1 . 已知无穷数列
,构造新数列
满足
,
满足
,
,
满足
,若
为常数数列,则称
为
阶等差数列;同理令
,
,
,
,若
为常数数列,则称
为
阶等比数列.
(1)已知
为二阶等差数列,且
,
,
,求
的通项公式;
(2)若
为
阶等差数列,
为一阶等比数列,证明:
为
阶等比数列;
(3)已知
,令
的前
项和为
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22e75bf99dcb0fe32f66fa90a74f9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc06ff2f65c456efb6a114e67b62cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d16e3ca4fb65342b0e9a0594d661ba3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaf623a6dd661f87cf64ea150072fd78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcbdf91bb5a49f293f9b52ac8dcfa35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc2b6b23da3e065820c15cf6c675e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1ca0ac3789432a3d1ce975a9a6f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ab5abd104649f9a3c231df9a55813a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1ca0ac3789432a3d1ce975a9a6f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69c653f3a05dd25f6affdba7baeab38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f0606df3b6fbc6fcf863f9c59e0e54f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc2b6b23da3e065820c15cf6c675e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab214e5f34d976717284bed52c645e10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020e796a0144ff9b3329c7064a01c5c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d8e8f821111de8075e5c3dfb22a5d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56a4b318fa151fab14b3857942ed3cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07418f1fa0f6569b50944b5a13ffa021.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b00f4eb7f1bd2ccefbabf0c1dfa8f69.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7778648d93a10ed66ddd99672d3ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a77316e06c00a9086be642f7f590684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2a5a414f3f5d724058a2e887f3d1c0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c3fec47d2dd2b8099d86c87b6e57de8.png)
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2 . 已知
,动点
满足
,动点
的轨迹为曲线
交
于另外一点
交
于另外一点
.
(1)求曲线
的标准方程;
(2)已知
是定值,求该定值;
(3)求
面积的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/107a80eeecf2efcb25cb008945c1c241.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cced7a3d18b398c1da1218d74a96542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ac4aa6db80d4edfd287abc4580e68b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c72be8e3e113103ca7de54ac39c2313.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da79ae7251aa6d5822b5396a632b01c7.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c28abb154f41e1ca9816c9c9c2433ca.png)
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7日内更新
|
634次组卷
|
3卷引用:浙江省宁波市镇海中学2024届高三下学期适应性测试数学试卷
名校
3 . 小明同学在计算出8个数的平均数后,不小心将这个数也混到数据中了,那么重新计算这些新数据后一定不变的量是( )
A.平均数 | B.中位数 | C.众数 | D.方差 |
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名校
解题方法
4 . 对于
,定义
,
,其中
为
中最大的数,例如:
,
,
. 给定正整数
,根据以上内容,对于
,请回答下列问题:
(1)
(用
和
表示);
(2)满足
的有序数对
有多少个?
(3)满足
的有序数对
有多少个?
(4)满足
的有序数对
有多少个?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24d7720b93b6a0ebf04ea3b8545901da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf7efd1e98a1bac7832ef6367c88c91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3a946cb466ad8db7174a8d318ce578.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dcb5694de40f2b01518fc88f0d556c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8436f067b7e4048dd0335f3fdb7e27b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca92c9a09bd82e0ebe8e065e09bfbc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/563d6edf4e17adf966f50a2e919f0212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18fbd87eb7ee8470dcce89f059473895.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be431af86fc0b0ba9b05d04c5586d82f.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/149c9303df43cbe149c0f02b0737688e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df09d267ae01dcf773ffbc14ead57740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a57d1215099fab4a97db12b2fa8f14.png)
(3)满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8586c1fac679cb347a28b2baeb988d7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a57d1215099fab4a97db12b2fa8f14.png)
(4)满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c259473293191a421065b88c80622359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a57d1215099fab4a97db12b2fa8f14.png)
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5 . 定义:若四边形有一组对角互补,一组邻边相等,且相等邻边的夹角为直角,像这样的图形称为“直角等邻对补”四边形,简称“直等补”四边形.
(1)如图1,正方形ABCD中,E是CD上的点,将
绕B点旋转,使BC与BA重合,此时点E的对应点F在DA的延长线上,则四边形
为“直等补”四边形,为什么?
(2)如图2,已知四边形
是“直等补”四边形,
,
,
,点
到直线
的距离为BE.
①求
的长;
②若
分别是
边上的动点,求
周长的最小值.
