1 . 若从无穷数列
中任取若干项
(其中
)都依次为数列
中的连续
项,则称
是
的“衍生数列".给出以下两个命题:
(1)数列
是某个数列的“衍生数列”;
(2)若
各项均为0或1,且是自身的“衍生数列”,则
从某一项起为常数列.下列判断正确的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d255743a932f013f8cd3c90942aea1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bacaf758c8b5c2f52624f80debc02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4429ffb4a826e1c7c474eea9c539391d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
A.(1)(2)均为真命题 |
B.(1)(2)均为假命题 |
C.(1)为真命题,(2)为假命题 |
D.(1)为假命题,(2)为真命题 |
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2023·上海浦东新·模拟预测
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解题方法
2 . 已知
,当
时,
是线段
的中点,点
在所有的线段
上,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338ab9fbf074bb0495f7130797464607.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ea59ed038abfbff5bc568d184e8463e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039af66355ed85ff4c204931b882b694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d159513efe8dc11305ff2fc3942110a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5d6940ef122dcb071e361c7161c82b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338ab9fbf074bb0495f7130797464607.png)
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2023·上海浦东新·模拟预测
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解题方法
3 . 若
的值域为
,则
至多有_______ 个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e4540345cf7aa5e09e49a3d91f306e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cb0b5499d5769e41b06010409db30f.png)
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2023·上海浦东新·三模
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4 . 某晚报曾刊登过一则生活趣事,某市民唐某乘坐出租车时,在半途中骂骂咧咧要求司机临时停靠,打表计价结账,然后重新计价,继续前行,该市民解释说,根据经验,这样分开支付车费比一次性付费便宜一些,他的这一说法有道理吗?确实,由于出租车运价上调,有些人出行时会估计一下可能的价格,再决定是否乘坐出租车.据了解,2018年上海出租车在5时到23时之间起租价为14元/3千米,超起租里程单价为2.50元/千米,总里程超过15千米(不含15千米)部分按超起租里程单价加50%.此外,相关部门还规定了低速等候费和其他时段的计价办法,以及适合其他车型的计价办法.你乘坐过出租车吗?你会仿效那位市民唐某的做法吗?为什么?
(1)根据上述情境你能提出什么数学问题?为了解决你的问题,你能否作出一些合理假设?
(2)你能否根据你的假设建立数学模型,并回答你所提出的问题.
(1)根据上述情境你能提出什么数学问题?为了解决你的问题,你能否作出一些合理假设?
(2)你能否根据你的假设建立数学模型,并回答你所提出的问题.
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2023·上海浦东新·模拟预测
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5 . 设
是定义域均为
的三个函数.
是
的一个子集.若对任意
,点
与点
都关于点
对称,则称
是
关于
的“
对称函数”.
(1)若
和
是关于
的“
对称函数”,求
;
(2)已知
是
关于
的“
对称函数”.且对任意
,存在
,使得
,求实数
的取值范围;
(3)证明:对任意
,存在唯一的
,使得
和
是关于
的“
对称函数”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9113f21d8ee013417ee7905d1b2fd585.png)
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db1a75c5fa4bcc70374c9148b3aba398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f400b879ec1c0ae07f984090c6cb2c76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe7522a3f232bd0b7a7850ae674db43f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3162d2c7b650bba3e401ffbb1e13bb45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74e7e79ac17c51c7a4aaf9d59ec9beb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd8fc312f6d5ea7d0e8d96d11c18b896.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/265f0662653525c979b3de4d60d75ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02b8cc78e3b92258e1114c0bbfa5e3b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bb62f5043ccd21a6e020a41947b13f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2187ee1ea3b7e47a6283314322e5decf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e334264a4da8fee53226266d558efd39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)证明:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c36b234ba460321e811de1729eadd4b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae1b87c23b45ce5e5e74d5b1d73234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db192285632d1991b4ee7a003a52205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46830ceaa0d61f63c9e415604567e243.png)
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2023·上海浦东新·模拟预测
6 . 已知
,
,
.
(1)若
,
,写出曲线
的一条水平切线的方程;
(2)若
,
使得
,
,
,
形成等差数列,证明:
;
(3)若存在
,使得函数
有唯一零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19339e3904e9541ff26b30ae5f1242b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2562a04795974b5fb1b1592e351e6122.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aed39f5aca78934fb383402433fe549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3604274ad6707a906eba371a9e884144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc9769116ec47353514e6b7fb7b17216.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/542893790445d6d888d9ff91fd215c9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1e5fb2d54a62f243bd5936a3f60386.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0ffdd04d5653d6ffae60559eb0e39ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/208d0c27b4a358f39abc6e12cfdeef64.png)
(3)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fcb5d3be7955ac79a959abad606a47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023·上海浦东新·模拟预测
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解题方法
7 . 设
,
.以点
为焦点,直线
为准线的抛物线
交抛物线
于
两点.则直线
的斜率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9db6b54803f4e65157f6be0e8427f5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09488419c9cef00b39a107ac81e706a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09c7fc8e284e4aafd93a630d50a53930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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解题方法
8 . 设
是定义在
上的奇函数.若
是严格减函数,则称
为“
函数”.
(1)分别判断
和
是否为
函数,并说明理由;
(2)若
是
函数,求正数
的取值范围;
(3)已知奇函数
及其导函数
定义域均为
.判断“
在
上严格减”是“
为
函数”的什么条件,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13c41afa095de249e257eed63fb4769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)分别判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4d1fad1b8feb80cd8bc9a4596c7439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3162d2c7b650bba3e401ffbb1e13bb45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/567869f9e9005fbbc59896e3c160e7da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)已知奇函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5a90aeba435af22d6bcdb7b91650b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adca47fb3667e6707265f5279688cf1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adca47fb3667e6707265f5279688cf1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5a90aeba435af22d6bcdb7b91650b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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2023·上海浦东新·模拟预测
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9 . 设
为无穷数列.若存在正整数
,使得对任意正整数
,均成立
,则称
为“
-低调数列”.有以下两个命题:①
是
-低调数列当且仅当
;②若存在
,使得
为2-低调数列,则
.那么( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6f55c8a09b177a0cc5596d4fee20c52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4b3e772d073df8c2334f51bf89be75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbeaed9ec21e090defafcfeefe0059c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15bde05677aa603411e4c00fa94241a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbc450d9fb1c6099c6de1cfcb99bc25b.png)
A.①是真命题,②是假命题 | B.①是假命题,②是真命题 |
C.①、②都是真命题 | D.①、②都是假命题 |
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2023·上海浦东新·模拟预测
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10 . 已知平面上的点
满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c33f815004ac8d0d569af555c66ff00.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d63368fb5c4feebe59c81bd5c90d8eaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6edb9940bd0cb006572825fce0f3377.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c33f815004ac8d0d569af555c66ff00.png)
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