![](https://img.xkw.com/dksih/QBM/2022/3/14/2927732832747520/2937564027559936/STEM/69418aa885c148baad8dd40f0ed7084e.png?resizew=297)
![](https://img.xkw.com/dksih/QBM/2022/3/14/2927732832747520/2937564027559936/STEM/c7574a95-f8a7-44e7-a7fd-3fb3a5f67026.png?resizew=376)
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2022-03-16更新
|
754次组卷
|
3卷引用:浙江省杭州第二中学滨江校区2021-2022学年高一上学期期末数学试题
21-22高三上·北京·期中
名校
10 . 已知函数
.
(1)求
的单调递增区间;
(2)若
在区间
上的最大值是
,求
的取值范围;
(3)令
,如果曲线
与直线
相邻两个交点间的距离为
,求
的所有可能取值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f734c7bab5a46c252054c0c7c58c1c38.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb37d173605f006df4c51ba63b1841d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2665cce8924f0d96c37e25ffdc982d7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9355031ea0b2dc9cef3777621bc6d38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d74c0570f3ef4fff3e0ba34204f8d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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