(1)如图1,正方形ABCD中,E是CD上的点,将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfa1a2af7e38d33634c462300df381f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2330c01a4d2b5b20f106e3e48834d5c0.png)
(2)如图2,已知四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59fe75f967e8915c9124a5d4ac420a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037b342a682cbd4241855a243da3c016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb6694f3443cc5f4d09948679251b61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df7fc746f8c4801d8f2f0471ba3297e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e856c15c61d7cb6ebd8daef542a4e7f.png)
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6 . 已知在平面直角坐标系中,直线
交坐标轴于A、B两点,直线
交坐标轴于C、D两点,已知点
,
.
与
交于点E,试判断
的形状,并说明理由;
(2)点P、Q在
的边上,且满足
与
全等(点Q异于点C),直接写出点Q的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85e24de76e6f9a6097f890bc2f395904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a01e2e3d40112fdeeb464f81eaac1c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eae074b97ec3ff58fbd9d556aea81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a5a48393681b882d719f5562235ba11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb49df05f2e31d005735c3f14a21d30.png)
(2)点P、Q在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb49df05f2e31d005735c3f14a21d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9dc427a01582ec222446b352d40ab0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
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7 . 如图,在平面直角坐标系中,抛物线
经过
、
、
.
(2)点D是线段BC上一动点,点D关于AC、AB的对称点分别为点M、N,连接MN交线段AC、AB于E、F.求
最小值;
(3)在(2)的条件下请直接写出线段MN的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da6bbbb53aaeab0ab7a242228cc510fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec0bc3a43265b63b6964476ca327fab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/850e01debd266a398b597a1876dbb3ea.png)
(2)点D是线段BC上一动点,点D关于AC、AB的对称点分别为点M、N,连接MN交线段AC、AB于E、F.求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13106b48acf096f7fc9ac1e49559b130.png)
(3)在(2)的条件下请直接写出线段MN的取值范围.
您最近一年使用:0次
名校
8 . 今年6月份,永州市某中学开展“六城同创”知识竞赛活动,赛后,随机抽取了部分参赛学生的成绩,按得分划为A,B,C,D四个等级,
,
,
,
,并绘制了如图两幅不完整的统计图,请结合图中所给信息,解答下列问题:
(2)扇形统计图中
______,
______,B等级所占扇形的圆心角度数为______.
(3)该校准备从上述获得A等级的四名学生中选取两人参加永州市举行的“六城同创”知识竞赛,已知这四人中有两名男生(用
,
表示),两名女生(用
,
表示),请利用树状图法或列表法,求恰好抽到1名男生和1名女生的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b788f849213c9bede89249019d87808d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59e507529b30a6ff85a1f089bd31a7b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cbfd347f5c3a2ae250f732fa9ab849f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4965f1128f8c5a418c24e39a51c364c0.png)
(2)扇形统计图中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
(3)该校准备从上述获得A等级的四名学生中选取两人参加永州市举行的“六城同创”知识竞赛,已知这四人中有两名男生(用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/024e2379c58191758f8bd7602a6bcb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b34a75c2a392f235c5f07b91d9fb58d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4450b959d69fdf09b38ba82fe132ec33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c89fcb4633216e492ed5a04cf45eed.png)
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名校
9 . 将正三角形、正方形、正五边形按如图所示的方式摆放,其中正方形和正五边形的下底边是水平共线的,如果
,那么
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcc3ef6a72ecee9efdca1f447fa243d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc310194575262fb45352c2fbc19868.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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10 . 如图,在矩形ABCD中,
,
,对角线AC、BD相交于点O,动点P、Q分别从点C、A同时出发,运动速度均为1cm/s,点P沿
运动.到点B停止,点Q沿
运动,到点C停止. 连接
,设
的面积为
(这里规定:线段是面积为0的几何图形),点Q的运动时间为x(s).
时,求x的值;
(2)当
时,求y与x之间的函数关系式;
(3)直接写出在整个运动过程中,使
的所有
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee5bd6f04872ef8d3d833d0e2056161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e40cc1f35e71e2abf5943a21fe448df4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82baca47182531f9f2135ef3056cc1ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3087da5c11909dab613378fee8d471fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ed47b8230bc383b2c167264f750d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012b14b48c09eb820c49c13dccb642bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b10bb426e00de29d8664ca5babb2f4f3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fc1a1c6781dc4554c47e2affb00405c.png)
(3)直接写出在整个运动过程中,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34ecd96adaec63c5bbd65f59f885ecfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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