1 . 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)
您最近一年使用:0次
7日内更新
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618次组卷
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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
解题方法
2 . 投掷一枚硬币(正反等可能),设投掷
次不连续出现三次正面向上的概率为
.
(1)求
,
,
和
;
(2)写出
的递推公式;
(3)单调有界原理:①若数列
单调递增,且存在常数
,恒有
成立,那么这个数列必定有极限,即
存在;②若数列
单调递减,且存在常数
,恒有
成立,那么这个数列必定有极限,即
存在.请根据单调有界原理判断
是否存在?有何统计意义?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee50575e3ebd56c4f46dd0bbf8e55d3.png)
(2)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
(3)单调有界原理:①若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5612ce06759d0f77ca029d10083f7d1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed169ec40816590af52f4ff8b1f5ea5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63cad0f23354aa754ade482d849557fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed169ec40816590af52f4ff8b1f5ea5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/675a2e9584f91900fa08f7808d44dcd7.png)
您最近一年使用:0次
名校
解题方法
3 . 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)
您最近一年使用:0次
4 . 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)
您最近一年使用:0次
5 . 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)
您最近一年使用:0次
6 . 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
7 . 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)
您最近一年使用:0次
解题方法
8 .
的角
对应边是 a,b,c ,三角形的重心是 O.已知
.
(1)求 a 的长.
(2)求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9fbd659c7e4424a2ea5a20a86c0cf7.png)
(1)求 a 的长.
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
9 . 若函数
满足以下三个条件,则称
为
函数.①定义域为
;②对任意
,
;③对任意正整数
,
,当
时,有
.若给定
函数
某几个函数值,在满足条件①②③的情况下,可能的
如果有
种,分别为
,
,
,
.
等于
,
,
,
的最大值.这样得到的
称为
的最大生成函数.
(1)若
为
函数,且
是在给定条件
,
下的
的最大生成函数,求
和
的值;
(2)若
为
函数,且满足
,求数列
的前10项和;
(3)若
为
函数,且
是在给定条件
,
下的
的最大生成函数,求数列
的前
项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f46f42b24d35609186c0051b125481c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59f63c9be8167a50ac3996e007b124df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62f133fb6340a11e7ba0240ac0e19339.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c2c8fda00e52527ee1472293c011eab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b7acae2f2543b05e3c5677bd755b136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12877ebeba622c766be60b77efea9eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f46f42b24d35609186c0051b125481c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/406957a919b3f16fb095aa9a8b7e2dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a42bf9afee931791911f748fd84d45f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b754b86e63e02f3faeebff9c18c7460b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b0749e3eddfb6056f19812d7fa713b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ddc3eab5cedbd4cba439126a8d2ea5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f43172b8f2f645afeada31271d6f2dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a788e92a6e3e5e721096e78cc112adf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02f196f6236188084f3b2c9f2b68c05c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f46f42b24d35609186c0051b125481c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02f196f6236188084f3b2c9f2b68c05c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67b17b16fdf70d2a885f5ab346afd18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ecae1c7e6e0dbb211105b27a0319c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/830acb3d191d323e9ea6e710c7de0061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1135b03537fa6527c9ba3f639f64474c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f46f42b24d35609186c0051b125481c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d31c3e1c4206e9bed7dd3c63d842080d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c46069372b8f2a59194dad5978e18445.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f46f42b24d35609186c0051b125481c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef7002fdc43f0d600cb517470ac65144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41678e5c9b510a2a4b798a0be444eb85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc095001df2e68af03d6ed197a8d4372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab050e103632618580d0ec8728b584a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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10 . 已知直线
与双曲线
相切于点
.
(1)试在集合
中选择一个数作为
的值,使得相应的
的值存在,并求出相应的
的值;
(2)过点
与
垂直的直线
分别交
轴于
两点,
是线段
的中点,求点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c287201dc8f4b7e1a8dd41920654656.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5bef93a53a2004910a8cac32f93c4b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)试在集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1196906fbdb1848b38b0419637041b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)过点
![](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/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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2024-05-20更新
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826次组卷
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2卷引用:浙江省温州市2024届高三第三次适应性考试数学试题