2023高三·全国·专题练习
1 . 曲线
上不同两点
,
处的切线的斜率分别是
,
,
是两点间距离,定义
为曲线
在点
与点
之间的“曲率”,给出以下命题:
任何曲线上两点
,
之间的曲率
均为正实数;
存在这样的函数,该函数图象上任意两点之间的“曲率”为常数;
抛物线
图象上两点
与
的横坐标分别为
,
,则“曲率”
;
函数
图象上任意两点
,
之间的“曲率”
其中正确命题的序号为________
填上所有正确命题的序号
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0ef244e9cd295656496929fbb46a9a5.png)
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2023高二·上海·专题练习
解题方法
2 . 已知函数
,其导函数
的图象经过点
,
,如图所示,则下列说法中正确结论的序号为_____ .
时函数取得极小值;
②
有两个极值点;
③当
时函数取得极小值;
④当
时函数取得极大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfb885b96ddbf9889de11e3339ca7704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d0c99ddd028f0bc3b1d64924ff0f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d599059e6b2c918ab15ee22611b6962.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
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23-24高二下·全国·课前预习
解题方法
3 . 判断正误,正确的写正确,错误的写错误.
(1)等差数列前
项和公式的推导方法是倒序相加.( )
(2)若数列
的前
项和
,则
为常数列.( )
(3)等差数列的前
项和,等于其首项、第
项的等差中项的
倍.( )
(4)
.( )
(1)等差数列前
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8271bf23009e445137406321047a142b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(3)等差数列的前
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0365855d9f439487911ff2391fb1ff70.png)
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4 . 对于实数a、b、c,有下列命题:
①若
,则a>b;
②若ab>c,则
;
③若a>b>0,且n为正数,则
.
其中,真命题的序号为______ .(写出所有满足要求的命题序号)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c22b9d08cf536bbb76bce1b0f135772.png)
②若ab>c,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65f904b61d1471c6076f322676ae9f0e.png)
③若a>b>0,且n为正数,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9361777ad9426527dd4650996fe9c3fc.png)
其中,真命题的序号为
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名校
5 . 下列说法中正确的有_______ (填正确说法的序号).
①回归直线
恒过点
,且至少过一个样本点;
②若样本数据
的方差为4,则数据
的标准差为4;
③已知随机变量
,且
,则
;
④若线性相关系数
越接近1,则两个变量的线性相关性越弱;
⑤
是用来判断两个分类变量是否相关的随机变量,当
的值很小时可以推断两个变量不相关.
①回归直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/929ef3bed0a4bdd22f39e036506dc481.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bda105ec292aac7ab1485bd5031783fb.png)
②若样本数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce0b4b61f09ac4f5e16b40f7c608402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/044cd011370eb6e1c50f4b701bfe5120.png)
③已知随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90f12392733f7d31b5dadaa7ec2e190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f008a4d0dc886d0138ff98f78686b2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/452ac2a59d469cb71f5ef336aa901233.png)
④若线性相关系数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fe9be2c6b3d8bf1e6ce9e9c0025ced7.png)
⑤
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b986e3613290b456532843d5ad4c6e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b986e3613290b456532843d5ad4c6e67.png)
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6 . 在吸烟与患肺病这两个分类变量的计算中,下列说法正确的是( )
附表:
附表:
![]() | 0.15 | 0.10 | 0.05 | 0.025 | 0.010 | 0.005 | 0.001 |
![]() | 2.072 | 2.706 | 3.841 | 5.024 | 6.635 | 7.879 | 10.828 |
A.若![]() ![]() |
B.从独立性检验可知有99%的把握认为吸烟与患肺病有关系时,我们说某人吸烟,那么他有99%的可能性患有肺病 |
C.从统计量中求出有95%的把握认为吸烟与患肺病有关系,是指有5%的可能性使得判断出现错误 |
D.以上三种说法都不正确 |
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名校
7 . 设直线系
:
,对于下列三个命题:
①
中所有直线均与一个定圆相切;
②
中所有直线均经过一个定点;
③存在点
不在
中的任一条直线上.
其中真命题的序号为____________ (写出所有真命题的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee014177faf3f62276d699606ca5bf05.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
③存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
其中真命题的序号为
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8 . 下列说法中,正确的序号为______ .
①可画一个平面,使它的长为4cm,宽为2cm;
②一条直线把它所在的平面分成两部分,一个平面把空间分成两部分;
③一个平面的面积为20cm2;
④经过面内任意两点的直线,如果直线上各点都在这个面内,那么这个面是平面.
①可画一个平面,使它的长为4cm,宽为2cm;
②一条直线把它所在的平面分成两部分,一个平面把空间分成两部分;
③一个平面的面积为20cm2;
④经过面内任意两点的直线,如果直线上各点都在这个面内,那么这个面是平面.
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解题方法
9 . 博览会安排了分别标有序号为“1号”“2号”“3号”的三辆车,等可能随机顺序前往酒店接嘉宾.某嘉宾突发奇想,设计两种乘车方案.方案一:不乘坐第一辆车,若第二辆车的车序号大于第一辆车的车序号,就乘坐此车,否则乘坐第三辆车;方案二:直接乘坐第一辆车.记方案一与方案二坐到“3号”车的概率分别为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e28d20fcedbc1072eac5fe902d2969bb.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5425108c557f0f21474c045334f97d9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e28d20fcedbc1072eac5fe902d2969bb.png)
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10 . 给出下列命题:
① ②
③
④
其中正确命题的序号为
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