解题方法
1 . 在棱长为2的正方体
中,
为
的中点,以
为原点,OB,OD,OO1所在直线分别为
轴、
轴、
轴,建立如何所示空间直角坐标系.若该正方体内一动点
,满足
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22a20b689283cc8b311eddae4c8c4242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49ea83a384f056dadaacfa349cc84130.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bfcaf2a345411411cf94422703e9269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e588cb555e36f28c5db66d213ef064d4.png)
A.点![]() ![]() | B.![]() ![]() |
C.![]() | D.三棱锥![]() ![]() |
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2 . 已知函数
,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/514df790653cf281af6323d283f72acd.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() |
C.存在![]() ![]() |
D.若![]() ![]() ![]() |
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3 . 设函数
.
(1)当
,求
在点
处的切线方程;
(2)证明:当
时,
;
(3)若函数
在
有唯一零点,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fa5e01a42421e4aabee073b6f552f18.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2763b57a7399653fbded5264f0cee150.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a2c484991fe4b01bd56c77a08a0e1da.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dbe1add7a58dbccdea4dbda1950fdae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e1c9c97de9198d47306216e9961b80.png)
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4 . 一只口袋中装有形状、大小都相同的6个小球,其中有红球1个,黑球2个,白球3个,分别从中两种不同方式摸出3个球,方式一:依次有放回:方式二:依次无放回.则( )
A.按方式一,则摸出是同一种颜色球的概率为![]() |
B.按方式一,设摸出黑色球的个数为X,则方差![]() |
C.按方式二,已知共有两种不同颜色的球的条件下,则2白1黑的概率为![]() |
D.若按方式一、二等可能,抽签决定,则最终摸出2白1黑的概率为![]() |
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5 . 如图,
是边长为2的正方形纸片,沿某动直线
为折痕将正方形在其下方的部分向上翻折,使得每次翻折后点
都落在边
上,记为
;折痕
与
交于点
,点
满足关系式
.以点
为坐标原点建立坐标系,若曲线
是由点
的轨迹及其关于边
对称的曲线组成的,等腰梯形
的
分别与曲线
切于点P、Q、
,且
在x轴上.则梯形
的面积最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828edf1530dce9c69d2e844b2bf4a81d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d659f763d2d33a685ba69df210dc1935.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e849e0ace8c1ca612978a716d15cc94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
A.6 | B.![]() | C.![]() | D.![]() |
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解题方法
6 . 已知函数
,
.
(1)当
时,求函数
的最小值;
(2)是否存在
,且
依次成等比数列,使得
,
,
依次成等差数列?请证明;
(3)当
时,函数
有两个零点
,是否存在
的关系?若存在,请证明;若不存在,请写出正确的关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/784548dbfa097ef19fd7a4e68739e478.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee4982f38cc607a43b9478e7e35a6330.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
(2)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1757236a5ef1fc70a18f31d6d2438b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22f0427915ac19bd2f9383d079b2a063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1f6718b4be26dd3274eddbbdf7dd29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b51b6ae7b103d7fa1d695f77e6c31e.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc93e6c831bd03403d423b88746e733.png)
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7 . 设O为坐标原点,定义非零向量
的“相伴函数”为
.向量
称为函数
的“相伴向量”.
(1)记
的“相伴函数”为
,若函数
与直线
有且仅有四个不同的交点,求实数k的取值范围;
(2)已知点
满足
,向量
的“相伴函数”
在
处取得最大值当点M运动时,求
的取值范围.
(3)当向量
时,伴随函数为
,函数
,求
在区间
上最大值与最小值之差的取值范围;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b84dac41f87e939f6cc39f38dc59b78d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e952eb24c100edc944c952fd804053f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b84dac41f87e939f6cc39f38dc59b78d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc54bc56c16baa3643686b85a6130e4.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3fa5a2ec0f43acc49c5f7f848f212c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0524e773cec51110a75e6735f4767fae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead6a3dbd03539ef5e0807be57bb1e17.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d6bb01f1044358cc5fee441bc62489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0bac149e19b3a4239cc2355c46f73d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e723e57753f0a4fe1ef8ca1aee0e2117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e0e24323fe73e5d9fc6136219306da.png)
(3)当向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bf212cb55c776481c675db9402d83cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9c691f19308f093ef6c3a77a519fb79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/123c14962305f0f9b98c60c14c36c42a.png)
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8 . 对于每项均是正整数的数列P:
,定义变换
,
将数列P变换成数列
:
.对于每项均是非负整数的数列
,定义
,定义变换
,
将数列Q各项从大到小排列,然后去掉所有为零的项,得到数列
.
(1)若数列
为2,4,3,7,求
的值;
(2)对于每项均是正整数的有穷数列
,令
,
.
(i)探究
与
的关系;
(ii)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e50dbc39a6a06eb8bd7b295f8cc95a6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4d9c1555c406f37a85ff5ddd2275af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed3926a18ee86236e7cf53467ac04f73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca3c54bcc0bd04c304d6513732584b51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29422ba63f79b2087f0dcce4879d8c78.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00061b36983bb547aa63f9a9f6222105.png)
(2)对于每项均是正整数的有穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131cac59d4d568a27dbb220810dbb014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef96396caccbf2f959e9d233f060317.png)
(i)探究
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00061b36983bb547aa63f9a9f6222105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c496ba1d329d5fd94f4fdb1da8c7cde.png)
(ii)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5de2726fe544faf83d4ab88e9116135.png)
您最近一年使用:0次
2024-03-12更新
|
1085次组卷
|
3卷引用:江苏省苏州市南京航空航天大学苏州附属中学2024届高三下学期五月阳光测试数学试题
9 . 国际象棋是国际通行的智力竞技运动.国际象棋使用
格黑白方格相间棋盘,骨牌为每格与棋盘的方格大小相同的
格灰色方格.若某种黑白相间棋盘与骨牌满足以下三点:①每块骨牌覆盖棋盘的相邻两格;②棋盘上每一格都被骨牌覆盖;③没有两块骨牌覆盖同一格,则称骨牌构成了棋盘的一种完全覆盖.显然,我们能够举例说明
格黑白方格相间棋盘能被骨牌完全覆盖.
格黑白方格相间棋盘的对角两格,余下棋盘不能被骨牌完全覆盖;
(2)请你切掉
格的黑白方格相间棋盘的任意两个异色方格,然后画出余下棋盘的一种骨牌完全覆盖方式,并证明:无论切掉的是哪两个异色方格,余下棋盘都能被骨牌完全覆盖;
(3)记
格黑白方格相间棋盘的骨牌完全覆盖方式数为
,数列
的前n项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a96e9c2e2a15130d1d56a1d0e16b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71fb79f6535ee15a3d41ca71cf72082b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a96e9c2e2a15130d1d56a1d0e16b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a96e9c2e2a15130d1d56a1d0e16b72.png)
(2)请你切掉
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a96e9c2e2a15130d1d56a1d0e16b72.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e70354d6ca5ad9f6b4592fac0b5e559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe5d94e748101eaf9aa5ae725b0040e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/485596f7fc2aa8d80466a7d02a00af15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6cfd722654be25b48b28ba0f6698e89.png)
您最近一年使用:0次
2024-03-06更新
|
787次组卷
|
4卷引用:江苏省苏州大学2024届高考新题型2月指导卷数学试题
江苏省苏州大学2024届高考新题型2月指导卷数学试题山东省菏泽第一中学人民路校区2024届高三下学期开学考试数学试题(已下线)第四套 最新模拟重组卷(已下线)压轴题08计数原理、二项式定理、概率统计压轴题6题型汇总
解题方法
10 . 记
为数列
的前n项积,已知 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7d0328f6138ed1ab82a5ed43716cab1.png)
(1)证明: 数列
是等差数列;
(2)若将集合
中的元素从小到大依次排列,构成数列
求数列
的前
项和
;
(3)已知等比数列
的首项为1,公比为
若
对任意的
恒成立,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7d0328f6138ed1ab82a5ed43716cab1.png)
(1)证明: 数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若将集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f856f09f3b4d6c1955d1436a8cfae890.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b24e1d66edb40d01fa1032f5d6a38068.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b17a9b9bb8bf6bb9865e37f204da5c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6ef48976a52cc4a2be7c46a98426c0a.png)
(3)已知等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9417f35a0db96335122490f49e304927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859832d40034c0c4d4f3e9a853458038.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
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